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Optics Letters

Entanglement in a four-wave mixing process

Zhan Zheng, Hailong Wang, Bing Cheng, Jietai Jing

Published Jul 7, 2017• 10 citations
Publisher

Abstract

We investigate different kinds of entanglement in a four-wave mixing process with a degenerate pump. After analyses on means and quantum fluctuations of the three output beams (Stokes, anti-Stokes, and pump), we verify the existence of genuine tripartite entanglement, and quantify bipartite, two-mode, as well as tripartite entanglement with the covariance matrix. We find out that the input pump power and the nonlinear coupling strength are the physical origins to enhance entanglement at a given photon loss.

DOI
10.1364/ol.42.002754

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We investigate different kinds of entanglement in a four-wave mixing process with a degenerate pump. After analyses on means and quantum fluctuations of the three output beams (Stokes, anti-Stokes, and pump), we verify the existence of genuine tripartite entanglement, and quantify bipartite, two-mode, as well as tripartite entanglement with the covariance matrix. We find out that the input pump power and the nonlinear coupling strength are the physical origins to enhance entanglement at a given photon loss.
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.
We experimentally demonstrate the various intermodal and intramodal four-wave mixing processes in a few-mode fiber with three modes using non-degenerate pumps. We distinguish the processes by calculating their phase mismatch and identify the intermodal spontaneous four-wave mixing process that generates entangled photon pairs in various modes. We achieve this using continuous-wave beams and the seeding technique due to the low efficiency of the spontaneous four-wave mixing effect in the fiber. We seeded the Stokes and anti-Stokes waves and measured the spectral content of each mode while moving the seed away from the perfect phase-matched condition in the fiber under test. We observe that the closer the seed gets to the pumps, the higher the efficiency of the four-wave mixing process.
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.
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.