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Physica Scripta

Enhanced multi-mode squeezing via a balanced regime in dual-four-wave mixing

Xing Heng, Weiyi Wang, Fan Wang, Wei Liu, Mingming Xia, Yueyang Zhai, Kai Wei

Published Feb 7, 2025• 2 citations
Publisher

Abstract

Abstract The generation of multi-mode squeezing using four-wave mixing process has attracted considerable attention, offering significant potential for advancements in quantum communication, quantum key distribution, and quantum-enhanced sensing. In this paper, we propose a balanced regime within the dual-four-wave mixing (DFWM) process to theoretically generate quantum-enhanced multi-mode squeezed light. By operating at a plane-balanced regime, the relative intensity squeezing noise factor of the multi-mode beams can be made to approach zero theoretically, thus achieving perfect multi-mode squeezed states. Moreover, the generated beams at the plane-balanced regime exhibit quantum-enhanced entanglement superior to that of conventional four-wave mixing processes, offering significant implications for quantum information processing. The DFWM process can also be extended to multi-spatial-mode squeezing with a spatial-balanced regime, where the attainable squeezing degree is enhanced by a factor of G N , where N denotes mode numbers and G denotes the gain, facilitating simply experimental implementation within a single atomic system. The proposed method paves the way for practical applications in high-precision measurements, robust quantum communication networks, and advanced quantum information processing systems.

DOI
10.1088/1402-4896/adb3e3

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Abstract The generation of multi-mode squeezing using four-wave mixing process has attracted considerable attention, offering significant potential for advancements in quantum communication, quantum key distribution, and quantum-enhanced sensing. In this paper, we propose a balanced regime within the dual-four-wave mixing (DFWM) process to theoretically generate quantum-enhanced multi-mode squeezed light. By operating at a plane-balanced regime, the relative intensity squeezing noise factor of the multi-mode beams can be made to approach zero theoretically, thus achieving perfect multi-mode squeezed states. Moreover, the generated beams at the plane-balanced regime exhibit quantum-enhanced entanglement superior to that of conventional four-wave mixing processes, offering significant implications for quantum information processing. The DFWM process can also be extended to multi-spatial-mode squeezing with a spatial-balanced regime, where the attainable squeezing degree is enhanced by a factor of G N , where N denotes mode numbers and G denotes the gain, facilitating simply experimental implementation within a single atomic system. The proposed method paves the way for practical applications in high-precision measurements, robust quantum communication networks, and advanced quantum information processing systems.
Quantum squeezed states, exhibiting noise reduction below the shot-noise limit, are important resources in quantum optics. The degree of quantum squeezing directly influences the performance of physical systems, making the achievement of higher squeezing levels essential. Here, by utilizing the phase-sensitive cascaded four-wave mixing (PSCFWM) processes, we experimentally demonstrate the enhancement of three-beam quantum squeezing. The intensity-difference squeezing among the three output beams from PSCFWM processes is about 8.2 dB, which is enhanced by about 1.3 dB compared with that generated by phase-insensitive cascaded four-wave mixing processes. Our scheme provides an effective way for enhancing multi-beam quantum squeezing and holds promise for applications in multimode quantum correlated imaging and multiparameter quantum precision measurement.
Multipartite quantum correlation is important for both fundamental science and quantum information processing. Its enhancement is critical to improve the performance of physical systems. Therefore, it is of great practical significance to study the enhancement of multipartite quantum correlation. Here, we theoretically investigate a scheme for enhancing quadripartite quantum correlation by utilizing a phase-sensitive cascaded four-wave mixing (CFWM) process. We find that the intensity-difference squeezing (IDS) among the four output beams generated by the phase-insensitive CFWM process can be largely enhanced by introducing the phase-sensitive CFWM process. We also find that our phase-sensitive CFWM process can be used to generate intensity-sum squeezing (ISS), which cannot be generated by the phase-insensitive CFWM process. Moreover, we find that the maximum squeezing value of ISS is equal to that of IDS when the intensity gains of the three four-wave mixing processes are equal in the phase-sensitive cascaded scheme. In the end, we discuss the effects of the losses and the phase fluctuations on the squeezing values of our phase-sensitive CFWM process and the corresponding phase-insensitive CFWM process with the same intensity gains. It can be seen that the squeezing enhancement of our phase-sensitive CFWM process holds also in presence of the losses and the phase fluctuations. Our results pave the way for experimental implementation and may find applications in quantum metrology and quantum communication.
Multimode quantum states, such as multipartite quantum entanglement or quantum correlations, are important for both fundamental science and the future development of quantum technologies. Here we theoretically propose and experimentally realize a scheme that can fully exploit the multi-spatial-mode nature of the four-wave-mixing (FWM) process, i.e., spatial multiplexing, and thus integrates multiple FWM processes into a single cell at each stage of the cascaded process. The number of generated quantum-correlated beams 2n{2}^{n}2n is exponentially dependent on the number of vapor cells nnn. In addition, the quantum correlations between the multiple beams also increase as the number of vapor cell increases. For the case of n=2n=2n=2, we experimentally show that the degree of intensity-difference squeezing between the four quantum-correlated beams in our scheme is enhanced to $\ensuremath{-}8.2\ifmmode\pm\else\textpm\fi{}0.2$ dB from $\ensuremath{-}5.6\ifmmode\pm\else\textpm\fi{}0.3$ and $\ensuremath{-}6.5\ifmmode\pm\else\textpm\fi{}0.2$ dB of squeezing obtained with a single FWM process. Our system may find applications in quantum information and precision measurement.
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.
The suitability of degenerate four-wave mixing (DFWM) as a source of squeezed-state (two-photon coherent state) light is investigated, both theoretically and experimentally. In previous semiclassical theory, which neglected pump quantization and loss in the nonlinear medium, Yuen and Shapiro [Opt. Lett. 4, 334 (1979)] showed that such states would be generated by 50%-50% combination of the transmitted probe (TP) and the phase-conjugate (PC) output beams of DFWM. Here the effects of quantum fluctuations in the amplitudes and phases of the pump beams are calculated in a traveling-wave finite-interaction-length DFWM configuration. It is shown that in the limit of strong pump beams and weak nonlinear coupling, the classical-pumps assumption of Yuen and Shapiro is valid. With use of this assumption, loss in the nonlinear medium is incorporated into the model by coupling the interacting modes to a set of reservoir modes. It is shown that loss presents an absolute limit on the degree of squeezing that can be achieved with DFWM. Also, for comparison with experimental work, the photoelectron statistics of the TP, PC, and 50%-50% combination modes are calculated for lossy DFWM; significant deviations are found from the predictions for lossless operation. Quantum-noise measurements on the PC and TP beams generated in sodiumvapor DFWM are described. The mixer is pumped and probed by the nearly transform-limited pulses produced by a continuous-wave-oscillator-pulse-amplifier chain dye laser at 589 nm wave-length. The normalized second-factorial moment g2{g}_{2}g2​ of the PC and TP beams is determined from photoelectron-counting measurements. Inability to simultaneously achieve high DFWM reflectivity and acceptably low scattered-plus-fluorescent background, coupled with low photomultiplier quantum efficiency, restrict the experiment to a DFWM regime wherein theory predicts Poisson statistics. Experimental g2{g}_{2}g2​ values corroborate this prediction, indicating that systematic and excess noises have been eliminated. No attempt was made to measure the quantum statistics of the 50%-50% combination mode.
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.