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Communications in Theoretical Physics

Entangled State Representation for Four-Wave Mixing

Ma Shan-Jun, Lu Hai-Liang, Fan Hong-Yi

Published Aug 1, 2008• 2 citations
Publisher

Abstract

We introduce the entangled state representation to describe the four-wave mixing. We find that the four-wave mixing operator, which engenders the correct input-output field transformation, has a natural representation in the entangled state representation. In this way, we see that the four-wave mixing process not only involves squeezing but also is an entanglement process. This analysis brings convenience to the calculation of quadrature-amplitude measurement for the output state of four-wave mixing process.

DOI
10.1088/0253-6102/50/2/42

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We introduce the entangled state representation to describe the four-wave mixing. We find that the four-wave mixing operator, which engenders the correct input-output field transformation, has a natural representation in the entangled state representation. In this way, we see that the four-wave mixing process not only involves squeezing but also is an entanglement process. This analysis brings convenience to the calculation of quadrature-amplitude measurement for the output state of four-wave mixing process.
A maximal joint quadrature squeezing of -6.8±0.4 dB is experimentally obtained by a scheme of cascaded four-wave mixing (FWM) processes, which gives strong proof about the inseparability or entanglement between output of the twin beams from the system. Here joint quadrature is the difference between the two quadratures of the twin beam output from the cascaded FWM processes. This result is enhanced by about 3.1 dB, compared with the one of the single FWM process. We also study the gain dependence of the entanglement enhancement in this cascaded system. Theoretical predictions with the considerations of the losses in the experiment are also studied, and a similar trend in the low-gain regime can be found between the experimental results and the theoretical predictions. The scheme of cascaded FWM processes, which can be used to improve or even manipulate the degree of the entanglement between the output fields from the single FWM process, may find its applications in the continuous-variable quantum communication protocols.
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.