Low-noise amplification of a continuous-variable quantum state

Orbital Angular Momentum Multiplexed Deterministic All-Optical Quantum Erasure-Correcting Code

Quantum erasure-correcting code, which corrects the erasure in the transmission of quantum information, is an important protocol in quantum information. In the continuous variable regime, the feed-forward technique is needed for realizing quantum erasure-correcting code. This feed-forward technique involves optic-electro and electro-optic conversions, limiting the bandwidth of quantum erasure-correcting code. Moreover, in the previous continuous variable quantum erasure-correcting code, only two modes are protected against erasure, limiting the applications of quantum erasure-correcting code in high-capacity quantum information processing. In this Letter, by utilizing the orbital angular momentum (OAM) multiplexed entanglement in the encoding part and replacing the feed-forward technique with OAM mode-matched phase-sensitive amplifier in the decoding part, we experimentally demonstrate a scheme of OAM multiplexed deterministic all-optical quantum erasure-correcting code. We experimentally demonstrate that four orthogonal modes can be simultaneously protected against one arbitrary erasure. Our results provide an all-optical platform to implement quantum erasure-correcting code and may have potential applications in implementing all-optical fault-tolerant quantum information processing.

Simultaneous three-wave and six-wave mixing of microwave and optical fields in an atomic medium

We experimentally investigate near-infrared optical field generation through simultaneous three-wave mixing (TWM) and six-wave mixing (SWM) processes in room-temperature ⁸⁵Rb atoms. The nonlinear processes are induced using three hyperfine levels in the D1 manifold, which cyclically interact with pump optical fields and an idler microwave field. The simultaneous appearance of TWM and SWM signals in discrete frequency channels is made possible by breaking the three-photon resonance condition. This gives rise to coherent population oscillations (CPO), which are observed experimentally. We explain through our theoretical model the role of CPO in the generation of the SWM signal and its enhancement due to parametric coupling with the input seed field in contrast to the TWM signal. Our experiment proves that a single tone microwave can be converted to multiple optical frequency channels. The simultaneous existence of TWM and SWM processes can potentially enable various types of amplification to be achieved with a single neutral atom transducer platform.

Optical-density enhanced quantum entanglement via four-wave mixing process

We theoretically propose a scheme to generate a strong continuous-variable quantum entangled light source in four-wave mixing (FWM) process by increasing the optical density of atomic medium. By properly choosing the input coupling field Rabi frequency and detuning, the optimized entanglement can be achieved to be better than -17 dB at an optical density of approximately 1, 000, which has been realized in atomic media. Besides, with the optimized one-photon detuning and coupling Rabi frequency, the optimum entanglement degree can be greatly enhanced with the increment of optical density. We also examine the effects of atomic decoherence rate and two-photon detuning on entanglement in a realistic setting, and evaluate the experimental feasibility. We find that the entanglement can be further improved by considering two-photon detuning. In addition, with optimum parameters the entanglement is robust against the decoherence. The strong entanglement provides a promising applications in continuous-variable quantum communications.

Phase-insensitive amplifier gain estimation at Cramér-Rao bound for two-mode squeezed state of light

Phase-insensitive amplifiers (PIAs), as a class of important quantum devices, have found significant applications in the subtle manipulation of multiple quantum correlation and multipartite quantum entanglement. Gain is a very important parameter for quantifying the performance of a PIA. Its absolute value can be defined as the ratio of the output light beam power to the input light beam power, while its estimation precision has not been extensively investigated yet. Therefore, in this work, we theoretically study the estimation precision from the vacuum two-mode squeezed state (TMSS), the estimation precision of the coherent state, and the bright TMSS scenario, which has the following two advantages: it has more probe photons than the vacuum TMSS and higher estimation precision than the coherent state. The advantage in terms of estimation precision of the bright TMSS compared with the coherent state is researched. We first simulate the effect of noise from another PIA with gain M on the estimation precision of the bright TMSS, and we find that a scheme in which the PIA is placed in the auxiliary light beam path is more robust than two other schemes. Then, a fictitious beam splitter with transmission T is used to simulate the noise effects of propagation loss and imperfect detection, and the results show that a scheme in which the fictitious beam splitter is placed before the original PIA in the probe light beam path is the most robust. Finally, optimal intensity difference measurement is confirmed to be an accessible experimental technique to saturate estimation precision of the bright TMSS. Therefore, our present study opens a new avenue for quantum metrology based on PIAs.

Telecom-wavelength conversion in a high optical depth cold atomic system

We experimentally investigate the frequency down-conversion through the four-wave mixing (FWM) process in a cold ⁸⁵Rb atomic ensemble, with a diamond-level configuration. An atomic cloud with a high optical depth (OD) of 190 is prepared to achieve a high efficiency frequency conversion. Here, we convert a signal pulse field (795 nm) attenuated to a single-photon level, into a telecom light at 1529.3 nm within near C-band range and the frequency-conversion efficiency can reach up to 32%. We find that the OD is an essential factor affecting conversion efficiency and the efficiency may exceed 32% with an improvement in the OD. Moreover, we note the signal-to-noise ratio of the detected telecom field is higher than 10 while the mean signal count is larger than 0.2. Our work may be combined with quantum memories based on cold ⁸⁵Rb ensemble at 795 nm and serve for long-distance quantum networks.

Comparison of SNR gain between quantum illumination radar and classical radar

It has been proved that quantum illumination (QI) radar has the quantum advantages in error-probability exponent. However, the error-probability exponent is not a recognized figure of merit in the radar literature, nor does it correspond in a straightforward manner to any such figure of merit. Signal to noise ratio (SNR) gain is an important criterion in radar theory. While, the theoretical analysis of quantum enhancement in SNR gain of QI radar has not been reported. In this paper, we compare the physical fundamental of matched filter (MF), which can achieve the optimal SNR gain under white noise in classical radar theory, and phase conjugation (PC) receiver. Furthermore, the quantum enhancement of SNR gain in QI radar is studied. It is shown that QI radar with practical receivers can achieve about 3dB quantum advantage in SNR gain. In addition, in the case of extremely weak signal, it can potentially achieve tens of dB enhancement in SNR gain compared with the MF based classical radar.

Multi-Mode Correlation in a Concurrent Parametric Amplifier

A concurrent parametric amplifier consisting of two pump beams is used to investigate the possibility of generating multi-mode correlation and entanglement. The existence of three-mode entanglement is demonstrated by analyzing the violation degree of three-mode entanglement criteria, including the sufficient criterion, i.e., two-condition and optimal single-condition criterion, and necessary and sufficient criterion, i.e., positivity under partial transposition (PPT) criterion. Besides, two-mode entanglement generated from any pair is also studied by using the Duan criterion and PPT criterion. We find that three-mode entanglement and two-mode entanglement of the two pairs are present in the whole parameter region. Our results pave the way for the realization and application of multi-mode correlation and entanglement based on the concurrent parametric amplifiers.

All-Optical Entanglement Swapping

Entanglement swapping, which is a core component of quantum network and an important platform for testing the foundation of quantum mechanics, can enable the entangling of two independent particles without direct interaction both in discrete variable and continuous variable systems. Conventionally, the realization of entanglement swapping relies on the Bell-state measurement. In particular, for entanglement swapping in continuous variable regime, such Bell-state measurement involves the optic-electro and electro-optic conversion, which limits the applications of the entanglement swapping for constructing broadband quantum network. In this Letter, we propose and demonstrate a measurement-free all-optical entanglement swapping. In our scheme, a high-gain parametric amplifier based on the four-wave mixing process is exploited to realize the function of Bell-state measurement without detection, which avoids the introduction of the optic-electro and electro-optic conversion. Our results provide an all-optical paradigm for implementing entanglement swapping and pave the way to construct a measurement-free all-optical broadband quantum network.

Phase manipulated two-mode entangled state from a phase-sensitive amplifier

The phase manipulation of the two-mode entangled state, which can flexibly control the combination of quadrature components on demand, is important for continuous variable (CV) quantum information and quantum metrology. Here, we experimentally demonstrate the phase manipulation of entangled state by using a phase-sensitive amplifier (PSA) based on four-wave mixing (FWM) process. The entanglement with different phase space squeezing orientations can be generated by directly changing the phase of the PSA. Our scheme is concise and can be expanded to generate multi-parties entangled states on demand. Our results here pave the way to realize a phase-coded quantum key distribution protocol and squeezing-enhanced Raman spectroscopy.

Multidimensional four-wave mixing signals detected by quantum squeezed light

Quantum light and its statistics provide powerful tools for the study of properties of matter that are difficult to retrieve with classical light. Novel spectroscopic and sensing techniques based on quantum light sources can reveal information about complex material systems that is not accessible by varying the frequencies or time delays of classical light pulses. Here, based on a four-wave mixing process, we report an experimental study of the 2D quantum noise spectra of two-beam intensity difference squeezing. External noise erodes the resolution of classical measurements, while quantum signals remain intact. Our results pave the way for exploiting quantum correlations of squeezed light for spectroscopic applications.

Four-wave mixing (FWM) of optical fields has been extensively used in quantum information processing, sensing, and memories. It also forms a basis for nonlinear spectroscopies such as transient grating, stimulated Raman, and photon echo where phase matching is used to select desired components of the third-order response of matter. Here we report an experimental study of the two-dimensional quantum noise intensity difference spectra of a pair of squeezed beams generated by FWM in hot Rb vapor. The measurement reveals details of the χ(3) susceptibility dressed by the strong pump field which induces an AC Stark shift, with higher spectral resolution compared to classical measurements of probe and conjugate beam intensities. We demonstrate how quantum correlations of squeezed light can be utilized as a spectroscopic tool which unlike their classical counterparts are robust to external noise.

Efficient Verification of Continuous-Variable Quantum States and Devices without Assuming Identical and Independent Operations

Continuous-variable quantum information, encoded into infinite-dimensional quantum systems, is a promising platform for the realization of many quantum information protocols, including quantum computation, quantum metrology, quantum cryptography, and quantum communication. To successfully demonstrate these protocols, an essential step is the certification of multimode continuous-variable quantum states and quantum devices. This problem is well studied under the assumption that multiple uses of the same device result in identical and independently distributed (i.i.d.) operations. However, in realistic scenarios, identical and independent state preparation and calls to the quantum devices cannot be generally guaranteed. Important instances include adversarial scenarios and instances of time-dependent and correlated noise. In this Letter, we propose the first set of reliable protocols for verifying multimode continuous-variable entangled states and devices in these non-i.i.d scenarios. Although not fully universal, these protocols are applicable to Gaussian quantum states, non-Gaussian hypergraph states, as well as amplification, attenuation, and purification of noisy coherent states.

Experimental Demonstration of a Multifunctional All-Optical Quantum State Transfer Machine

Quantum information protocol with quantum resources shows a great advantage in substantially improving security, fidelity, and capacity of information processing. Various quantum information protocols with diverse functionalities have been proposed and implemented. However, in general, the present quantum information system can only carry out a single information protocol or deal with a single communication task, which limits its practical application in the future. Therefore, it is essential to develop a multifunctional platform compatible with multiple different quantum information protocols. In this Letter, by utilizing an all-optical platform consisting of a gain-tunable parametric amplifier, a beam splitter, and an entanglement source, we experimentally realize the partially disembodied quantum state transfer protocol, which links the all-optical quantum teleportation protocol and the optimal 1→N coherent state cloning protocol. As a result, these three protocols, which have different physical essences and functionalities, are implemented in a single all-optical machine. In particular, we demonstrate that the partially disembodied quantum state transfer protocol can enhance the state transfer fidelity compared with all-optical quantum teleportation under the same strength of entanglement. Our all-optical quantum state transfer machine paves a way to implement the multifunctional quantum information system.

Nonlinear interferometric surface-plasmon-resonance sensor

A nonlinear interferometer can be constructed by replacing the beam splitter in the Mach-Zehnder interferometer with four-wave mixing (FWM) process. Meanwhile, the conventional surface plasmon resonance (SPR) sensors can be extensively used to infer the information of refractive index of the sample to be measured via either angle demodulation technique or intensity demodulation technique. Combined with a single FWM process, a quantum SPR sensor has been realized, whose noise floor is reduced below standard quantum limit with sensitivity unobtainable with classical SPR sensor. Therefore, in this work we have theoretically proposed a nonlinear interferometric SPR sensor, in which a conventional SPR sensor is placed inside nonlinear interferometer, which is called as I-type nonlinear interferometric SPR sensor. We demonstrate that near resonance angle I-type nonlinear interferometric SPR sensor has the following advantages: its degree of intensity-difference squeezing, estimation precision ratio, and signal-noise-ratio are improved by the factors of 4.6 dB, 2.3 dB, and 4.6 dB respectively than that obtained with a quantum SPR sensor based on a single FWM process. In addition, the theoretical principle of this work can also be expanded to other types of sensing, such as bending, pressure, and temperature sensors based on a nonlinear interferometer.

All-Optical Optimal N-to-M Quantum Cloning of Coherent States

The laws of quantum mechanics forbid the perfect copying of an unknown quantum state, known as the no-cloning theorem. In spite of this, approximate cloning with imperfect fidelity is possible, which opens up the field of quantum cloning. In general, quantum cloning can be divided into discrete variable and continuous variable (CV) categories. In the CV regime, all-optical implementation of the optimal N→M quantum cloning has been proposed in two original parallel works, which involves a parametric amplifier and a set of beam splitters and thus avoids the optic-electro and electro-optic conversions in the current CV quantum cloning technologies. However, such original proposal of all-optical CV optimal N→M quantum cloning scheme has never been experimentally implemented. Here, we show that optimal N→M quantum cloning of coherent states can be realized by utilizing a parametric amplifier based on four-wave mixing process in a hot atomic vapor and a set of beam splitters. In particular, we realize 1→M, 2→M, and 4→M quantum cloning. We find that the fidelity of N→M quantum cloning increases with the decrease of clone number M and the increase of original replica number N. The best cloning fidelity achieved in our experiment is about 93.3% ±1.0% in the 4→5 case. Our results may find potential applications in realizing all-optical high-fidelity quantum state transfer and all-optical high-compatibility eavesdropping attack in quantum communication networks.

Generation of quantum entanglement based on electromagnetically induced transparency media

Quantum entanglement is an essential ingredient for the absolute security of quantum communication. Generation of continuous-variable entanglement or two-mode squeezing between light fields based on the effect of electromagnetically induced transparency (EIT) has been systematically investigated in this work. Here, we propose a new scheme to enhance the degree of entanglement between probe and coupling fields of coherent-state light by introducing a two-photon detuning in the EIT system. This proposed scheme is more efficient than the conventional one, utilizing the ground-state relaxation (population decay or dephasing) rate to produce entanglement or two-mode squeezing which adds far more excess fluctuation or noise to the system. In addition, maximum degree of entanglement at a given optical depth can be achieved with a wide range of the coupling Rabi frequency and the two-photon detuning, showing our scheme is robust and flexible. It is also interesting to note that while EIT is the effect in the perturbation limit, i.e. the probe field being much weaker than the coupling field and treated as a perturbation, there exists an optimum ratio of the probe to coupling intensities to achieve the maximum entanglement. Our proposed scheme can advance the continuous-variable-based quantum technology and may lead to applications in quantum communication utilizing squeezed light.

Characterization of quantum squeezing generated from the phase-sensitive and phase-insensitive amplifiers in the ultra-low average input photon number regime

We give the general expressions of intensity-difference squeezing (IDS) generated from two types of optical parametric amplifiers [i.e. phase-sensitive amplifier (PSA) and phase-insensitive amplifier (PIA)] based on the four-wave mixing process, which clearly shows the IDS transition between the ultra-low average input photon number regime and the ultra-high average input photon number regime. We find that both the IDS of the PSA and the IDS of the PIA get enhanced with the decrease of the average input photon number especially in the ultra-low average input photon number regime. This result is substantially different from the result in the ultra-high average input photon number regime where the IDS does not vary with the average input photon number. Moreover, under the same intensity gain, we find that the optimal IDS of the PSA is better than the IDS of the PIA in the ultra-low average input photon number regime. Our theoretical work predicts the presence of strong quantum correlation in the ultra-low average input photon number regime, which may have potential applications for probing photon-sensitive biological samples.

Orbital angular momentum multiplexed deterministic all-optical quantum teleportation

Quantum teleportation is one of the most essential protocol in quantum information. In addition to increasing the scale of teleportation distance, improving its information transmission capacity is also vital importance for its practical applications. Recently, the orbital angular momentum (OAM) of light has attracted wide attention as an important degree of freedom for realizing multiplexing to increase information transmission capacity. Here we show that by utilizing the OAM multiplexed continuous variable entanglement, 9 OAM multiplexed channels of parallel all-optical quantum teleportation can be deterministically established in experiment. More importantly, our parallel all-optical quantum teleportation scheme can teleport OAM-superposition-mode coded coherent state, which demonstrates the teleportation of more than one optical mode with fidelity beating the classical limit and thus ensures the increase of information transmission capacity. Our results open the avenue for deterministically implementing parallel quantum communication protocols and provide a promising paradigm for constructing high-capacity all-optical quantum communication networks.

Reconfigurable Hexapartite Entanglement by Spatially Multiplexed Four-Wave Mixing Processes

Multipartite entanglement serves as a vital resource for quantum information processing. Generally, its generation requires complex beam splitting processes which limit scalability. A promising trend is to integrate multiple nonlinear processes into a single device via frequency or time multiplexing. The generated states in these schemes are useful for quantum computation. However, they are confined in one or two beams and hard to be spatially separated for applications in quantum communication. Here, we experimentally demonstrate a scheme to generate spatially separated hexapartite entangled states by means of spatially multiplexing seven concurrent four-wave mixing processes. In addition, we show that the entanglement structure characterized by subsystem entanglement distribution can be modified by appropriately shaping the pump characteristics. Such reconfigurability of the entanglement structure gives the possibility to target a desired multipartite entangled state for a specific quantum communication protocol. Our results here provide a new platform for generating large scale spatially separated reconfigurable multipartite entangled beams.

Polarization-based truncated SU(1,1) interferometer based on four-wave mixing in Rb vapor

We propose and demonstrate a polarization-based truncated SU(1,1) interferometer that outputs the desired optical joint-quadrature of a two-mode squeezed vacuum field and allows its measurements using a single balanced homodyne detector. Using such a setup, we demonstrate up to ≈2dB of quantum noise suppression below the shot-noise limit in intensity-difference and phase-sum joint-quadratures, and confirm entanglement between the two quantum fields. Our proposed technique results in a better balance between the two ports of the detector and, consequently, in better common noise suppression for differential measurements. As a result, we are able to observe flat joint-quadrature squeezing and entanglement at a wide range of detection frequencies: from several MHz (limited by the photodiode gain bandwidth) down to a few hundred Hz (limited by electronic noises).

Phase-sensitive amplification of an optical field using microwaves

We report phase-sensitive amplification (PSA) of a near-infrared electromagnetic field using room-temperature ⁸⁵Rb atoms possessing ground-state coherence. Our novelty is in achieving significant optical PSA by manipulating the intensity and phase of a frequency-separated microwave field. PSA is obtained by inducing a three-wave mixing nonlinear process utilising a three-level cyclic scheme in the D1 manifold. We achieve a near-ideal PSA with a gain of 7 dB over a range of 500 kHz bandwidth with very low pump-field intensities and with low optical depths. Such a hybrid, ground-state-coherence-assisted PSA is the first such demonstration using atomic ensembles.

Interference-Induced Quantum Squeezing Enhancement in a Two-beam Phase-Sensitive Amplifier

We experimentally demonstrate a method for realizing quantum squeezing enhancement which is induced by the interference in a two-beam phase-sensitive amplifier (PSA) based on a four-wave mixing process. Compared to the normal phase-insensitive amplifier with an intensity-difference squeezing (IDS) of 8.97±0.24  dB or 8.76±0.26  dB, the IDS of our two-beam PSA is enhanced to 10.13±0.21  dB under the same experimental situation. Furthermore, we study how various parameters influence the quantum squeezing enhancement of the PSA. These results clearly show that the physical mechanism inducing the IDS enhancement of the two-beam PSA is its intrinsic interference nature. Our results may find potential applications in improving the fidelity of quantum information processing and the precision of quantum metrology.

Atomic dispensers for thermoplasmonic control of alkali vapor pressure in quantum optical applications

Alkali metal vapors enable access to single electron systems, suitable for demonstrating fundamental light-matter interactions and promising for quantum logic operations, storage and sensing. However, progress is hampered by the need for robust and repeatable control over the atomic vapor density and over the associated optical depth. Until now, a moderate improvement of the optical depth was attainable through bulk heating or laser desorption – both time-consuming techniques. Here, we use plasmonic nanoparticles to convert light into localized thermal energy and to achieve optical depths in warm vapors, corresponding to a ~16 times increase in vapor pressure in less than 20 ms, with possible reload times much shorter than an hour. Our results enable robust and compact light-matter devices, such as efficient quantum memories and photon-photon logic gates, in which strong optical nonlinearities are crucial.

Robust and fast control of the atomic vapor pressure in alkali vapor cells would greatly extend their use for many quantum technologies. Here, the authors exploit plasmonic absorption in a cell coating containing gold nanoparticles to control the vapor pressure with milliseconds response time.

Test One to Test Many: A Unified Approach to Quantum Benchmarks

Quantum benchmarks are routinely used to validate the experimental demonstration of quantum information protocols. Many relevant protocols, however, involve an infinite set of input states, of which only a finite subset can be used to test the quality of the implementation. This is a problem, because the benchmark for the finitely many states used in the test can be higher than the original benchmark calculated for infinitely many states. This situation arises in the teleportation and storage of coherent states, for which the benchmark of 50% fidelity is commonly used in experiments, although finite sets of coherent states normally lead to higher benchmarks. Here, we show that the average fidelity over all coherent states can be indirectly probed with a single setup, requiring only two-mode squeezing, a 50-50 beam splitter, and homodyne detection. Our setup enables a rigorous experimental validation of quantum teleportation, storage, amplification, attenuation, and purification of noisy coherent states. More generally, we prove that every quantum benchmark can be tested by preparing a single entangled state and measuring a single observable.

Eight-wave mixing parametrical amplification

We investigate parametrically amplified eight-wave mixing (PA-EWM). The double dressed PA-four-wave mixing (PA-FWM) is the superposition of one PA-FWM process, two different PA-six-wave mixing (PA-SWM) processes (PA-SWM1 and PA-SWM2 with external dressing field 776nm and 795nm, respectively) and one PA-EWM process. When the phases among FWM, SWM1, SWM2 and EWM change from 0 to π, the double dressed PA-FWM could gradually satisfy the pure enhancement (all 0), partial enhancement and suppression (mixture of 0 and π), or pure suppression condition (all π). The outcomes of the investigation can potentially contribute to the development of multi-channel quantum information processing and high dimensional stereoscopic imaging.

Phase-sensitive cascaded four-wave mixing processes for generating continuous-variable entanglement

Quantum entanglement shared by different parties enhances their capabilities to communicate, which is the core content of continuous-variable quantum optics and quantum information science. Here, we study an experimentally feasible scheme for generating quantum entanglement of bipartite and tripartite cases based on phase-sensitive cascaded four-wave mixing processes in rubidium vapor. Quantum entanglement of bipartite and tripartite cases in our system, which can be manipulated by the phases and the intensity gains of the input beams, is predicted. We also find a sufficient optimal single-condition criterion to give a valid description for genuine tripartite quantum entanglement in our system. The sufficient optimal single-condition criterion is convenient and can be extended to genuine multipartite entanglement.

Multi-mode of Four and Six Wave Parametric Amplified Process

Multiple quantum modes in correlated fields are essential for future quantum information processing and quantum computing. Here we report the generation of multi-mode phenomenon through parametric amplified four- and six-wave mixing processes in a rubidium atomic ensemble. The multi-mode properties in both frequency and spatial domains are studied. On one hand, the multi-mode behavior is dominantly controlled by the intensity of external dressing effect, or nonlinear phase shift through internal dressing effect, in frequency domain; on the other hand, the multi-mode behavior is visually demonstrated from the images of the biphoton fields directly, in spatial domain. Besides, the correlation of the two output fields is also demonstrated in both domains. Our approach supports efficient applications for scalable quantum correlated imaging.

Enhancement of entanglement using cascaded four-wave mixing processes

A maximal joint quadrature squeezing of -6.8±0.4  dB is experimentally obtained by a scheme of cascaded four-wave mixing (FWM) processes, which gives strong proof about the inseparability or entanglement between output of the twin beams from the system. Here joint quadrature is the difference between the two quadratures of the twin beam output from the cascaded FWM processes. This result is enhanced by about 3.1 dB, compared with the one of the single FWM process. We also study the gain dependence of the entanglement enhancement in this cascaded system. Theoretical predictions with the considerations of the losses in the experiment are also studied, and a similar trend in the low-gain regime can be found between the experimental results and the theoretical predictions. The scheme of cascaded FWM processes, which can be used to improve or even manipulate the degree of the entanglement between the output fields from the single FWM process, may find its applications in the continuous-variable quantum communication protocols.

Characterization of Pairwise Correlations from Multiple Quantum Correlated Beams Generated from Cascaded Four-Wave Mixing Processes

We theoretically characterize the performance of the pairwise correlations (PCs) from multiple quantum correlated beams based on the cascaded four-wave mixing (FWM) processes. The presence of the PCs with quantum corre- lation in these systems can be verified by calculating the degree of intensity difference squeezing for any pair of all the output fields. The quantum correlation characteristics of all the PCs under different cascaded schemes are also discussed in detail and the repulsion effect between PCs in these cascaded FWM processes is theoretically predicted. Our results open the way for the classification and application of quantum states generated from the cascaded FWM processes.

Generation of tripartite entanglement from cascaded four-wave mixing processes

We investigate the possibility of an experimentally feasible cascaded four-wave mixing (FWM) system [Phys. Rev. Lett. 113, 023602 (2014)] to generate tripartite entanglement. We verify that genuine tripartite entanglement is present in this system by calculating the covariances of three output beams and then considering the violations of the inequalities of the three-mode entanglement criteria, such as two-condition criterion, single-condition criterion, optimal single-condition criterion and the positivity under partial transposition (PPT) criterion. We also consider the possibilities of the bipartite entanglement of any pair of the three output beams using the Duan-Giedke-Cirac-Zoller criterion and PPT criterion. We find that the tripartite entanglement and the bipartite entanglement for the two pairs are present in the whole gain region. The entanglement characteristics under different entanglement criteria are also considered. Our results pave the way for the realization and application of multipartite entanglement based on the cascaded FWM processes.

Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics

We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.

Dressed Gain from the Parametrically Amplified Four-Wave Mixing Process in an Atomic Vapor

With a forward cone emitting from the strong pump laser in a thermal rubidium atomic vapor, we investigate the non-degenerate parametrically amplified four-wave mixing (PA-FWM) process with dressing effects in a three-level “double-Λ” configuration both theoretically and experimentally. By seeding a weak probe field into the Stokes or anti-Stokes channel of the FWM, the gain processes are generated in the bright twin beams which are called conjugate and probe beams, respectively. However, the strong dressing effect of the pump beam will dramatically affect the gain factors both in the probe and conjugate channels, and can inevitably impose an influence on the quantum effects such as entangled degree and the quantum noise reduction between the two channels. We systematically investigate the intensity evolution of the dressed gain processes by manipulating the atomic density, the Rabi frequency and the frequency detuning. Such dressing effects are also visually evidenced by the observation of Autler-Townes splitting of the gain peaks. The investigation can contribute to the development of quantum information processing and quantum communications.

Experimental generation of multiple quantum correlated beams from hot rubidium vapor

Quantum correlations and entanglement shared among multiple quantum modes are important for both fundamental science and the future development of quantum technologies. This development will also require an efficient quantum interface between multimode quantum light sources and atomic ensembles, which makes it necessary to implement multimode quantum light sources that match the atomic transitions. Here, we report on such a source that provides a method for generating quantum correlated beams that can be extended to a large number of modes by using multiple four-wave mixing (FWM) processes in hot rubidium vapor. Experimentally, we show that two cascaded FWM processes produce strong quantum correlations between three bright beams but not between any two of them. In addition, the intensity-difference squeezing is enhanced with the cascaded system to -7.0±0.1  dB from the -5.5±0.1/-4.5±0.1  dB squeezing obtained with only one FWM process. One of the main advantages of our system is that as the number of quantum modes increases, so does the total degree of quantum correlations. The proposed method is also immune to phase instabilities due to its phase insensitive nature, can easily be extended to multiple modes, and has potential applications in the production of multiple quantum correlated images.

Parametric amplification and cascaded-nonlinearity processes in common atomic system

For the first time, we study the parametric amplification process of multi-wave mixing (PA-MWM) signal and cascaded-nonlinearity process (CNP) in sodium vapors both theoretically and experimentally, based on a conventional phase-conjugate MWM and a self-diffraction four-wave mixing (SD-FWM) processes, which are pumped by laser or amplified spontaneous emission (ASE), respectively. For laser pumping case, SD-FWM process serves as a quantum linear amplifier (a CNP) out (inside) of the resonant absorption region. While for ASE case, only the CNP occurs and the output linewidth is much narrower than that of the MWM signal due to the second selected effect of its electromagnetically induced transparency window. In addition, the phase-sensitive amplifying process seeded by two MWM processes is discussed for the first time. Theoretical fittings agree well with the experiment. The investigations have important potential applications in quantum communication.

Cancellation of internal quantum noise of an amplifier by quantum correlation

Quantum noise is usually added in an amplification process through the internal degrees of the amplifier. Coupling the squeezed state to the internal degree can suppress the extra noise. Here, we demonstrate another method: when the internal degree of the amplifier is correlated with the input signal via quantum entanglement, quantum destructive interference between the input and the internal degree may result in noise reduction at the amplified output. We achieve a quantum noise reduction of 2.3 dB at the output and an improvement of 4.0±0.2 dB in signal-to-noise ratio during the amplification process with a quantum noise gain of 4.5 dB.

Suppression and enhancement of coexisting super-fluorescence and multi-wave mixing processes in sodium vapor

Different aspects of the properties of the coexisting super-fluorescence (SFL), multi-wave mixing with the fluorescence signal in the sodium vapor are studied both theoretically and experimentally. First, by scanning the dressed-state, the properties of these coexisting processes, such as the SFL signal modulated by using the dark and bright states, the interplay between dressed-states, are observed for the first time. Then, by scanning the probe field, the interplay between the one-photon and two-photon processes of the coexisting signals is obtained with or without the external dressing fields. Such control on each process in such coexisting system has an important potential application in quantum communication.

Compact diode-laser-pumped quantum light source based on four-wave mixing in hot rubidium vapor

Using a nondegenerate four-wave mixing process in hot rubidium vapor, we demonstrate a compact diode-laser-pumped system for the generation of intensity-difference squeezing down to 8 kHz with a maximum squeezing of -7 dB. To the best of our knowledge, this is the first demonstration of kilohertz-level intensity-difference squeezing using a semiconductor laser as the pump source. This scheme is of interest for experiments involving atomic ensembles, quantum communications, and precision measurements. The diode-laser-pumped system would extend the range of possible applications for squeezing due to its low cost, ease of operation, and ease of integration.

Noiseless optical amplifier operating on hundreds of spatial modes

We implement a noiseless optical amplifier using a phase-sensitive four-wave mixing process in rubidium vapor. We observe performance near the quantum limit for this type of amplifier over a range of experimental parameters and show that the noise figure is always better than would be obtained with a phase-insensitive amplifier with the same gain. Additionally, we observe that the amplifier supports hundreds of spatial modes, making it possible to amplify complex two-dimensional spatial patterns with less than a 10% degradation of the input signal-to-noise ratio for gains up to 4.6. To confirm the multimode character of the amplifier, we study the noise figure as a function of spatially-varying losses. Additionally, we investigate the spatial resolution of the amplifier and show that it supports a range of spatial frequencies from 1.3 to more than 35 line pairs per millimeter.

Intensity-dependent effects on four-wave mixing based on electromagnetically induced transparency

We extend the study on a four-wave mixing (FWM) scheme of contiuous-wave lasers in a hot rubidium vapor when the probe and coupling fields work in the electromagnetically induced transparency (EIT) regime while the pump and signal fields work in the two-photon Raman regime. Our experimental results show that the generated signal field is well contained in an EIT dip of the incident probe field as a result of efficient FWM. We find, in particular, that an optimal FWM process can only be attained when the coupling and pump fields are well matched in intensity. If the probe intensity is far beyond the EIT condition, however, the nonlinear efficiency of energy transfer from the probe field to the signal field will be greatly reduced.

Multi-spatial-mode single-beam quadrature squeezed states of light from four-wave mixing in hot rubidium vapor

We present experimental results on the generation of multi-spatial-mode, single-beam, quadrature squeezed light using four-wave mixing in hot Rb vapor. Squeezing and phase-sensitive deamplification are observed over a range of powers and detunings near the (85)Rb D1 atomic transition. We observe -3 dB of vacuum quadrature squeezing, comparable to the best single-spatial mode results previously reported using atomic vapors, however, produced here in multiple spatial modes. We confirm that the squeezing is present in more than one transverse mode by studying the spatial distribution of the noise properties of the field.

Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor

We experimentally demonstrate the creation of two correlated beams generated by a nondegenerate four-wave-mixing amplifier at λ=795 nm in hot rubidium vapor. We achieve intensity difference squeezing at frequencies as low as 1.5 kHz which is so far the lowest frequency to observe squeezing in an atomic system. The squeezing spans from 5.5 to 16.5 MHz with a maximum squeezing of -5 dB at 1 MHz. We can control the squeezing bandwidth by changing the pump power. Both low frequency and controllable bandwidth squeezing show great potential in sensitivity detection and precise control of the atom optics measurement.

Relative intensity squeezing by four-wave mixing with loss: an analytic model and experimental diagnostic

Four-wave mixing near resonance in an atomic vapor can produce relative intensity squeezed light suitable for precision measurements beyond the shot-noise limit. We develop an analytic distributed gain/loss model to describe the competition of mixing and absorption through the non-linear medium. Using a novel matrix calculus, we present closed-form expressions for the degree of relative intensity squeezing produced by this system. We use these theoretical results to analyze experimentally measured squeezing from a 85Rb vapor and demonstrate the analytic model's utility as an experimental diagnostic.

Continuous variable entanglement enhancement and manipulation by a subthreshold Type II optical parametric amplifier

We experimentally demonstrate that the quantum entanglement between amplitude and phase quadratures of optical modes produced from a nondegenerate optical parametric amplifier (NOPA) can be enhanced and manipulated phase sensitively by means of another NOPA. When both NOPAs operate at deamplification, the entanglement degree is increased at the cavity resonance of the second NOPA. When the first NOPA operates at deamplification and the second one at amplification, the spectral features of the correlation variances are significantly changed. The experimental results are in good agreement with the theoretical expectation.

Quantum correlated light beams from non-degenerate four-wave mixing in an atomic vapor: the D1 and D2 lines of 85Rb and 87Rb

We present experimental results showing that quantum correlated light can be produced using non-degenerate, off-resonant, four-wave mixing (4WM) on both the D1 (795 nm) and D2 (780 nm) lines of (85)Rb and (87)Rb, extending earlier work on the D1 line of (85)Rb. Using this 4WM process in a hot vapor cell to produce bright twin beams, we characterize the degree of intensity-difference noise reduction below the standard quantum limit for each of the four systems. Although each system approximates a double-lambda configuration, differences in details of the actual level structure lead to varying degrees of noise reduction. The observation of quantum correlations on light produced using all four of these systems, regardless of their substructure, suggests that it should be possible to use other systems with similar level structures in order to produce narrow frequency, non-classical beams at a particular wavelength.