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Physical Review A

Generation of hexapartite entanglement in a four-wave-mixing process with a spatially structured pump: Theoretical study

Hailong Wang, Kai Zhang, Nicolas Treps, Claude Fabre, Jun Zhang, Jietai Jing

Published Aug 21, 2020• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.102.022417

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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.
Multipartite entanglement serves as a vital resource for quantum information processing. Generally, its generation requires complex beam splitting processes which limit scalability. A promising trend is to integrate multiple nonlinear processes into a single device via frequency or time multiplexing. The generated states in these schemes are useful for quantum computation. However, they are confined in one or two beams and hard to be spatially separated for applications in quantum communication. Here, we experimentally demonstrate a scheme to generate spatially separated hexapartite entangled states by means of spatially multiplexing seven concurrent four-wave mixing processes. In addition, we show that the entanglement structure characterized by subsystem entanglement distribution can be modified by appropriately shaping the pump characteristics. Such reconfigurability of the entanglement structure gives the possibility to target a desired multipartite entangled state for a specific quantum communication protocol. Our results here provide a new platform for generating large scale spatially separated reconfigurable multipartite entangled beams.
Multimode quantum resources or states, in which quantum correlations are shared and distributed among multiple parties, are important not only for fundamental tests of quantum effects but also for their numerous possible applications in quantum technologies, such as quantum imaging and quantum metrology. Here we demonstrate the single-step fabrication of a multimode quantum resource from four-wave mixing (FWM) process in hot Rb vapor using a spatially structured pump, which consists of a coherent combination of two tilted pump beams. During this FWM process, one probe beam is amplified, three conjugate and two new probe beams are generated. The measured degrees of the intensity squeezing for the four-beam case and six-beam case are around $\ensuremath{-}4.1\ifmmode\pm\else\textpm\fi{}0.1$ dB and $\ensuremath{-}4.7\ifmmode\pm\else\textpm\fi{}0.1$ dB, respectively. The generated multiple quantum correlated beams are naturally separated with distinct directions, which is crucial for sending them out to quantum nodes at different locations in quantum communication. Our scheme is compact, simple, phase insensitive, and easily scalable to larger number of quantum-correlated modes.
We propose an experimentally feasible scheme to produce bright quadricolor continuous-variable (CV) entanglement by a four-wave mixing process (FWM) with four-level atoms inside the optical ring cavities operating above threshold. The Stokes and anti-Stokes beams are generated via the pump beam (tuned close to one atomic transition) and the coupling beam (tuned to the resonance of another atomic transition), respectively. The quadruply resonant and narrowed linewidth of the cavity fields with different frequencies are achieved and quadricolor CV entanglement among the four cavity fields is demonstrated according to the criterion proposed by van Loock and Furusawa [Phys. Rev. A 67, 052315 (2003)]. This scheme provides a way to generate bright quadricolor CV entanglement and will be significant for applications in quantum information processing and quantum networks.
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.
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.
Quantum correlations and entanglement shared among multiple modes are fundamental ingredients of most continuous-variable quantum technologies. Recently, a method used to generate multiple quantum correlated beams using cascaded four-wave mixing (FWM) processes was theoretically proposed and experimentally realized by our group [Z. Qin et al., Phys. Rev. Lett. 113, 023602 (2014)]. Our study of triple-beam quantum correlation paves the way to showing the tripartite entanglement in our system. Our system also promises to find applications in quantum information and precision measurement such as the controlled quantum communications, the generation of multiple quantum correlated images, and the realization of a multiport nonlinear interferometer. For its applications, the degree of quantum correlation is a crucial figure of merit. In this letter, we experimentally study how various parameters, such as the cell temperatures, one-photon, and two-photon detunings, influence the degree of quantum correlation between the triple beams generated from the cascaded two-FWM configuration.