Method for cooling atomic objects confined by atomic object confinement means

Abstract

An atomic object confined in a particular region of an atomic object confinement device is cooled using an EIT cooling operation from S to P to D. A controller associated with the atomic object confinement device controls a first steering source and a second steering source to provide a first steering signal and a second steering signal, respectively, to the particular region. The first steering signal is characterized by a first wavelength corresponding to a transition between an S manifold and a P manifold of a first component of the atomic object, and the S to P transition is detuned by a first detuning amount. The second steering signal is characterized by a second wavelength corresponding to a transition between the P manifold and a D manifold of the first component, and the P to D transition is detuned by a second detuning amount. The first detuning amount and the second detuning amount are selected to establish a dark state associated with a two-photon transition between the S manifold and the D manifold.

Description

TECHNICAL FIELD

[0001] Various embodiments relate to laser cooling of atomic objects confined by atomic object confinement devices. For example, various embodiments relate to sympathetic EIT cooling using S to P to D transitions. For example, various embodiments relate to sympathetic EIT cooling using atomic object clock states. CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Application No. 63 / 228,486, filed August 2, 2021, the contents of which are incorporated by reference in their entirety. BACKGROUND

[0003] In various instances, it is desirable to cool ions captured by an ion trap so that various operations (e.g., experiments, controlled quantum evolution, etc.) can be performed on the ions. However, conventional laser cooling techniques tend to be complex and / or require high power laser beams. Through the application of effort, ingenuity, and innovation, many of the deficiencies of such conventional laser cooling systems have been addressed by developing solutions structured in accordance with embodiments of the present invention, many examples of which are described in detail herein. SUMMARY

[0004] Example embodiments provide quantum computers, systems, apparatuses, etc. and corresponding methods for performing EIT cooling based on one or more states of an S manifold of a first component of an atomic object, through a P manifold of the first component of the atomic object, to a two-photon resonance transition between one or more states of a D manifold of the first component of the atomic object. Example embodiments provide quantum computers, systems, apparatuses, etc. and corresponding methods for performing EIT cooling based on a clock state of a first component of an atomic object. In various embodiments, the atomic object is an atomic crystal, a group of atoms (neutral and / or ionized), or a group of molecules (neutral and / or ionized), and a component (e.g., the first component) of the atomic object is at least one atom or molecule of a particular type (e.g., element type, chemical formula, etc.) of the atomic object. For example, in one example embodiment, the atomic object includes cooling ions of a first element type and qubit ions of a second element type, where the cooling ions are referred to herein as the first component of the example atomic object. For example, in one example embodiment, a first component of the atomic object is cooled by EIT cooling, and a second component of the atomic object is cooled by sympathetic cooling through interaction with the first component of the atomic object. In one example embodiment, the second component is used as a qubit of a quantum computer.

[0005] According to one aspect, a method for cooling an atomic object confined by an atomic object confinement device is provided. In one example embodiment, the method includes, by a controller associated with the atomic object confinement device, controlling a first manipulation source to provide a first manipulation signal to a particular region of the atomic object confinement device. The method also includes, by the controller, controlling a second manipulation source to provide a second manipulation signal to the particular region of the atomic object confinement device. The atomic object to be cooled is located in the particular region of the atomic object confinement device. The first manipulation signal is characterized by a first wavelength corresponding to a transition between an S manifold and a P manifold of a first component of the atomic object and is detuned from the transition between the S manifold and the P manifold by a first detuning amount. The second manipulation signal is characterized by a second wavelength corresponding to a transition between the P manifold and a D manifold of the first component of the atomic object and is detuned from the transition between the P manifold and the D manifold by a second detuning amount. The first detuning amount and the second detuning amount are selected to establish a dark state related to a two-photon transition between the S manifold and the D manifold.

[0006] In one example embodiment, the atomic object is an ionic crystal including two or more ions, and the first component of the atomic object is at least one of the two or more ions of a first atomic object type.

[0007] In one example embodiment, the first component of the atomic object is configured to function as a coolant ion in a cooperative cooling scheme for a crystal.

[0008] In one example embodiment, the second component of the atomic object is at least one of two or more ions of a second atomic object type, the second atomic object type being different from the first atomic object type, and wherein the at least one of the two or more ions of the second atomic object type is configured to function as a qubit of a quantum computer including the atomic object confinement device.

[0009] In one example embodiment, the first detuning amount and the second detuning amount are approximately equal. In one example embodiment, the first manipulation signal is a pi-polarized laser beam and the second manipulation signal is a sigma-polarized laser beam.

[0010] In one example embodiment, a polarization of the first manipulation signal and a polarization of the second manipulation signal correspond to the two-photon transition associated with the dark state.

[0011] In one example embodiment, the method further includes causing a magnetic field having a magnetic field direction to be generated in the particular region of the atomic object confinement device, wherein one of the atomic object or the particular region of the atomic object confinement device defines an atomic object axis, and the magnetic field direction is transverse to the atomic object axis.

[0012] In one example embodiment, the magnetic field direction and the atomic object axis form an angle of thirty to sixty degrees.

[0013] In one example embodiment, the first manipulation signal defines a first direction of propagation transverse to an axis of the atomic object, and the second manipulation signal defines a second direction of propagation transverse to the axis of the atomic object.

[0014] In one example embodiment, the first direction of propagation and the second direction of propagation are approximately anti-parallel to each other, and the magnetic field direction is transverse to both the first direction of propagation and the second direction of propagation.

[0015] In one example embodiment, both the first direction of propagation and the second direction of propagation are approximately perpendicular to the magnetic field direction.

[0016] In one example embodiment, (a) a polarization of the first manipulation signal is approximately transverse to a plane defined by the atomic object confinement device, (b) a polarization of the second manipulation signal is approximately transverse to the plane defined by the atomic object confinement device, and (c) the first direction of propagation, the second direction of propagation, and the magnetic field direction are approximately parallel to the plane defined by the atomic confinement device, respectively.

[0017] According to another aspect, there is provided a device configured to cause and / or control cooling of an atomic object confined by an atomic object confinement device. In one example embodiment, the device comprises at least one processor and a memory storing computer-executable instructions. The computer-executable instructions are configured to, when executed by the at least one processor, cause the device to at least control a first manipulation source to provide a first manipulation signal to a particular region of the atomic object confinement device; control a second manipulation source to provide a second manipulation signal to the particular region of the atomic object confinement device. The atomic object to be cooled is located within the particular region of the atomic object confinement device. The first manipulation signal and the second manipulation signal are configured to collectively cool the atomic object. The first manipulation signal is characterized by a first wavelength corresponding to a transition between an S manifold and a P manifold of a first component of the atomic object, and is detuned from the transition between the S manifold and the P manifold by a first detuning amount. The second manipulation signal is characterized by a second wavelength corresponding to a transition between the P manifold and a D manifold of the first component of the atomic object, and is detuned from the transition between the P manifold and the D manifold by a second detuning amount. The first and second detuning amounts are selected to establish a dark state related to a two-photon transition between the S manifold and the D manifold.

[0018] In one example embodiment, the device is a controller of a quantum computer comprising the atomic object confinement device.

[0019] In one example embodiment, the atomic object is an ion crystal comprising two or more ions, and the first component of the atomic object is at least one of the two or more ions of a first atomic object type.

[0020] In one example embodiment, the first set of components of the atomic object is configured to function as a coolant ion in a sympathetic cooling scheme for a crystal.

[0021] In one example embodiment, the second set of components of the atomic object is at least one of two or more ions of a second atomic object type, the second atomic object type being different from the first atomic object type, and wherein the at least one of the two or more ions of the second atomic object type is configured to function as a qubit of a quantum computer comprising the atomic object confinement device.

[0022] In one example embodiment, the first detuning amount and the second detuning amount are approximately equal. In one example embodiment, the first manipulation signal is a pi-polarized laser beam and the second manipulation signal is a sigma-polarized laser beam.

[0023] In one example embodiment, the polarization of the first manipulation signal and the polarization of the second manipulation signal correspond to a two-photon transition associated with the dark state.

[0024] In one example embodiment, the computer-executable instructions are further configured to, when executed by the at least one processor, cause the apparatus to cause at least generation of a magnetic field having a magnetic field direction in a particular region of the atomic object confinement device, wherein one of the atomic object or the particular region of the atomic object confinement device defines an atomic object axis, the magnetic field direction being transverse to the atomic object axis.

[0025] In one example embodiment, the magnetic field direction and the atomic object axis form an angle of thirty to sixty degrees.

[0026] In one example embodiment, the first manipulation signal defines a first propagation direction transverse to the atomic object axis, and the second manipulation signal defines a second propagation direction transverse to the atomic object axis.

[0027] In one example embodiment, the first propagation direction and the second propagation direction are approximately antiparallel to each other, and the magnetic field direction is transverse to both the first propagation direction and the second propagation direction.

[0028] In one example embodiment, both the first propagation direction and the second propagation direction are approximately perpendicular to the magnetic field direction.

[0029] In one example embodiment, (a) the polarization of the first manipulation signal is approximately transverse to a plane defined by the atomic object confinement device, (b) the polarization of the second manipulation signal is approximately transverse to the plane defined by the atomic object confinement device, and (c) the first propagation direction, the second propagation direction, and the magnetic field direction are approximately parallel to the plane defined by the atomic confinement device, respectively.

[0030] According to another aspect, a system is provided. In one example embodiment, the system comprises: an atomic object confinement device configured to confine an atomic object in a particular region of the atomic object confinement device; a first manipulation source controllable by a controller of the system and configured to provide a first manipulation signal to the particular region of the atomic object confinement device; a second manipulation source controllable by the controller of the system and configured to provide a second manipulation signal to the particular region of the atomic object confinement device; and, the controller. The controller comprises at least one processor and a memory storing computer-executable instructions configured to, when executed by the at least one processor, cause the controller to at least control the first manipulation source to provide the first manipulation signal to the particular region of the atomic object confinement device; and, control the second manipulation source to provide the second manipulation signal to the particular region of the atomic object confinement device. The first manipulation signal and the second manipulation signal are configured to collectively cool the atomic object. The first manipulation signal is characterized by a first wavelength corresponding to a transition between an S manifold and a P manifold of a first component of the atomic object, and is detuned from the transition between the S manifold and the P manifold by a first detuning amount. The second manipulation signal is characterized by a second wavelength corresponding to a transition between the P manifold and a D manifold of the first component of the atomic object, and is detuned from the transition between the P manifold and the D manifold by a second detuning amount. The first and second detuning amounts are selected to establish a dark state related to a two-photon transition between the S manifold and the D manifold.

[0031] In one example embodiment, the system is a quantum computer based on a quantum charge coupled device (QCCD).

[0032] In one example embodiment, the device is a controller of a quantum computer comprising the atomic object confinement device.

[0033] In one example embodiment, the atomic object is an ion crystal comprising two or more ions, and the first component of the atomic object is at least one of the two or more ions of a first atomic object type.

[0034] In one example embodiment, the first component of the atomic object is configured to function as a coolant ion in a collective cooling scheme of the crystal.

[0035] In one example embodiment, the second component of the atomic object is at least one of two or more ions of a second atomic object type, the second atomic object type being different from the first atomic object type, and wherein the at least one of the two or more ions of the second atomic object type is configured to function as a qubit of a quantum computer comprising the atomic object confinement device.

[0036] In one example embodiment, the first detuning amount and the second detuning amount are approximately equal.

[0037] In one example embodiment, the first steering signal is a pi polarized laser beam and the second steering signal is a sigma polarized laser beam.

[0038] In one example embodiment, the polarization of the first steering signal and the polarization of the second steering signal correspond to a two-photon transition associated with a dark state.

[0039] In one example embodiment, the computer executable instructions are further configured to, when executed by the at least one processor, cause the apparatus to at least cause generation of a magnetic field having a magnetic field direction in a particular region of the atomic object confinement apparatus, wherein one of the atomic object or the particular region of the atomic object confinement apparatus defines an atomic object axis, the magnetic field direction being transverse to the atomic object axis.

[0040] In one example embodiment, the magnetic field direction and the atomic object axis form an angle of thirty to sixty degrees.

[0041] In one example embodiment, the first steering signal defines a first propagation direction transverse to the atomic object axis and the second steering signal defines a second propagation direction transverse to the atomic object axis.

[0042] In one example embodiment, the first propagation direction and the second propagation direction are approximately anti-parallel to each other and the magnetic field direction is transverse to both the first propagation direction and the second propagation direction.

[0043] In one example embodiment, both the first propagation direction and the second propagation direction are approximately perpendicular to the magnetic field direction.

[0044] In one example embodiment, (a) the polarization of the first steering signal is approximately transverse to a plane defined by the atomic object confinement apparatus, (b) the polarization of the second steering signal is approximately transverse to the plane defined by the atomic object confinement apparatus, and (c) the first propagation direction, the second propagation direction, and the magnetic field direction are each approximately parallel to the plane defined by the atomic object confinement apparatus.

[0045] According to another aspect, there is provided a method for cooling an atomic object confined by an atomic object confinement apparatus. In one example embodiment, the method includes, by a controller associated with the atomic object confinement apparatus, controlling a first manipulation source to provide a first manipulation signal to a particular region of the atomic object confinement apparatus. The method also includes, by the controller, controlling a second manipulation source to provide a second manipulation signal to the particular region of the atomic object confinement apparatus. The atomic object to be cooled is located within the particular region of the atomic object confinement apparatus. The first manipulation signal is characterized by a first wavelength corresponding to a first transition between a first clock state of an S manifold and a P manifold of a first component of the atomic object, and is detuned from the first transition by a first detuning amount. The second manipulation signal is characterized by a second wavelength corresponding to a second transition between a second clock state of the S manifold and the P manifold of the first component of the atomic object, and is detuned from the second transition by a second detuning amount. The first detuning amount and the second detuning amount are selected to establish a dark state related to a two-photon transition between the first clock state and the second clock state.

[0046] In one example embodiment, the atomic object is an ionic crystal including two or more ions, and the first component of the atomic object is at least one of the two or more ions of a first atomic object type.

[0047] In one example embodiment, the first component of the atomic object is configured to function as a coolant ion in a cooperative cooling scheme for the crystal.

[0048] In one example embodiment, the second component of the atomic object is at least one of two or more ions of a second atomic object type, the second atomic object type being different from the first atomic object type, and wherein the at least one of the two or more ions of the second atomic object type is configured to function as a qubit of a quantum computer including the atomic object confinement apparatus.

[0049] In one example embodiment, the first atomic object type is singly ionized ytterbium.

[0050] In one example embodiment, the first detuning amount and the second detuning amount are approximately equal.

[0051] In one example embodiment, the method further includes causing or controlling generation of a magnetic field having a magnetic field direction in the particular region of the atomic object confinement apparatus, and the magnetic field direction is transverse to a direction of propagation of the first manipulation signal.

[0052] In one example embodiment, the first manipulation signal is characterized by a first polarization that is a linear polarization approximately parallel to a plane defined by the atomic object confinement apparatus, and the second manipulation signal is characterized by a second polarization that is a linear polarization approximately perpendicular to the plane defined by the atomic object.

[0053] In one example embodiment, the method further comprises causing a magnetic field having a magnetic field direction to be generated in the particular region of the atomic object confinement device, wherein the magnetic field direction is transverse to the first polarization.

[0054] In one example embodiment, the first manipulation signal is characterized by a first polarization and the second manipulation signal is characterized by a second polarization, the first polarization being transverse to the second polarization.

[0055] In one example embodiment, the first clock state is an F = 1, m = 0 state and the second clock state is an F = 0, m = 0 state.

[0056] According to another aspect, there is provided an apparatus configured to cause / control cooling of an atomic object confined by an atomic object confinement device. In one example embodiment, the apparatus comprises at least one processor and a memory storing computer-executable instructions. The computer-executable instructions are configured to, when executed by the at least one processor, cause the apparatus at least to control a first manipulation source to provide a first manipulation signal to a particular region of the atomic object confinement device; and, control a second manipulation source to provide a second manipulation signal to the particular region of the atomic object confinement device. The atomic object to be cooled is located within the particular region of the atomic object confinement device. The first manipulation signal and the second manipulation signal are configured to collectively cool the atomic object. The first manipulation signal is characterized by a first wavelength corresponding to a first clock state to a P manifold of an S manifold of a first component of the atomic object and is detuned from the first clock state by a first detuning amount. The second manipulation signal is characterized by a second wavelength corresponding to a second clock state to the P manifold of the S manifold of the first component of the atomic object and is detuned from the second clock state by a second detuning amount. The first detuning amount and the second detuning amount are selected to establish a dark state related to a two-photon transition between the first clock state and the second clock state.

[0057] In one example embodiment, the atomic object is an ion crystal comprising two or more ions and the first component of the atomic object is at least one of the two or more ions of a first atomic object type.

[0058] In one example embodiment, the first component of the atomic object is configured to function as a coolant ion in a collective cooling scheme for the crystal.

[0059] In one example embodiment, the second component of the atomic object is at least one of two or more ions of a second atomic object type, the second atomic object type being different from the first atomic object type, and wherein the at least one of the two or more ions of the second atomic object type is configured to function as a qubit of a quantum computer comprising the atomic object confinement device.

[0060] In one example embodiment, the first atomic object type is singly ionized ytterbium.

[0061] In one example embodiment, the first detuning and the second detuning are approximately equal.

[0062] In one example embodiment, a magnetic field having a magnetic field direction is present in a particular region of the atomic object confinement device, and the magnetic field direction is transverse to a propagation direction of the first manipulation signal.

[0063] In one example embodiment, the first manipulation signal is characterized by a first polarization, which is a linear polarization approximately parallel to a plane defined by the atomic object confinement device, and the second manipulation signal is characterized by a second polarization, which is a linear polarization approximately perpendicular to the plane defined by the atomic object.

[0064] In one example embodiment, a magnetic field having a magnetic field direction is present in a particular region of the atomic object confinement device, and the magnetic field direction is transverse to the first polarization.

[0065] In one example embodiment, the first manipulation signal is characterized by a first polarization, and the second manipulation signal is characterized by a second polarization, the first polarization being transverse to the second polarization.

[0066] In one example embodiment, the first clock state is an F = 1, m = 0 state, and the second clock state is an F = 0, m = 0 state.

[0067] In one example embodiment, the device is a controller for a quantum computer based on a quantum charge coupled device (QCCD).

[0068] According to yet another aspect, a system is provided. In one example embodiment, the system comprises: an atomic object confinement device configured to confine an atomic object in a particular region of the atomic object confinement device; a first manipulation source controllable by a controller of the system and configured to provide a first manipulation signal to the particular region of the atomic object confinement device; a second manipulation source controllable by the controller of the system and configured to provide a second manipulation signal to the particular region of the atomic object confinement device; and, the controller comprising at least one processor and a memory storing computer-executable instructions. The computer-executable instructions are configured to, when executed by the at least one processor, cause the controller to at least control the first manipulation source to provide the first manipulation signal to the particular region of the atomic object confinement device; and, control the second manipulation source to provide the second manipulation signal to the particular region of the atomic object confinement device. The first manipulation signal and the second manipulation signal are configured to collectively cool the atomic object. The first manipulation signal is characterized by a first wavelength corresponding to a first transition between a first clock state of an S manifold and a P manifold of a first component of the atomic object, and is detuned from the first transition by a first detuning amount. The second manipulation signal is characterized by a second wavelength corresponding to a second transition between a second clock state of the S manifold and the P manifold of the first component of the atomic object, and is detuned from the second transition by a second detuning amount. The first detuning amount and the second detuning amount are selected to establish a dark state related to a two-photon transition between the first clock state and the second clock state.

[0069] In one example embodiment, the atomic object is an ion crystal comprising two or more ions, and the first component of the atomic object is at least one of the two or more ions of a first atomic object type.

[0070] In one example embodiment, the first component of the atomic object is configured to function as a coolant ion in a collective cooling scheme for the crystal.

[0071] In one example embodiment, the second component of the atomic object is at least one of two or more ions of a second atomic object type, the second atomic object type being different from the first atomic object type, and wherein the at least one of the two or more ions of the second atomic object type is configured to function as a qubit of a quantum computer comprising the atomic object confinement device.

[0072] In one example embodiment, the first atomic object type is singly ionized ytterbium.

[0073] In one example embodiment, the first detuning amount and the second detuning amount are approximately equal.

[0074] In one example embodiment, a magnetic field having a magnetic field direction is present in the particular region of the atomic object confinement device, and the magnetic field direction is transverse to a direction of propagation of the first manipulation signal.

[0075] In one example embodiment, the first manipulation signal is characterized by a first polarization, which is a linear polarization substantially parallel to a plane defined by the atomic object confinement device, and the second manipulation signal is characterized by a second polarization, which is a linear polarization substantially perpendicular to the plane defined by the atomic object.

[0076] In one example embodiment, there is a magnetic field having a magnetic field direction in a particular region of the atomic object confinement device, and the magnetic field direction is transverse to the first polarization.

[0077] In one example embodiment, the first manipulation signal is characterized by a first polarization, and the second manipulation signal is characterized by a second polarization, the first polarization being transverse to the second polarization.

[0078] In one example embodiment, the first clock state is an F = 1, m = 0 state, and the second clock state is an F = 0, m = 0 state.

[0079] In one example embodiment, the system is a quantum computer based on a quantum charge coupled device (QCCD). BRIEF DESCRIPTION OF DRAWINGS

[0080] Having thus described the application in general terms, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and wherein:

[0081] Figure 1 A block diagram of an example atomic object quantum computer according to an example embodiment is provided.

[0082] Figure 2A An energy level diagram of a first component of an atomic object illustrating performance of a cooling operation according to an example embodiment is provided.

[0083] Figure 2B An energy level diagram of a first component of an atomic object illustrating performance of a cooling operation according to another example embodiment is provided.

[0084] Figure 3A A schematic diagram illustrating performance of a cooling operation corresponding to the energy level diagram shown in Figure 2A FIG. 1 according to an example embodiment is provided.

[0085] Figure 3B A schematic diagram illustrating performance of another cooling operation corresponding to the energy level diagram shown in Figure 2B FIG. 1 according to an example embodiment is provided.

[0086] Figure 4 An energy level diagram of a first component of an atomic object illustrating performance of a cooling operation according to another example embodiment is provided.

[0087] Figure 5 A flowchart showing various processes and / or procedures of a cooling operation in accordance with one example embodiment is provided. Figure 4 A schematic diagram of the execution of a cooling operation shown in the energy level diagram of FIG. 1.

[0088] Figure 6 A flowchart showing various processes and / or procedures of a cooling operation in accordance with one example embodiment is provided.

[0089] Figure 7 A schematic diagram of an example controller of a quantum computer including an atomic object confinement device configured to confine an atomic object therein in accordance with one example embodiment is provided.

[0090] Figure 8 A schematic diagram of an example computing entity of a quantum computer system that can be used in accordance with one example embodiment is provided. DETAILED DESCRIPTION

[0091] The present application will now be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the application are shown. Indeed, the application can be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. The term "or" as used in this document (also represented as " / ") is to be interpreted as an inclusive or, meaning any one or any combination of the listed items. The terms "illustrative" and "exemplary" are used to mean example, and are not to be construed as limiting. The terms "generally" and "about" are used to mean within an acceptable range of engineering and / or manufacturing tolerances and / or within a range that is acceptable for the user at hand. Like numbers refer to like elements throughout.

[0092] In various scenarios, an atomic object is confined within an atomic object confinement device. In various embodiments, the atomic object confinement device is an ion trap, such as a surface ion trap, a Paul ion trap, and / or the like. In various embodiments, the atomic object is an ion, an atom, an ion crystal, an atom crystal, and / or the like. In one example embodiment, the atomic object includes two or more ions, where a first component of the atomic object is one or more ions of a first atomic type (e.g., a first chemical element, an ion of a first atomic number, and / or the like). In one example embodiment, the atomic object includes two or more ions, where a second component of the atomic object is one or more ions of a second atomic type (e.g., a second chemical element, an ion of a second atomic number, and / or the like). In one example embodiment, the first component of the atomic object (the ions of the first atomic type) are one or more cooling ions used in a sympathetic cooling scheme of the atomic object. In one example embodiment, the second component of the atomic object (e.g., the ions of the second atomic object type) are one or more qubit ions used as qubits of a quantum computer.

[0093] In various embodiments, the atomic objects confined within the atomic object confinement device are used to perform experiments, controlled quantum state evolution, quantum computation, etc. In various embodiments, in order for the atomic objects confined within the atomic object confinement device to be used to perform experiments, controlled quantum state evolution, quantum computation, etc., the atomic objects need to be at low temperature and / or cooled near the motional ground state of the atomic objects and / or their constituents. In various embodiments, laser cooling is used to reduce the motional energy of the atomic objects and / or their constituents. For example, in an example embodiment, the first component of the atomic objects are cooling ions used to cooperatively cool the qubit ions, and the second component of the atomic objects are qubit ions used as qubits of a quantum computer.

[0094] Conventional types of laser cooling include Doppler cooling and resolved sideband cooling. Doppler cooling includes cooling an atomic object by a wider optical transition compared to the atomic object's long term frequency. The long term frequency of an atomic object is the frequency at which the atomic object oscillates in response to the confining potential and / or pseudopotential of the atomic object confinement device, such as the frequency produced by applying a radio frequency voltage signal to the orbit of a radio frequency electrode and / or a Paul surface ion trap. Doppler cooling is relatively easy to perform, but generally cannot be used to cool the atomic objects and / or their components to a sufficiently low temperature. Resolved sideband cooling refers to cooling an atomic object by a narrow optical transition compared to the atomic object's long term frequency. However, resolved sideband cooling is technically demanding and requires a relatively high power laser beam to perform sufficient cooling.

[0095] EIT cooling is another form of laser cooling. EIT cooling includes applying two laser fields and a magnetic field to the atomic object. The laser fields are detuned from respective transitions of the first component of the atomic object. Cooling occurs when stronger photon absorption occurs on a red-detuned motional sideband compared to a blue-detuned motional sideband.

[0096] Two example EIT cooling operations are described herein. The first is an S-to-P-to-D EIT cooling operation, which can be used, for example, for atomic objects in which the first component is singly ionized barium (138Ba) atoms or another atomic object component with a similar energy structure (e.g., similar fine structure and / or hyperfine structure, such as singly ionized 88Sr). The S-to-P-to-D EIT cooling operation can be used, for example, for atomic objects in which the first component has a low-lying D manifold. As used herein, a low-lying D manifold is a manifold of states with orbital angular momentum quantum number = 2 that are lower in energy than a manifold of states P with orbital angular momentum quantum number = 1, respectively.

[0097] A second example EIT cooling operation described herein is a clock state EIT cooling operation. For example, the clock state EIT cooling operation is configured for use with an atomic object in which the first component is a singly ionized ytterbium (e.g., 171Yb) atom or another atomic object component having a similar energy structure (e.g., a similar fine structure and / or hyperfine structure). For example, the clock state EIT cooling operation can be performed with an atomic object in which the first component has an electronic spin of ½ and a nuclear spin of ½. For example, the energy structure of the first component of the atomic object includes one low-energy manifold that includes two states forming a pair of "clock" states, which are defined by the characteristic that the energy difference between the two states is insensitive to fluctuations in the magnetic field. For example, the S 1 / 2 , F = 0, M = 0 and S 1 / 2 , F = 1, M = 0 states are examples of such a pair of clock states. This pair of clock states allows for a transition to a common high-energy manifold, such as the P manifold in 171Yb, which has a linewidth large enough to allow for convenient laser coupling. In the example described with respect to Figure 4 , the clock states are coupled to the P manifold by a sigma + / - transition. Another example first component of an atomic object having a similar energy structure is singly ionized 133Ba.

[0098] Exemplary quantum computer system

[0099] Laser cooling of an atomic object confined by an atomic object confinement device can be performed in a variety of environments and / or for a variety of applications. One example context is a quantum computer based on quantum charge coupled devices (QCCDs). Figure 1 A block diagram of an example quantum computer system 100 is provided. In various embodiments, the quantum computer system 100 includes a computing entity 10 and a quantum computer 110.

[0100] In various embodiments, the quantum computer 110 includes a controller 30, a cryogenic and / or vacuum chamber 40 enclosing an atomic object confinement device 50 in which atomic objects are confined, and one or more manipulation sources 64 (e.g., 64A, 64B, 64C). In one example embodiment, the one or more manipulation sources 64 can include one or more lasers (e.g., optical lasers, microwave sources, and / or microwave masers, etc.) or another manipulation source. In various embodiments, the one or more manipulation sources 64 are configured to manipulate and / or cause controlled quantum state evolution of one or more atomic objects within the device 50. For example, a first manipulation source 64A is configured to generate and / or provide a first manipulation signal and a second manipulation source 64B is configured to generate and / or provide a second manipulation signal, where the first and second manipulation signals are configured to collectively laser cool an atomic object confined by the atomic object confinement device.

[0101] In various embodiments, the atomic object confinement apparatus 50 is an ion trap, such as a surface ion trap, a Paul ion trap, etc. In various embodiments, the atomic object is an ion, an atom, an ion crystal, an atom crystal, etc. In one example embodiment, the atomic object includes two or more ions, where a first component of the atomic object is one or more ions of a first atomic type (e.g., ions of a first chemical element, a first atomic number, etc.). In one example embodiment, the atomic object includes two or more ions, where a second component of the atomic object is one or more ions of a second atomic type (e.g., ions of a second chemical element, a second atomic number, etc.). In one example embodiment, the first component of the atomic object (ions of the first atomic type) are one or more cooling ions used in a sympathetic cooling scheme of the atomic object. In one example embodiment, the second component of the atomic object (e.g., ions of the second atomic object type) are one or more qubit ions used as qubits of a quantum computer. For example, in one example embodiment, the atomic object is an ion crystal that includes singly ionized Ba atoms used as cooling ions and singly ionized Yb ions used as qubit ions. In another example embodiment, the atomic object is an ion crystal that includes singly ionized Yb atoms used as cooling ions and singly ionized Ba ions used as qubit ions.

[0102] In one example embodiment, the one or more manipulation sources 64 each provide a manipulation signal (e.g., a laser beam, etc.) to one or more regions of the atomic object confinement apparatus 50 through a respective optical beam path 66 (e.g., 66A, 66B, 66C). In various embodiments, at least one optical beam path 66 includes a modulator configured to modulate the manipulation signal provided to the apparatus 50 via the optical beam path 66. In various embodiments, the manipulation sources 64, the modulators, and / or other components of the quantum computer 110 are controlled by the controller 30.

[0103] In various embodiments, the quantum computer 110 includes one or more magnetic field generators 70 (e.g., 70A, 70B). For example, the magnetic field generators can be internal magnetic field generators 70A disposed within the cryogenic and / or vacuum chamber 40 and / or external magnetic field generators 70B disposed outside of the cryogenic and / or vacuum chamber 40. In various embodiments, the magnetic field generators 70 are permanent magnets, Helmholtz coils, electromagnets, etc. In various embodiments, the magnetic field generators 70 are configured to produce a magnetic field in one or more regions of the atomic object confinement apparatus 50 having a particular magnitude and a particular magnetic field direction in the one or more regions of the atomic object confinement apparatus 50.

[0104] In various embodiments, the controller 30 is configured to control the voltage source, the electrical signal source, and / or a driver that controls the transport of the atomic objects within the atomic object confinement device 50 and / or the atomic object confinement device 50 (cryogenic system), and / or a cryogenic system and / or a vacuum system that controls the temperature and pressure within the cryogenic and / or vacuum chamber 40, the manipulation source 64, the magnetic field generator 70, and / or other systems configured to manipulate and / or cause a controlled evolution of the quantum state of one or more atomic objects within the atomic object confinement device 50.

[0105] In various embodiments, the computing entity 10 is configured to allow a user to provide input to the quantum computer 110 (e.g., through a user interface of the computing entity 10) and receive, view output from the quantum computer 110, etc. The computing entity 10 can communicate with the controller 30 of the quantum computer 110 through one or more wired or wireless networks 20 and / or through direct wired and / or wireless communication. In one example embodiment, the computing entity 10 can translate, configure, format information / data, quantum computing algorithms, quantum circuits, etc., into a computing language, executable instructions, command sets, and / or the like that the controller 30 can understand and / or implement.

[0106] Example S to P to D EIT cooling operation

[0107] Various embodiments provide quantum computers, systems, devices, and the like, and corresponding methods for performing EIT cooling based on a two-photon resonance transition between one or more states of a S manifold of a first component of an atomic object to one or more states of a D manifold of the first component of the atomic object via a P manifold of the first component of the atomic object.

[0108] Generally, EIT cooling of an ion having a Ba+like energy structure (e.g., a fine and / or hyperfine energy structure similar to a singly ionized Ba atom) includes using a single laser for both couplings, coupling a first state (Zeeman, Zeeman) in a ground state manifold (e.g., a S manifold corresponding to angular momentum quantum number l = 0) to an excited state in an excited state manifold, and coupling the excited state in the excited state manifold to a second state (Zeeman, Zeeman) in the ground state manifold (e.g., S manifold). In other words, conventional EIT cooling uses a two-photon transition to couple two states within the same manifold together.

[0109] However, for atomic objects or first components of atomic objects having low-lying D manifolds, the atomic objects or first components of atomic objects can get "stuck" in the D manifold. As used herein, a low-lying D manifold is a manifold of states with orbital angular momentum quantum number l = 2 that is energetically lower than a manifold of states P with orbital angular momentum quantum number l = 1, respectively. Thus, conventional EIT cooling requires additional elements and steps to effectively cool atomic objects containing first components having low-lying D manifolds. Accordingly, there exists a technical problem as to how to efficiently, effectively, and robustly cool atomic objects to near their motional ground state.

[0110] Various embodiments provide technical solutions to these technical problems. In various embodiments, an EIT cooling operation is performed using a first manipulation signal that couples one or more states of an S manifold to one or more states of a P manifold and a second manipulation signal that couples one or more states of the P manifold to one or more states of a D manifold. In various embodiments, both the first manipulation signal and the second manipulation signal are detuned above the one or more states of the P manifold to establish a dark state associated with a two-photon transition between the S manifold and the D manifold. By coupling the S manifold to the P manifold and coupling the P manifold to the D manifold, efficient cooling of atomic objects to near the motional ground state (e.g., to temperatures significantly below the Doppler cooling limit) can be achieved in a manner that has lower laser power requirements than resolved sideband cooling and is simpler than conventional EIT cooling techniques. Moreover, in various embodiments, the first and second manipulation sources used to generate and / or provide the first and second manipulation signals can also be used to perform Doppler cooling. Thus, various embodiments are able to use both Doppler cooling and EIT cooling without requiring additional lasers or other manipulation sources. Accordingly, various embodiments provide technical improvements to conventional laser cooling of atomic objects including first components having low-lying D manifolds.

[0111] Furthermore, the detuning amounts of various embodiments are less than conventional detuning amounts of conventional EIT cooling operations, which enables simultaneous cooling of multiple modes of atomic objects. For example, in various embodiments, by adjusting the first and second detuning amounts (while in various embodiments maintaining the first and second detuning amounts substantially equal to each other) and the strengths of the first and second manipulation signals, an optimal set of parameters can be determined for an atomic object that enables simultaneous cooling of a large range of crystal modes of the atomic object having different frequencies (e.g., varying between ~1 MHz and ~3 MHz). For example, various embodiments provide the additional advantage of being able to simultaneously cool multiple modes of an atomic object having different mode frequencies (e.g., a frequency range exceeding 1-3 MHz) in a broadband manner.

[0112] Figure 2AA partial energy level diagram of an example first component of an atomic object (e.g., a cooled ion) illustrating an example EIT cooling operation is provided in accordance with various embodiments. The partial energy level diagram illustrates an S manifold 210. In various embodiments, the EIT cooling operation utilizes one or more states of the S manifold 210 (e.g., one or two states of the S manifold). The partial energy level diagram also illustrates a P manifold 220. In various embodiments, the EIT cooling operation utilizes one or more states of the P manifold 220 (e.g., one or two states of the P manifold). The partial energy level diagram further illustrates a low-lying D manifold 230. In various embodiments, the EIT cooling operation utilizes one or more states of the D manifold 230 (e.g., one, two, three, or four states of the D manifold).

[0113] Figure 2B A partial energy level diagram of an example first component of an atomic object (e.g., a cooled ion) illustrating another example EIT cooling operation is provided in accordance with various embodiments. Figure 2B The illustrated partial energy level diagram includes the same S manifold 210, P manifold 220, and low-lying D manifold 230 as Figure 2A illustrated, since, for example, the diagram corresponds to the energy levels of the same cooled ion. However, a polarization of a first manipulation signal 215' used to couple the S manifold 210 to the P manifold 220 is σ polarized in Figure 2B , rather than π polarized as illustrated in Figure 2A .

[0114] Performance of the EIT cooling operation of various embodiments includes application of the first manipulation signal 215, 215' and the second manipulation signal 225, 225' to the atomic object. In an example embodiment, the first manipulation signal 215 is characterized by a first wavelength λ1 and is π polarized, as illustrated in Figure 2A . In another example embodiment, the first manipulation signal 215' is characterized by a first wavelength λ1 and is σ polarized, as illustrated in Figure 2B . The first wavelength λ1 corresponds to a transition between the S manifold 210 and the P manifold 220. In various embodiments, the first wavelength λ1 corresponds to a resonant frequency of the transition between the S manifold 210 and the P manifold 220, and is detuned therefrom by a first detuning amount Δ SP .

[0115] In an example embodiment, the second manipulation signal 225, 225' is characterized by a second wavelength λ2 and is σ polarized. For example, the second manipulation signal 225 is linearly polarized (σ + / - polarization) in a direction perpendicular to the magnetic field. The second wavelength λ2 corresponds to a transition between the P manifold 220 and the D manifold 230. In various embodiments, the second wavelength λ2 corresponds to a resonant frequency of the transition between the P manifold 220 and the D manifold 230, and is detuned therefrom by a second detuning amount Δ PD .

[0116] In various embodiments, the first and second detunings are substantially equal to each other (e.g., Δ SP ≈ Δ PD ). In an example embodiment, the first constituent of the atomic object is singly ionized Ba, the first wavelength λ1≈ 493 nm, the second wavelength λ2≈ 650 nm, the first and second detunings Δ SP ≈ 20 MHz ≈ Δ PD In various embodiments, the frequency of the first manipulation signal 215, 215' and the frequency of the second manipulation signal 225, 225' are stable relative to each other within a tolerance Δω / (2π) < 100 kHz. It will be appreciated that various other polarization schemes, wavelengths, and detunings are used in various other embodiments based on the energy structure of the first constituent of the atomic object and the selected dark state.

[0117] As used herein, the term dark state refers to a coherent superposition of two states formed by an appropriate two-photon transition. For the embodiments shown in FIGS. 1A and IB, the corresponding dark state is formed by a superposition of a state in the S manifold and a state in the D manifold, which are coupled by the first manipulation signal 215, 215' and the second manipulation signal 225, 225'. Figure 2A and 2B For the embodiments shown in FIGS. 1A and IB, the corresponding dark state is formed by a superposition of a state in the S manifold and a state in the D manifold, which are coupled by the first manipulation signal 215, 215' and the second manipulation signal 225, 225'.

[0118] It will be appreciated that as used herein, a transition between a first manifold and a second manifold (e.g., the S manifold and the P manifold, the P manifold and the D manifold) indicates a transition between a state of the first manifold and a state of the second manifold. As used herein, a manifold of states refers to a group of states having the same total angular momentum, where each manifold includes multiple states that are different in energy due to the application of a magnetic field through Zeeman splitting. The total angular momentum of a state corresponds to the sum of the spin angular momentum and the orbital angular momentum of the state (including the nuclear angular momentum through hyperfine coupling when the nuclear angular momentum is non-zero).

[0119] In various embodiments, the S-to-P-to-D EIT cooling operation involves the Zeeman states of the S 1 / 2 manifold 210, the Zeeman states of the P 1 / 2 manifold 220, and the Zeeman states of the D 3 / 2 manifold 230. In one example embodiment, the S-to-P-to-D EIT cooling operation involves states and / or manifolds that tend to be used for Doppler cooling. Thus, for a system configured to perform Doppler cooling, the same manipulation source can be readily reused in an example embodiment of the S-to-P-to-D EIT cooling operation. Under the finite magnetic field and fixed frequency (e.g., fixed wavelength λ2) of the second manipulation signal 225, 225', scanning the frequency of the first manipulation signal 215, 215' reveals a transition from the S 1 / 2 manifold 210 to the D3 / 2 Four dark state resonances are associated with the two-photon resonance transitions of manifold 230. Dark states are states of atomic objects and / or components of atomic objects that cannot absorb or emit photons. When the first wavelength λ1 of the first manipulation signals 215, 215' and the second wavelength λ2 of the second manipulation signals 225, 225' are tuned to one of these two-photon resonances, preferential scattering is induced on the red-sideband transitions that remove kinetic energy from the atomic objects and / or the first components of atomic objects (e.g., cooling ions), and EIT cooling is achieved when the scattering rate of the blue side (e.g., the shorter wavelength, higher frequency side) of the two-photon resonance is less than the scattering rate of the red side (e.g., the longer wavelength, lower frequency side) of the two-photon resonance.

[0120] exist Figure 2A In the diagram, the coupling of the first control signal 215 (shown by solid lines) and the second control signal 225 (shown by solid lines) illustrates the operation of S... 1 / 2 m of manifold 210 j = 1 / 2 states and D 3 / 2 m of manifold 230 j = An example two-photon resonance consisting of 3 / 2 states can be used for EIT cooling operations from S to P to D in the example embodiment.

[0121] The frequency bandwidth of the two-photon resonance depends on P l / 2 The single-photon detuning of the manifold state (e.g., Δ) SP Δ PD For example, as the first and / or second detuning decreases, the width of the two-photon resonance widens, while as the first and / or second detuning increases, the width of the two-photon resonance narrows. The narrower frequency width of the two-photon resonance provides faster cooling to lower temperatures (compared to the wider frequency width of the two-photon resonance), while the wider frequency width of the two-photon resonance provides a wider cooling bandwidth (compared to the narrower frequency width of the two-photon resonance).

[0122] In various embodiments, the first detuning amount Δ SP Second detuning Δ PD The detuning amount is set in the range of 10-450MHz. For example, in one example embodiment, ΔSP = Δ PD ≈ 20 MHz, which provides a sufficiently large cooling bandwidth to effectively cool many motion modes of atomic objects (e.g., ionic crystals, such as ionic crystals containing four ions), while still maintaining a cooling rate and final temperature sufficient for a variety of applications, including cooling atomic objects confined within an atomic object confinement device of a quantum computer, wherein the atomic objects include qubit ions used as qubits in the quantum computer.

[0123] In each embodiment, the first and second detuning amounts ΔSP = Δ PD The first and second detunings of various embodiments are smaller than a traditional detuning used in a traditional EIT cooling operation. The smaller first and second detunings of various embodiments (as compared to the traditional detuning of a traditional EIT cooling operation) enable simultaneous cooling of multiple modes of an atomic object. For example, in various embodiments, by adjusting the first and second detunings (while maintaining Δ SP = Δ PD ) and the intensities of the first and second manipulation signals, an optimal set of parameters can be determined for an atomic object that enables simultaneous cooling of a large range of crystal modes of the atomic object having different frequencies (e.g., varying between ~1 MHz and ~3 MHz). For example, various embodiments enable simultaneous cooling of multiple modes of an atomic object having different mode frequencies (e.g., a frequency range exceeding 1-3 MHz).

[0124] In various embodiments, the efficiency of the S-to-P-to-D EIT cooling operation of various embodiments is improved when the first and second wavelengths λ1, λ2 characterizing the first and second manipulation signals, respectively, are relatively stable with respect to each other. In one example embodiment, the first manipulation source and the second manipulation source are configured such that the first wavelength λ1 and the second wavelength λ2 are independently stabilized such that their frequency difference is stabilized to a tolerance of For example, in one example embodiment, the relative stabilization of the first and second wavelengths is performed by independently stabilizing the first and second manipulation sources 64A, 64B. In various embodiments, stabilization of the first and / or second manipulation sources 64A, 64B and / or stabilization of the first and / or second wavelengths is achieved by using a resonant cavity, coupling the first and second manipulation signals to a frequency comb (examples of which are described in U.S. Patent No. 10,951,002, issued March 16, 2021 (the contents of which are incorporated by reference in their entirety herein)); using servo and / or feedback loops, etc.

[0125] Figure 3A One example geometry for performing the S-to-P-to-D EIT cooling operation of the example embodiment shown in Figure 2A is shown. Figure 3AAn atomic object 308 is shown positioned and / or arranged in the particular region 55 of the atomic object confinement device 50. The atomic object 308 includes two first components 310 and two second components 312. The first components 310 are of a first atomic type and the second components 312 are of a second atomic type, the first atomic type being different than the second atomic type. For example, in one example embodiment, the first components 310 are singly ionized Ba atoms and the second components 312 are singly ionized Yb atoms. The first and second components 310, 312 are positioned and / or arranged along the atomic object axis 305 to define the atomic object axis 305. In one example embodiment, the atomic object axis 305 is substantially parallel to a radio frequency null 350 of the particular region 55 of the atomic object confinement device 50. The radio frequency null 350 is a zero point line of a pseudo-potential generated by applying a radio frequency voltage signal to radio frequency electrodes and / or tracks of the atomic object confinement device 50.

[0126] In various embodiments, the magnetic field B is generated such that, in the particular region 55, the magnetic field B has a finite and substantially stable (e.g., not varying with time) magnitude (e.g., 2-10 Gauss and / or 5 Gauss in one example embodiment). In various embodiments, the magnetic field B in the particular region 55 has a magnetic field direction that forms an angle a with the atomic object axis 305. In one example embodiment, the angle a is 30 to 60 degrees. In one example embodiment, the angle a is approximately 45 degrees.

[0127] In various embodiments, the first manipulation signal 215 has a polarization 218 (e.g., a pi polarization). In an example embodiment, the polarization 218 of the first manipulation signal 215 is substantially parallel to the magnetic field direction. In various embodiments, the first propagation direction is transverse to the atomic object axis 305. In one example embodiment, the first manipulation signal 215 propagates in the first propagation direction that forms an angle b with the atomic object axis 305. In various embodiments, the angle b is configured such that the propagation of the first manipulation signal 215 is non-parallel or anti-parallel to the magnetic field direction. In various embodiments, the angle b is 30 to 60 degrees. In one example embodiment, the angle b is approximately 45 degrees.

[0128] In various embodiments, the second manipulation signal 225 has a polarization 228 (e.g., a sigma + / - polarization). In one example embodiment, the polarization 228 of the second manipulation signal 225 is transverse to the magnetic field direction. In various embodiments, the second propagation direction is transverse to the atomic object axis 305. In one example embodiment, the second manipulation signal 225 propagates in the second propagation direction that forms an angle g with the atomic object axis 305. In various embodiments, the angle g is 0 to 90 degrees. In one example embodiment, the angle g is approximately 45 degrees.

[0129] In various embodiments, the first propagation direction is substantially anti-parallel to the second propagation direction. In various embodiments, both the first propagation direction and the second propagation are transverse to the magnetic field direction. In one example embodiment, the first propagation direction and the second propagation direction are substantially perpendicular to the magnetic field direction.

[0130] Figure 3B Another example geometry for performing the S-to-P-to-D EIT cooling operation of the example embodiment shown in FIG. 2 is shown. Figure 2B Another example geometry for performing the S-to-P-to-D EIT cooling operation of the example embodiment shown in FIG. 2 is shown. Figure 3B An atomic object 308 is shown positioned and / or disposed in the particular region 55 of the atomic object confinement device 50. The atomic object 308 includes two first components 310 and two second components 312. The first components 310 are of a first atomic type and the second components 312 are of a second atomic type, the first atomic type being different than the second atomic type. For example, in one example embodiment, the first components 310 are singly ionized Ba atoms and the second components 312 are singly ionized Yb atoms. The first and second components 310, 312 are positioned and / or disposed along an atomic object axis 305 to define the atomic object axis 305. In one example embodiment, the atomic object axis 305 is substantially parallel to the radio frequency null 350 of the particular region 55 of the atomic object confinement device 50.

[0131] In various embodiments, the magnetic field B is generated such that in the particular region 55, the magnetic field B has a finite and substantially stable (e.g., not varying with time) magnitude (e.g., 2-10 Gauss and / or 5 Gauss in one example embodiment). In various embodiments, the magnetic field B in the particular region 55 has a magnetic field direction that forms an angle a' with the atomic object axis 305. In one example embodiment, the angle a' is 0 to 360 degrees. In one example embodiment, the angle a' is approximately 45 degrees. In particular, the magnetic field direction is substantially not parallel or anti-parallel to the polarization 228' of the second manipulation signal 225'. In various embodiments, the magnetic field B is substantially parallel to a plane defined by the atomic object confinement device.

[0132] In various embodiments, the first manipulation signal 215' has a first polarization 218' (e.g., σ + / - In one example embodiment, the first polarization 218' of the first manipulation signal 215' is substantially not parallel and / or transverse to the magnetic field direction. In one example embodiment, the first polarization 218' is perpendicular to the magnetic field direction. In various embodiments, the first propagation direction is transverse to the atomic object axis 305. In one example embodiment, the first manipulation signal 215' propagates in a first propagation direction that forms an angle β' with the atomic object axis 305. In various embodiments, the angle β' is 0 to 90 degrees. In one example embodiment, the angle β' is approximately 45 degrees. In one example embodiment, the angle β' is approximately 90 degrees.

[0133] In various embodiments, the second manipulation signal 225' has a second polarization 228' (e.g., σ + / - polarization). In one example embodiment, the second polarization 228' of the second manipulation signal 225' is transverse to the magnetic field direction. In one example embodiment, the second polarization 228' is perpendicular to the magnetic field direction. In various embodiments, the second propagation direction is transverse to the atomic object axis 305. In one example embodiment, the second manipulation signal 225' propagates in the second propagation direction at an angle γ to the atomic object axis 305. In various embodiments, the angle γ is 30 to 60 degrees. In one example embodiment, the angle γ is approximately 45 degrees.

[0134] In various embodiments, the first propagation direction is approximately anti-parallel to the second propagation direction. In the illustrated embodiment, the first propagation direction and the second propagation direction are approximately anti-parallel to each other (e.g., β'≈γ').

[0135] In various embodiments, the first propagation direction (in a unit vector in the direction of the wave vector of the respective first manipulation signal 215, 215') and the second propagation direction (in a unit vector in the direction of the wave vector of the respective second manipulation signal 225, 225') have a non-zero projection in the direction of motion to be cooled. For example, when the mode of the atomic object 308 to be cooled is an axial mode (e.g., corresponding to motion along the atomic object axis 305), where is a unit vector along the atomic object axis 305, and In another example, when the mode of the atomic object 308 to be cooled is a radial mode (e.g., corresponding to motion orthogonal to the atomic object axis 305), where is a radial unit vector (e.g., ), and .

[0136] Figure 3A and 3B two example geometries for performing the S-to-P-to-D EIT cooling operation of the example embodiments are shown. It will be appreciated that other geometries can be used in various other embodiments. For example, in one example embodiment, the magnetic field direction can be parallel or anti-parallel to the atomic object axis 305. In one example embodiment, the first propagation direction and the second propagation direction are each parallel to the atomic object axis 305. In various embodiments, the magnetic field direction is transverse to both the first and second propagation directions. In various embodiments, the magnetic field direction, the first propagation direction, and / or the second propagation can be transverse to a plane defined by the atomic object confinement device.

[0137] Generally, the EIT cooling operation of S to P to D can be performed using a first manifold, a second manifold, and a third manifold, where the first, second, and third manifolds are each different fine-structure manifolds, the first and second manifolds are lower-energy manifolds, and both the first and second manifolds can be coupled to the third (higher-energy) manifold by a dipole transition. The illustrated embodiment shows the case where the first manifold is the S manifold, the second manifold is the D manifold, and the third manifold is the P manifold.

[0138] Clock state EIT cooling operation example

[0139] Various embodiments provide quantum computers, systems, apparatuses, and the like, and corresponding methods for performing EIT cooling using clock states of a first component of an atomic object.

[0140] Previously, with the class 171Yb + EIT cooling of ions of an energy structure (e.g., a fine- and / or hyperfine energy structure similar to singly-ionized 171Yb atoms) is performed by coupling multiple F = 1 states to an excited manifold. For example, by coupling to the P 1 / 2 , F = 0, m = 0 state, the S 1 / 2 , F = 1, m = +1 state of the ground-state manifold is coupled to the S 1 / 2 , F = 1, m = 0 state of the ground-state manifold. However, the S 1 / 2 , F = 1, m = +1 state to the P1 / 2, F = 0, m = 0 state requires sigma polarization, while the S 1 / 2 , F = 1, m = 0 state to the P 1 / 2 , F = 0, m = 0 requires pi polarization, thus requiring a certain orientation of the magnetic field with respect to the direction of propagation. Furthermore, the ion can get “stuck” in the S 1 / 2 , F = 0, m = 0 state, and must be repumped into the S 1 / 2 , F = 1 manifold, requiring an additional operational signal to couple the S 1 / 2 , F = 0 manifold to the P manifold. Thus, conventional EIT cooling requires a high degree of technical sophistication to effectively cool an atomic object containing a first component of an energy structure of the class 171Yb+. Furthermore, resolving sideband cooling would require a high-bandwidth control capability beyond that required for EIT, thus requiring additional technical sophistication if one wanted to use both cooling methods simultaneously. Thus, there exists a technical problem as to how to efficiently, effectively, and robustly cool an atomic object to near its motional ground state.

[0141] Various embodiments provide technical solutions to these technical problems. In various embodiments, an EIT cooling operation is performed using a first manipulation signal that couples a first clock state in an S manifold of a first component of an atomic object to one or more states of a P manifold and a second manipulation signal that couples a second clock state in the S manifold of the first component of the atomic object to one or more states of the P manifold. In various embodiments, the first clock state in the S manifold of the first component of the atomic object is an F = 1, m = 0 state and the second clock state in the S manifold of the first component of the atomic object is an F = 0, m = 0 state. The first and second clock states have much less impact on the environment than the F = 1, m = + / - 1 states. In various embodiments, both the first manipulation signal and the second manipulation signal are detuned above the one or more states of the P manifold to establish a dark state associated with a two-photon transition between the first clock state in the S manifold and the second clock state in the S manifold.

[0142] By coupling the first and second clock states in the S manifold to produce a dark state, effective cooling of the motional ground state of the atomic object (e.g., at a temperature significantly below the Doppler cooling limit) can be achieved with lower laser power requirements than resolved sideband cooling and with less technical complexity than traditional EIT cooling. Moreover, in various embodiments, the first and second manipulation sources used to produce and / or provide the first and second manipulation signals can also be used to perform sideband cooling of the first component of the atomic object. Thus, various embodiments are able to use both sideband cooling and EIT cooling without requiring additional lasers or other manipulation sources.

[0143] Moreover, the efficacy of the various embodiments of clock state EIT cooling operations is not sensitive to the relative positioning of the magnetic field and the first and second manipulation signals. Thus, various embodiments provide the additional technical advantage of providing efficient cooling without requiring strict requirements regarding the relative positioning of the magnetic field and the first and second manipulation signals.

[0144] Moreover, the amount of detuning of various embodiments is less than the amount of detuning of conventional EIT cooling operations, which enables simultaneous cooling of multiple modes of the atomic object. For example, various embodiments provide the additional advantage of being able to simultaneously cool multiple modes of the atomic object having different mode frequencies (e.g., a frequency range exceeding 1-3 MHz) in a broadband fashion. Thus, various embodiments provide a technical improvement over conventional laser cooling of the atomic object.

[0145] Figure 4Partial energy level diagrams of an example first component of an atomic object (e.g., cooled ions) illustrating example EIT cooling operations according to various embodiments are provided. The partial energy level diagrams illustrate an S-manifold 410. In various embodiments, the EIT cooling operation utilizes two clock states of the S-manifold 410 (e.g., the m=0 state of the S-manifold). The partial energy level diagrams also illustrate a P-manifold 420. In various embodiments, the EIT cooling operation utilizes one or more states of the P-manifold 420. The partial energy level diagrams further illustrate transitions between corresponding clock states and states of the P-manifold 420 with first and second manipulation signals 415, 425 blue detuning of the P-manifold 420.

[0146] The execution of the EIT cooling operation in various embodiments includes applying a first manipulation signal 415 and a second manipulation signal 425 to the atomic object. In one example embodiment, the first manipulation signal 415 is characterized by a first wavelength λ. A It also possesses the first polarization. The first wavelength λ A This corresponds to the transition between the first clock state 412 of the S-manifold 410 and the P-manifold 420. In various embodiments, the first wavelength λ A The resonant frequency corresponding to the transition between the first clock state 412 of the S-manifold 410 and the P-manifold 420, and the first detuning amount Δ from its detuning. A .

[0147] In one example embodiment, the second manipulation signal 425 is characterized by a second wavelength λ. B It also exhibits a second polarization. The second wavelength λ B This corresponds to the transition between the second clock state 414 of the S-manifold 410 and the P-manifold 420. In various embodiments, the second wavelength λ B The resonant frequency corresponding to the transition between the second clock state 414 of the S-manifold 410 and the P-manifold 420, and the second detuning amount Δ from its detuning. B .

[0148] In various embodiments, when measured relative to a specific set of the three energy levels, the first and second detuning amounts are substantially equal to each other (e.g., Δ). A ≈Δ B In one example embodiment, the first component of the atomic object is monoionized Yb, with a first wavelength λ. A The first wavelength is approximately 369.5 nm (e.g., 369.5193 nm), the second wavelength is approximately 369.5 nm (e.g., 369.5251 nm), and the detuning of the first and second wavelengths is Δ. A ≈ 30-450 MHz ≈ Δ B In one example embodiment, Δ A ≈55MHz≈ΔB It should be appreciated that based on the energy structure of the first component of atomic objects and the selected dark state, various other polarization schemes, wavelengths, and detunings are used in various other embodiments. In various embodiments, the amount of detuning, Δ A ≈ Δ B , can be adjusted during the execution of the clock state EIT operation in order to cool different (crystal) modes of motion of the atomic objects. In various embodiments, multiple modes of the atomic objects can be simultaneously cooled, including modes of the atomic objects having different mode frequencies (e.g., a frequency range exceeding 1-3 MHz).

[0149] In various embodiments, the first polarization and the second polarization are transverse to each other. For example, in example embodiments in which the first polarization and the second polarization are linear polarizations, a first direction along which the first polarization is oriented and a second direction along which the second polarization is oriented are transverse to each other. For example, in one example embodiment, an orthogonal coordinate system is definable such that the first manipulation signal propagates in a positive z direction, the first polarization is oriented along an x direction, and the second manipulation signal propagates in a negative z direction, the second polarization is oriented along a y direction. In various embodiments, the first polarization and the second polarization can be linear or circular polarizations.

[0150] It should be appreciated that as used herein, a transition between a first manifold and a second manifold (e.g., a S 1 / 2 , F = 1 manifold and a P 1 / 2 , F = 1 manifold, and a P 1 / 2 , F = 1 manifold and a S 1 / 2 , F = 1 manifold) refers to a transition between a state of the first manifold and a state of the second manifold. As used herein with respect to the clock state EIT cooling operation, a manifold of states refers to a particular hyperfine energy level, where each manifold includes multiple states that are different in energy due to the applied magnetic field by Zeeman splitting.

[0151] The frequency width of the two-photon resonance depends on the one-photon that is detuned from the state of the P 1 / 2 manifold (e.g., Δ A , Δ B ). For example, as the first and / or second amount of detuning decreases, the width of the two-photon resonance widens, while as the first and / or second amount of detuning increases, the width of the two-photon resonance narrows. A narrower frequency width of the two-photon resonance provides faster cooling to lower temperatures (as compared to a wide frequency width of the two-photon resonance), while a wider frequency width of the two-photon resonance provides a wider cooling bandwidth (as compared to a narrow frequency width of the two-photon resonance). Various embodiments provide broadband EIT cooling by using varying amounts of detuning that are less than conventional and varying the intensity of the first and second manipulation signals to achieve simultaneous cooling of multiple atomic object modes, including modes of the atomic objects having different mode frequencies (e.g., a frequency range exceeding 1-3 MHz).

[0152] In various embodiments, the first detuning Δ A and the second detuning Δ B are set to detunings in the range of 30-450 MHz. For example, in one example embodiment, Δ A = Δ B ≈ 55 MHz, which provides a sufficiently large cooling bandwidth to effectively cool the motional modes of the atomic object (e.g., an ion crystal, such as an ion crystal containing four ions), while still maintaining a cooling speed and final temperature sufficient for various applications, including cooling atomic objects confined within atomic object confinement devices of a quantum computer, where the atomic objects include qubit ions that serve as qubits of the quantum computer.

[0153] In various embodiments, the efficiency of various embodiments of the clock state EIT cooling operation is improved when the first and second wavelengths λ A , λ B characterizing the first and second manipulation signals, respectively, are relatively stable with respect to each other. In one example embodiment, the first manipulation source and the second manipulation source are configured such that the first wavelength and the second wavelength are independently stabilized. In one example embodiment, the first manipulation signal and the second manipulation signal are generated by the same manipulation source 64, such that the respective wavelengths of the two manipulation signals are substantially stable with respect to each other.

[0154] In Figure 4 , an example two-photon resonance consisting of the m = 0 state of the S 1 / 2 manifold 410 (e.g., clock states 412, 414) and the state of the P 1 / 2 manifold 420 is shown by the coupling of the first manipulation signal 415, shown by the solid line, and the second manipulation signal 425, shown by the solid line, which can be used in the clock state EIT cooling operation of example embodiments.

[0155] Figure 4It is also shown that the atomic objects are optically pumped out of the Zeeman states 416A, 416B (m = + / - 1) of the S manifold 410 by the first manipulation signal 415. In various embodiments, spontaneous decay of the atomic objects outside of the P manifold 420 can lead to population of the uncoupled Zeeman (e.g., m = + / - 1) states 416A, 416B of the S manifold 410. However, application of the first manipulation signal 415 and the second manipulation signal 425 to the atomic objects also removes population from these uncoupled Zeeman states 416A, 416B, as shown by the dashed transition line 450. For example, application of the first manipulation signal 415 to the atomic objects optically pumps the atomic objects (e.g., m = + / -1) states 416A, 416B in the uncoupled Zeeman back to the clock states 412, 414. Thus, any atomic objects (e.g., including one or more of the clock states 412, 414 and the P manifold 420) that leak from the dark state cooling cycle will be quickly returned by this optical pumping process.

[0156] In one example embodiment, the first manipulation signal 415 is generated and / or provided by a first manipulation source 64A and the second manipulation signal 425 is generated and / or provided by a second manipulation source 64B, where the first manipulation source 64A and the second manipulation source 64B are different manipulation sources. In one example embodiment, the first manipulation signal 415 and the second manipulation signal 425 are generated by the same manipulation source (e.g., the same laser). For example, in one example embodiment, the first manipulation source and the second manipulation source are the same manipulation source or are overlapping manipulation sources (e.g., include the same laser but can include different optical components for preparing the respective manipulation signals).

[0157] Figure 5 One example geometry for performing a clock state EIT cooling operation of an example embodiment is shown. Figure 5 An atomic object 508 is shown positioned and / or disposed in the particular region 55 of the atomic object confinement device 50. The atomic object 508 includes two first components 510 and two second components 512. The first components 510 are of a first atomic type and the second components 512 are of a second atomic type, the first atomic type being different than the second atomic type. For example, in one example embodiment, the first components 510 are singly ionized Yb atoms and the second components 512 are singly ionized Ba atoms. The first and second components 510, 512 are positioned and / or disposed along an atomic object axis 505 to define the atomic object axis 505. In one example embodiment, the atomic object axis 505 is substantially parallel to a radio frequency null 550 of the particular region 55 of the atomic object confinement device 50. The radio frequency null 550 is a zero point line of a pseudo-potential created by application of a radio frequency voltage signal to radio frequency electrodes and / or tracks of the atomic object confinement device 50.

[0158] In various embodiments, the magnetic field B is generated such that in the particular region 55, the magnetic field B has a finite and generally stable (e.g., not changing over time) magnitude (e.g., 2-10 Gauss and / or 5 Gauss in one example embodiment). In various embodiments, the magnetic field B in the particular region 55 has a magnetic field direction that forms an angle Θ with the atomic object axis 505. In one example embodiment, the angle Θ is in the range of 0 to 90 degrees or in the range of 180 to 270 degrees. In one example embodiment, the angle Θ is approximately 45 degrees.

[0159] In various embodiments, the magnetic field direction is not substantially parallel or anti-parallel to the direction of propagation of the first manipulation signal 415. In various embodiments, the efficiency of the clock state EIT cooling operation is not dependent on the relative angle between the magnetic field direction and the first and second manipulation signals 415, 425, so long as the magnetic field direction is not substantially parallel or anti-parallel to the polarization 418 of the first manipulation signal 415.

[0160] In various embodiments, the first manipulation signal 415 has a first polarization 418 (e.g., linear polarization in the illustrated embodiment). In one example embodiment, the polarization 418 of the first manipulation signal 415 is transverse to the magnetic field direction.

[0161] In various embodiments, the first manipulation signal 415 propagates in a first direction of propagation that is transverse to the atomic object axis 505. In one example embodiment, the first manipulation signal 415 propagates in the first direction of propagation that forms an angle φ with the atomic object axis 505. In various embodiments, the angle φ is in the range of 0 to 90 degrees. In one example embodiment, the angle φ is approximately 45 degrees.

[0162] In various embodiments, the second manipulation signal 425 has a second polarization 428 (e.g., linear polarization in the illustrated embodiment). In one example embodiment, the second polarization 428 of the second manipulation signal 425 is transverse to the magnetic field direction and the first polarization 418.

[0163] In various embodiments, the second manipulation signal 425 propagates in a second direction of propagation that is transverse to the atomic object axis 505. In one example embodiment, the second manipulation signal 425 propagates in the second direction of propagation that forms an angle ψ with the atomic object axis 505. In various embodiments, the angle ψ is in the range of 90 to 180 degrees. In one example embodiment, the angle ψ is approximately 135 degrees.

[0164] In various embodiments, the first propagation direction is transverse or anti-parallel to the second propagation direction. Generally, the first and second propagation directions are substantially non-parallel (e.g., transverse or anti-parallel to one another). In the illustrated embodiment, the first and second propagation directions are substantially anti-parallel to one another (e.g., φ + ψ = 180°). In various embodiments, φ + ψ is 135 to 225 degrees.

[0165] In various embodiments, the first propagation direction is transverse to the second propagation direction In various embodiments, the difference between the first propagation direction (corresponding to a unit vector in the wave vector direction of the respective first manipulation signal 415) and the second propagation direction (corresponding to a unit vector in the wave vector direction of the respective second manipulation signal 425) has a non-zero projection in the direction of motion to be cooled. For example, when the mode of the atomic object 508 to be cooled is an axial mode (e.g., corresponding to motion along the atomic object axis 505), where is a unit vector along the atomic object axis 505, and In another example, when the mode of the atomic object 508 to be cooled is a radial mode (e.g., corresponding to motion orthogonal to the atomic object axis 505), where is a radial unit vector (e.g., ), and

[0166] . Figure 5

[0167] An example geometry for performing a clock state EIT cooling operation of an example embodiment is shown. It will be appreciated that other geometries can be used in various other embodiments. For example, in one example embodiment, the magnetic field direction can be parallel or anti-parallel to the atomic object axis 505. In example embodiments, the first and second propagation directions are each parallel to the atomic object axis 505. In various embodiments, the magnetic field direction, the first propagation direction, and / or the second propagation can be transverse to a plane defined by the atomic object confinement device. Example method of performing EIT cooling operation

[0168] Figure 6 Flowcharts showing various processes, procedures, and / or the like for performing S-to-P-to-D EIT cooling operations and / or clock state EIT cooling operations in accordance with various embodiments are provided. Figure 6 The illustrated example embodiments correspond to S-to-P-to-D EIT cooling operations and / or clock state EIT cooling operations performed by a QCCD-based quantum computer (e.g., quantum computer 110). Figure 6 The illustrated embodiments, processes, procedures, and / or the like are performed by controller 30 of quantum computer 110.

[0169] From step / operation 602, the controller 30 causes the quantum computer 110 to begin executing and / or implementing a quantum circuit. For example, the controller 30 can control voltage sources, manipulation sources 64, magnetic field generators 70, etc. of the quantum computer 110 to cause the quantum computer 110 to perform a controlled quantum state evolution of a qubit ion of an atomic object that is confined by the atomic object confinement apparatus 50.

[0170] At step / operation 604, the controller 30 determines that a cooling trigger has been identified. For example, as the controller 30 controls the quantum computer 110 and / or its components, the controller 30 determines that a cooling trigger has been identified. In one example embodiment, a cooling trigger is identified in response to performing a transport operation (e.g., a linear transport, a transport through a junction of a two-dimensional atomic object confinement apparatus, a reordering of components within an atomic object, combining atomic objects, splitting atomic objects, swapping atomic objects, etc.) and determining that excess heat obtained during the transport operation is to be removed from the atomic object. In one example embodiment, a cooling trigger is identified in preparation for performing a quantum gate. In various embodiments, various actions and / or planned actions can cause the controller 30 to determine that a cooling trigger has been identified. In various embodiments, a cooling trigger indicates a particular region 55 of the atomic object confinement apparatus 50 in which a cooling operation is to be performed.

[0171] At step / operation 606, the controller 30 controls the magnetic field generator 70 to generate a magnetic field having a magnetic field direction and a particular magnitude in the particular region 55. In one example embodiment, the magnetic field generator 70 is a permanent magnet and the controller 30 does not need to control the magnetic field generator 70. In one example embodiment, the magnetic field generator 70 is configured to produce and / or maintain a magnetic field having a magnetic field direction and a particular magnitude that is approximately stable throughout operation of the quantum computer 110 and / or execution of a quantum circuit and / or algorithm. Thus, in one example embodiment, the controller 30 controls the magnetic field generator 70 to maintain the magnetic field in the particular region 55 having the magnetic field direction and the particular magnitude.

[0172] At step / operation 608, the controller 30 controls the first manipulation source 64A to generate and provide the first manipulation signal 215, 415 to the particular region 55, and controls the second manipulation source 64B to generate and provide the second manipulation signal 225, 425 to the particular region 55.

[0173] In various embodiments, the EIT cooling operation is an S-to-P-to-D EIT cooling operation, and the first manipulation signal 215 is characterized by a first wavelength λ1 that corresponds to a transition between the S manifold and the P manifold of the first component 310 of the atomic object 308, and the first detuning amount Δ1 by which the transition between the S manifold and the P manifold is detuned is SPIn various embodiments, the second manipulation signal 225 is characterized by a second wavelength λ2, which corresponds to and is detuned from a transition between the P manifold and the D manifold of the first constituent 310 of the atomic object 308 by a second detuning amount Δ PD .

[0174] In various embodiments, the EIT cooling operation is a clock state EIT cooling operation and the first manipulation signal 415 is characterized by a first wavelength λ A which corresponds to and is detuned from a transition between the first clock state 412 of the S manifold and the P manifold 420 of the first constituent 510 of the atomic object 408 by a first detuning amount Δ A In various embodiments, the second manipulation signal 425 is characterized by a second wavelength λ B which corresponds to and is detuned from a transition between the second clock state 414 of the S manifold and the P manifold 420 of the first constituent 510 of the atomic object 508 by a second detuning amount Δ B .

[0175] In various embodiments, the first and second detuning amounts correspond to (e.g., are tuned to and / or based on) a (selected) dark state associated with a two-photon transition between the S manifold and the D manifold in the case of an S-to-P-to-D EIT cooling operation, or a (selected) dark state associated with a two-photon transition between the first clock state 412 and the second clock state 414 in the case of a clock state EIT cooling operation. In various embodiments, the first and second manipulation signals 215, 415, 225, 425 are provided such that an atomic object disposed in the particular region 55 has the first and second manipulation signals incident thereon in a time-overlapping manner. For example, for at least some period of time, both the first and second manipulation signals are incident on the atomic object disposed in the particular region 55 at the same time.

[0176] In various embodiments, a Doppler cooling operation is performed prior to performing the S-to-P-to-D EIT cooling operation or the clock state EIT cooling operation. For example, in one example embodiment, in response to determining that a cooling trigger is identified, the Doppler cooling operation is performed, and then the S-to-P-to-D EIT cooling operation or the clock state EIT cooling operation is performed, depending on the atomic object and / or its constituents. In one example embodiment, the cooling trigger is identified in response to determining that a Doppler cooling operation has been performed in the particular region 55 until the atomic object disposed in the particular region 55 has reached a Doppler limit.

[0177] In step / operation 610, controller 30 determines whether sufficient cooling has been performed. For example, controller 30 may control one or more components of quantum computer 110 to perform one or more measurements to determine the temperature and / or motion pattern of an atomic object positioned in a specific region 55. For example, controller 30 may determine whether an S-to-P-to-D EIT cooling operation or a clock-state EIT cooling operation has been performed long enough to cause sufficient cooling. For example, in one example embodiment, controller 30 is configured to perform an S-to-P-to-D EIT cooling operation or a clock-state EIT cooling operation during the cooling time, and determining whether sufficient cooling has been performed is determining whether an S-to-P-to-D EIT cooling operation or a clock-state EIT cooling operation was performed during the cooling time. In various embodiments, the cooling time is 0.2 to 1.5 milliseconds.

[0178] In each embodiment, the S to P to D EIT cooling operation of each embodiment cools the atomic object 308 from the Doppler limit to [temperature value] in less than 1.5 milliseconds. ≈0.1, where This is the average number of photons in a specific mode of the atomic object. In various embodiments, the S-P-D EIT cooling operation of each embodiment cools the atomic object 308 from the Doppler limit to [a specific value] within 0.2 to 1.25 milliseconds. ≈0.1. In one example embodiment, the S to P to D EIT cooling operation of each embodiment cools the atomic object 308 from the Doppler limit to within 0.2 to 0.5 milliseconds. ≈0.1. For example, in one example embodiment, the S to P to D EIT cooling operations of the various embodiments cool the atomic object 308 from the Doppler limit to approximately 0.25 milliseconds. ≈0.1. Therefore, the controller 30 can determine whether a cooling time has elapsed since the first and second manipulation signals 215, 225 were first applied to the specific region 55. In various embodiments, the cooling time is 0.25 milliseconds, 0.5 milliseconds, 1 millisecond, 1.25 milliseconds, 1.5 milliseconds, etc.

[0179] In various embodiments, the clock-state cooling operation is configured to cool the atomic object 508 from the Doppler limit to below within approximately 0.7 milliseconds for axial gate mode and approximately 0.13 milliseconds for axial centroid mode. ≈0.1. In various embodiments, the clock-state cooling operation is configured to cool all radial modes to within less than 0.55 ms. ≈1. Thus, the controller 30 can determine whether the cool-down time has elapsed since the first and second manipulation signals 415, 425 were applied to the particular region 55. In various embodiments, the cool-down time is 0.25 milliseconds, 0.55 milliseconds, 0.8 milliseconds, 1 millisecond, 1.25 milliseconds, etc.

[0180] When it is determined that sufficient cooling has not occurred (e.g., the S-to-P-to-D EIT cooling operation or the clocked state EIT cooling operation has been performed for less than the cool-down time), the process returns to step / operation 608 and the first and second manipulation signals 215, 225 continue to be applied to the particular region 55. When it is determined that sufficient cooling has occurred (e.g., the S-to-P-to-D EIT cooling operation or the clocked state EIT cooling operation has been performed for the cool-down time), the process continues to step / operation 612.

[0181] At step / operation 612, the controller 30 controls the first manipulation source 64A and the second manipulation source 64B to cause the first manipulation signal 215 and the second manipulation signal 225 to stop being applied to the particular region 55. For example, the controller 30 can cause the first manipulation source 64A and / or the second manipulation source 64B to stop generating the first manipulation signal 215 and / or the second manipulation signal 225, respectively. For example, the controller 30 can control one or more modulators to cause the first manipulation signal 215 and / or the second manipulation signal 225 to stop being provided and / or applied to the particular region 55.

[0182] At step / operation 614, the controller 30 controls various elements of the quantum computer 110 (e.g., voltage sources, manipulation sources 64, magnetic field generators 70, etc.) to continue to execute and / or implement the quantum circuit. For example, the controller 30 can control various elements of the quantum computer 110 to cause one or more atomic objects to be transferred into, out of, and / or within the particular region 55, perform one or more quantum gates on one or more atoms, read the state of one or more atomic objects and / or components of the atomic objects, etc.

[0183] Technical advantages

[0184] In various embodiments, S-to-P-to-D EIT cooling operations are performed. In various embodiments, systems capable of performing S-to-P-to-D EIT cooling (e.g., quantum computers) and / or controllers configured to cause respective systems to perform S-to-P-to-D EIT cooling are provided. For example, various embodiments provide systems in which a first group of components of an atomic object has a low-lying D manifold and the atomic object is cooled at least in part using S-to-P-to-D EIT cooling operations. The S-to-P-to-D EIT cooling operations of various embodiments provide technical advantages over traditional laser cooling techniques and provide technical solutions to technical problems related to traditional laser cooling techniques.

[0185] For example, Doppler cooling is only able to cool atomic objects to the Doppler limit, which is not low enough for various applications, including QCCD-based quantum computing applications. In addition, Doppler cooling is relatively slow compared to EIT cooling. The S-to-P-to-D EIT cooling operations of various embodiments are able to efficiently cool atomic objects to well below the Doppler limit (e.g., ~0.1) in cooling times of 0.2 to 1.5 milliseconds. ≈0.1). While resolved sideband cooling is able to cool below the Doppler limit, resolved sideband cooling is technically complex to implement, requires high laser power, and is sensitive to fluctuations in laser intensity. Resolved sideband cooling is particularly technically complex to implement when the atomic object includes multiple components and / or is a crystal including multiple ions and / or atoms. The S-to-P-to-D EIT cooling operations of various embodiments provide improvements over resolved sideband cooling, including lower technical implementation complexity and lower laser power requirements, while maintaining fast and efficient cooling performance. The S-to-P-to-D EIT cooling operations of various embodiments further avoid the complexity of performing conventional EIT cooling on components of atomic objects having a low-lying D manifold. For example, in traditional EIT cooling of atoms and / or ions having a low D manifold, the atoms and / or ions can become “stuck” in the low D manifold, requiring a re-pumping back into the cooling cycle between the S manifold and the P manifold. Thus, for atomic objects having a first group of components with a low-lying D manifold and / or for atoms and / or ions having a low-lying D manifold, the S-to-P-to-D EIT cooling operations of various embodiments reduce technical complexity compared to traditional EIT cooling.

[0186] The S-to-P-to-D EIT cooling operations of various embodiments provide an additional technical advantage that the manipulation sources used to generate the first and second manipulation signals can be the same manipulation sources used to perform Doppler cooling. Thus, for example, the system can be configured to perform Doppler cooling and S-to-P-to-D EIT cooling using the same two lasers, which further reduces technical complexity implemented in various embodiments.

[0187] In various embodiments, a clock state EIT cooling operation is performed. In various embodiments, a system (e.g., a quantum computer) capable of performing clock state EIT cooling and / or a controller configured to cause a respective system to perform a clock state EIT cooling operation is provided. For example, various embodiments provide a system in which a first set of components of an atomic object has an energy structure similar to singly ionized Yb, and the atomic object is cooled at least in part using a clock state EIT cooling operation. The clock state EIT cooling operation of various embodiments provides a technical advantage over traditional laser cooling techniques, and provides a technical solution to technical problems related to traditional laser cooling techniques.

[0188] For example, as discussed elsewhere herein, laser cooling techniques are relatively slow processes (e.g., as compared to other processes performed by a QCCD quantum processor, such as quantum gates, atomic object transport, etc.). Moreover, traditional laser cooling techniques require a large amount of laser power. Furthermore, previous EIT cooling of ions having a 171Yb+ energy structure (e.g., a fine and / or hyperfine energy structure similar to a singly ionized 171Yb atom) works by coupling multiple F = 1 states to the excited manifold. For example, by coupling to the P 1 / 2 , F = 0, m = 0 state, the S 1 / 2 , F = 1, m = +1 state of the ground state manifold is coupled to the S 1 / 2 , F = 1, m = 0 state of the ground state manifold. However, coupling the S 1 / 2 , F = 1, m = +1 state to the S 1 / 2 , F = 0, m = 0 state of the ground state manifold requires sigma polarization, whereas coupling the S 1 / 2 , F = 1, m = 0 state to the P 1 / 2 , F = 0, m = 0 requires pi polarization, thus requiring a certain orientation of the magnetic field with respect to the direction of propagation. Furthermore, the ions can get “stuck” in the S 1 / 2 , F = 0, m = 0 state, and must be repumped into the S 1 / 2 , F = 1 manifold, requiring an additional operational signal to couple the S 1 / 2 , F = 0 manifold to the P state. Thus, traditional EIT cooling requires a high degree of technical sophistication to effectively cool an atomic object having a first set of components having a 171Yb+ energy structure. Moreover, resolving sideband cooling would require a high bandwidth control capability beyond that required for EIT, thus requiring additional technical sophistication if one wanted to use both cooling methods simultaneously. Thus, there are technical problems related to how to efficiently, effectively, and robustly cool an atomic object to near its motional ground state.

[0189] Various embodiments provide technical solutions to these technical problems. In various embodiments, an EIT cooling operation is performed using a first manipulation signal that couples a first clock state in an S manifold of a first component of an atomic object to one or more states of a P manifold and a second manipulation signal that couples a second clock state in the S manifold of the first component of the atomic object to one or more states of the P manifold. In various embodiments, the first clock state in the S manifold of the first component of the atomic object is the F = 0, m = 0 state and the second clock state in the S manifold of the first component of the atomic object is the F = 1, m = 0 state. The first and second clock states are less susceptible to environmental changes than the F = 1, m = + / - 1 states. In various embodiments, both the first manipulation signal and the second manipulation signal are detuned above the one or more states of the P manifold to establish a dark state associated with a two-photon transition between the first clock state in the S manifold and the second clock state in the S manifold. By coupling the first and second clock states in the S manifold to produce a (selected) dark state, efficient cooling of the atomic object near the motional ground state (e.g., significantly below the Doppler cooling limit) can be achieved with lower laser power requirements than resolved sideband cooling and is technically simpler than traditional EIT cooling. Moreover, in various embodiments, first and second manipulation sources used to generate and / or provide the first and second manipulation signals can also be used to perform sideband cooling of the first component of the atomic object. Thus, various embodiments are able to use both sideband cooling and EIT cooling without requiring additional lasers or other manipulation sources. Moreover, various embodiments result in faster cooling of the atomic object while using less power than traditional laser cooling techniques. Thus, various embodiments provide technical improvements over conventional laser cooling of atomic objects.

[0190] Example controller

[0191] In various embodiments, the quantum computer 110 includes a controller 30 configured to control various elements of the quantum computer 110. In various embodiments, the controller 30 may be configured to cause the quantum computer 110 to perform various operations (e.g., computational operations such as gate operations, cooling operations, transfer operations, qubit interaction operations, qubit measurement operations, leakage suppression / conversion operations, etc.). For example, the controller 30 may be configured to recognize cooling triggers, causing the execution of cooling operations (e.g., S-to-P-to-D EIT cooling operations, clock-state EIT cooling operations, and / or Doppler cooling, followed by S-to-P-to-D or clock-state EIT cooling operations), control first and / or second manipulation sources to provide first and / or second manipulation signals, etc. For example, controller 30 may be configured to control cryogenic and / or vacuum systems, control temperature and pressure within cryogenic and / or vacuum chamber 40, manipulation source 64, voltage source configured to apply voltage signals to electrodes of atomic object confinement device 50, magnetic field generator 70, and / or control environmental conditions (e.g., temperature, humidity, pressure, etc.) within cryogenic and / or vacuum chamber 40, and / or be configured to manipulate and / or cause the controlled evolution of the quantum states of one or more atomic objects within atomic object confinement device 50.

[0192] like Figure 7 As shown, in various embodiments, controller 30 may include various controller elements, including processing element 705, memory 710, driver controller element 715, communication interface 720, analog-to-digital converter element 725, etc. For example, processing element 705 may include programmable logic device (CPLD), microprocessor, coprocessor entity, application-specific instruction set processor (ASIP), integrated circuit, application-specific integrated circuit (ASIC), field-programmable gate array (FPGA), programmable logic array (PLA), hardware accelerator, other processing devices and / or circuits, etc., and / or controllers. The term circuit can refer to a completely hardware embodiment or a combination of hardware and computer program products. In one example embodiment, processing element 705 of controller 30 includes a clock and / or communicates with a clock.

[0193] For example, the memory 710 can include non-transitory memory, such as volatile memory, and / or non-volatile memory, such as one or more of the following: a hard disk, a ROM, a PROM, an EPROM, an EEPROM, a flash memory, an MMC, an SD memory card, a memory stick, a CBRAM, a PRAM, a FeRAM, a RRAM, a SONOS, a racetrack memory, a RAM, a DRAM, a SRAM, a FPM DRAM, an EDO DRAM, an SDRAM, a DDR SDRAM, a DDR2 SDRAM, a DDR3 SDRAM, a RDRAM, a RIMM, a DIMM, a SIMM, a VRAM, a cache memory, a register memory, etc. In various embodiments, the memory 710 can store qubit records corresponding to qubits of a quantum computer (e.g., in a qubit record data store, a qubit record database, a qubit record table, etc.), calibration tables, executable file queues, computer program code (e.g., in one or more computer languages, one or more special purpose controller languages, etc.), etc. In one example embodiment, execution of at least a portion of the computer program code stored in the memory 710 (e.g., by the processing element 705) causes the controller 30 to perform one or more steps, operations, processes, procedures, etc. described herein.

[0194] In various embodiments, the driver controller element 715 can include one or more drivers and / or controller elements each configured to control one or more drivers. In various embodiments, the driver controller element 715 can include a driver and / or a driver controller. For example, the driver controller can be configured to cause one or more respective drivers to operate in accordance with executable instructions, commands, etc. scheduled and executed by the controller 30 (e.g., by the processing element 505). In various embodiments, the driver controller element 715 can enable the controller 30 to operate and / or control one or more steering sources 64, control one or more magnetic field generators 70, operate vacuum and / or cryogenic systems, etc. In various embodiments, the drivers can be laser drivers; vacuum component drivers; voltage sources (e.g., alternating voltage sources, arbitrary waveform generators (AWGs), direct digital synthesizers (DDSs), etc.); cryogenic and / or vacuum system component drivers, etc. In various embodiments, the controller 30 includes means for communicating and / or receiving signals from one or more optical receiver components, such as cameras, MEMS cameras, CCD cameras, photodiodes, photomultiplier tubes, etc. For example, the controller 30 can include one or more analog-to-digital converter elements 725 configured to receive signals from one or more optical receiver components, calibration sensors, etc. For example, the controller 30 can receive, through the analog-to-digital converter element 725, measurements corresponding to conditions in particular regions 55 of the atomic object confinement device 50 and / or corresponding to various atomic objects 308.

[0195] In various embodiments, the controller 30 can include a communication interface 720 for interfacing and / or communicating with the computing entity 10. For example, the controller 30 can include a communication interface 720 for receiving executable instructions, command sets, etc. from the computing entity 10 and providing the computing entity 10 with outputs received from the quantum computer 110 (e.g., from an optical collection system or other measurement system) and / or processed results of the outputs. In various embodiments, the computing entity 10 and the controller 30 can communicate through a direct wired and / or wireless connection and / or one or more wired and / or wireless networks 20.

[0196] Exemplary computing entity

[0197] Figure 8An illustrative schematic of a representative computing entity 10 that can be used in conjunction with embodiments of the present application is provided. In various embodiments, the computing entity 10 is configured to allow a user to provide input to the quantum computer 110 (e.g., through a user interface of the computing entity 10) and to receive, display, analyze, and / or similarly process output from the computer 110. For example, a user can operate the computing entity 10 to generate and / or program a quantum algorithm and / or quantum circuit, which can be provided so that the controller 30 can receive the quantum algorithm and / or quantum circuit and cause the quantum computer 110 to execute the quantum algorithm and / or quantum circuit.

[0198] As Figure 8As shown, computing entity 10 can include an antenna 812, a transmitter 814 (e.g., radio), a receiver 806 (e.g., radio), and a processing device and / or element 808 that provides signals to and receives signals from transmitter 814 and receiver 806, respectively. The signals provided to and received from transmitter 814 and receiver 806, respectively, can include signaling information / data in accordance with the air interface standard of the applicable wireless system, such as the air interface standards illustrated by controller 30, other computing entities 10, and so on. In this regard, the computing entity 10 can be capable of operating with one or more air interface standards, communication protocols, modulation types, and access types. For example, computing entity 10 can be configured to receive and / or provide communications using a wired data transmission protocol, such as fiber optic distributed data interface (FDDI), digital subscriber line (DSL), Ethernet, asynchronous transfer mode (ATM), frame relay, data over cable service interface specification (DOCSIS), or any other wired transmission protocol. Similarly, computing entity 10 can be configured to communicate using any of a plurality of protocols, such as general packet radio service (GPRS), universal mobile telecommunications system (UMTS), code division multiple access 2000 (CDMA2000), CDMA2000 IX (lxRTT), wideband code division multiple access (WCDMA), global system for mobile communications (GSM), enhanced data rates for GSM evolution (EDGE), time division-synchronous code division multiple access (TD-SCDMA), long term evolution (LTE), evolved universal terrestrial radio access network (E-UTRAN), evolution-data optimized (EVDO), high-speed packet access (HSPA), high-speed downlink packet access (HSDPA), IEEE 802.11 (Wi-Fi), Wi-Fi Direct, 802.16 (WiMAX), ultra-wideband (UWB), infrared (IR) protocols, near-field communication (NFC) protocols, Wibree, Bluetooth protocols, wireless universal serial bus (USB) protocols, and / or any other wireless protocol.The computing entity 10 can use such protocols and standards to communicate using Border Gateway Protocol (BGP), Dynamic Host Configuration Protocol (DHCP), Domain Name System (DNS), File Transfer Protocol (FTP), HyperText Transfer Protocol (HTTP), HTTPS / SSL / encrypted protocols, Internet Message Access Protocol (IMAP), Network Time Protocol (NTP), Simple Mail Transfer Protocol (SMTP), Telnet, Transport Layer Security (TLS), Secure Sockets Layer (SSL), Internet Protocol (IP), Transmission Control Protocol (TCP), User Datagram Protocol (UDP), Datagram Congestion Control Protocol (DCCP), Stream Control Transmission Protocol (SCTP), HyperText Markup Language (HTML), and the like.

[0199] Through these communication standards and protocols, the computing entity 10 can communicate with various other entities using concepts such as Unstructured Supplementary Service Data (USSD), Short Message Service (SMS), Multimedia Message Service (MMS), Dual-Tone Multi-Frequency Signaling (DTMF), and / or Subscriber Identity Module Dialer (SIM dialer). The computing entity 10 can also download changes, add-ons, and updates to its firmware, software (e.g., including executable instructions, applications, program modules), and operating system.

[0200] The computing entity 10 can also include user interface devices that include one or more user input / output interfaces (e.g., a display 816 and / or speaker / speaker driver coupled to the processing device and / or elements 808, and a touchscreen, keyboard, mouse, and / or microphone coupled to the processing device and / or elements 808). For example, the user output interface can be configured to provide applications, browsers, user interfaces, interfaces, dashboards, screens, webpages, pages, and / or similar words used herein interchangeably, that are executed on the computing entity 10 or are accessible by the computing entity 10 to cause display or aural presentation of information / data and to interact therewith through one or more user input interfaces. The user input interface can include any of a number of devices allowing the computing entity 10 to receive data, such as a keypad 818 (hard or soft), touch display, voice / speech or motion interfaces, scanners, readers, or other input devices. In embodiments including a keypad 818, the keypad 818 can include (or cause display of) the conventional numeric (0-9) and related keys (#, *), and other keys used for operating the computing entity 10, and can include a complete set of alphabetic keys or a set of keys that can be activated to provide a complete alphabetic set, and / or other keys. In addition to providing input, the user input interface can be used, for example, to activate or deactivate certain functions, such as screen savers and / or sleep modes. Through such input, the computing entity 10 can gather information / data, user interactions / inputs, and the like.

[0201] The computing entity 10 can also include volatile storage or memory 822 and / or non-volatile storage or memory 824, which can be internal and / or removable. Non-volatile storage can be ROM, PROM, EPROM, EEPROM, flash memory, MMCs, SD memory cards, Memory Sticks, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, etc. Volatile storage can be RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, etc. The volatile and non-volatile storage or memory can store databases, database instances, database management system entities, data, applications, programs, program modules, scripts, source code, object code, byte code, compiled code, interpreted code, machine code, executable instructions, etc. to implement the functionality of the computing entity 10.

[0202] CONCLUSION

[0203] Many modifications and other embodiments with respect to the inventions set forth herein will occur to those skilled in the art upon reading the foregoing description and understanding the teachings presented herein. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments. While specific terms have been employed herein, they should not be construed as limiting the scope of the embodiments, unless otherwise explicitly so specified.

[0204] The following additional clauses are part of the specification:

[0205] 1. A method for cooling an atomic object confined by an atomic object confinement device, the method comprising:

[0206] controlling, by a controller associated with the atomic object confinement device, a first steering source to provide a first steering signal to a particular region of the atomic object confinement device; and

[0207] controlling, by the controller, a second steering source to provide a second steering signal to the particular region of the atomic object confinement device,

[0208] wherein:

[0209] the atomic object to be cooled is located in the particular region of the atomic object confinement device,

[0210] the first manipulation signal is characterized by a first wavelength corresponding to a transition between the S manifold and the P manifold of the first component of the atomic object, and is detuned from the transition between the S manifold and the P manifold by a first detuning amount,

[0211] the second manipulation signal is characterized by a second wavelength corresponding to a transition between the P manifold and the D manifold of the first component of the atomic object, and is detuned from the transition between the P manifold and the D manifold by a second detuning amount,

[0212] the first detuning amount and the second detuning amount are selected to establish a dark state associated with a two-photon transition between the S manifold and the D manifold.

[0213] 2. The method of item 1, wherein the atomic object is an ion crystal comprising two or more ions, and the first component of the atomic object is at least one of the two or more ions of a first atomic object type.

[0214] 3. The method of item 2, wherein the first component of the atomic object is configured to function as a cooling ion in a cooperative cooling scheme for the crystal.

[0215] 4. The method of item 2, wherein a second component of the atomic object is at least one of the two or more ions of a second atomic object type, the second atomic object type being different from the first atomic object type, and wherein the at least one of the two or more ions of the second atomic object type is configured to function as a qubit for a quantum computer comprising the atomic object confinement device.

[0216] 5. The method of item 1, wherein the first detuning amount and the second detuning amount are approximately equal.

[0217] 6. The method of item 1, wherein a polarization of the first manipulation signal and a polarization of the second manipulation signal correspond to the two-photon transition associated with the dark state.

[0218] 7. The method of item 1, further comprising causing a magnetic field having a magnetic field direction to be generated in a particular region of the atomic object confinement device, wherein one of the atomic object or the particular region of the atomic object confinement device defines an atomic object axis, and the magnetic field direction is transverse to the atomic object axis.

[0219] 8. The method of item 7, wherein the magnetic field direction and the atomic object axis form an angle of thirty to sixty degrees.

[0220] 9. The method of item 7, wherein the first manipulation signal defines a first propagation direction that is transverse to the atomic object axis, and the second manipulation signal defines a second propagation direction that is transverse to the atomic object axis.

[0221] 10. The method of item 9, wherein the first propagation direction and the second propagation direction do not co-propagate, and the magnetic field direction is transverse to both the first propagation direction and the second propagation direction.

[0222] 11. The method of item 10, wherein both the first propagation direction and the second propagation direction are substantially perpendicular to the magnetic field direction.

[0223] 12. The method of item 9, wherein (a) a polarization of the first manipulation signal is substantially transverse to a plane defined by the atomic object confinement device, (b) a polarization of the second manipulation signal is substantially transverse to the plane defined by the atomic object confinement device, and (c) the first propagation direction, the second propagation direction, and the magnetic field direction are each substantially parallel to the plane defined by the atomic confinement device.

[0224] 13. An apparatus comprising at least one processor and a memory storing computer executable instructions that, when executed by the at least one processor, cause the apparatus to at least:

[0225] control a first manipulation source to provide a first manipulation signal to a particular region of an atomic object confinement device; and

[0226] control a second manipulation source to provide a second manipulation signal to the particular region of the atomic object confinement device,

[0227] wherein:

[0228] an atomic object is located in the particular region of the atomic object confinement device,

[0229] the first manipulation signal and the second manipulation signal are configured to co-cool the atomic object,

[0230] the first manipulation signal is characterized by a first wavelength corresponding to a transition between an S manifold and a P manifold of a first component of the atomic object, and is detuned from the transition between the S manifold and the P manifold by a first detuning amount,

[0231] the second manipulation signal is characterized by a second wavelength corresponding to a transition between the P manifold and a D manifold of the first component of the atomic object, and is detuned from the transition between the P manifold and the D manifold by a second detuning amount,

[0232] the first detuning amount and the second detuning amount are selected to establish a dark state associated with a two-photon transition between the S manifold and the D manifold.

[0233] 14. The apparatus of item 13, wherein (a) the apparatus is a controller of a quantum computer comprising the atomic object confinement apparatus, (b) the atomic object is an ion crystal comprising two or more ions, and the first component of the atomic object is at least one of the two or more ions of a first atomic object type, and (c) the first component of the atomic object is configured to function as a cooling ion in a sympathetic cooling scheme of the ion crystal.

[0234] 15. The apparatus of item 14, wherein the second component of the atomic object is at least one of two or more ions of a second atomic object type, the second atomic object type being different from the first atomic object type, and wherein the at least one of the two or more ions of the second atomic object type is configured to function as a qubit of a quantum computer comprising the atomic object confinement apparatus.

[0235] 16. The apparatus of item 13, wherein the polarization of the first manipulation signal and the polarization of the second manipulation signal correspond to a two-photon transition associated with a dark state.

[0236] 17. The apparatus of item 13, wherein the computer-executable instructions are further configured to, when executed by the at least one processor, cause the apparatus to at least generate a magnetic field having a magnetic field direction in a particular region of the atomic object confinement apparatus, wherein one of the atomic object or the particular region of the atomic object confinement apparatus defines an atomic object axis, and the magnetic field direction is transverse to the atomic object axis.

[0237] 18. The apparatus of item 17, wherein the first manipulation signal defines a first direction of propagation that is transverse to the atomic object axis, and the second manipulation signal defines a second direction of propagation that is transverse to the atomic object axis.

[0238] 19. The apparatus of item 18, wherein the first manipulation signal and the second manipulation signal do not co-propagate, and the magnetic field direction is transverse to both the first direction of propagation and the second direction of propagation.

[0239] 20. A system comprising:

[0240] an atomic object confinement apparatus configured to confine an atomic object in a particular region of the atomic object confinement apparatus;

[0241] a first manipulation source controllable by a controller of the system and configured to provide a first manipulation signal to the particular region of the atomic object confinement apparatus;

[0242] a second manipulation source controllable by the controller of the system and configured to provide a second manipulation signal to the particular region of the atomic object confinement apparatus; and

[0243] the controller including at least one processor and memory storing computer-executable instructions configured to, when executed by the at least one processor, cause the controller to at least:

[0244] control a first manipulation source to provide a first manipulation signal to a particular region of the atomic object confinement device; and

[0245] control a second manipulation source to provide a second manipulation signal to the particular region of the atomic object confinement device,

[0246] wherein:

[0247] the first manipulation signal and the second manipulation signal are configured to collectively cool the atomic object,

[0248] the first manipulation signal is characterized by a first wavelength corresponding to a transition between an S manifold and a P manifold of a first component of the atomic object, and is detuned from the transition between the S manifold and the P manifold by a first detuning amount,

[0249] the second manipulation signal is characterized by a second wavelength corresponding to a transition between the P manifold and a D manifold of the first component of the atomic object, and is detuned from the transition between the P manifold and the D manifold by a second detuning amount,

[0250] the first detuning amount and the second detuning amount are selected to establish a dark state associated with a two-photon transition between the S manifold and the D manifold.

Claims

1. A method for cooling an atomic object confined by an atomic object confinement device, the method comprising: controlling, by a controller associated with the atomic object confinement device, a first manipulation source to provide a first manipulation signal to a particular region of the atomic object confinement device; and controlling, by the controller, a second manipulation source to provide a second manipulation signal to the particular region of the atomic object confinement device, wherein: the atomic object to be cooled is located in the particular region of the atomic object confinement device, the first manipulation signal is characterized by a first wavelength corresponding to a transition between a S manifold and a P manifold of a first component of the atomic object, and is detuned from the transition between the S manifold and the P manifold by a first detuning amount, the second manipulation signal is characterized by a second wavelength corresponding to a transition between the P manifold and a D manifold of the first component of the atomic object, and is detuned from the transition between the P manifold and the D manifold by a second detuning amount, the first detuning amount and the second detuning amount are selected to establish a dark state associated with a two-photon transition between the S manifold and the D manifold. (a) the atomic object is an ion crystal comprising two or more ions, (b) the first component of the atomic object is at least one of the two or more ions of a first atomic object type, (c) the first component of the atomic object is configured to function as a cooling ion in a scheme for cooperative cooling of a crystal, (d) the second component of the atomic object is at least one of the two or more ions of a second atomic object type, (e) the second atomic object type is different from the first atomic object type, and (f) at least one of the two or more ions of the second atomic object type is configured to function as a qubit of a quantum computer comprising the atomic object confinement device.

2. The method of claim 1, wherein, the first detuning amount and the second detuning amount are equal.

3. The method of claim 1, wherein, a polarization of the first manipulation signal and a polarization of the second manipulation signal correspond to the two-photon transition associated with the dark state.

4. The method of claim 1, wherein, one of the particular region of the atomic object or the atomic object confinement device defines an atomic object axis, and a magnetic field direction is transverse to the atomic object axis.

5. The method of claim 1, further comprising generating a magnetic field having a magnetic field direction in a particular region of the atomic object confinement device, wherein, the magnetic field direction and the atomic object axis form an angle of thirty to sixty degrees.

6. The method of claim 5, wherein, the first manipulation signal defines a first propagation direction that is transverse to the atomic object axis, and the second manipulation signal defines a second propagation direction that is transverse to the atomic object axis.

7. The method of claim 5, wherein, the first manipulation signal and the second manipulation signal do not co-propagate, and the magnetic field direction is transverse to both the first propagation direction and the second propagation direction.

8. The method of claim 7, wherein, both the first propagation direction and the second propagation direction are perpendicular to the magnetic field direction.

9. The method of claim 8, wherein, (a) a polarization of the first manipulation signal is transverse to a plane defined by the atomic object confinement device, (b) a polarization of the second manipulation signal is transverse to the plane defined by the atomic object confinement device, and (c) the first propagation direction, the second propagation direction, and the magnetic field direction are respectively parallel to the plane defined by the atomic confinement device.

10. The method of claim 7, wherein, ​

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