High-bandwidth photonic memory using high-temperature atomic vapor

Abstract

Described herein is a technique for enabling the storage and retrieval of quantum bits in a high-temperature atomic vapor system, which includes emitting a first control pulse having a bandwidth based on a bandwidth of an optical quantum bit to modify a transmission characteristic of the atomic vapor system, receiving the optical quantum bit in the atomic vapor system, emitting a second control pulse having a characteristic based on a target bandwidth of the retrieved optical quantum bit to modify a transmission characteristic of the atomic vapor system, and decoupling the retrieved optical quantum bit from a control laser.

Description

[Background technology]

[0001] Quantum networks enable the transmission of information in the form of quantum bits ("qubits") between physically separated quantum processors or other quantum devices (e.g., quantum sensors). Quantum networks can be used to enable optical quantum communication over long distances and can be implemented over standard telecommunication optical fiber through the transmission of single photons in which information is encoded (e.g., in polarization). Additional components may be required to enable reliable transmission of quantum information over arbitrary distances. Summary of the Invention

[0002] The following is a non-limiting summary of some embodiments of the present application: Some embodiments provide a method for improving the bandwidth of optical quantum bits stored in atomic vapor, the method comprising: preparing a control laser pulse to store optical quantum bits using a high-temperature atomic vapor system, the optical quantum bits having a bandwidth, wherein preparing the control laser pulse includes generating the control laser pulse having a bandwidth based on a temporal profile of the optical quantum bits, adjusting a pulse energy of the control laser pulse based on the temporal profile of the optical quantum bits; transmitting the control laser pulse through the high-temperature atomic vapor system to change a transmission characteristic of the atomic vapor; and receiving the optical quantum bits in the high-temperature atomic vapor system while the control laser pulse is transmitting through the high-temperature atomic vapor system.

[0003] In some embodiments, adjusting the bandwidth of the control laser pulses based on the temporal profile of the optical quantum bits comprises modulating a light source of the control laser pulses to adjust the bandwidth of the control laser pulses.

[0004] In some embodiments, a fiber-coupled electro-optic modulator is used to modulate the source of the control laser pulses. In some embodiments, the bandwidth of the control laser pulse is adjusted to have approximately the same temporal profile as the optical quantum bit.

[0005] In some embodiments, adjusting the pulse energy of the control laser pulse is further based on properties of the atomic vapor and a beam shape of the control laser pulse. In some embodiments, the amplitude of the control laser pulse is adjusted such that the pulse intensity in the atomic vapor produces a transparency window having a linewidth approximately the same as the bandwidth of the optical quantum bit.

[0006] In some embodiments, adjusting the pulse energy of the control laser pulse comprises amplifying the control laser pulse after adjusting the bandwidth of the control laser pulse.

[0007] In some embodiments, the atomic vapor comprises rubidium atomic vapor. In some embodiments, transmitting the control laser pulse through the high temperature atomic vapor system modifies the three-level system of the rubidium atomic vapor creating a transparency window.

[0008] In some embodiments, the transparent window has a bandwidth of 10 to 100 GHz. Some embodiments provide a method for controlling the bandwidth of optical quantum bits retrieved from atomic vapor storage, the method comprising: determining a target bandwidth for the retrieved optical quantum bits; providing a control laser to retrieve stored optical quantum bits from a high-temperature atomic vapor system such that the retrieved optical quantum bits have the target bandwidth; transmitting the control laser through the high-temperature atomic vapor system to change a transmission characteristic of the high-temperature atomic vapor system; receiving the retrieved optical quantum bits from the high-temperature atomic vapor system in response to the control laser; and decoupling the retrieved optical quantum bits from the control laser.

[0009] In some embodiments, the control laser is arranged to generate the retrieved optical quantum bit having the same bandwidth as the previously stored optical quantum bit. In some embodiments, the control laser is arranged to generate the retrieved optical quantum bit having a different bandwidth than the previously stored optical quantum bit.

[0010] In some embodiments, the target bandwidth of the extracted optical quantum bit is based on the bandwidth of a second optical quantum bit, such as to improve interference caused by the extracted optical quantum bit interfering with the second optical quantum bit.

[0011] In some embodiments, preparing the control laser to retrieve the stored optical quantum bits from the high temperature atomic vapor system such that the retrieved optical quantum bits have the target bandwidth includes modulating the control laser with a fiber-mounted electro-optic modulator.

[0012] In some embodiments, preparing the control laser to retrieve the stored optical quantum bits from the high temperature atomic vapor system such that the retrieved optical quantum bits have the target bandwidth includes modulating the control laser with an acousto-optic modulator.

[0013] In some embodiments, the atomic vapor comprises rubidium atomic vapor. In some embodiments, transmitting the control laser pulse through the high temperature atomic vapor system modifies the three-level system of the rubidium atomic vapor creating a transparency window.

[0014] Some embodiments provide a system for improving storage and retrieval of optical quantum bits stored in atomic vapor, the system comprising: a high-temperature atomic vapor system containing atomic vapor; a control laser configured to emit first control pulses having a bandwidth based on a bandwidth of the optical quantum bit and emit second control pulses having characteristics based on a target bandwidth of the optical quantum bit to change a transmission characteristic of the high-temperature atomic vapor system; and an optical filtering system configured to separate the extracted optical quantum bit from the control laser, the optical filtering system including: a first etalon configured in a first double-pass configuration, the first etalon having a first bandwidth; and a second etalon configured in a second double-pass configuration, the second etalon being positioned to receive an output of the first etalon and having a second bandwidth different from the first bandwidth.

[0015] In some embodiments, the first etalon receives light output from the high temperature atomic vapor system, the first etalon configured with a first polarizing beam splitter such that light returning after passing twice through the first etalon and a wave plate is directed to the second etalon, and the second etalon configured with a second polarizing beam splitter such that light returning after passing twice through the second etalon is directed to a detector. [Brief explanation of the drawings]

[0016] [Figure 1] FIG. 1 illustrates a quantum memory module 100 in accordance with some embodiments of the techniques described herein. [Figure 2] FIG. 2 illustrates an example of an optical quantum bit storage process 200 according to some embodiments of the techniques described herein. [Figure 3] FIG. 3 shows an example of an optical quantum bit storage process 300 according to some embodiments of the techniques described herein. [Figure 4] FIG. 4 illustrates an example of an optical qubit extraction process 400 according to some embodiments of the techniques described herein. [Figure 5A] FIG. 5A shows an example of an absorption spectrum 500 corresponding to the EIT regime at the low bandwidth limit. [Figure 5B] FIG. 5B shows an example of an absorption spectrum 504 corresponding to the ATS regime at the high bandwidth limit. [Figure 6A] FIG. 6A shows an EIT window as transmission of a weak probe field through room temperature steam under different control field intensities, according to some embodiments of the techniques described herein. [Figure 6B] FIG. 6B shows multiple time traces of photons extracted in a memory operation using different optical powers of the control field according to some embodiments of the techniques described herein. [Figure 7A] FIG. 7A shows a plot 700 of an input time profile 702 and an output time profile 704 according to some embodiments of the techniques described herein. [Figure 7B] FIG. 7B shows a plot 710 of an input time profile 712 and an output time profile 714 according to some embodiments of the techniques described herein. [Figure 7C] FIG. 7C shows a plot 720 of modified input pulse widths and the corresponding FWHM of extracted qubits, according to some embodiments of the techniques described herein. [Figure 8] FIG. 8 illustrates an example of a control pulse generation module 800 in accordance with some embodiments of the techniques described herein. [Figure 9] FIG. 9 illustrates an example of a memory unit 900 in accordance with some embodiments of the techniques described herein. [Figure 10] FIG. 10 shows an example of a filter unit 1000 according to some embodiments of the technology described herein. [Figure 11] FIG. 11 shows an example of an optical filter configuration 1100 for filtering a control laser from an extracted qubit, according to some embodiments of the techniques described herein. [Figure 12] FIG. 12 shows an acousto-optic modulator-based configuration 1200 for modulating the bandwidth of a laser to generate control pulses, according to some embodiments of the techniques described herein. [Figure 13A] FIG. 13A shows acousto-optic modulation performance for an 80 MHz shifted and focused beam according to some embodiments of the techniques described herein. [Figure 13B] FIG. 13B shows memory performance using the AOM configuration of FIG. 13A in accordance with some embodiments of the techniques described herein. [Figure 14] FIG. 14 shows a direct electro-optic modulator configuration 1400 for controlling a control laser, in accordance with some embodiments of the techniques described herein. [Figure 15A] FIG. 15A shows electro-optic modulation performance according to some embodiments of the techniques described herein. [Figure 15B] FIG. 15B shows memory performance using the EOM configuration of FIG. 15A in accordance with some embodiments of the techniques described herein. [Figure 16] FIG. 16 shows a low-power EOM phase-switching configuration 1600 with optical amplification in accordance with some embodiments of the techniques described herein. [Figure 17A] FIG. 17A shows an RF pulse recorded by a photodiode according to some embodiments of the techniques described herein. [Figure 17B]FIG. 17B shows the Fourier transform of the pulse shown in FIG. 17A. [Figure 18] FIG. 18 shows photon bandwidth as a function of control field power according to some embodiments of the techniques described herein. [Figure 19] FIG. 19 shows an example of a low-power EOM intensity switching configuration 1900 with optical amplification, in accordance with some embodiments of the techniques described herein. [Figure 20] FIG. 20 shows an example of a pulse generated using an intensity modulator and a TA, according to some embodiments of the techniques described herein. [Figure 21A] FIG. 21A is an example of memory fidelity in the high bandwidth region using phase modulation with fEOM and TA amplification, according to some embodiments of the techniques described herein. [Figure 21B] FIG. 21B shows an example plot of bandwidth in a qubit extraction process according to some embodiments of the techniques described herein. DETAILED DESCRIPTION OF THE INVENTION

[0017] The present inventors have developed techniques for improving the storage and retrieval of quantum bits (qubits) to advance quantum information science, including methods and systems for adjusting the bandwidth of control pulses used in storing quantum bits in a hot atomic gas.

[0018] Quantum repeaters have been proposed as a solution to overcome transmission losses in adapting existing extensive long-distance communication fiber infrastructure for use in quantum networks. Quantum repeaters split long communication channels into multiple elementary links and use pair-wise entanglement swapping to distribute entanglement between two remote parties. In the most common quantum repeater scheme, quantum memory is the central device that allows single photons to be temporarily stored in long-lived matter states and retrieved when needed, enabling temporary storage of entanglement in the elementary links. Because the entanglement process is probabilistic, the use of quantum mechanics can improve the implementation of entanglement swapping, significantly increasing the entanglement distribution rate and serving as the foundation for global-scale quantum networks.

[0019] Quantum memories are devices that can store and retrieve photonic qubits on demand. This capability can be characterized by three parameters: fidelity, f, which indicates the degradation of the input quantum state of a photon; storage efficiency, η, which is defined as the probability that a photon can be stored and retrieved; and storage time, T, which measures the time it takes for the storage efficiency to significantly decay. For quantum memories in a quantum network, these parameters determine the entanglement distribution rate and distance scaling and can therefore be used to indicate the "quantum performance" of a quantum memory.

[0020] For implementation into existing telecommunications infrastructure, additional metrics apply: fiber-hub compatibility, favoring devices with smaller size, weight, and power consumption (SWaP); Robustness against environmental noise (e.g., electromagnetic noise, thermal noise, mechanical noise), · Adaptable to mass deployment.

[0021] These parameters can be used to indicate the "hardware performance" of a quantum memory. Quantum memories that are deployed in real-world settings and serve large-scale quantum networks must meet both quantum and hardware performance criteria.

[0022] Quantum memories with high quantum performance have been realized in a variety of physical systems, including ensembles of atoms or ions, rare-earth-doped crystals, defects in diamonds, and quantum dots. However, the supporting technologies required to achieve high quantum performance from these systems are resource-intensive and include cryogenic cooling systems, ultra-high vacuum systems, and sophisticated laser-cooled trapping systems. The requirements for each of these systems, including energy consumption, space requirements, use of refrigerants, and vibration isolation, pose significant obstacles to deploying these quantum memories in the field or in large-scale quantum networks.

[0023] The present inventors have recognized and appreciated that warm atomic vapor systems are a promising platform for implementing quantum memories with improved quantum and hardware performance. This is because warm atomic vapor systems are simple and robust physical platforms that operate at room temperature or above (e.g., in the range of 18°C ​​to 25°C or higher) without the need for cryogenic or vacuum technology. For example, one embodiment utilizes an ensemble of room-temperature atoms with an internal three-level structure in a lambda configuration. A strong external laser field (called the "control" field), specifically its electric field, changes the properties of three-level atoms that interact with photons to be stored (called the "probe" field), a phenomenon known as "electromagnetically induced transparency" (EIT). This mechanism allows signal photons to be transformed (mapped) into long-lived matter states and recalled by turning the control field off and on.

[0024] The three-level atom mainly determines the wavelength of the optical pulse that can be stored, and the frequency difference between the intrinsic energy difference and the optical field is called detuning D. The lifetime of the excited state is naturally selected as the benchmarking bandwidth, which is called G. The memory protocol can function within a wide detuning range. When D>>G, it is usually called the Raman protocol, and when D<G, it is called EIT. Despite the proposed differences in the mechanics of fundamental physics, both regimes are experimentally treated as the same process and can be adequately explained by a unified theory. A non-limiting explanation is described in "Quantum optical memory for entanglement distribution, Optica 10, 1511-1528 (2023)" by Yisheng Lei, Faezeh Kimiaee Asadi, Tian Zhong, Alex Kuzmich, Christoph Simon, and Mahdi Hosseini, which is hereby incorporated by reference in its entirety. Thus, regardless of the fundamental physics (either by the Raman protocol or the EIT phenomenon), the optical field changes the transmission characteristics of the three-level atomic system.

[0025] The inventors recognized that in order to achieve optimal storage, the spectral characteristics of the atomic medium should match the photons to be stored. A transform-limited pulse has a bandwidth B defined as the full width at half-maximum of its spectral peak. In the EIT regime, the transparency peak has a width Δω c determined by the intensity of the control field (Ω EIT ). By adjusting the power of the control field under the same conditions, the transparency window can be changed, and as a result, the bandwidth

[0026]

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[0027] Photons with The inventors further recognized that bandwidth plays a critical role in photon-based quantum communication applications. Therefore, the inventors developed a physical system for controlling bandwidth in optical quantum communication systems. To store photons with a low (temporal) bandwidth (e.g., less than 1 MHz), the power of the control field can be reduced to reduce the size of the EIT window. However, to store photons with a high (temporal) bandwidth (e.g., greater than 100 MHz), both an increase in the power of the control field and matching the bandwidth of the control pulse to the bandwidth of the stored photons may be required to optimize storage and retrieval. The inventors further recognized that controlling the bandwidth of the control pulse for storage / retrieval operations can be difficult due to technological limitations regarding the on- and off-switching of the control field, including the finite time required to complete the switching operation. The switching bandwidth can be characterized by measuring the 10% to 90% rise / fall time. Instead of using a switch to turn the laser on and off in a binary manner, storage / retrieval can be performed by pulsing the control field, in which case the FWHM of the pulse represents the switching bandwidth. In either case, one must ensure that the switching bandwidth is comparable to or larger than the photon bandwidth B. Failure to maintain such a match between these bandwidths can reduce storage efficiency due to bandwidth mismatch. Thus, high bandwidth storage requires a control field (or its Rabi frequency Ω) c ) and its temporal bandwidth, which is on the same order as the photons to be stored. For example,

[0028]

number

[0029] For a typical beam size and Rb atoms, 200 mW and

[0030]

number

[0031] A control field with a duration of is required. 1 shows a quantum memory module 100 in accordance with some embodiments of the techniques described herein. Quantum memory module 100 receives qubits 102 via input module 104. The received qubits are stored in atomic vapor cells 106 such that the qubits are retrieved after a time delay. After retrieval, retrieved qubits 116 are sent from quantum memory module 100 via output module 114.

[0032] Input module 104 includes optical components for enabling it to receive and direct optical qubits to atomic vapor cell 106. The optical components for enabling it to receive the optical qubits may include free-space optics and / or fiber optics. In some embodiments, input module 104 receives the optical qubits from an optical qubit source. For example, input module 104 may receive the optical qubits from an entanglement source.

[0033] The storage and retrieval of qubits in atomic vapor cell 106 is controlled by control laser 108. When the control laser is used to retrieve a qubit, the control laser light and the retrieved qubit propagate along a shared optical path. Accordingly, filter unit 112 is configured to filter the control laser such that the retrieved qubit is sent out of quantum memory module 100 for use and / or detection.

[0034] Output module 114 receives the extracted qubit from filter unit 112 and includes multiple optical components to enable directing extracted qubit 116 from quantum memory module 100. In some embodiments, output module 114 may direct the extracted qubit to a detector. In some embodiments, output module 114 can direct the extracted qubit to a destination for quantum communication. For example, output module 114 can direct the extracted qubit into a fiber for transmission over a long distance to a quantum communication detector.

[0035] Control laser 108 generates one or more control beams to enable storage and retrieval of multiple optical quantum bits in atomic vapor cell 106. In some embodiments, control laser 108 includes a pulse generating unit 110 for generating control laser pulses, which may be implemented in any suitable manner, including the configurations described herein in connection with FIGS.

[0036] FIG. 2 illustrates an example of an optical quantum bit storage process 200 according to some embodiments of the techniques described herein. Process 200 begins with operation 202, where a first control pulse having a bandwidth based on the bandwidth of an optical quantum bit is emitted to change the transmission characteristics of an atomic vapor system in accordance with some embodiments of the techniques described herein. Operation 202 may be implemented using process 300, described below in connection with FIG.

[0037] Process 200 then proceeds to operation 204, where a second control pulse having characteristics based on a target bandwidth of the extracted optical quantum bit is transmitted in accordance with some embodiments of the techniques described herein. Operation 204 may be performed in accordance with process 400, described below in connection with FIG.

[0038] Process 200 then proceeds to operation 206, where the extracted optical quantum bit is isolated from the control laser in accordance with some embodiments of the techniques described herein. Isolating the extracted optical quantum bit from the control laser may be accomplished using any suitable filter as described herein, including the filters described in connection with FIGS. 10 and 11.

[0039] After act 206, process 200 ends. FIG. 3 shows an example of an optical quantum bit storage process 300 according to some embodiments of the techniques described herein.

[0040] Process 300 begins at operation 302 with preparing a control laser pulse based on a temporal profile of an optical quantum bit to store the quantum bit using an atomic vapor system in accordance with some embodiments of the techniques described herein. As described above, the performance of the store operation (e.g., the ability to retrieve the quantum bit with a high signal-to-noise ratio) depends at least in part on the temporal profile of the optical quantum bit. Thus, preparing the control laser pulse includes generating a control laser pulse having optical properties to enable storage of the quantum bit. The optical properties of the control laser pulse may include a bandwidth of the control laser pulse, a pulse energy of the control laser pulse, and a center frequency of the control laser pulse.

[0041] In some embodiments, preparing the control laser pulse includes generating a control laser pulse having a bandwidth based on the temporal profile of the optical quantum bit. The bandwidth of the control laser pulse can be generated to have approximately the same temporal profile as the optical quantum bit. The temporal profile of the quantum bit can be measured as the temporal bandwidth as measured by the full width at half maximum (FWHM) of the quantum bit's duration relative to its intensity. For example, the approximately same temporal profile can be a control laser pulse having an FWHM within ±1%, ±2%, ±5%, ±10%, or ±15% of the FWHM of the optical quantum bit.

[0042] In some embodiments, generating the bandwidth of the laser pulses to have approximately the same temporal profile as the optical quantum bits includes modulating a source of control laser pulses with a fiber-coupled electro-optical modulator, as further described in connection with Figures 16-21B below. In some embodiments, generating the bandwidth of the laser pulses to have approximately the same temporal profile as the optical quantum bits includes using an acousto-optical modulator or an electro-optical modulator, as further described in connection with Figures 12-15 below.

[0043] Because the energy levels of the atomic gas system depend on the composition of the atomic gas, the frequency and bandwidth of the control laser pulse can be generated based on the frequency of each energy level of the three-level system of the atomic gas system. For example, the control laser pulse can be generated based on a desired detuning D between the laser and the energy level of the lambda atomic system.

[0044] In some embodiments, preparing the control laser pulse includes generating a control laser pulse having a Rabi frequency based on the temporal profile of the optical quantum bit. The Rabi frequency is described by Equation 1 below:

[0045]

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[0046] In Equation 1 above, μ is the transition dipole moment of the atom or molecule, E is the electric field strength of the laser, and h is Planck's constant. Because the Rabi frequency depends on the electric field strength, the Rabi frequency can be adjusted by adjusting the pulse energy of the control laser pulse. The pulse energy of the control laser pulse can be adjusted to have a Rabi frequency approximately equal to the bandwidth of the optical quantum bit. For example, the Rabi frequency being approximately equal to the bandwidth of the optical quantum bit can be within ±1%, ±2%, ±5%, ±10%, or ±15% of the bandwidth of the optical quantum bit.

[0047] In some embodiments, adjusting the pulse energy of the control laser pulse based on the temporal profile of the optical quantum bit comprises adjusting the gain of an amplifier to increase or decrease the pulse energy of the control laser pulse, hi some embodiments, adjusting the pulse energy of the control laser pulse based on the temporal profile of the optical quantum bit comprises adjusting the attenuation of the control laser pulse to decrease the intensity of the control laser pulse.

[0048] In some embodiments, adjusting the pulse energy of the control laser pulse is based on an atomic gas system. The composition of the atomic gas system can change the Rabi frequency of the system when the control laser pulse is transmitted through the atomic gas. For example, the dipole moment of the atomic gas affects the Rabi frequency as described in Equation 1 above. Therefore, adjusting the pulse energy of the control laser pulse is based on the properties of the atomic gas. For example, the atomic gas system can be 87 It may also be atomic vapor containing vapor of Rb atoms.

[0049] In some embodiments, preparing the control laser pulse includes adjusting pulse energy based at least in part on beam geometry. Light intensity depends on pulse energy and beam size. Thus, preparing the control laser pulse includes adjusting pulse energy based on beam size in the atomic gas so that the control laser pulse has a target intensity for generating a desired Rabi frequency in the atomic gas.

[0050] In some embodiments, generating a control laser pulse having a bandwidth based on the temporal profile of the optical quantum bit includes generating the control laser pulse before amplifying the pulse, and after generating the control pulse having a bandwidth based on the temporal profile of the optical quantum bit, the pulse energy of the control laser pulse is adjusted.

[0051] In some embodiments, generating a control laser pulse having a bandwidth based on the temporal profile of the optical quantum bits includes adjusting the bandwidth of a seed pulse (e.g., a pulse sent to an optical amplifier) ​​so that, upon amplification, the amplified pulse has a desired bandwidth based on the temporal profile of the optical quantum bits. After amplification, the pulse energy can be adjusted by attenuation.

[0052] In some embodiments, the bandwidth of the control laser pulse may be adjusted after amplification of the seed pulse. The bandwidth of the amplified control laser pulse may be adjusted by a nonlinear optical process. For example, an optical parametric amplifier may be used to adjust the pulse bandwidth. As another example, a nonlinear optical parametric amplifier may be used to adjust the pulse bandwidth. In some embodiments, other nonlinear optical processes may be used to adjust the bandwidth, and aspects of the techniques described herein are not limited in this respect.

[0053] In some embodiments, compression optics may be used to compress the temporal bandwidth of the control laser pulse. For example, multiple chirped mirrors may be used to compress the temporal bandwidth of the control laser pulse. In some embodiments, multiple optical components may be used to increase the dispersion of the optical pulse and expand the temporal bandwidth of the control laser pulse.

[0054] Next, process 300 proceeds to operation 304, where a control laser pulse is transmitted through the atomic vapor system to change the transmission properties of the atomic vapor in accordance with some embodiments of the techniques described herein. The control laser pulse is transmitted through the atomic vapor system to change the transmission properties of the atomic vapor, thereby creating a transparency window, as shown below in connection with FIGS. 5A and 5B. The control laser pulse is transmitted through the atomic vapor system, thereby creating a transparency window during the period when the system expects to receive an optical quantum bit. An exemplary configuration of components for transmitting a control laser pulse through the atomic vapor system is included below in connection with memory unit 900 depicted in FIG. 9.

[0055] Next, process 300 proceeds to operation 306, where an optical quantum bit is received in an atomic vapor system according to some embodiments of the techniques described herein. The atomic vapor system is a high-temperature atomic vapor system. To store an optical quantum bit using the atomic vapor system, the optical quantum bit is received in the atomic vapor system while a control laser pulse is transmitted through the atomic vapor system.

[0056] In some embodiments, the atomic vapor system is rubidium (Rb) atomic vapor. For example, the atomic vapor system is 87 In some embodiments, other atomic vapor systems may be used, and aspects of the techniques described herein are not limited in this respect.

[0057] In some embodiments, the optical quantum bit is a polarization quantum bit. A polarization quantum bit contains quantum information encoded in any polarization state of a photon. Therefore, due to the effective storage of polarization quantum bits, any polarization state of a photon can be retrieved from an atomic vapor system. In some embodiments, the optical quantum bit is a spatial quantum bit.

[0058] In some embodiments, the high temperature atomic vapor system is a room temperature atomic vapor system (e.g., 20°C). In some embodiments, the high temperature atomic vapor system is between 20°C and 40°C. In some embodiments, the high temperature atomic vapor system is between 18°C ​​and 25°C. In some embodiments, the high temperature vapor system is between 45°C and 65°C. In some embodiments, the high temperature atomic vapor system is between 18°C ​​and 40°C. In some embodiments, the high temperature vapor system is between 10°C and 100°C. In some embodiments, the high temperature atomic vapor system is between 0°C and 100°C. In some embodiments, the high temperature atomic vapor system may be above 40°C, although aspects of the technology described herein are not limited in this respect. By way of example, the high temperature atomic vapor may be operated at about 50°C to 60°C.

[0059] After operation 306, process 300 ends. After process 300 for storing a qubit is completed, the qubit can be extracted from the atomic vapor using a qubit extraction process. In some embodiments, the qubit extraction process can be process 400, described below in connection with FIG. 4. In some embodiments, other extraction processes may be used in combination with optical qubit storage process 300, and aspects of the techniques described herein are not limited in this respect.

[0060] As a non-limiting example illustrating the storage of received optical quantum bits, the inventors have recognized that a control laser pulse can convert (map) the optical quantum bit into a set of atomic excitations. For example, the control laser pulse can convert (map) any polarization of the optical quantum bit into a spin wave excitation in an atomic vapor. Thus, upon extraction, a control field is applied to convert the spin waves into photons with the same arbitrary polarization as the stored photons. The extracted photons can have a different bandwidth than the stored photons. The bandwidth of the extracted photons is determined by the power of the control field.

[0061] The inventors have recognized that the bandwidth of the extracted quantum bit may depend on the characteristics of the control field used to enable the quantum bit to be extracted from the atomic vapor in which it is stored. The inventors have further recognized that for multiple interfering quantum bits in a quantum communication network, matching the bandwidth between pulses can provide a better signal-to-noise ratio for subsequent detection and analysis. Therefore, controlling the bandwidth of the extracted quantum bit can improve quantum communication methods by enabling matching between optical quantum bits generated from different light sources. Therefore, the inventors have developed a method for controlling the bandwidth of the extracted quantum bit.

[0062] 4 shows an example of an optical quantum bit extraction process 400 according to some embodiments of the techniques described herein. Prior to the start of process 400, the optical quantum bit may be stored in a high-temperature atomic vapor system using an optical quantum bit storage process, such as process 300 described above. In some embodiments, process 400 may include determining a target bandwidth for the extracted optical quantum bit. Determining the target bandwidth includes determining a temporal profile of the extracted optical quantum bit. In some embodiments, the target bandwidth may be based on optimizing the signal-to-noise of the extracted quantum bit. An example of a noise profile and target bandwidth is further described in connection with FIGS. 21A and 21B below.

[0063] In some embodiments, the target bandwidth may be based on the bandwidth of the second optical qubit to optimize the signal-to-noise of the interference between the extracted qubit and the second qubit. For example, the target bandwidth may be a spatial-temporal mode selected to effectively interfere with the second qubit to produce projection-based entanglement.

[0064] Process 400 begins at operation 402 with preparing a control laser to extract optical quantum bits from an atomic vapor system such that the extracted photons have a target bandwidth, according to some embodiments of the techniques described herein. The target bandwidth is a target temporal profile of the extracted photons. Preparing the control laser includes generating laser control light based on the target bandwidth. In some embodiments, the laser control light is a laser control pulse. The laser control pulse may be generated to have approximately the same bandwidth as the target temporal profile of the extracted quantum bit. In some embodiments, the laser control pulse is generated and / or adjusted as described above in connection with FIG. 3 .

[0065] In some embodiments, a quasi-continuous wave controlled laser may be used. A quasi-continuous wave controlled laser uses a continuous wave (CW) laser that is modulated so that the optical field provided to the atomic vapor system is turned on and off (e.g., pulsed). For example, a CW laser may be pulsed using an fEOM driven by a fast digital delay generator (DDG), as described herein.

[0066] Next, process 400 proceeds to operation 404, where a control laser is transmitted through the atomic vapor system to change the transmission properties of the atomic vapor, according to some embodiments of the techniques described herein. The control laser is transmitted through the atomic vapor system to change the transmission properties of the atomic vapor, thereby creating a transparency window, as shown below in conjunction with FIGS. 5A and 5B. The control laser is transmitted through the atomic vapor system, thereby creating a transparency window through which the quantum bit is received. An exemplary configuration of components for transmitting a control laser pulse through the atomic vapor system is included below in conjunction with FIGS. 8 and 9.

[0067] Next, process 400 proceeds to operation 406, where an extracted optical quantum bit is received from the atomic vapor system in response to a control laser, according to some embodiments of the techniques described herein. The atomic vapor system is a high-temperature atomic vapor system. The extracted optical quantum bit is received following transmission of the control laser.

[0068] Process 400 then proceeds to operation 408, where the extracted optical quantum bit is separated from the control laser according to some embodiments of the techniques described herein. Following extraction of the optical quantum bit, the extracted quantum bit and the control laser may propagate in the same direction. Thus, before detecting, interfering with, and / or processing the extracted optical quantum bit, the quantum bit is separated from the control laser. In some embodiments, the extracted optical quantum bit is separated using dual-pass etalons, as described herein in connection with FIGS. 10 and 11 . In some embodiments, other separation techniques may be used, although aspects of the techniques described herein are not limited in this respect.

[0069] After operation 406, process 400 ends. After process 400 ends, the extracted qubit may be detected. The detection may include detecting the qubit using a polarizing beam splitter and one or more single-photon detectors. In some embodiments, the detection may include interfering with the extracted qubit and interfering the extracted qubit with a second qubit.

[0070] With respect to the transparency window generated by the control laser, the Rabi frequency Ω c There are two regimes that scale differently with . The first regime, the EIT regime, corresponds to the low-bandwidth limit. The low-bandwidth limit can be considered when the bandwidth is smaller than the excited state lifetime G. In the EIT regime, the bandwidth varies linearly with the power of the control field:

[0071]

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[0072] 5A shows an example of an absorption spectrum 500 corresponding to the EIT region, where the transparency window is characterized by the FWHM of an absorption dip, shown as dip 502 in absorption spectrum 500.

[0073] The second regime, the Autler-Townes splitting (ATS) regime, corresponds to the high-bandwidth limit, which can be considered when the bandwidth is larger than the excited state lifetime G. In the ATS regime, the bandwidth scaling is given by

[0074]

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[0075] 5B shows an example of an absorption spectrum 504 corresponding to the ATS region at the limit of high bandwidth. In the ATS region, the transparency window is the separation (spacing) between two absorption peaks 506 and 508, as shown in the absorption spectrum 504.

[0076] In atomic vapor systems implemented for memory storage, the difference between ATS and EIT may not be experimentally detectable. Therefore, according to some embodiments of the techniques described herein, either regime may be used depending on the target bandwidth for storage.

[0077] As mentioned above, the pulse energy of the control laser can be adjusted based on the bandwidth of the optical quantum bits for storage or extraction. The relationship between the pulse energy (e.g., power) and both the transparency window and the bandwidth of the extracted photons is shown in Figures 6A and 6B. Figures 6A and 6B show that the size of the transparency window and the bandwidth of the extracted photons increases with increasing power of the control field.

[0078] 6A shows an EIT window as a transmission of a weak probe field through room-temperature steam under different control field intensities, according to some embodiments of the techniques described herein. Plot 600 shows the normalized transmittance of the probe field (having a power of about 5 μW) for different control field powers as a function of two-photon detuning δ. The traces in FIG. 6A are vertically offset.

[0079] 6B shows multiple time traces of extracted photons in memory operations using different optical powers of the control field according to some embodiments of the techniques described herein. While illustrated in the EIT regime, a similar phenomenon is observed in the Raman regime. As shown in plot 602, the time profile represents the bandwidth of extracted photons at different control field powers of the control laser. The multiple traces in FIG. 6B are vertically offset.

[0080] The inventors have recognized and appreciated that the input qubit (e.g., the stored qubit) and the output qubit (e.g., the retrieved qubit) may have different bandwidth characteristics based on the dependence of the retrieved qubit's bandwidth on the control laser. Thus, the memory functions as a bandwidth converter. Figures 7A, 7B, and 7C illustrate the difference in bandwidth characteristics of the input qubit and the output qubit, as well as the effectiveness of the control laser to maintain consistent output bandwidth characteristics across multiple input qubits.

[0081] 7A shows a plot 700 of an input time profile 702 and an output time profile 704. The input time profile 702 includes a peak 706 corresponding to an input qubit. The output time profile 704 includes a peak 708 corresponding to an output qubit.

[0082] Figure 7B shows a plot 710 of an input time profile 712 and an output time profile 714. The input time profile 712 includes a peak 716 corresponding to the input qubit. The output time profile 714 includes a peak 718 corresponding to the output qubit. As shown by a comparison of Figures 7A and 7B, the input qubits are very different, yet the same control field is used to extract the qubits. Therefore, as reflected in Figures 7A and 7B, the extracted qubits 708 and 718 have similar bandwidths.

[0083] 7C shows a plot 720 of varied input pulse widths and the corresponding FWHM of the extracted qubit, according to some embodiments of the techniques described herein. As shown in plot 720 by curve 722, the input pulse width is varied over a range of one or more orders of magnitude, while the control laser for extraction is held nearly constant. Thus, despite the variability of the input pulse, the FWHM of the output pulse remains nearly constant. While shown as an example of varying the input qubit to produce a constant output qubit bandwidth, in some embodiments, the reverse implementation may be used. For example, a constant input bandwidth may be used, and the output bandwidth may be varied by varying the control laser for extraction.

[0084] 8 shows an example of a control pulse generation module 800 according to some embodiments of the techniques described herein. The control pulse generation module 800 includes a laser source 802. The laser source 802 includes a diode laser 804. The diode laser generates continuous wave laser light. A half-wave plate 806 and a polarizing beam splitter 808 split the output from the diode laser 804. A first portion of the continuous wave laser light enters a fiber 824, where it is modulated by an fEOM 818 according to a modulation signal generated by an arbitrary waveform generator (AWG) 822. The modulated light exits the fiber at an end 826 and is amplified by a tapered amplifier (TA) 828. According to some embodiments of the techniques described herein, the amplified light passes through a variable Bragg grating 830 and an etalon 832 before being sent to a memory module and used as a control pulse for the storage process.

[0085] A second portion of the continuous wave laser light passes through an AOM before being split by a 90:10 splitter 820. One output of the 90:10 splitter includes a lock-in detector 812, and the other output is sent to a fiber for modulation by an fEOM 814 driven by a digital delay generator (DDG) 816. The resulting pulses may be quasi-continuous wave pulses used for memory retrieval processes, according to some embodiments of the technology described herein. In some embodiments, the laser source 802 is a Toptica TA Pro amplified laser. In some embodiments, another amplified laser system may be used, and aspects of the technology described herein are not limited in this respect.

[0086] FIG. 9 illustrates an example of a memory unit 900 according to some embodiments of the techniques described herein. The memory unit 900 receives a control laser pulse for enabling the quantum bit storage process from a control pulse generation module, such as the control pulse generation module 800 shown in FIG. 8, via an optical fiber 902. The control pulse passes through an etalon 904, a Glan-Laser prism 906, and a quarter waveplate 912 before entering an atomic vapor system 914. The Glan-Laser prism 906 couples the control laser pulse and the input quantum bit into a shared optical path so that both are directed toward the atomic vapor system 914. The control laser pulse changes the transmission properties of the atomic vapor, thereby enabling the storage of the quantum bit in the atomic vapor. The memory unit 900 receives the quantum bit from an optical fiber 910 and stores it in the atomic vapor system 914. The qubits pass through Glan-laser prism 906 and quarter-wave plate 912 before entering vapor storage system 914. Memory unit 908 receives a control pulse to enable the extraction process from optical fiber 908. Following vapor storage system 914, the control laser pulse and the extracted qubit pass through quarter-wave plate 916, half-wave plate 918, quarter-wave plate 920, and Glan-laser prism 922. Glan-laser prism 922 directs the control light to beam block 924 and the extracted qubit to filter system 926.

[0087] Although shown as a single beam configuration, a dual beam configuration such as that described at # may also be used. The inventors recognized and understood that an ideal filter should have a bandwidth wider than the maximum photon bandwidth at which the memory is designed to operate. At the same time, the filter must sufficiently suppress the strong control laser to achieve high SNR and fidelity. Therefore, the inventors developed a multi-double-pass filter that uses two etalons, each with a different bandwidth, to filter the control laser while maintaining the bandwidth.

[0088] FIG. 10 shows an example of a filter unit 1000 according to some embodiments of the techniques described herein. The filter unit 1000 receives input light from a memory unit via an optical fiber 1002. The input light includes the quantum bit to be extracted and residual laser light of a control laser pulse. The input light passes through a Glan-laser polarizer 1004 configured to separate orthogonal polarizations of the light. An etalon 1006 is configured in a dual-pass configuration with a quarter-wave plate 1008 and a retroreflector 1010. Thus, the input light passes through the etalon 1006, travels toward the quarter-wave plate 1008, and is then reflected by the retroreflector 1010. Following reflection by the retroreflector 1010, the input light passes through the quarter-wave plate 1008 a second time and then through the etalon 1006 a second time. After obtaining the phase shift from passing twice through the quarter-wave plate 1009, the Glan-Laser prism 1004 directs the input light to the second Glan-Laser prism 1012. The Glan-Laser prism 1012 receives the input light from the first Glan-Laser prism 1012, allowing the input light to pass through the Glan-Laser prism 1004 and reach the etalon 1014. The etalon 1014 is configured in a dual-path configuration with a quarter-wave plate 1016 and a retroreflector 1018. Thus, the input light passes through the etalon 1014, travels toward the quarter-wave plate 1016 and retroreflector 1018, and is then reflected by the retroreflector 1018. Following reflection by the retroreflector 1018, the input light passes through the quarter-wave plate 1016 a second time and then passes through the etalon 1014 a second time. After obtaining a second phase shift from the second pass through the quarter wave plate 1016, the Glan-Laser prism 1012 directs the filtered light to a detector 1022. In some embodiments, a third, single-pass etalon 1020 may be included in the optical path between the Glan-Laser prism 1012 and the detector 1022.

[0089] 11 shows an example of an optical filter configuration 1100 for filtering the control laser from the extracted quantum bit in accordance with some embodiments of the techniques described herein. The optical filter configuration 1100 includes an input 1102, Glan-Taylor prisms 1104 and 1112, etalons 1106 and 1114, quarter-wave plates 1108 and 1116, retroreflectors 1110 and 1118, and an output 1120. The input 1102 receives input light from the atomic vapor system, including the extracted quantum bit and the control laser light. The input light passes through the Glan-Taylor prism 1104 and reaches the etalon 1106. Following the etalon 1106, the filtered light passes through the quarter-wave plate 1108 to the retroreflector 1110 and returns through the quarter-wave plate 1108 for a second pass through the etalon 1106. After obtaining a phase shift by passing twice through etalon 1106 and twice through the quarter-wave plate, the input light is directed from Glan-Taylor prism 1104 to Glan-Taylor prism 1112. Glan-Taylor prism 1112 directs the input light to etalon 1114. After passing once through etalon 1114, the light passes through quarter-wave plate 1116 and is then reflected by retroreflector 1118, passing through quarter-wave plate 1116 and etalon 1114 a second time. After passing twice through etalon 1114, the light becomes filtered light. The filtered light passes through Glan-Taylor prism 1112 to output 1120.

[0090] In some embodiments, etalons 1106 and 1114 are flat etalons. In some embodiments, etalon 1106 has a 15 GHz free spectral range, and etalon 1114 has a 30 GHz free spectral range. In some embodiments, etalons 1106 and 1114 provide 120 dB suppression and 50% transmission. Light passes through each etalon twice by retroreflecting itself in opposite directions (retroreflecting) off mirrors and QWPs to avoid interference. Retroreflecting also ensures that the two passes hit the same surface area, so they share the same resonance conditions (temperature dependent). A Glan-Taylor prism (instead of a PBS) is used to prevent light filtered by the etalon from recombining into the filtered path. This single-rail configuration can be easily extended to a dual-rail configuration by incorporating a previously developed Sagnac-type interferometer. The dual-rail configuration can also be easily adapted to the rest of the optical elements.

[0091] For high bandwidth memories, operation depends on two conditions: 1) a high control field strength (e.g., Ω c 1) and 2) high-bandwidth control of such electric fields (to maximize efficiency). Laser amplifier technology can be used to provide high control field strengths. For example, high control field strengths can be achieved using solid-state tapered amplifiers (TAs). TAs can provide several watts of power, which, combined with a focused beam (approximately 1 mm), can produce Rabi frequencies in the 100 MHz range. To provide high-bandwidth control while maintaining high control field strengths, we developed several configurations that operate over different bandwidth ranges. Therefore, depending on the characteristics of the stored photons (e.g., whether the qubits originate from a narrow-band source such as a Rydberg atom or a broad-band source such as SPDC), an appropriate configuration can be used.

[0092] FIG. 12 shows an acousto-optic modulator-based configuration 1200 for modulating the bandwidth of a laser to generate control pulses, according to some embodiments of the techniques described herein. The acousto-optic modulator (AOM) uses the acousto-optic effect to diffract and frequency-shift light using traveling acoustic waves at RF frequencies generated by a piezoelectric transducer. The intensity of the diffracted light can be adjusted by modulating the RF power (and frequency). For example, the speed of sound in a TeO crystal is approximately 4,260 m / s. When diffracting light to generate laser pulses, the cross section of the light determines the switching bandwidth. The damage threshold of an AOM is generally higher than other methods because diffraction occurs within the bulk material of the crystal. Therefore, the AOM can directly handle high laser powers (e.g., 1 watt). The acousto-optic modulator-based configuration 1200 includes a high-power laser 1202, an acousto-optic crystal 1204, and an acousto-optic driver 1206. A high-power laser 1202 generates a high-power continuous wave output that enters an acousto-optic crystal 1204. An acousto-optic driver 1206 provides an RF source to create the acousto-optic effect in the acousto-optic crystal 1204, modulating the continuous wave light to generate pulsed light.

[0093] 13A shows the acousto-optic modulation performance for an 80 MHz shifted and focused beam according to some embodiments of the techniques described herein. The switching time is measured as the time from 10% to 90% intensity. As shown in FIG. 13A, for an 80 MHz AOM with a 50 μm focal spot size, a switching time of approximately 60 ns is obtained.

[0094] Among commercially available AOM materials, TeO2 has the highest acoustic velocity. The bandwidth of pulses using TeO2 crystals depends on the beam cross section. However, when using a Gaussian beam, its divergence is inversely proportional to the focal spot size, resulting in practical limits on how small the light can be focused. For example, if the beam divergence becomes comparable to the diffraction angle (corresponding to the RF frequency), interference between the unshifted and shifted light can occur, potentially causing unintended power modulation.

[0095] FIG. 13B shows memory performance using the AOM configuration of FIG. 13A according to some embodiments of the techniques described herein. The memory performance of the AOM configuration of FIG. 13A is shown for different optical powers. The EIT linewidth is measured using CW light and provides a guideline for the highest bandwidth that can be expected for each optical power. The divergence between the photon bandwidth and the EIT linewidth is due to the finite switching time of the AOM. Based on FIG. 13B, the suitable bandwidth for memory operation using direct AOM switching is 0-5 MHz.

[0096] FIG. 14 shows a direct electro-optic modulator configuration 1400 for controlling a control laser in accordance with some embodiments of the technology described herein. Electro-optic modulators (EOMs) rely on nonlinear optical materials whose refractive index is a function of the local electric field. Light traveling through the nonlinear optical material assumes a phase determined by the refractive index (e.g., the effective speed of light in the material). Thus, a time-varying electric field applied to the nonlinear optical material is used to modulate the phase of light traveling through the crystal. In some embodiments, a free-space modulator based on a bulk material EOM is used. In some embodiments, a waveguide modulator is used. In some embodiments, other types of EOMs may be used, and aspects of the technology described herein are not limited in this respect. The direct electro-optic modulator configuration 1400 includes a high power laser 1402, a Pockels cell 1404, an EOM driver 1406, polarizers 1408 and 1406, and wave plates 1410, 1412, and 1414.

[0097] A high-power laser 1402 generates laser light that passes through a polarizer 1408, then a waveplate 1410, and then a Pockels cell 1404. The Pockels cell 1404 receives a drive RF signal from an EOM driver 1406. The Pockels cell modulates the phase of the laser light. The phase modulation of the laser light is converted to intensity modulation via waveplates 1412 and 1414 in combination with a polarizer 1416.

[0098] Free-space modulators rely on the Pockels electro-optic effect (e.g., a Pockels cell). In a Pockels cell, the electric field is applied along the direction of light propagation and can be thought of as a voltage-controlled waveplate. The voltage required to achieve a π phase shift is the half-wave voltage, V π In commercially available products, it is called V πis typically in the range of several hundred volts to several kilovolts. The π phase can be converted to intensity modulation using a polarizer and an additional waveplate, as shown in Figure 14. This allows the optical intensity to be modulated by applying an electric field. The high optical damage threshold of the bulk material allows for direct high-power optical field modulation.

[0099] Compared to AOMs, the switching bandwidth of a Pockels cell is primarily limited by the bandwidth of the driver electronics, since the speed of the electric field traveling through the crystal is typically a fraction of the speed of light, c. The Pockels cell acts like a capacitor; therefore, significant voltage is required to achieve full modulation. Special circuitry is included in EOM designs to handle high currents and operate at high speeds. Commercially available drivers provide bandwidths of several MHz for kV applications. In some embodiments, the EOM driver 1404 is configured with gallium nitride (GaN) field effect transistors (FETs) in a step-down (buck) converter configuration. For example, the EOM driver 1404 controls the V of the Pockels cell. π The EOM driver 1404 can output either 0 V or 160 V with fast switching times approaching 1 V. Therefore, a low-voltage TTL signal can be used to trigger the switching of the EOM driver. In some embodiments, the EOM driver 1404 can use evaluation board model EPC9099 to perform the EOM driver switching. In some embodiments, other suitable EOM drivers capable of providing sufficiently fast driving of the nonlinear optical material may be used, and aspects of the technology described herein are not limited in this respect.

[0100] In some embodiments, the Pockels cell 1404 is a Conoptics M360-40 Pockels cell. In some embodiments, other Pockels cells may be used, and aspects of the technology described herein are not limited in this respect.

[0101] Figure 15A shows electro-optic modulation performance according to some embodiments of the techniques described herein, which corresponds to the configuration described in connection with Figure 14. The switching time, measured from the switching time from 10% to 90% of the optical field, is about 29 ns.

[0102] 15B shows memory performance using the EOM configuration of FIG. 15A, according to some embodiments of the techniques described herein. The memory performance of the EOM configuration of FIG. 15A is shown for different optical powers. The deviation between the EIT window and the photon bandwidth indicates that a range around 0 to 12.5 MHz is a suitable bandwidth for memory operation.

[0103] FIG. 16 shows a low-power EOM phase switching configuration 1600 with optical amplification according to some embodiments of the techniques described herein. EOM on a waveguide can be used to avoid the use of stringent electronics drive requirements and provide larger switching bandwidths. EOM on a waveguide may be packaged and implemented in a fiber-coupled configuration (fEOM). The smaller field confinement provided by the fiber allows for larger field strengths to be obtained with smaller input voltages. For example, V π may be about 2 to 3 V. Thus, the options for driving electronic devices are expanded compared to the EOM described in connection with FIG.

[0104] The low-power EOM phase switching configuration 1600 includes a low-power laser 1602, an fEOM 1604 for phase modulation, an RF source 1608, an RF amplifier 1606, an RF switch 1614, a TA 1610, and an etalon 1612. The RF source 1608 generates an RF signal that is amplified by the RF amplifier 1606. The amplifier's RF signal passes through a high-speed RF switch 1614 that is triggered by a TTL pulse. The output from the RF switch 1614 drives the fEOM 1604. The fEOM 1604 modulates the phase of low-power laser light (e.g., less than 50 mW) received from the low-power laser 1602. The output of the fEOM is filtered using the etalon 1612 before being amplified by the TA 1610. In some embodiments, the etalon 1612 has a bandwidth of 100 MHz. In other embodiments, the etalon has other bandwidths based on the bandwidth achievable through the use of RF switch 1614 .

[0105] In some embodiments, multiple intensity modulator fEOMs are used. In some embodiments, multiple phase modulator fEOMs are used. The phase modulator fEOMs imprint a modulating phase from the electric field to the optical field. The imprinted phase generates RF sidebands for a monochromatic laser field. Passive frequency-selective elements such as optical cavities (e.g., etalons) can be used to filter out light with specific sideband frequencies and eliminate the rest of the laser field. The intensity of the resulting sidebands can be modulated by modulating the RF field.

[0106] Low voltage compatibility provides high hardware compatibility compared to EOM technology. Commercially available RF amplifiers offer low V at RF frequencies up to several GHz. πIt can deliver approximately 30-36 dBm of output power, exceeding 100 MHz. To maximize the switching bandwidth, an active RF switch is placed after the RF amplifier. For example, a voltage variable attenuator (VVA) can be placed after the RF amplifier. In some embodiments, the ADF5020 RF switch is used, which provides a few nanoseconds of switching capability for high-power RF fields. In this configuration, the resulting bandwidth is approximately 100 MHz. Compared to bulk EOMs, the photorefractive effect limits the optical power they can support, and this effect is more pronounced for photons with longer wavelengths (e.g., near-infrared photons). Therefore, most fEOMs are limited to an input power of approximately 30 mW. Considering insertion loss and a modulation efficiency of 30%, the output power is approximately 3 mW. This power amplification is insufficient for broadband operation. Optical amplifiers such as TAs are highly nonlinear devices. Therefore, noise generated during RF switching can introduce large noise fluctuations and even damage the device. Therefore, to ensure that the field is truly zero when it is assumed to be zero, RF switching with excitation greater than 60 dB should be used. Similarly, optical sideband suppression is important to prevent amplification of the carrier field. In some embodiments, multiple etalons can be used for optical sideband suppression. The use of a high-finesse cavity can be insufficient because it can reduce the bandwidth of transmitted photons. Therefore, for high bandwidths, one or more etalons are used that match the photon bandwidth and sufficiently suppress undesired frequency components by more than 40 dB.

[0107] A typical fEOM can achieve a response time as low as 0.2 ns (e.g., at a modulation bandwidth of 10 GHz). Therefore, the bandwidth limitations of fEOMs are likely due to their electronic circuitry. In some embodiments, high-power RF switches with rise times of 3-5 ns may be used. In some embodiments, to circumvent RF switch speed limitations, a high-speed AWG may be used to generate the RF waveform directly. For example, a 0.1 ns pulse contains a full-cycle sinusoidal function with a frequency of 10 GHz, corresponding to a sampling rate of at least 50 GSa / s.

[0108] 17A and 17B show the performance of the fEOM system shown in FIG. 16 in accordance with some embodiments of the techniques described herein. To evaluate the performance of the fEOM system, a TTL pulse with a 5 ns width is generated and used to control a high-power RF switch. Because this is near the limit of the RF switch, the rise and fall times are not rectangular, and take a finite amount of time to complete. The resulting peaks are recorded by a high-speed photodiode, such as a Thorlabs APD430.

[0109] 17A shows an RF pulse recorded by a photodiode according to some embodiments of the techniques described herein. As shown in FIG. 17A, the pulse has a FWHM of 5.3 ns due to the speed limitation of the RF switch.

[0110] Figure 17B shows the Fourier transform of the pulse shown in Figure 17A. As shown in Figure 17B, the spectral components have a FWHM in the frequency domain of 74.8 MHz. The power of the pulse has a CW value of up to 500 mW.

[0111] 18 shows the photon bandwidth as a function of control field power according to some embodiments of the techniques described herein. Based on the photon bandwidth plot, the appropriate photon bandwidth for memory operation is 0-70 MHz.

[0112] FIG. 19 shows an example of a low-power EOM intensity switching configuration 1900 with optical amplification, according to some embodiments of the techniques described herein. A waveguide EOM can be used to avoid the use of stringent electronics drive requirements and provide larger switching bandwidths. A waveguide EOM can be packaged and implemented in a fiber-coupled configuration (fEOM). Similar to the fEOM for phase adjustment shown in FIG. 16, an fEOM for intensity adjustment provides larger field strengths with smaller input voltages. The fEOM intensity modulator includes a Mach-Zehnder interferometer (MZI) with a phase modulator in one arm (or both arms). Modulating the phase from 0 to 2π results in fully constructive / destructive optical interference at the output port. Thus, the phase modulation by the interferometer is converted to intensity modulation.

[0113] The low-power EOM intensity switching configuration 1900 includes a low-power laser 1902, an fEOM 1904, an AWG 1906, and a TA 1908. In some embodiments, the low-power laser 1902 generates light of less than 50 mw and sends the light to the fEOM 1904. The AWG 1906 drives the fEOM by generating pulses to modulate the intensity of the light received from the laser 1902. After modulation by the fEOM, the modulated light is amplified by the TA 1908.

[0114] The transfer function between the applied electrical signal and the optical output is sin 2 Therefore, to generate short pulses, the -V generated on a fast time scale π ~V π Electrical signals in the range of are used. Low-power optical pulses (on the order of a few mW) are amplified by the TA to several watts. Unlike phase modulators, intensity modulators do not generate extraneous frequency components. Therefore, no filtering components are required to separate the amplified signal.

[0115] To produce pulses with high contrast, the off state is Vπ +V O The on-state should correspond to V O In some embodiments, the transfer function cannot be adjusted depending on the fEOM structure. In some embodiments, a DC bias can be applied to shift the voltage offset and thus the transfer function. For example, a high-speed programmable DAC can be used to control the transfer function. As another example, a commercially available high-speed AWG can be used to control the transfer function.

[0116] Figure 20 shows an example of a pulse generated using an intensity modulator and TA according to some embodiments of the techniques described herein. To generate the plot in Figure 20, a Tektronix 10 G Sa / s AWG (7101) was operated in normal mode. Normal mode produces a -2 to 2 V function with a 350 ps rise time. A Jenopik AM795 intensity modulator was used, with an extinction voltage of 1.5 V. The resulting pulse shown in Figure 20 has a FWHM of 1.37 ns. This configuration may limit the pulse size based on the modulator response (approximately 200 ps) and the AWG rise time (350 ps). When using an intensity modulator with an external CD bias, such as an iXblue intensity modulator, the modulator can be driven in the AWG's direct mode instead of normal mode. In direct mode, a -1 to 1 V function is output with a rise time of 70 ps. Therefore, pulses as short as 0.1 ns are supported by such a configuration.

[0117] The inventors have recognized and understood that multiple atomic noise processes have different time scales, and therefore, through appropriate preparation of the control laser, the bandwidth of the extracted qubit can be tuned to temporally filter the extracted qubit from the noise.

[0118] FIG. 21A is an example of memory fidelity in the high-bandwidth regime using phase modulation by an fEOM and TA amplification, according to some embodiments of the techniques described herein. To improve the signal-to-noise ratio of the extracted qubit, the target bandwidth of the extracted qubit can be determined based on the noise profile so that the signal-to-noise ratio can be increased. For example, atomic noise processes such as four-wave mixing (FWM) and spontaneous Raman scattering (SRS) involve spontaneous processes and therefore typically have a time scale that depends on the lifetime of the excited state. For the D1 transition in Rb, this time scale is approximately 27.7 ns. By arranging the control laser to generate an extracted qubit with a bandwidth higher than the time scale of the noise (e.g., only a few nanoseconds), a mismatch between the extracted qubit and the noise occurs, resulting in a degree of temporal separation between the noise signal and the qubit, as shown in FIG. 21A. In FIG. 21A, the extracted qubit signal is shown as a dashed line and the noise is shown as a solid line. The extracted qubit signal peaks rapidly, while the noise signal still rises slowly. As a result, the SNR reaches a maximum of 41, corresponding to 98% fidelity in the polarization-agnostic setting. The storage efficiency was 6 / 8%. The storage and extraction, reflected by Figure 21A, is <n>= 0.2. The experiment was performed with the input photons blocked to obtain the noise signal shown as a solid line. The results are magnified by a factor of 5 for easier visualization. The vertical line indicates the detection window with a width of 5 ns.

[0119] 21B shows an example plot of bandwidth in the qubit extraction process according to some embodiments of the techniques described herein. As shown in FIG. 21B, the bandwidth can be sub-1 ns, which can improve the signal-to-noise ratio by avoiding FWM noise. A non-limiting explanation of the SNR improvement is that the extraction process is a first-order process and FWM is a second-order process. Therefore, extraction precedes the onset of noise.

[0120] As shown in Figure 21B, the dashed line is the memory retrieval signal, and the orange line is the noise signal (e.g., a measurement made in the absence of stored / retrieved photons). Figure 21B shows the dashed line rising faster than the solid line, which has beneficial effects on SNR (e.g., by integrating the signal collection between the vertical lines). Collisional fluorescence is automatically avoided (the slowly decaying tail seen to the right of the vertical lines).

[0121] Having thus described several aspects of at least one embodiment, it should be understood that various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure and are intended to be within the spirit and scope of the principles described herein. Accordingly, the foregoing description and drawings are by way of example only.

[0122] The phrase "and / or," as used in the specification and claims, should be understood to mean "either or both" of the elements so conjoined, i.e., elements present conjunctively in some cases and disjunctively in other cases. Multiple elements listed with "and / or" should be construed in the same manner, i.e., as "one or more" of the elements so conjoined. Other elements, whether related or unrelated to those elements specifically identified by the "and / or" clause, may optionally be present. Thus, as a non-limiting example, a reference to "A and / or B," when used in conjunction with open-ended language such as "comprising," can refer in one embodiment to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements), etc.

[0123] The indefinite articles "a" and "an," as used in the specification and claims, unless expressly indicated to the contrary, should be understood to mean "at least one." As used in this specification and claims, the phrase "at least one," in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed in the list of elements, or excluding any combination of elements in the list of elements. This definition also allows for elements other than those specifically identified in the list of elements to which the phrase "at least one" refers, whether related or unrelated to those specifically identified elements, may optionally be present. Thus, as a non-limiting example, "at least one of A and B" (or, equivalently, "at least one of A or B," or, equivalently, "at least one of A and / or B") can refer in one embodiment to at least one, optionally two or more, A, and no B (and optionally including elements other than B); in another embodiment to at least one, optionally two or more, B, and no A (and optionally including elements other than A); in yet another embodiment to at least one, optionally two or more, A, and at least one, optionally two or more, B (and optionally including other elements); etc.

[0124] The use of ordinal terms such as "first," "second," and "third" in the claims to modify claim elements does not, by itself, imply any priority, precedence, or ordering of one claim element relative to another claim element, or any chronological order in which method actions are performed, but is merely used as a label to distinguish an element of one claim having a particular name from an element of another claim having the same name (except for the use of ordinal terms) to distinguish claim elements.

[0125] The terms "substantially," "approximately," and "about" may be used in some embodiments to mean within ±20% of a target value, in some embodiments within ±10% of a target value, in some embodiments within ±5% of a target value, and even in some embodiments within ±2% of a target value. The terms "and" and "about" may be inclusive of the target value.

[0126] Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of "including," "comprising," "having," "containing," "involving," and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof, as well as additional items.

[0127] All definitions defined and used herein should be understood to be interpreted in accordance with dictionary definitions, definitions in documents incorporated by reference, and / or ordinary meanings of the defined terms.< / n>

Claims

1. 1. A method for improving storage of optical qubits in atomic vapor, comprising: providing a control laser pulse to store an optical quantum bit using a high temperature atomic vapor system, the optical quantum bit having a bandwidth; Providing the control laser pulse comprises: generating the control laser pulse having a bandwidth based on a temporal profile of the optical quantum bit; preparing a control laser pulse, the control laser pulse including adjusting a pulse energy of the control laser pulse based on the temporal profile of the optical quantum bit; transmitting the control laser pulse through the high temperature atomic vapor system to change the transmission characteristics of the atomic vapor; receiving the optical quantum bit at the high temperature atomic vapor system while the control laser pulse is transmitted through the high temperature atomic vapor system.

2. 10. The method of claim 1 , wherein adjusting the bandwidth of the control laser pulses based on the temporal profile of the optical quantum bits comprises modulating a light source of the control laser pulses to adjust the bandwidth of the control laser pulses.

3. The method of claim 2 , wherein a fiber-coupled electro-optic modulator is used to modulate the light source of the control laser pulses.

4. 10. The method of claim 1, wherein the bandwidth of the control laser pulse is adjusted to have approximately the same temporal profile as the optical quantum bit.

5. The method of claim 1 , wherein adjusting the pulse energy of the control laser pulse is further based on properties of the atomic vapor and a beam shape of the control laser pulse.

6. 6. The method of claim 5, further comprising adjusting an amplitude of the control laser pulse such that the pulse intensity in the atomic vapor produces a transparency window having a linewidth approximately the same as the bandwidth of the optical quantum bit.

7. 6. The method of claim 5, wherein adjusting the pulse energy of the control laser pulse comprises amplifying the control laser pulse after adjusting the bandwidth of the control laser pulse.

8. The method of claim 1 , wherein the atomic vapor comprises rubidium atomic vapor.

9. 9. The method of claim 8, wherein transmitting the control laser pulse through the high temperature atomic vapor system modifies the three-level system of the rubidium atomic vapor to create a transparency window.

10. The method of claim 9, wherein the transparent window has a bandwidth of 10 to 100 GHz.

11. 1. A method for controlling bandwidth of optical quantum bits retrieved from atomic vapor storage, comprising: determining a target bandwidth of the extracted optical quantum bit; providing a control laser to extract the stored optical quantum bits from the high temperature atomic vapor system such that the extracted optical quantum bits have the target bandwidth; transmitting the control laser through the high temperature atomic vapor system to change a transmission characteristic of the high temperature atomic vapor system; receiving the extracted optical quantum bit from the high temperature atomic vapor system in response to the control laser; decoupling the extracted optical quantum bit from the control laser.

12. 12. The method of claim 11, wherein the control laser is arranged to generate the retrieved optical quantum bit having the same bandwidth as the previously stored optical quantum bit.

13. 12. The method of claim 11, wherein the control laser is arranged to generate the retrieved optical quantum bit having a different bandwidth than the previously stored optical quantum bit.

14. 12. The method of claim 11 , wherein the target bandwidth of the extracted optical quantum bit is based on a bandwidth of the second optical quantum bit, such as to improve interference caused by the extracted optical quantum bit interfering with the second optical quantum bit.

15. 12. The method of claim 11 , wherein preparing the control laser to retrieve the stored optical quantum bits from the high temperature atomic vapor system such that the retrieved optical quantum bits have the target bandwidth comprises modulating the control laser with a fiber-mounted electro-optic modulator.

16. 12. The method of claim 11 , wherein preparing the control laser to retrieve the stored optical quantum bits from the high temperature atomic vapor system such that the retrieved optical quantum bits have the target bandwidth comprises modulating the control laser with an acousto-optic modulator.

17. The method of claim 11 , wherein the atomic vapor comprises rubidium atomic vapor.

18. 18. The method of claim 17, wherein transmitting the control laser pulse through the high temperature atomic vapor system modifies the three-level system of the rubidium atomic vapor to create a transparency window.

19. 1. A system for improving storage and retrieval of optical quantum bits stored in atomic vapor, comprising: a high temperature atomic vapor system containing atomic vapor; a control laser, emitting a first control pulse having a bandwidth based on a bandwidth of an optical quantum bit to change a transmission characteristic of the high-temperature atomic vapor system; emitting a second control pulse having characteristics based on a target bandwidth of the extracted optical quantum bit; an optical filtering system configured to separate the extracted optical quantum bit from the control laser; a first etalon configured in a first double-pass configuration, the first etalon having a first bandwidth; the optical filtering system including a second etalon configured in a second double-pass configuration, the second etalon positioned to receive the output of the first etalon, the second etalon having a second bandwidth different from the first bandwidth.

20. the first etalon receives light output from the high temperature atomic vapor system, the first etalon being configured with a first polarizing beam splitter such that light returning after passing through the first etalon and a wave plate twice is directed to the second etalon; 20. The system of claim 19, wherein the second etalon is configured with a second polarizing beam splitter such that light returning from passing through the second etalon twice is directed to a detector.

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