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

Near-resonant twin-beam generation from degenerate four-wave mixing in hot 133Cs vapor enabled by field-dressed energy levels

Squeezed light near an atomic resonance is beneficial for efficient atom-light quantum interfaces. It is desirable but challenging to directly generate in atoms due to excess noise from spontaneous emission and reabsorption. Here, we report on the use of energy-level modulation to actively control atomic coherence and interference in degenerate four-wave mixing (DFWM) and then to enhance the DFWM gain process for the generation of near-resonant squeezed twin beams. With this technique, we obtain a -2.6 dB intensity-difference squeezing detuned 100 MHz from the D1 F = 4 to F' = 4 transition of 133Cs.

Optimal bright multimode quantum squeezing via multi-seeding energy-level cascaded four-wave mixing

Quantum Squeezing is one of the most important quantum resources in quantum optics and quantum information. In particular, multimode quantum squeezing, with ultra-low quantum fluctuations and quantum correlations amongst many optical modes, is essential for realizing multipartite entanglement and quantum precision measurements. In this paper, we propose an all-optically controlled scheme to generate three-mode bright quantum correlated beams from energy-level cascaded four-wave mixing (ELC-FWM). By using a linear modes transform approach, the input-output relation and the covariance matrix of the produced states are obtained. Moreover, single-, double- and triple-seeding conditions are investigated to measure the quantum squeezing properties. We find that various permutations of two- and three-mode quadrature squeezing can be generated and optimized to reach the corresponding limit, via only modulating the ratio of the multiple seeds, without need of any post-operating linear optics, e.g., beam splitters. Such weak seeding light controlled scheme suggests the modulation and the optimization of multimode quantum states might be operated at photons-level, providing a reconfigurable and integrated strategy for complex quantum information processing and quantum metrology.

Multi-Way Noiseless Signal Amplification in a Symmetrical Cascaded Four-Wave Mixing Process

According to the fundamental laws of quantum optics, vacuum noise is inevitably added to the signal when one tries to amplify a signal. However, it has been recently shown that noiseless signal amplification can be realized when a phase-sensitive process is involved. Two phase-sensitive schemes, a correlation injection scheme and a two-beam phase-sensitive amplifier scheme, are both proposed to realize multi-way noiseless signal amplification in a symmetrical cascaded four-wave mixing process. We theoretically study the possibility of the realization of four-way noiseless signal amplification by using these two schemes. The results show that the correlation injection scheme can only realize one-way noiseless signal amplification, but that the two-beam phase-sensitive amplifier scheme can lead to four-way noise figure values below 1. Our results here may find potential applications in quantum information processing, e.g., the realization of quantum information tap and quantum non-demolition measurement, etc.

Two-beam coupling in the production of quantum correlated images by four-wave mixing

We investigate the effect of 2-beam coupling in different imaging geometries in generating intensity-difference squeezing from four-wave mixing (4WM) in Rb atomic vapors. A recently-introduced dual-seeding technique can cancel out the classical noise in a seeded four-wave mixing process. This dual-seeding technique, however, can introduce new complications that involve 2-beam coupling between different seeded spatial modes in the atomic vapor and can ruin squeezing at frequencies on the order of the atomic linewidth and below. This complicates some forms of quantum imaging using these systems. Here we show that seeding the 4WM process with skew rays can eliminate the excess noise caused by 2-beam coupling. To avoid 2-beam coupling in bright, seeded images, it is important to re-image the object in the gain medium, instead of focussing through it.

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.

Multimode entanglement generation with dual-pumped four-wave-mixing of Rubidium Atoms

Multimode entanglement is essential for the generation of quantum networks, which plays a central role in quantum information processing and quantum metrology. Here, we study the spatial multimode entanglement characteristics of the large scale quantum states via a dual-pumped four-wave-mixing (FWM) process of Rubidium atomics vapors. A linear mode transform approach is applied to solve the four- and six-mode Gaussian states and the analytical input-output relations are presented. Moreover, via reconstructing the full covariance matrix of the produced states, versatile entanglement with from two up to six modes is analyzed. The results show that most of the 1 versus n-mode and m versus n-mode states are entangled, and the amount of entanglement can be regulated due to the competitions of mode components caused by different interaction strengths of co-existing FWMs. Our study could be applied for any multimode Gaussian states with a quadratic Hamiltonian.

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.

Twin-beam intensity-difference squeezing below 10 Hz

We report the generation of strong, bright-beam intensity-difference squeezing down to measurement frequencies below 10 Hz. We generate two-mode squeezing in a four-wave mixing (4WM) process in Rb vapor, where the single-pass-gain nonlinear process does not require cavity locking and only relies on passive stability. We use diode laser technology and several techniques, including dual seeding, to remove the noise introduced by seeding the 4WM process as well as the background noise. Twin-beam intensity-difference squeezing down to frequencies limited only by the mechanical and atmospheric stability of the lab is achieved. These results should enable important low-frequency applications such as direct intensity-difference imaging with bright beams on integrating detectors.

Optical bistablility in six-wave mixing parametrical amplification

We investigate the nonreciprocity "∞"-shape optical bistability (OB) induced by the feedback dressing effect of six-wave mixing parametrically amplified process in a four-level atomic system. Compared to the traditional OB by scanning power, the "∞"-shape OB is scanning probe frequency and demonstrated by "∞"-shape non-overlapping region. More, this non-overlapping region in the x direction (frequency difference) and in the y direction (intensity difference) could demonstrate the degree of this OB phenomenon of dressed probe and conjugate signals, which can be changed by the intensity of feedback dressing. Further, we find the feedback intensity can be controlled by experimental parameters include powers of external-dressing, frequency detuning, incident phase and the nonlinear phase shift of internal-dressing beam. As a result, the nonreciprocity "∞"-shape OB is more sensitive and multiple than traditional OB. These outcomes have potential applications in logic-gate devices and quantum information processing.

Dependence of measured audio-band squeezing level on local oscillator intensity noise

We investigate the dependence of the measured squeezing level on the local oscillator (LO) intensity noise. The theoretical results indicate that it produces a large measurement error with the increase of the LO intensity noise, but the measurement error has immunity to the product P of the common mode rejection ratio (CMRR) with the LO intensity noise. According to the investigation results and the LO intensity noise, we employ a detector with the CMRR of 67 dB to detect the quantum noise at audio frequencies, the product P of the CMRR with the LO intensity noise is 20 dB below the shot noise limit (SNL), which can induce the measurement error of 0.1 dB for 10 dB of squeezing. Finally, the squeezing level measured at 15.2 kHz is 9.9 ± 0.2 dB. The influence of the intensity noise of the LO, and the electronic noise of the detector is subtracted, the inferred squeezing level is approximately 10.2 ± 0.2 dB. It is extremely important to quantify the requirements of the CMRR of the detector for measuring the squeezing at audio frequency and inferring the real squeezing level.

Polarization squeezing at the audio frequency band for the Rubidium D1 line

A 2.8-dB polarization squeezing of the Stokes operatorS^₂for the rubidium D₁ line (795 nm) is achieved, with the lowest squeezing band at an audio frequency of 2.6 kHz. It is synthetized by a bright coherent beam and a squeezed vacuum, which are orthogonally polarized and share same frequency. Two methods are applied to support the optical parametric oscillator: an orthogonally-polarized locking beam that precludes residual unwanted interference and quantum noise locking method that locks the squeezing phase. Besides, the usage of low noise balanced detector, mode cleaner and the optical isolator helped to improve the audio frequency detection. The squeezing level is limited by absorption-induced losses at short wavelengths, which is 397.5 nm. The generated polarization squeezed light can be used in a quantum enhanced magnetometer to increase the measurement sensitivity.

Hybrid interferometer with nonlinear four-wave mixing process and linear beam splitter

Optical interferometer has played an important role in optics. Up to now, many kinds of interferometers have been realized and found their applications. In this letter, we experimentally construct an interferometer by using parametric amplifier as a wave splitter and beam splitter as a wave combiner. We make measurements of interference fringes and explore the relationships between the interference visibility of the interferometer and various system parameters, such as the gain of the parametric amplifier, the one-photon detuning and the temperature of the Rb-85 vapor cell.

Experimental observation of quantum correlations in four-wave mixing with a conical pump

Generation of multimode quantum states has drawn much attention recently due to its importance for both fundamental science and the future development of quantum technologies. Here, by using a four-wave mixing process with a conical pump beam, we have experimentally observed about -3.8  dB of intensity-difference squeezing between a single-axial probe beam and a conical conjugate beam. The multi-spatial-mode nature of the generated quantum-correlated beams has been shown by comparing the variation tendencies of the intensity-difference noise of the probe and conjugate beams under global attenuation and local cutting attenuation. Due to its compactness, phase-insensitive nature, and easy scalability, our scheme may find potential applications in quantum imaging, quantum information processing, and quantum metrology.

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.

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.

Nonlinear optical magnetometry with accessible in situ optical squeezing

We demonstrate compact and accessible squeezed-light magnetometry using four-wave mixing in a single hot rubidium vapor cell. The strong intrinsic coherence of the four-wave mixing process results in nonlinear magneto-optical rotation (NMOR) on each mode of a two-mode relative-intensity squeezed state. This framework enables 4.7 dB of quantum noise reduction while the opposing polarization rotation signals of the probe and conjugate fields add to increase the total signal to noise ratio.

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.

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.