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Physical Review A

Hexapartite coherent feedback control in four-wave mixing with a spatially structured pump

Haiyan He, Kai Zhang, Jietai Jing

Published Jun 7, 2024• 4 citations
Publisher

Abstract

Quantum coherent feedback control (CFC) has been widely applied to prepare and manipulate nonclassical beams. In this paper, we utilize an optical beam splitter with tunable reflectivity $k$ as a feedback controller and theoretically construct a CFC system based on four-wave mixing (FWM) processes with a spatially structured pump. After considering absorption loss in the atoms, beam propagation loss in the feedback loop, and detection loss in the detectors, we derive an input-output relationship and theoretically study the manipulation of feedback strength, gain of the FWM processes, and phase to the degree of hexapartite quantum correlation of the system. We find that the relative intensity-difference squeezing degree of all the six output fields from this system is enhanced within a certain range of feedback ratio and phase. Furthermore, there exists an optimal feedback ratio and phase to maximize the intensity-difference squeezing. In addition, we also study the entanglement properties of this CFC system by the positivity under the partial transposition criterion and find that the feedback ratio and phase can tailor the entanglement structure of the hexapartite state. The proposed CFC scheme has realized quantum correlation enhancement and entanglement manipulation, which can be expanded to a large-scale quantum network for more practical applications in quantum information processing.

DOI
10.1103/physreva.109.062409

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Quantum coherent feedback control (CFC) has been widely applied to prepare and manipulate nonclassical beams. In this paper, we utilize an optical beam splitter with tunable reflectivity kkk as a feedback controller and theoretically construct a CFC system based on four-wave mixing (FWM) processes with a spatially structured pump. After considering absorption loss in the atoms, beam propagation loss in the feedback loop, and detection loss in the detectors, we derive an input-output relationship and theoretically study the manipulation of feedback strength, gain of the FWM processes, and phase to the degree of hexapartite quantum correlation of the system. We find that the relative intensity-difference squeezing degree of all the six output fields from this system is enhanced within a certain range of feedback ratio and phase. Furthermore, there exists an optimal feedback ratio and phase to maximize the intensity-difference squeezing. In addition, we also study the entanglement properties of this CFC system by the positivity under the partial transposition criterion and find that the feedback ratio and phase can tailor the entanglement structure of the hexapartite state. The proposed CFC scheme has realized quantum correlation enhancement and entanglement manipulation, which can be expanded to a large-scale quantum network for more practical applications in quantum information processing.
Coherent feedback control (CFC) has been proven to be a promising approach for manipulating nonclassical light beams. In this paper, a CFC scheme based on the spatial multiplexing cascaded four-wave mixing (FWM) process is proposed, employing a beam splitter as a feedback controller. Considering the absorption loss of the atomic vapor and the transmission loss of the feedback loop, the input–output relationship of the CFC system is derived. Based on this, the quadripartite quantum correlation of the CFC system versus the feedback strength, phase delay of the feedback loop, gain of the FWM process, and the losses is studied. It is found that the quadripartite quantum correlation can be enhanced within a certain range of feedback ratio and phase. Furthermore, there always exists an optimal feedback ratio to maximize the correlation. In addition, the bipartite correlation present in the multiple quantum correlated beams is also investigated. The numerical calculation based on feasible physical parameters of realistic systems provides direct references for the experimental design, which may find applications in quantum communication and quantum metrology.
Quantum steering, as a fundamental resource in quantum information science, is a key resource for secure quantum communication networks. Coherent feedback control (CFC) has been widely used to enhance squeezing. In this paper, we utilize a variable beam splitter (VBS) with a reflectivity of k as the feedback controller to build a coherent feedback control system in four-wave mixing (FWM) processes with a spatially structured pump (SSP). We investigate the influence of feedback strength and interaction intensity on quantum steering across different modes under specific phase delay conditions. The results show that the coherent feedback control system can flexibly control quantum steering. By adjusting the parameters, we can achieve various quantum steering types, especially collective multipartite steering and genuine multipartite steering. It has significant practical application value for secure quantum information processing and offers a theoretical reference for the construction of large-scale, secure quantum networks.
Based on the cascaded four wave mixing processes, a coherent-feedback control system is constructed by utilizing a linear beam splitter as the feedback controller. Considering the loss of optical propagation in the coherent feedback loop and the absorption effect of Rb vapor cells to beams, we theoretically investigate the entanglement properties of this system under different feedback ratio, gain and phase by calculating the covariance matrix of system and applying the positivity under partial transpose (PPT) criterion to all possible bipartitions. The result shows that the genuine tripartite entanglement exists in the coherent feedback control system, but the entanglement structure of system will be destroyed by the excessive feedback. In addition, when the phase is π, we find that the tripartite entanglement can be enhanced by changing the gains and the reflectivity of the beam splitter in the range of 0.1 to 0.4. The results pave the way for manipulating multipartite entanglement by coherent feedback control and have potential application in quantum communication.
Measurement-free coherent feedback control is promising to manipulate various quantum optical systems for preparing nonclassical states of light. In this paper, three different coherent feedback control systems are constructed based on cascaded four-wave mixing processes. By utilizing a beam splitter as the feedback controller, we theoretically investigate the enhancement of tripartite quantum correlation and its pairwise correlation. The absorption effect of Rb vapor cells and the loss of optical propagation in the coherent feedback loop are also taken into account. The quantum correlation in the three structures can be characterized by the degree of relative intensity squeezing of the output fields. We find that the tripartite quantum correlation can be maximally enhanced by an optimal feedback ratio. In addition, two of the three pairwise correlations in the quantum regime can also be improved by tuning the strength of feedback, while the other pairwise correlation remains in the classical regime. Our results pave the way for the experimental implementation and may find potential applications in quantum communication and quantum metrology.
Coherent feedback control (CFC) of multipartite optical entangled states produced by a nondegenerate optical parametric amplifier is theoretically studied. The features of the quantum correlations of amplitude and phase quadratures among more than two entangled optical modes can be controlled by tuning the transmissivity of the optical beam splitter in the CFC loop. The physical conditions to enhance continuous variable multipartite entanglement of optical fields utilizing the CFC loop are obtained. The numeric calculations based on feasible physical parameters of realistic systems provide direct references for the design of experimental devices.
We have experimentally shown in a recent paper [Wang et al., Phys. Rev. A 95, 051802(R) (2017)] that a four-wave mixing (FWM) process in a Rb vapor with a spatially structured pump (SSP), consisting of a coherent combination of two tilted pump beams, can generate six well-separated bright beams that are quantum correlated. The experimental setup is compact, simple, phase insensitive, and easily scalable to a larger number of quantum correlated beams. For applications to quantum information processing, multipartite entanglement is needed in addition to quantum correlations. Very recently, we have also experimentally demonstrated the generation of the hexapartite entanglement from this SSP-based FWM process [Zhang et al., Phys. Rev. Lett. 124, 090501 (2020)]. The purpose of this theoretical paper is to extensively investigate the hexapartite entanglement properties by using different entanglement witnesses such as the van Loock-Furusawa criterion and the positivity under partial transposition criterion. We find that hexapartite entanglement is indeed present among the six beams. In addition, we also study the supermodes of this system using basis change.