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Journal of the Optical Society of America B

Entanglement enhancement from single-port and two-port feedback optical parametric amplifiers

Zhao Zhang, Yashuai Han, Jun Qu

Published Jun 7, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.1364/josab.490019

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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.
In the paper, the intensity-difference squeezing enhancement from a two-port feedback optical parametric amplifier (TFPA) is theoretically discussed. The performance of squeezing enhancement with the TFPA is compared with that of a one-port feedback optical parametric amplifier (OFPA) and a phase-sensitive optical amplifier. For the ideal case, the infinite squeezing can be achieved for both TFPA and OFPA by manipulating the strength of the feedback and the phase delay induced by the feedback loops. Furthermore, the TFPA can realize the all-phase squeezing enhancement. For the lossy case, the TFPA shows unique advantages in squeezing enhancement against the other two schemes. Our results provide new ideas on the generation of high-quality intensity-difference squeezed light, which may find potential applications in quantum information and quantum metrology.
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.
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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.
We present a cascaded system consisting of three nondegenerate optical parametric amplifiers (NOPAs) for the generation and the enhancement of quantum entanglement of continuous variables. The entanglement of optical fields produced by the first NOPA is successively enhanced by the second and the third NOPAs from $\ensuremath{-}5.3$ to $\ensuremath{-}8.1$ dB below the quantum noise limit. The dependence of the enhanced entanglement on the physical parameters of the NOPAs and the reachable entanglement limitation for a given cascaded NOPA system are calculated. The calculation results are in good agreement with the experimental measurements.