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Coherent feedback enabled distributed generation of entanglement between propagating Gaussian fields

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Abstract

In this paper, we show how Einstein–Podolsky–Rosen-like entanglement between a pair of spatially separated propagating continuous-mode Gaussian fields can be generated via a coherent feedback loop that connects two spatially distant nondegenerate optical parametric amplifiers (NOPAs) over two transmission channels. In particular, the scheme generates entanglement in a distributed manner using spatially distributed resources. It is shown that similar to a single NOPA, the coherent feedback scheme has parameters that determine the achievable frequency-dependent two-mode squeezing and entanglement bandwidth between the pair of continuous-mode fields. It is also shown that in ideal scenarios, the feedback connection is able to yield an increase in the quality of the entanglement while consuming less power, compared to conventional distribution of entanglement using a single NOPA and a two-cascaded NOPA system. Furthermore, in contrast to the two conventional systems, under the same pump power, the coherent feedback system provides more entanglement in the presence of transmission losses, which indicates that the feedback scheme increases tolerance to transmission losses.

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Notes

  1. Note that [4] and the formula (6) takes \(\xi ^q_{\mathrm{out},a}-\xi ^q_{\mathrm{out},b}\) and \(\xi ^p_{\mathrm{out},a}+\xi ^p_{\mathrm{out},b}\) as the squeezed two-mode quadratures rather than \(\xi ^q_{\mathrm{out},a}+\xi ^q_{\mathrm{out},b}\) and \(\xi ^p_{\mathrm{out},a}-\xi ^p_{\mathrm{out},b}\), respectively. To obtain squeezing in the latter quadratures, as in this paper, in the single NOPA one need only take \(\epsilon <0\) and the formula (6) is modified to be \(V_{\pm }(0)= 2\frac{(1+k)^2}{(1-k)^2}\).

  2. See [21, 22] for experiments on the entanglement produced by cascading two or more NOPAs.

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Authors and Affiliations

  1. School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, NSW, 2052, Australia

    Zhan Shi & Hendra I. Nurdin

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  1. Zhan Shi
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  2. Hendra I. Nurdin
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Correspondence to Hendra I. Nurdin.

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Shi, Z., Nurdin, H.I. Coherent feedback enabled distributed generation of entanglement between propagating Gaussian fields. Quantum Inf Process 14, 337–359 (2015). https://doi.org/10.1007/s11128-014-0845-4

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