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Acta Physica Sinica

Quantum entanglement in coherent feedback system based on the cascaded four wave mixing processes

Yinyin Zhong, Xiaozhou Pan, Jietai Jing

Published Jan 1, 2020• 2 citations
Publisher

Abstract

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.

DOI
10.7498/aps.69.20200042

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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.
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.
We investigate the possibility of an experimentally feasible cascaded four-wave mixing (FWM) system [Phys. Rev. Lett. 113, 023602 (2014)] to generate tripartite entanglement. We verify that genuine tripartite entanglement is present in this system by calculating the covariances of three output beams and then considering the violations of the inequalities of the three-mode entanglement criteria, such as two-condition criterion, single-condition criterion, optimal single-condition criterion and the positivity under partial transposition (PPT) criterion. We also consider the possibilities of the bipartite entanglement of any pair of the three output beams using the Duan-Giedke-Cirac-Zoller criterion and PPT criterion. We find that the tripartite entanglement and the bipartite entanglement for the two pairs are present in the whole gain region. The entanglement characteristics under different entanglement criteria are also considered. Our results pave the way for the realization and application of multipartite entanglement based on the cascaded FWM processes.
As a crucial quantum resource in quantum information processing, multipartite entanglement plays an important role not only in the field of testing basic quantum effects, but also in the applications of quantum network, quantum communication and quantum computing. The generation of multipartite entanglement usually involves many complex linear processes and nonlinear processes. In this paper, we theoretically propose a scheme for generating genuine quadripartite entanglement by linking two independent four-wave mixing (FWM) processes with one linear beam splitter (BS). Here, we use one linear BS to mix the probe beams amplified by two independent FWM processes. We first set the transmissivity of the linear BS to be 0.5 and study the effect of the intensity gain of the system on quadripartite entanglement by applying the positivity under partial transposition (PPT) criterion. The results show that there exists genuine quadripartite entanglement in all gain regions, and the degree of entanglement increases with intensity gain increasing. And then, the dependence of quadripartite entanglement on the transmissivity of the linear BS is studied when the intensity gains of two independent FWM processes are both set to be 3. We find that the transmissivity of the linear BS can affect the entanglement properties of the system. At the same time, we also find that the system can generate genuine quadripartite entanglement when the transmissivity of the linear BS is not equal to 0 or 1. Finally, in order to reveal the entanglement structure of the system, we further investigate the dependence of the possible tripartite entanglement and bipartite entanglement on the intensity gain of the system by using the PPT criterion. The results show that there exists the genuine tripartite entanglement in this system, and the degree of entanglement increases as the intensity gain increases. However, there exists no genuine bipartite entanglement in this system, some of bipartite states are always separable, and the entanglement of the other bipartite states gradually become weak and eventually disappear with the increase of the intensity gain. Our theoretical result provides a simple and reliable scheme for generating genuine quadripartite entanglement by using FWM process in atomic ensemble and linear BS.
Multipartite entanglement is an important resource in quantum information. For its generation and manipulation, optical losses are inevitable experimental imperfections that cannot be ignored. In this paper, by using the positivity under partial transposition criterion, we theoretically characterize the effect of losses on two multipartite entanglement cases, tripartite entanglement and quadripartite entanglement, which are generated by cascaded four-wave mixing processes. The characterization of entanglement is made possible by calculating the smallest symplectic eigenvalues of the partially transposed covariance matrix. It is verified that when the power gains are smaller than 5, both the tripartite and the quadripartite entanglement can be maintained under the realistic experimental condition (less than 20% losses). In addition, we also study how the losses will affect the entanglement of subsystems in both cases. Our results pave the way for the experimental implementation of multipartite entanglement in cascaded four-wave mixing processes.