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Australian Control Conference

End-to-end entanglement in a coherent feedback interconnection of three nondegenerate optical parametric amplifiers

Zhan Shi, Hendra I. Nurdin

Published Nov 1, 2014• 0 citations
Publisher

Abstract

In previous work we have shown that a dual nondegenerate optical parametric amplifier (NOPA) coherent feedback network tolerates transmission losses better and has stronger entanglement (i.e., enhanced two-mode squeezing) than a single NOPA over the same transmission distance. The aim of this paper is to investigate stability, entanglement degree and power consumption of a coherent feedback interconnection of three NOPAs, which connects two spatially separated parties over two transmission channels. The influence of transmission losses in the transmission channels is considered and numerical calculations are given to illustrate advantages for entanglement generation of the triple-NOPA coherent feedback network over a dual-NOPA coherent feedback system.

DOI
10.1109/aucc.2014.7358676

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In previous work we have shown that a dual nondegenerate optical parametric amplifier (NOPA) coherent feedback network tolerates transmission losses better and has stronger entanglement (i.e., enhanced two-mode squeezing) than a single NOPA over the same transmission distance. The aim of this paper is to investigate stability, entanglement degree and power consumption of a coherent feedback interconnection of three NOPAs, which connects two spatially separated parties over two transmission channels. The influence of transmission losses in the transmission channels is considered and numerical calculations are given to illustrate advantages for entanglement generation of the triple-NOPA coherent feedback network over a dual-NOPA coherent feedback system.
This paper is concerned with linear quantum networks of NNN nondegenerate optical parametric amplifiers (NOPAs), with NNN up to 6, which are interconnected in a coherent feedback chain. Each network connects two communicating parties (Alice and Bob) over two transmission channels. In previous work we have shown that a dual-NOPA coherent feedback network generates better Einstein-Podolsky-Rosen (EPR) entanglement (i.e., more two-mode squeezing) between its two outgoing Gaussian fields than a single NOPA, when the same total pump power is consumed and the systems undergo the same transmission losses over the same distance. This paper aims to analyze stability, EPR entanglement between two outgoing fields of interest, and bipartite entanglement of two-mode Gaussian states of cavity modes of the NNN-NOPA networks under the effect of transmission and amplification losses, as well as the effect of time delays on the outgoing fields. It is numerically shown that, in the absence of losses and delays, the network with more NOPAs in the chain requires less total pump power to generate the same degree of EPR entanglement. Moreover, we report on the internal entanglement synchronization that occurs in the steady state between certain pairs of Gaussian oscillator modes inside the NOPA cavities of the networks.
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In this paper we show how Einstein-Podolski-Rosen (EPR)-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 shown that in ideal scenarios, in the absence and presence of transmission losses, the feedback connection is able to provide a moderate increase in the quality of entanglement while achieving this in a more efficient manner by consuming less power, compared to conventional distribution of entanglement using a single NOPA.
This paper presents formulae for Einstein-Podolsky-Rosen (EPR) entanglement generated from N nondegenerate optical parametric amplifiers (NOPAs) interconnected in a linear coherent feedback (CFB) chain in the idealized lossless scenario and infinite bandwidth limit. The lossless scenario sets the ultimate EPR entanglement (two-mode squeezing) that can be achieved by this linear chain of NOPAs while the infinite bandwidth limit simplifies the analysis but gives an accurate approximation to the EPR entanglement at low frequencies of interest. Two adjustable phase shifts are placed at the outputs of the system to achieve the best EPR entanglement by selecting appropriate quadratures of the output fields.
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.
How to achieve the maximal entanglement, for given finite entanglement resources? In this paper, we propose a two-port feedback optical parametric amplifier (TFPA) consisting of a nondegenerate optical parametric amplifier (NOPA) and two linear beam splitters. The former is an entanglement resource, and the latter serve as feedback controllers that feed the two entangled beams generated from the NOPA back into its input ports. By manipulating the reflectivity of the beam splitters and the phase delays introduced by the feedback paths, an entanglement enhancement can be achieved by the TFPA. Furthermore, we demonstrate that such entanglement enhancement can happen at all phase points for the ideal case, and the maximal entanglement can be infinitely large. For the lossy case, our TFPA also has its unique advantages in the robustness of the losses of the system.