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New Journal of Physics

Generation of tripartite squeezed state by cascaded four-wave mixing in single hot rubidium atomic system

Changbiao Li, Yufeng Li, Wei Li, Kangkang Li, Yuliang Liu, Yin Cai, Yanpeng Zhang

Published Aug 30, 2022• 11 citations
Publisher

Abstract

Abstract We report the quantum correlated triple beams via cascaded four-wave mixing (CFWM) amplified in single hot atomic vapor. Experimentally, we show that strong quantum correlation of three light beams, among them any two’s quantum correlation is characterized by the maximum value of intensity-difference squeezing (IDS) about −7.8 ± 0.3 dB. We found there is IDS between two idler beams, because two pairs of Einstein–Podolsky–Rosen injections potentially exist in our system. Besides, CFWM can emit three-mode beams at three different frequencies, in which these beams can be well separated in the spatial domain. Moreover, much difference with other methods, the injecting probe field can manipulate the gain and IDS of output three-mode light beams, which is resulting from competition relationship between cascaded two four-wave mixing processes. More interestingly, Autler–Townes splitting of gain peaks of output signals due to dressing effect of pumping fields, will lead to the evolution of measured two- and three-mode IDS from single-mode to multi-mode at frequency domain. This result will provide a multimode quantum resource which can potentially realize multimode entanglement and quantum networks.

DOI
10.1088/1367-2630/ac8db2

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Abstract We report the quantum correlated triple beams via cascaded four-wave mixing (CFWM) amplified in single hot atomic vapor. Experimentally, we show that strong quantum correlation of three light beams, among them any two’s quantum correlation is characterized by the maximum value of intensity-difference squeezing (IDS) about −7.8 ± 0.3 dB. We found there is IDS between two idler beams, because two pairs of Einstein–Podolsky–Rosen injections potentially exist in our system. Besides, CFWM can emit three-mode beams at three different frequencies, in which these beams can be well separated in the spatial domain. Moreover, much difference with other methods, the injecting probe field can manipulate the gain and IDS of output three-mode light beams, which is resulting from competition relationship between cascaded two four-wave mixing processes. More interestingly, Autler–Townes splitting of gain peaks of output signals due to dressing effect of pumping fields, will lead to the evolution of measured two- and three-mode IDS from single-mode to multi-mode at frequency domain. This result will provide a multimode quantum resource which can potentially realize multimode entanglement and quantum networks.
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.
Abstract In this paper, we demonstrate that the intensity difference squeezing (IDS) of parametric amplified four-wave mixing (PA-FWM) can be modulated by the phase-sensitive dressed effect in a hot rubidium (Rb) atomic system. The introduction of phase-sensitive dressed effect can enhance the degree of IDS of PA-FWM to −8.1 dB, as compared to that in the phase-insensitive dressed PA-FWM of −6.6 dB. The phase-sensitive dressing field can not only enhance the degree of IDS of PA-FWM by the dressed effect, but can also be treated as the seed beam of the PA-six wave mixing process. So, double-injected three-mode IDS obviously has a bigger degree of IDS compared with the single-injection case. One advantage of the current scheme for enhancing the generated IDS is that the experimental setup is simple and mechanically stable. These outcomes can be used in the fabrication of quantum devices and the realization of quantum metrology.
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.
We propose a two-beam pumped cascaded four-wave-mixing (CFWM) scheme with a double-$\mathrm{\ensuremath{\Lambda}}$ energy-level configuration in 85Rb^{85}\mathrm{Rb}85Rb vapor cell and experimentally observe the emission of up to 10 quantum correlated beams from such CFWM scheme. During this process, the seed beam is amplified; four new signal beams and five idler beams are generated. The 10 beams show strong quantum correlation which is characterized by the intensity-difference squeezing of about $\ensuremath{-}6.7\ifmmode\pm\else\textpm\fi{}0.3$ dB. Then, by altering the angle between the two pump beams, we observe the notable transition of the number of the output beams from 10 to eight, and even to six. We find that both the number of the output quantum correlated beams and their degree of quantum correlation from such two-beam pumped CFWM scheme increase with the decrease of the angle between the two pump beams. Such system may find potential applications in quantum information and quantum metrology.
Theoretical studies and experimental implementations of quantum correlation are the important contents of continuous variables quantum optics and quantum information science. There are various systems for the study of quantum correlation. Here, we study an experimental scheme for generating three quantum correlated beams based on phase-sensitive cascaded four-wave-mixing (FWM) processes in rubidium vapor. Quantum correlation including intensity difference or sum squeezing, two other combinatorial squeezing, and quantum entanglement among the three output light fields are theoretically analyzed in this paper. Also, the comparison of the quantum correlations have been made between the phase-sensitive cascaded FWM processes and the phase-insensitive cascaded FWM processes. By changing the phases and intensities of the input beams, it is interesting to find that the maximum degrees of various combinatorial squeezing are equal when the two FWM processes share a common intensity gain. When the common intensity gain of the two FWM processes changes, the maximum degrees of different combinatorial squeezing will be synchronously controlled. At last we discuss the genuine tripartite entanglement and steering in our phase-sensitive cascaded scheme, and compare them with the cases of the phase-insensitive cascaded scheme.
Abstract Level-cascaded four-wave mixing systems with multimode quantum state squeezing are of great significance for non-Hermitian exceptional control. In this paper, based on non-Hermitian systems, we couple the energy level dressing to generate multimode quantum correlated beams. We have conducted an in-depth discussion on the quantum squeezing characteristics of the cascaded four-mode system. We use the gain squeezing matrix of the Hamiltonian matrix to introduce a pair of Einstein–Podolsky–Rosen (EPR) injections and two pairs of EPR injections at different positions in the cascaded four-mode system. We found several key phenomena: (1) In covariance squeezing, dual EPR injections not only disrupt the original squeezing strength but also produce varying numbers of Hamiltonians depending on injection location; (2) For intensity-difference squeezing, multiple coherent injections enhance squeezing coherence proportionally to injection count, while increased Hamiltonians strengthen intensity-difference correlations. Particularly noteworthy is the equivalence between single EPR injections and E 2 E 3 dual injections, as well as between position-B dual EPR injections and E 2 E 3 E 4 triple injections. The results establish that EPR injections exhibit superior intensity hierarchy compared to multiple coherent or Hamiltonian injections, with their configuration capable of actively modifying inter-mode hierarchical relationships.