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Physical Review A

Generation of non-Gaussian states in a cyclic four-wave-mixing system with photon-number projections

Boxuan Jing, Feng-Xiao Sun, Yu Xiang, Qiongyi He

Published Apr 11, 2025• 1 citation
Publisher

Abstract

Continuous-variable entanglement, especially in the non-Gaussian states exhibiting Wigner negativity, is essential for realizing quantum advantages in quantum information processing tasks. Here, we propose a method to efficiently generate multimode non-Gaussian entangled states using a single Rb vapor cell integrated with a cyclic optical system. By employing multiple pump light pulses and recycling the output signal light as a seed light, our system is equivalent to implementing the multiple cascaded four-wave mixing processes while maintaining resource efficiency. Through the analysis of the properties of multipartite steering and entanglement in the cyclic system, we find a hierarchical Gaussian steering structure, which enables the photon number projection on superior signal mode to prepare a multimode entangled non-Gaussian state in the idler modes. Conversely, the projection on each subordinate idler mode can induce more negativity in the signal mode. More importantly, our approach significantly improves the success probability of photon number projections, thereby augmenting the yield of non-Gaussian states and enhancing their potential for delivering robust quantum advantages.

DOI
10.1103/physreva.111.043515

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Journal of the Optical Society of America B•Sep 1, 2022•6 citations
Continuous-variable entanglement, especially in the non-Gaussian states exhibiting Wigner negativity, is essential for realizing quantum advantages in quantum information processing tasks. Here, we propose a method to efficiently generate multimode non-Gaussian entangled states using a single Rb vapor cell integrated with a cyclic optical system. By employing multiple pump light pulses and recycling the output signal light as a seed light, our system is equivalent to implementing the multiple cascaded four-wave mixing processes while maintaining resource efficiency. Through the analysis of the properties of multipartite steering and entanglement in the cyclic system, we find a hierarchical Gaussian steering structure, which enables the photon number projection on superior signal mode to prepare a multimode entangled non-Gaussian state in the idler modes. Conversely, the projection on each subordinate idler mode can induce more negativity in the signal mode. More importantly, our approach significantly improves the success probability of photon number projections, thereby augmenting the yield of non-Gaussian states and enhancing their potential for delivering robust quantum advantages.
Non-Gaussian quantum states of light are important resources for implementing quantum information tasks, ranging from fault-tolerant optical quantum information processing to long distance quantum communication. These states can be generated by applying non-Gaussian operations, such as photon addition and subtraction, to an input Gaussian quantum state. Also, the use of Gaussian operations (like homodyne measurement) allows the transformation of non-Gaussian input quantum states while maintaining their non-Gaussianity. It has been shown that in such context, iterative tailoring of arbitrary quantum states is possible, by cascading elementary operation blocks. This invitably comes at the cost of increasing the protocol complexity. Spectral modes, on the other hand, can be used to handily carry multiple quantum states in a single spatial mode. Moreover, multimode states populating such modes are readily available in commonly exploited processes such as spontaneous parametric down conversion.In this work, we propose a protocol to generate non-Gaussian quantum states using spectral multiplexing of input states and Gaussian operations. We give the analytical expression of the output non-Gaussian state as a function of the number of input state, the Gaussian operation and the properties of spectral modes carrying the input quantum states. Taking as an example the cat breeding operation, we show that with a single mixing and measurement operation, we can obtain an amplified output cat state comparable to the one obtained using iterative breeding scheme with multiple mixing operations and measurements with the same number of input states. We show also that the generation of approximated GKP states is possible with this protocol. We believe that the proposed protocol will have a major impact on the field of non-Gaussian quantum states generation, and can be used to extend the study beyond the cases considered in our work.
Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.
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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.
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.
Multimode quantum squeezing plays an essential role in the fields of quantum metrology and quantum information. In this paper, we first construct a three- and four-mode energy-level cascaded four-wave mixing system in a single 85 R b vapor, and then analyze the quantum properties of the produced states, including the covariance matrix and the intensity squeezing with 11 possible Hamiltonians. In addition, the dressing field is applied to modulate the nonlinear susceptibility and the multimode quantum states. Our scheme allows active modulation of the quantum states integrated within the generation step, without the need for any post-operation of the optics. The mode number of the states also can be extended using more pump fields and the dressing effect. Our study provides a promising candidate to generate multimode quantum states and multimode quantum squeezing within a quantum device involved in the construction of practical quantum networks.