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arXiv:1201.1163 · Physical Review A

Coherent feedback control of multipartite quantum entanglement for optical fields

Zhihui Yan, Xiaojun Jia, Changde Xie, Kunchi Peng

Published Dec 6, 2011• 43 citations
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Abstract

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.

DOI
10.1103/physreva.84.062304

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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.
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.
The non-measurement based coherent feedback control (CFC) is a control method without introducing any backaction noise into the controlled system, thus is specially suitable to manipulate various quantum optical systems for preparing nonclassical states of light. By simply tuning the transmissivity of an optical controller in a CFC loop attached to a non-degenerate optical parametric amplifier (NOPA), the quantum entanglement degree of the output optical entangled state of the system is improved. At the same time, the threshold pump power of the NOPA is reduced also. The experimental results are in reasonable agreement with the theoretical expectation.
Quantum entanglement shared by more than two partites is the essential bases for developing quantum communication networks and quantum computation. The multipartite entanglement of continuous variables can be generated by distributing or combining squeezed states of light using linear optics. We experimentally obtained a tripartite entangled state of bright optical field by means of a nondegenerate optical parametric amplifier (NOPA) and optical beam-splitters. The NOPA is operated in the state of parametric deamplification by locking the relative phase between the pump laser and the injected seed wave to (2n+1)π, so the generated Einstein-Podolsky-Rosen (EPR) beam for continuous variables is an entangled state of light with the quantum correlation of phase quadratures and the quantum anticorrelation of amplitude quadratures [1]. The output EPR beam consists of two frequency-degenerate optical modes with horizontal and vertical polarizations which are distributed to three parties with two linear beam-splitters. We have theoretically and experimentally demonstrated the three parties are in a tripartite entangled state with three-mode “position” (amplitude quadrature) correlation and relative “momentum” (phase quadrature) correlation [2]-[4]. The obtained GHZ-like state is a fully inseparable tripartite continuous-variables state violating the three inequalities used for the criterion of the inseparability [5][6]. The controlled dense coding quantum communication is experimentally accomplished by exploiting the tripartite entanglement. The three entangled modes are sent to a sender (Alice), a receiver (Bob) and a controller (Claire), respectively. The information transmission capacity of the quantum channel between Alice and Bob is controlled by Claire. The channel capacity completed under Claire’s help is always larger than that without her help.
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.
Abstract This study is based on a theoretical proposal for the generation and enhancement of multipartite entanglements of indirectly coupled modes using the coherent feedback loop scheme. The coherent feedback‐control mechanism that is presented here significantly improves the bipartite and tripartite entanglements among the indirectly coupled modes. The numerical study shows that the entanglements can be sufficiently tuned by the effective couplings and the reflective parameter of the beam splitter. In addition, the robustness and survival of the generated entanglement in the proposed system have shown to be significantly dependent on the reflectivity parameter. The existence of a genuine tripartite entanglement state in the dynamical state of the system is proven. Finally, the effect of the reflective parameter on three different tripartite entanglements is observed. The findings pave the way for tuning and enhancing multipartite entanglements of indirectly coupled modes in current cavity Opto‐magnomechanical systems and may have various vital applications in quantum information.
Coherent feedback control has been proved to be an effective approach in entanglement enhancement of the entangled states produced by a nondegenerate optical parametric amplifier (NOPA). However, the present research mainly focuses on a two-port feedback NOPA (TFPA). In this study, a scheme of single-port feedback NOPA (SFPA) is proposed and investigated. For the ideal case, both SFPA and TFPA have the potential to realize an infinite degree of entanglement. For the practical case with feasible physical parameters of realistic systems, the features of entanglement enhancement for two schemes are compared. The effect of entanglement enhancement for SFPA is relatively weaker than that of TFPA, but has a loose phase-locking accuracy requirement. Our results may provide useful references on the control of nonclassical light fields.