Microwave photon counter without quantum destruction based on the Cross-Kerr nonlinearity of a Josephson junction embedded in a superconducting circuit

Abstract

Microwave unit (100) comprising: a dispersive nonlinear element; a pump resonator (102) whose first end is connected to both the dispersive nonlinear element and a first stub line (120A) and capacitively coupled to a pump terminal (111) at a second end of the pump resonator (102), the first stub line (120A) terminating in an open circuit; and a quantum signal resonator (104) whose first end is connected to both the dispersive nonlinear element and a second stub line (120B) and capacitively coupled to a signal terminal (113) at a second end of the signal resonator, the second stub line (120B) being connected to ground (405).

Description

BACKGROUND OF THE INVENTION

[0001] The present invention relates to measurement techniques for quantum systems operating in the microwave frequency range, for example superconducting quantum circuits, and non-destructive detection and / or counting of individual microwave photons.

[0002] A photon is an elementary particle, the light quantum, and all other forms of electromagnetic radiation. A photon possesses energy proportional to its radiation frequency, and its rest mass is zero.

[0003] One reason why detecting individual microwave photons is so extremely challenging is that the energy of a single microwave photon is very low. The energy of a photon in the microwave range, for example in the 1 to 20 gigahertz range, is at least 10 times lower. 4less than the energy of a photon in the visible light range.

[0004] Circuit quantum electrodynamics (cQED) is one of the leading architectures for realizing a quantum computer based on superconducting microwave circuits. It uses artificial atoms consisting of nonlinear superconducting units called qubits, which are dispersively coupled to microwave resonators, meaning the frequencies of the qubits and the resonators are not matched. In one example, each superconducting qubit can have one or more Josephson junctions, with capacitors connected in parallel to the junctions. The qubits are capacitively coupled to two-dimensional (2D) planar waveguide resonators or three-dimensional (3D) microwave resonators. The electromagnetic energy associated with the qubit is stored in the Josephson junctions and in the capacitive and inductive components that make up the qubit.To date, the main focus has been on extending the lifetime of qubits so that calculations (i.e., processing and reading) can be performed before the information is lost due to qubit decoherence.

[0005] By dispersively coupling a superconducting qubit to a microwave resonator in a cQED architecture, the resonator is charged, causing its resonant frequency to become dependent on the quantum state of the qubit (i.e., the resonator's resonant frequency differs depending on whether the qubit is in its ground state or excited state). This property enables non-destructive quantum measurement of the qubit state by sending a microwave signal of a few photons near the resonator frequency to the cQED and measuring the amplitude and / or phase of the emitted microwave field, which contains information about the qubit state. Thus, a potential application of a functional and reliable single-photon detector in the microwave range is to measure this weak emission signal inside the mixing cryostat (i.e.,, to detect the qubit state), without using highly isolated, highly sensitive and low-noise detection chains that are commonly used for such measurements today. SUMMARY

[0006] According to one embodiment, a microwave unit is provided. The microwave unit includes a dispersive nonlinear element and a pump resonator, the first end of which is connected to both the dispersive nonlinear element and a first stub line. The second end of the pump resonator is capacitively connected to a pump terminal, where the first stub line terminates in an open circuit. Furthermore, the microwave unit includes a quantum signal resonator, the first end of which is connected to both the dispersive nonlinear element and a second stub line. The second end of the quantum signal resonator is capacitively connected to a signal terminal, with the second stub line being connected to ground.

[0007] According to one embodiment, a method for non-destructive photon counting is provided. This method involves coupling a pump resonance mode of a pump resonator and a signal resonance mode of a quantum signal resonator with a dispersive, nonlinear element in response to a pump signal at a pump resonance frequency and a quantum signal at a signal resonance frequency. The pump resonance mode of the pump resonator has the pump resonance frequency, and the signal resonance mode of the quantum signal resonator has the signal resonance frequency. Furthermore, the method involves generating a nonlinear interaction between the pump signal and the quantum signal by exciting the pump resonance mode with the pump signal at the pump resonance frequency and detecting, based on the pump resonance frequency, whether photons are present in the quantum signal, thereby measuring an output pump signal.

[0008] According to one embodiment, a method for operating a microwave unit is provided. The method includes receiving a pump signal at a pump resonant frequency by the microwave unit, wherein the pump resonant frequency corresponds to a pump resonant mode of a pump resonator. The method also includes receiving a quantum signal at a signal resonant frequency by the microwave unit, wherein the signal resonant frequency corresponds to a signal resonant mode of a signal resonator, and outputting the pump signal with a phase shift by the microwave unit in response to a number of photons in the quantum signal. List of characters

[0009] Further features and advantages are realized through the techniques of the present invention. Other embodiments and aspects of the invention, which are considered part of the claimed invention, are described in detail herein. For a better understanding of the invention, its advantages, and features, reference is made to the description and the drawings, wherein: Fig. 1 a schematic representation of a microwave unit according to one embodiment of the invention; Fig. 2 a schematic representation of an equivalent circuit of the microwave unit from the perspective of the pump connection; Fig. 3 is a schematic representation of an equivalent circuit of the microwave unit from the point of view of the signal connection; Fig. 4 is a schematic representation of an exemplary implementation of the microwave unit using a coplanar waveguide geometry; Fig. 5 is a schematic representation of an exemplary implementation of the microwave unit using a microstrip geometry; Fig. 6. A flowchart of a procedure for the non-destructive counting and / or detection of photons using the microwave unit; and Fig. 7 is a flowchart of a procedure for the microwave unit. DETAILED DESCRIPTION

[0010] In the optical frequency range, the use of reliable single-photon detectors, such as photomultipliers, kinetic microwave inductance detectors, and superconducting single-photon nanowire detectors, is widespread in various experiments and applications. However, a disadvantage of these devices is that they destroy (i.e., absorb) the photons to be detected.

[0011] In the microwave range, i.e., the gigahertz (GHz) range, research and development of reliable and usable photon detectors is still ongoing. A usable microwave photon detector based on Josephson junctions (referred to as a Josephson photomultiplier) has been experimentally investigated. Similar to single-photon detectors in the optical range, this device also absorbs the photons to be detected. Furthermore, this microwave device under development does not count the number of photons present in an incoming signal, but can only distinguish between zero photons or at least one photon in the signal.

[0012] Embodiments of the invention provide a usable design for a microwave unit and a measuring method for counting individual microwave photons. Embodiments are designed to 1) determine the number of individual photons within a specific bandwidth in the microwave range (i.e., in the gigahertz range (GHz), e.g., in the range of 10 ... 1 1) to detect and count photons up to 20 GHz, and 2) to perform the detection and counting of photons non-destructively, i.e., without destroying (or absorbing) the photons to be detected or counted.

[0013] Among the characters is Fig. 1. A schematic representation of a microwave unit 100 according to one embodiment. The microwave unit 100 It contains a λ / 4 resonator 102 for pump excitation and a λ / 4 resonator 104 for quantum signals. One end of the pump resonator 102 is equipped with a coupling capacitor 106Aconnected, and this is connected to a pump feed line 108 connected. The pump feed line 108 is equipped with a pump connection 111 connected, and / or the pump connection 111 is located on the pump feed line 108 The pump feed line 108 receives a microwave pump signal 130 (i.e., a strong microwave tone) from a microwave generator (referred to as a pump). 135 The other end of the pump resonator 102 is both with a dispersive, nonlinear element, e.g. a Josephson transition (JJ) 110 as well as with a λ / 2 stub line at the pump frequency 120A connected. The connection between the pump resonator 102 , the Josephson transition (JJ) 110 and the branch line 120A This can be designated as node A. The branch line ends on the side opposite node A. 120Ain an open circuit (OC). Beyond the coupling capacitor 106A is the pump feed line 108 with a microwave measuring / analysis unit 150 connected. The microwave measurement / analysis unit 150 serves to transmit the pump signal 130 to measure in reflection after the pump signal 130 with the microwave unit 100 has interacted. The microwave measurement / analysis unit 150 It may contain and / or be connected to a computer for determining the phase shift (frequency) in the pump signal, which is discussed in more detail here. The microwave measurement / analysis unit 150 It can contain and / or be connected to one or more processors, memory (e.g., a computer-readable storage medium), display screens, input devices (e.g., mouse, keyboard, touchscreen, etc.). The pump 135 and the microwave measuring / analysis unit 150are via a rotation unit 180A functional with the microwave unit 100 connected, but not part of the microwave unit 100 .

[0014] In the microwave unit 100 is one end of the λ / 4 signal resonator 104 with a coupling capacitor 106B and this with a signal feed line 109 connected. The signal feed line 109 is equipped with a signal connection 113 connected, and / or the signal connection 113 is located on the signal feed line 109 The signal feed line 109 It serves to generate a microwave quantum signal 140 , i.e., a microwave signal to be measured / tested, from a quantum unit 145 to receive. At the quantum unit 145 It could be a qubit, a resonator connected to a qubit, etc. The other end of the signal resonator 104 is with the Josephson transition (JJ)110 and a λ / 2 spur line at the pump frequency 120B connected. The connection between the pump resonator 102 , the Josephson transition (JJ) 110 and the branch line 120B This can be referred to as node B. The branch line ends beyond node B. 120B in a short-circuit circuit. The signal feed line 109 can be done via a rotary unit 180B with the quantum unit 145 and a measurement / analysis unit 144 be connected. The measurement / analysis unit 144 can be used for further processing. According to one implementation, the unit 144 Represent a 50-ohm connection. The one with the measurement / analysis unit 144 connected connection of the rotary unit 180B ensures that no reflected signal reaches the quantum unit 145 is transferred back.

[0015] The pump resonator 102It has a fundamental mode, which can also be called the pump mode or pump resonance mode. The pump mode of the pump resonator 102 has a resonant frequency, which is known as the pump resonant frequency ƒ P can be described as the pump mode of the pump resonator. 102 has a wavelength λ P , where λ P = c' / ƒ P and c' is equal to the speed of light in the transmission line or waveguide used to build the unit 102 is used. In the pump resonator 102 fed-in pump signal 130 It is a strong coherent resonance tone (i.e., its frequency matches the resonance frequency of the pump resonator). 102 (agree). The pump resonator 102 is designed such that its length λ p / 4 corresponds to one-quarter of the wavelength of the pump signal. The two spur lines 120A and 120B are designed such that their length λ p / 2 corresponds to half the wavelength of the pump signal.

[0016] The signal resonator 104 It has a fundamental mode, which can be called the signal mode or signal resonance mode. The signal mode of the signal resonator 104 has a resonant frequency, which is called the signal resonant frequency ƒ S can be described as follows: The quantum microwave signal fed into the signal resonator 140 This is a weak resonance tone on the order of a few individual photons, whose frequency ƒ S coincides with the resonant frequency of the signal mode. The signal mode of the signal resonator 104 has a wavelength λ S , where λ S = c' / ƒ S and c' is equal to the speed of light in the transmission line or waveguide used to construct the unit. The signal resonator 104 is designed such that its length λ S / 4 corresponds to one quarter of the wavelength of the quantum signal.

[0017] The microwave unit 100 is subject to a frequency condition between the pump resonance frequency of the pump resonator 102 and the signal resonance frequency of the signal resonator 104 The frequency condition is that the pump resonance frequency ƒ P of the pump resonator 102 twice as high as the signal resonance frequency ƒ S of the signal resonator 104 In other words, the frequency condition is ƒ P = 2•ƒ S Accordingly, the input signal 130 a frequency f P , which is twice as high as the frequency ƒ S of the quantum signal 140 .

[0018] The microwave unit 100 is configured so that the reflected pump signal 130 (e.g., as a reflected pump signal) 130'(designated) information about the number of quantum particles in the input quantum signal 140 contains photons and is therefore used to count the photons in the quantum signal 140 can be used. Furthermore, the reflected quantum signal contains 140 (e.g., as a reflected quantum signal) 140' (designated) information about the number of components in the input pump signal 130 contained photons and can therefore be used to count the photons in the pump signal 130 This information about the number of photons in the quantum signal can be used. 140 are in the phase shift of the reflected pump signal 130' from the connection 108 as a result of the resonance frequency shift of the pump resonator 102 depending on the number of photons in the signal resonator 104 encoded. The phase shift of the reflected pump signal. 130' is done by the microwave measurement / analysis unit150 measured and analyzed.

[0019] The microwave unit 100 (and / or their operation via the pump signal) 130 and the quantum signal 140 ) is configured so that it (with the exception of the control and feed lines) is controlled by the effective Hamiltonian H eff = ℏω̃ P N P + ℏω̃ S N S + ℏ K N P 2 + ℏ K ' N P N S can be described, where ℏω̃ P N P the (as a harmonic oscillator with the adapted resonant frequency ω̃) P (of the pump resonance mode modeled) Pump resonance mode term, ℏω̃ S N S the (as a harmonic oscillator with the adapted resonant frequency ω̃) S (signal resonance mode modeled) signal resonance mode term, ℏ K N P 2 the Eigen-Kerr nonlinearity of the unit and ℏK'N P N SThis represents the Cross-Kerr nonlinearity of the unit. Furthermore, K is equal to the Eigen-Kerr constant (i.e., equal to the Kerr frequency shift per photon) and K' is equal to the Cross-Kerr constant (i.e., equal to the Cross-Kerr frequency shift per photon). Additionally, N P equal to the operator of the pump mode for the number of photons N P = a P † a P (whose eigenvalue is equal to the number of photons in the pump resonance mode) and N S equal to the operator of the signal mode for the number of photons N S = a S † a S (whose eigenvalue is equal to the number of photons in the signal resonance mode), and ℏ = h 2 π , where h is equal to Planck's constant. Furthermore, a P and a S Quantum operators (i.e., annihilation operators associated with the pump and signal resonance modes). It should be noted that in this disclosure the symbols N P , N SThey can be used to represent the eigenvalues ​​of the number operators instead of the number operators themselves. Furthermore, it is pointed out that any person skilled in the art can recognize this difference from the context.

[0020] Fig. Figure 2 is a schematic representation of the equivalent circuit of the microwave unit. 100 according to one embodiment in the area of ​​the pump connection 111 . Apart from the depiction of the area around the pump connection. 111 illustrative Fig. 2 simultaneously, the incoming pump signal 130 with the pump resonance frequency ƒ P Perceived circuit. Accordingly, the discussion regarding the pump connection applies. 111 for the incoming pump signal 130 .

[0021] In the pump replacement circuit of Fig. 2 shows that the pump feed line 108 (including the pump connection) 111 ) via the coupling capacitor 106Awith the part of the pump resonator's transmission line 102 coupled and the other end of part of the pump resonator's transmission line via the Josephson junction 110 is connected to ground. To explain this equivalent circuit, it should be noted that 1) the spur line 120A , which serves as an impedance converter, terminates in an open circuit and has a length of half the wavelength of the pump signal 130 corresponds, so that node A perceives an open circuit at the pump frequency, and that 2) the spur line 120B , which serves as an impedance converter, terminates in an open circuit and has a length of half the wavelength of the pump signal 130 This corresponds to node B perceiving an open circuit at the pump frequency.

[0022] An advantageous result of this pump equivalent circuit is that it shows that the pump resonance mode is the signal resonator. 104does not recognize it. In other words, the pump resonator 102 is from the signal resonator 104 isolated.

[0023] Another advantageous result is that the RF current I associated with the pump resonance mode P at the site of the Josephson Crossing 110 has an antinode.

[0024] Fig. Figure 3 is a schematic representation of the equivalent circuit of the microwave unit. 100 in the area of ​​quantum signal connection 113 according to one embodiment. Fig. 3 illustrates not only what the signal connection 113 perceives, but simultaneously shows the effect of the incoming quantum signal 140 at the signal resonance frequency ƒ S Perceived equivalent circuit. Accordingly, the discussion regarding the signal connection 113 also on the incoming quantum signal 140 applicable.

[0025] Fig. Figure 3 shows the equivalent circuit of the microwave unit. 100 , as it is perceived through the signal connection, the signal feed line 109 (including the signal connection) 113 ), which is connected via the coupling capacitor 106B with the part of the transmission line of the signal resonator 104 is connected, and the other end of the part of the signal resonator's transmission line. 104 , which is via the Josephson crossing 110 is connected to ground. Since the frequency condition for the pump frequency ƒ P = 2 • ƒ S is (the fundamental resonance mode of the pump resonator) 102 corresponds to the pump frequency ƒ P , and the fundamental resonance mode of the signal resonator 104 corresponds to the signal frequency ƒ S ), the signal connection 113 (Quantum signal) 140 at the signal resonance frequency ƒ S ) the opposite side of the pump connection 111 true.

[0026] In this case (i.e., the case of the signal connection), the spur line ends. 120B , which acts as an impedance converter in a short-circuit circuit, and its length corresponds to a quarter of the signal wavelength, so that node B perceives an open circuit at the signal frequency. Likewise, the stub line ends 120A , which acts as an impedance converter in an open circuit, and its length corresponds to a quarter of the signal wavelength, so that node A perceives a short circuit at the signal frequency.

[0027] An advantageous result of this signal equivalent circuit is that the signal resonance mode is the pump resonator. 102 does not perceive. In other words, the signal resonator 104 is from the pump resonator 102 isolated.

[0028] Another advantageous result is that the RF current I associated with the signal resonance mode Sat the site of the Josephson Crossing 110 has an antinode.

[0029] Based on the Fig. 2 and Fig. 3. It should be clarified here that 1) the pump resonator 102 (apart from the coupling capacitor and the feed line) consists of the λ / 4 transmission line at the pump frequency, which is via the Josephson junction. 110 is short-circuited to ground, and 2) the signal resonator 104 (apart from the coupling capacitor and the feed line) consists of the λ / 4 transmission line at the signal frequency, which passes through the Josephson junction. 110 is short-circuited to ground.

[0030] The microwave unit 100 is configured to have two microwave resonance modes (i.e., the pump resonance mode and the signal resonance mode) with a common dispersive, nonlinear element, i.e., a Josephson transition. 110 couples.

[0031] The microwave unit 100 is configured to operate in one mode, i.e., the pump mode at the pump resonance frequency ƒ P , used as a photon detector to count the photons present in the second mode, i.e., the quantum signal mode at the signal resonance frequency. In the microwave unit 100 corresponds to the signal resonance frequency ƒ S the signal mode of the microwave frequency of the microwave photons that are to be detected and / or counted.

[0032] By stimulating the pump mode (of the pump resonator) 102 ) using a strong coherent microwave tone (i.e., the pump signal) 130 ) at the pump resonance frequency ƒ P The microwave unit causes 100 , that a nonlinear Cross-Kerr effect occurs in the Josephson junction, leading to a nonlinear interaction between the pump mode and the signal mode (and consequently between the pump signal) 130at the pump resonance frequency ƒ P and the quantum signal 140 at the signal resonance frequency ƒ S ) leads.

[0033] Because of this cross-kerr effect, the microwave unit 100 configured so that the pump resonance frequency ƒ P The pump mode depends on the number of photons in the signal resonance mode at frequency ƒ. S depends and vice versa.

[0034] The microwave unit 100 is configured so that the measurement / analysis unit 150 by monitoring the phase of the reflected pump signal 130' at the frequency ƒ P in a non-destructive quantum measurement, the presence or absence of signal photons in the signal mode can be detected (i.e., the presence or absence of signal photons in the quantum signal). 140 at the frequency ƒ S ).

[0035] The microwave unit 100is configured so that the number of photons in signal mode is derived / determined from the magnitude of the phase shift caused by the (at the pump feed line) 108 through the measurement / analysis unit 150 (measured in reflection) output pump signal 130' was obtained. Thus, the microwave unit serves 100 as a non-destructive microwave photon detector and counter. By introducing a frequency shift into the resonant frequency of the pump mode, it is achieved that in the microwave unit 100 the signal photons in the quantum signal 140 It is neither absorbed nor destroyed. Rather, the quantum signal is transmitted to the signal feed line. 109 through the microwave unit 100 reflects 104', after it is in the unit 100 via the Josephson crossing 110 with the pump signal 130 has interacted.

[0036] It is pointed out that the microwave unit100 Besides the pump mode and the signal mode, which are measured in reflection and explained in detail above, the unit has two common-mode resonance modes that can be measured in transmission between the pump and signal terminals. However, these common-mode resonance modes do not play a role in the interaction between the signal and pump modes described above, because their frequencies differ significantly from the pump and signal resonance modes (and can therefore be filtered out if necessary). For example, in a unit with a pump resonance frequency of approximately 16 GHz and a signal resonance frequency of approximately 8 GHz, common-mode resonances of the unit would be expected at approximately 3 GHz and 13 GHz.

[0037] From the above description, the following advantages of the microwave unit can easily be derived. 100 can be derived from: 1) the strong pump excitation (i.e. the pump signal) 130), which enables the detection of the signal photons, is connected to a different terminal than the detected weak signal (e.g., the quantum signal). 140 ) fed in; and 2) The pump mode and the signal mode are completely isolated from each other (due to the use of stub lines). They only interact through the JJ (or JJs) connected to their respective resonators. Therefore, no direct leakage currents should occur between the pump terminal and the signal terminal.

[0038] Fig. Figure 4 is a schematic representation of the microwave unit 100 , which, according to one embodiment, is realized as a coplanar waveguide. In Fig. 4 is a pump feed line 108 through the coupling capacitor 106A with the pump resonator 102 connected. The pump feed line 108 and the pump resonator 102They consist of superconductors made from a low-loss dielectric substrate. The coupling capacitor 106A is used as an air gap capacitor between the conductors of the pump feed line 108 and the pump resonator 102 executed. The pump resonator 102 has a length of approximately λ P / 4 (at a given pump resonance frequency, this length can vary depending on the inductance of the Josephson junction 110 (contributes, which is located at the end of the pump resonator's transmission line). On both sides of the pump resonator 102 and the pump feed line 108 is a mass surface 405 educated.

[0039] A quantum signal feed line 109 is through the coupling capacitor 106B with the signal resonator 104 connected. The signal feed line 109 and the signal resonator 104They also consist of superconductors made from a low-loss dielectric substrate. The coupling capacitor 106B is in turn an air gap capacitor between the conductors of the signal feed line. 109 and the signal resonator 104 realized. The signal resonator 104 has a length that is approximately λ S / 4 corresponds (at a specific signal resonance frequency, this length can vary depending on the inductance of the Josephson junction 110 (contributes, which is located at the end of the signal resonator's transmission line). On both sides of the signal resonator. 104 and the signal feed line 109 is a mass surface 405 educated.

[0040] The pump resonator is located at node A. 102 with the Josephson transition 110 and the branch line 120A connected. The other end of the branch line 120A remains open (i.e., ends in an open circuit).

[0041] The signal resonator is located at node B. 104 with the Josephson transition 110 and the branch line 120B connected. The other end of the branch line 120B is with the mass area 405 connected. At the branch lines 120A and 120B These are superconducting transmission lines, which in this embodiment are realized in the form of a coplanar waveguide on the low-loss dielectric substrate, and the center conductors of the branch lines 120A and 120B each have a λ P / 2 corresponding length.

[0042] At the Josephson crossing 110 This is a dispersive, nonlinear inductor consisting of two superconducting electrodes separated by a barrier (e.g., an insulating tunnel barrier). For example, a superconducting electrode of the Josephson junction... 110one electrode is connected to node A and the other superconducting electrode is connected to node B.

[0043] Fig. Figure 5 is a schematic representation of the microwave unit 100 , which, according to one embodiment, is realized in the form of strip lines. Fig. 5 resembles Fig. 4 insofar as, in the embodiment, superconducting striplines are mounted on a low-loss dielectric substrate of the microwave unit 100 are formed. A key difference between the embodiments with striplines and coplanar waveguides concerns the arrangement of the ground plane. In the configuration with coplanar waveguides ( Fig. 4) the ground plane is located on the same side of the dielectric substrate as the center conductor, whereas in the configuration with strip conductors ( Fig. 5) the mass area is located on the opposite side of the dielectric substrate.

[0044] In Fig. 5 is a pump feed line 108 through the coupling capacitor 106A with the pump resonator 102 connected to the pump feed line 108 and the pump resonator 102 These are superconductors formed on a low-loss dielectric substrate. The coupling capacitor 106A is used as an air gap capacitor between the conductors of the pump feed line 108 and the pump resonator 102 realized. The pump resonator 102 has a λ P / 4 corresponding length (at a specific pump resonance frequency, this length can depend on the homologous inductance of the Josephson junction) 110 (vary where the pump resonator terminates with its transmission line). In contrast to Fig. 4 here is not a mass surface on both sides of the pump resonator 102 and the pump feed line 108formed, but the mass surface is formed on the other side of the dielectric substrate.

[0045] A quantum signal feed line 109 is through the coupling capacitor 106B with the signal resonator 104 connected. At the signal feed line 109 and the signal resonator 104 These are also superconductors formed on a low-loss dielectric substrate. The coupling capacitor is similar. 106B as an air gap capacitor between the conductors of the signal feed line 109 and the signal resonator 104 realized. The signal resonator 104 has a λ S / 4 corresponding length (at a specific signal resonance frequency, this length can depend on the homologous inductance of the Josephson junction) 110 (vary where the signal resonator ends with its transmission line). In contrast to Fig. 4 here is not a ground plane on both sides of the signal resonator 104 and the signal feed line 109 formed, but the mass surface is formed on the other side of the dielectric substrate.

[0046] The pump resonator is located at node A. 102 with the Josephson transition 110 and the branch line 120A connected. The other end of the branch line 120A remains open (i.e., ends in an open circuit).

[0047] The signal resonator is located at node B. 104 with the Josephson transition 110 and the branch line 120B connected. The other end of the branch line 120B is with the mass area 405 connected. At the branch lines 120A and 120BThese are superconducting transmission lines, which in this embodiment are realized in the form of a strip conductor on the low-loss dielectric substrate, and the center conductors of the branch lines 120A and 120B each have a λ P / 2 corresponding length.

[0048] Other implementations or variants of the invention are also possible. According to one implementation, the pump resonator 102 and the signal resonator 104 Alternatively, homologous inductances (e.g., thin superconducting wires or an array of large Josephson junctions) and homologous capacitances (e.g., planar capacitors or comb capacitors) can be used. A particular requirement for the various implementations is to ensure that the maximum RF currents of the pump mode and the signal mode are within the range of the Josephson junction. 110 to maintain.

[0049] According to another implementation, the λ / 2 branch lines 120A and 120B of the microwave unit can be used. 100 can also be implemented using their equivalent circuit with homologous components near the pump resonance frequency.

[0050] According to another implementation, the single Josephson transition 110 be replaced by an arrangement of large Josephson transitions.

[0051] According to yet another implementation, the single Josephson transition 110 by replacing it with a DC-SQUID (superconducting DC quantum interference unit) (or an array of DC-SQUIDs), which allows the linear inductance of the mixing element (i.e., the inductance of the Josephson junctions in the DC-SQUID) to be tuned in place by changing the magnetic flux passing through the DC-SQUID loop (or loops of the array of DC-SQUIDs).

[0052] According to one implementation, the frequency of the microwave unit can be 100 tuning is achieved by adjusting the resonators, stub lines, and the nonlinear mixing element (i.e., the Josephson transition). 110 or the arrangement of Josephson transitions) DC-SQUIDs are used.

[0053] The following describes the theory for counting and detecting photons in the microwave unit. 100 This will be discussed in more detail. For better understanding, subheadings have been included below. It is clear that these subheadings serve only as explanations and are not intended to represent any limitations. The energy of the Josephson transition

[0054] A supercurrent flowing in a Josephson junction satisfies the current-phase relation I J = I0sinδ, where I0 is the critical current of the Josephson transition and δ is the transformation-invariant phase difference. The energy of the Josephson transition can be expressed as E j= E J [1 - cosδ] are written, where E J I0φ0 is equal to the Josephson energy and φ0 = ℏ / 2e is equal to the reduced flux quantum (e is equal to the charge of the electron). Using the trigonometric identity cos x = 1 − x 2 can the energy of the Josephson transition take the form E j = E J [ 1 − 1 − ( I J I 0 ) 2 ] to be written.

[0055] Extending the expression for the energy of the Josephson transition to the fourth order of the current yields E j ≃ E J 2 ( I J I 0 ) 2 − E J 24 ( I J I 0 ) 4 . By substituting the inductance L J = E J I 0 2 the transition results E j ≃ L J 2 I J 2 − L J 24 I J 4 I 0 2 , where the first term ( ∝ I J 2 ) the pure resonance frequencies of the pump resonator and the signal resonator are modified, while the second term ( ∝ I J 4 ) represents the nonlinear mixing term. II. Quantization

[0056] Based on the equivalent circuits of the microwave unit from the perspective of the pump and signal connections according to the Fig. 2, Fig. 3. The RF current flowing in the Josephson junction is equal to I. J = I P - I S , where I P and I S The RF currents of the microwave pump and signal resonance modes flow in the Josephson junction.

[0057] Expressions of flows I P , I S through the quantum operators a P , a S , which represent the annihilation operators belonging to the pump resonance mode and the signal resonance mode, leads to I P = i Î P ( a P † − a P ) I S = i Î S ( a S † − a S ) where Î P , Î S equal to the current amplitudes of the zero-point fluctuations (ZPF) caused by Î P = ω P ℏ 2 Z P and Î S = ω S ℏ 2 Z S are given, where ω P and ω S the angular resonance frequencies of the pump resonator and the signal resonator and Z P and Z S the characteristic impedances of the corresponding resonators.

[0058] Using the following expressions for the angular resonance frequencies ω P 2 = 1 L P C P , ω S 2 = 1 L S C S and the resonator impedances Z P 2 = L P C P , Z S 2 = L S C S The ZPF current amplitudes can be rewritten as I ^ p 2 = ℏ 2 ω P L P , und I ^ s 2 = ℏ 2 ω S L S , where L P , L S and C P , C S the inductances and capacitances of the LC equivalent circuit of the resonating pump resonator and signal resonator. III. Effective Hamiltonian of the system

[0059] Without considering the feed lines, the control lines and environmental losses, the effective Hamiltonian of the system is given by the sum H eff = H res + E j , where H res = ℏω P N P + ℏω S N S and N P = a p † a p , N S = a S † a S The photon number operators for the pump mode and the signal mode are.

[0060] Now equations 2 and 3 are substituted into the expression for E j (i.e., equation 1) and equations 4 and 5, the photon number operators N P , N S , the specified frequency condition ω P = 2ω S and the rotational wave approximation is used, so that the effective Hamiltonian of the system (equation 6) is in the form H eff = ℏ ω ˜ P N P + ℏ ω ˜ S N S + ℏ K N p 2 + ℏ K ' N P N S , can be written as ω̃ P , ω̃ Sin the first and second terms are equal to the adapted angular resonance frequencies of the pump mode and the signal mode, which contain the inductive loading of the resonator due to the Josephson junction (represented by the first term in Equation 1), and K, K' in the third and fourth terms, which represent the Eigen-Kerr and Cross-Kerr nonlinearity, correspond to the Eigen-Kerr and Cross-Kerr constants, respectively.

[0061] In deriving equation 7, the fact that the pump mode is more strongly excited than the signal mode was also taken into account, and the boson operators of the two modes a P , a S among themselves and those of the same fashion subject to the usual exchange relationships of form [ a P , a P † ] = 1, [ a S , a S † ] = 1 sufficient.

[0062] The Eigen-Kerr constant in equation 7 is given by K = − L J 4 I 0 2 I ^ P 4 ℏ given, which using the ratio P P = L J L P the linear inductance of the JJ to the total inductance of the pump resonator and the plasma frequency ω J = I 0 2 e of JJ can be rewritten to K = − P P 2 ω P 2 16 ω J

[0063] Similarly, the Cross-Kerr constant in equation 7 is given by k ' = − L J I 0 2 I ^ p 2 I ^ S 2 ℏ , which using p P , ω J and the relationship P S = L J L S the linear inductance of the JJ to the total inductance of the signal resonator K ' = − P P P S ω P ω S 4 ω J umgeschrieben werden kann . IV. Resonance frequency shift per photon

[0064] To better understand the basic idea of ​​the microwave unit, the terms in equation 7 are rearranged so that the effective Hamiltonian of the system looks like this: H eff = ℏ ( ω ˜ P + K N p + K ' N S ) N P + ℏ ω ˜ S N S .

[0065] This form shows that when operating the unit in nonlinear mode, where the Kerr effect is pronounced, the eigen-Kerr and cross-Kerr nonlinearities cause the adapted angular resonance frequency of the pump mode to shift depending on the number of photons present in the pump resonance and signal resonance modes. Since the pump mode is externally excited at a specific operating point, signal photons entering the signal resonator would also shift the pump resonance frequency by K'N. S shift, which is proportional to their number; thus, the Cross-Kerr constant K' corresponds to the frequency shift per photon.

[0066] It is pointed out that in order to detect (i.e. resolve the presence of) a single microwave photon using this unit, the frequency shift per photon due to the cross-Kerr nonlinearity (i.e. K') must be equal to or greater than the linewidth (i.e. bandwidth) of the pump resonance mode at the operating point. Example implementation using typical numerical values

[0067] For an embodiment of the proposed microwave unit 100 Realistic numerical values ​​are used for the various parameters. The adjusted resonant frequency for the pump mode is... ω ˜ P 2 π = 16 GHz . The adjusted resonant frequency for the signal mode is ω ˜ S 2 π = 8 GHz . The impedance of the resonators is Z P = Z S= 50 Ω (note that lower characteristic impedances are possible and should be more advantageous in terms of the unit's performance). Using the relationship L P , S = Z P , S ω ˜ P , S <?page 12=""?> This results in an estimated value of L P = 0.5 nanohenry (nH) and of L S = 1 nH. Assuming I0 = 1 microampere (µA), L J = 0.3 nH and ω J 2 π = 497 GHz . Using the values ​​for L P,S and L J This yields an estimated value for the contributions of the pump resonator and the signal resonator of p P ≃ 0.38 and p S ≃ 0.23. Substituting these values ​​into equations 8 and 9 yields K 2 π ≃ − 4,6 MHz and K ' 2 π ≃ − 5,6 MHz . If the linewidth of the pump resonance mode is set narrower than these frequency shifts per photon (which is quite achievable with state-of-the-art superconducting microwave circuits), the microwave unit 100 able to measure individual measurements through the measurement / analysis unit 150 To detect measured quantum signal photons.

[0068] For the unit to function correctly according to an implementation, it must meet two additional requirements. The first requirement is that the internal quality factor of both resonators at the single-photon level must be >10 5The external quality factor of the resonators, determined by the coupling capacitors between the resonators and the feed lines and their characteristic impedances, should be as large as possible and at least two orders of magnitude greater. This requirement is sufficient to ensure that the detected signal photons and the pump photons detecting them are not destroyed by internal loss mechanisms faster than they reach and leave both resonators. An obvious consequence of this requirement is that the overall quality factor of both resonators is determined by the external quality factor.

[0069] The second requirement is that the bandwidth of the pump resonator at the operating point should be equal to or greater than the bandwidth of the signal resonator. In other words, the response time of the pump resonator should be equal to or shorter than the response time of the signal resonator. This requirement is intended to ensure that the pump photons have sufficient time to detect the signal photons before they leave the unit through the signal feed line. It is noted that both of these requirements are met in the superconducting microwave circuits discussed herein.

[0070] According to one embodiment, a technique for (experimental) calibrating the Cross-Kerr constant K' for a given pump excitation consists of varying the input power of a coherent tone introduced into the signal resonator at the signal frequency and simultaneously measuring, for each input power, the complex reflection parameters of the pump resonator as a function of frequency using a very weak probe (on average less than one photon) superimposed on the pump excitation. By determining the rise of the measured pump resonant frequency as a function of the signal power and using the already known signal resonant frequency and signal resonator bandwidth, the constant K' can be calculated.

[0071] According to one embodiment, a technique for (experimental) detection of individual signal photons using this unit consists of monitoring the phase of the reflected pump excitation, which occurs without an input signal (i.e., N). S = 0) was injected at the pump resonance frequency. When signal photons on the order of 1 to 3 photons enter the signal resonator and interact with the pump mode via the JJ (i.e., the dispersive, nonlinear element), the pump mode's resonance frequency is shifted downwards by a multiple of K' / 2π, which is proportional to the number of signal photons in the signal resonator. As a consequence of this resonance frequency shift of the pump mode, the phase of the reflected pump excitation is also shifted accordingly. By measuring this phase shift, the number of signal photons entering the unit (on the order of 1 to 3) can be derived.

[0072] To count a larger number of incoming signal photons, e.g., between 3 and 10, in real time using the unit, a more sophisticated measurement technique can be employed. For example, the reflected phase of several relatively weak tones (so as not to affect the unit's function) can be continuously monitored. These tones are fed to the pump resonator at frequencies around [value missing in original text]. K ' 2 π , 2 K ' 2 π , … N S K ' 2 π below the pump resonance frequency without an input signal (i.e., N) S =0). If a phase shift is detected in the reflected tone at this frequency using this method. N S K ' 2 π If the signal is injected below the pump resonance frequency without an input signal, this indicates with a high probability that the incoming signal N S contained photons.

[0073] Measurements of not just a few, but a larger number of microwave photons may not be as useful for certain quantum applications, so the unit cannot be tailored accordingly. It is also noted that the derivation of the system's effective Hamiltonian operator was explicitly restricted to signals that are very weak compared to the pump excitation. Thus, for stronger signals beyond just a few photons, other undesired nonlinear terms could come into play, which were neglected in the derivation of the Hamiltonian operator (Equation 10).The exact number of input signal photons that can be detected or counted by the unit without significant loss of performance can, of course, vary depending on system parameters such as the critical current of the JJ(s), the proportion quotients, the bandwidths of the resonators, the characteristic impedances of the resonators, and the respective implementation of the resonators from unit to unit and from implementation to implementation.

[0074] Fig. 6 represents a flowchart of a procedure 600 for non-destructive counting and / or detection of microwave photons using the microwave unit 100 ready according to one embodiment.

[0075] In block 605 is the microwave unit 100 configured to produce a pump resonance mode (fundamental resonance mode) of the pump resonator 102and a signal resonance mode (e.g., the fundamental resonance mode) of the quantum signal resonator 104 in response to the pump signal 130 at a pump resonance frequency ƒ P and on the quantum signal 140 at a signal resonance frequency ƒ S with a dispersive, nonlinear element (e.g. a Josephson transition) 110 ) couples. The pump resonance mode of the pump resonator 102 The pump resonance frequency ƒ P and the signal resonance mode of the quantum signal resonator determines the signal resonance frequency.

[0076] In block 610 is the microwave unit 100 configured to allow a nonlinear interaction / mixing (e.g., through the Josephson junction) 110 ) between the pump signal 130 and the quantum signal 104 by strongly exciting the pump resonance mode (i.e., the pump mode) with the coherent pump signal 130 at the pump resonance frequency ƒ Pgenerated.

[0077] In block 615 is the microwave unit 100 configured to detect the presence or absence of photons in the quantum signal 140 according to the resonant frequency of the pump mode, which allows the phase of the (from the microwave unit) 100 reflected) output pump signal 130' influenced.

[0078] The microwave unit 100 is configured to excite a nonlinear cross-kerr effect in the dispersive, nonlinear element, thereby creating a nonlinear interaction between the pump signal 130 and the quantum signal 140 The microwave unit causes this. 100 is configured such that the pump resonance frequency of the pump mode depends on the number of photons in the quantum signal due to the nonlinear cross-Kerr effect generated in the unit. 140depends (this can be shown using the unit's input / output ratios).

[0079] The number of photons in the quantum signal 140 The frequency shift is determined by the magnitude of the pump resonance frequency shift. This shift is a multiple of a Cross-Kerr coefficient. A zero line of the frequency shift is determined, and a shift is present if its value is greater than the previously determined zero line. The frequency shift indicates the number of photons in the quantum signal, and this zero line is determined before the quantum signal is received. Each multiple of the frequency shift above the zero line in the pump signal represents a count for a single photon of the quantum signal, such that 0 to N photons 0up to M correspond to multiples of the frequency shift above the zero line, where N is a final number of photons and M is a final multiple of the frequency shift above the zero line.

[0080] Fig. 7 is a flowchart of a procedure 700 for the microwave unit 100 according to one embodiment. See also the Fig. 1 to Fig. 5.

[0081] In block 705 is the microwave unit 100 configured to produce a strong, coherent pump signal 130 at the pump resonance frequency ƒ P receives, where the pump resonance frequency of a pump resonance (fundamental) mode of a pump resonator 102 corresponds.

[0082] In block 710 is the microwave unit 100 configured to generate a quantum signal 140 at the signal resonance frequency ƒ Sreceives, wherein the signal resonance frequency of a signal resonance (fundamental) mode of a signal resonator 104 corresponds.

[0083] In block 715 is the microwave unit 100 configured to respond to the shift in the pump resonance frequency of the pump mode, which is generated by a number of photons in the quantum signal 140 depends on the pump signal 130' outputs with a phase shift.

[0084] It is clear that various microelectronic manufacturing methods can be used to produce the components / elements discussed herein. Four types of processes are relevant for the fabrication of superconducting and bonded conductor devices: deposition, ablation, structuring, and modification of electrical properties.

[0085] Deposition refers to any process in which a material is deposited onto a wafer by growing, coating, or other means. Available technologies include PVD (physical vapor deposition), CVD (chemical vapor deposition), ECD (electrochemical deposition), MBE (molecular beam epitaxy), and, more recently, ALD (atomic layer deposition).

[0086] Removal refers to any process in which material is removed from the wafer: examples include etching processes (wet or dry etching) and CMP (chemical-mechanical planarization), etc.

[0087] Structuring refers to the shaping or modification of deposited materials, a process generally known as lithography. In conventional lithography, the wafer is coated with a chemical substance called photoresist; then, a stepper machine focuses, adjusts, and moves a mask, exposing selected areas of the wafer underneath with short-wavelength light. After etching and further processing, the remaining photoresist is removed. Electron beam lithography is also used in structuring.

[0088] To modify electrical properties, doping, for example, doping the source and drain regions of transistors, is generally possible via diffusion and / or ion implantation. These doping processes are followed by furnace annealing or rapid thermal annealing (RTA). Annealing serves to activate the implanted dopants.

[0089] The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. Accordingly, each block in the drive assembly or block diagrams can represent a module, segment, or section of instructions comprising one or more executable instructions for performing the specified logical function(s). According to some alternative implementations, the functions specified in the block may occur in a different order than shown in the figures. For example, depending on the intended functionality, two blocks shown consecutively may in reality be executed essentially simultaneously, or the blocks may sometimes be executed in reverse order.It is also pointed out that each block of the block diagrams and / or flowcharts and combinations of blocks in the block diagrams and / or flowcharts can be implemented by special hardware systems that perform the specified functions or actions or combinations of special hardware and computer instructions.

[0090] The descriptions of the various embodiments of the present invention serve only for illustration and do not claim to be exhaustive or to limit the disclosed embodiments. Many modifications and variants are obvious to those skilled in the art without deviating from the scope of protection of the invention. The terms used herein have been chosen to explain the basic concepts of the embodiments, their practical application, or technical improvements over commercially available technologies as clearly as possible, or to facilitate the understanding of the embodiments of the invention disclosed herein by other skilled persons.

Claims

[1] Microwave unit which features: a dispersive, nonlinear element; a pump resonator, the first end of which is connected to both the dispersive, nonlinear element and a first stub line and capacitively coupled to a second end of the pump resonator with a pump terminal, the first stub line terminating in an open circuit; and a quantum signal resonator, the first end of which is connected to both the dispersive, nonlinear element and a second stub line, and capacitively coupled to a signal terminal at a second end of the signal resonator, with the second stub line being connected to ground. [2] Microwave unit according to claim 1, wherein the dispersive nonlinear element has a Josephson junction. [3] Microwave unit according to claim 2, wherein the dispersive nonlinear element comprises an arrangement of Josephson junctions. [4] Microwave unit according to claim 1, wherein the pump resonator has a pump resonance mode with a pump resonance frequency and a pump wavelength; where one length of the pump resonator λ / 4 corresponds to the pump wavelength; wherein the quantum signal resonator has a signal resonance mode with a signal resonance frequency and a signal wavelength; where one length of the quantum signal resonator corresponds to λ / 4 of the signal wavelength; and where the pump resonance mode and the signal resonance mode are coupled to the dispersive, nonlinear element. [5] Microwave unit according to claim 4, wherein the pump terminal and the signal terminal are spatially separated and the pump resonant mode and the signal resonant mode are isolated from each other by the first and the second spur line in such a way that no leakage current flows between the pump terminal and the signal terminal; and wherein the pump resonator and the quantum signal resonator are configured such that the pump resonance mode undergoes a frequency shift at the signal resonance frequency according to a number of photons in an input quantum signal. [6] Microwave unit according to claim 5, wherein the pump resonator and the quantum signal resonator are configured such that, in response to an input pump signal, a nonlinear cross-kerr effect is generated in the dispersive nonlinear element, thereby generating a nonlinear interaction between the pump resonance mode and the signal resonance mode. [7] Microwave unit according to claim 6, wherein the nonlinear Cross-Kerr effect causes a reflected pump signal at the pump resonance frequency to depend on the number of photons in the input quantum signal at the signal resonance frequency. [8] Microwave unit according to claim 6, wherein the nonlinear Cross-Kerr effect causes a reflected quantum signal at the signal resonance frequency to depend on a number of photons in the input pump signal at the pump resonance frequency. [9] Microwave unit according to claim 7, wherein the pump resonator is configured such that the reflected pump signal at the pump resonant frequency contains information about the presence or absence of photons in the input quantum signal. [10] Microwave unit according to claim 5, wherein the pump resonator is configured such that the magnitude of the frequency shift in the pump resonance frequency is given by the number of photons in the input quantum signal. [11] Microwave unit according to claim 5, wherein the pump resonator, the quantum signal resonator, the first and second stub lines and the dispersive nonlinear element are configured such that the photons in the input quantum signal are neither destroyed nor absorbed, while the number of photons in the input quantum signal is counted by the frequency shift of the pump resonance mode. [12] Method for non-destructive counting of photons by a microwave unit according to claim 1, wherein the method comprises: Coupling a pump resonance mode of the pump resonator and a signal resonance mode of the quantum signal resonator with the dispersive, nonlinear element in response to a pump signal at a pump resonance frequency and a quantum signal at a signal resonance frequency, wherein the pump resonance mode of the pump resonator has the pump resonance frequency and the signal resonance mode of the quantum signal resonator has the signal resonance frequency; Generating a nonlinear interaction between the pump signal and the quantum signal by exciting the pump resonance mode with the pump signal at the pump resonance frequency; and Detecting the presence or absence of photons in the quantum signal based on the pump resonance frequency, thereby influencing an output pump signal to be measured. [13] Method according to claim 12, further comprising excitation of a nonlinear Cross-Kerr effect in the dispersive nonlinear element, thereby causing the nonlinear interaction between the pump signal and the quantum signal. [14] Method according to claim 12, wherein the pump resonance frequency of the output pump signal as a result of the nonlinear Cross-Kerr effect depends on a number of photons in the quantum signal. [15] Method according to claim 14, comprising determining the number of photons in the quantum signal by the magnitude of a phase shift in the output pump signal. [16] Method according to claim 14, wherein a frequency shift is equal to a multiple of a Cross-Kerr coefficient. [17] Method according to claim 16, comprising determining a zero line of the frequency shift, wherein a frequency shift is present if its value is greater than the previously determined zero line. [18] Method according to claim 17, wherein the frequency shift indicates the number of photons in the quantum signal after the zero line of the frequency shift has been determined prior to receiving the quantum signal. [19] Method according to claim 18, wherein each multiple of the zero line of the frequency shift of the pump resonance frequency indicates a count value of a single photon of the quantum signal, such that 0 to N photons correspond to 0 to M multiples of the zero line of the frequency shift, where N is a final number of photons and M is a final multiple of the zero line of the frequency shift. [20] Method for operating a microwave unit according to claim 1, wherein the method comprises: Receiving a pump signal at a pump resonant frequency by the microwave unit, wherein the pump resonant frequency corresponds to a pump resonant mode of the pump resonator; Receiving a quantum signal at a signal resonance frequency, where the signal resonance frequency corresponds to a signal resonance mode of the signal resonator; and Output of the pump signal with a phase shift by the microwave unit in response to a number of photons in the quantum signal.