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Journal of the Optical Society of America B

Generating multiplexed entanglement frequency comb in a nondegenerate optical parametric amplifier

Rongguo Yang, Jing Zhang, Shuqin Zhai, Kui Liu, Junxiang Zhang, Jiangrui Gao

Published Jan 9, 2013• 11 citations
Publisher

Abstract

In this paper, we propose a scheme to produce a multiplexed entanglement frequency comb in a type II phase-matching nondegenerate optical parametric amplifier (NOPA) operating below threshold. The entanglement of the signal and idler frequency combs in the wide frequency range, which is limited by the phase-matching bandwidth of the NOPA, is investigated by the inseparability criterion. Furthermore, N Einstein–Podolsky–Rosen pairs can be created from the two combs without any reduction in the correlations by using frequency-dependent beam splitters.

DOI
10.1364/josab.30.000314

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In this paper, we propose a scheme to produce a multiplexed entanglement frequency comb in a type II phase-matching nondegenerate optical parametric amplifier (NOPA) operating below threshold. The entanglement of the signal and idler frequency combs in the wide frequency range, which is limited by the phase-matching bandwidth of the NOPA, is investigated by the inseparability criterion. Furthermore, N Einstein–Podolsky–Rosen pairs can be created from the two combs without any reduction in the correlations by using frequency-dependent beam splitters.
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.
The quantum fluctuations and correlations of the output signal and idler beams from a type-II polarization nondegenerate optical parametric amplifier (NOPA) inside an optical cavity are investigated theoretically, which is driven by the different kinds of quantized fields such as the two-mode thermal field, the phase-conjugate state, and a pair of EPR beams at the signal and idler frequency. Spectral line shapes due to quantum interferences between the input quantum fields and the generated down-converted subharmonic fields of NOPA are studied by scanning the length of the NOPA cavity. The entanglement degree of the EPR entangled beams injected into the NOPA as signal and idler beams can be increased or decreased, which are realized by controlling the relative phase between the pump beam and the injected beams for the NOPA. The results demonstrate coherent phenomena of NOPA in the quantum regime and show phase-sensitive manipulations of quantum entanglement for quantum information processing.
We experimentally demonstrate that the quantum entanglement between amplitude and phase quadratures of optical modes produced from a nondegenerate optical parametric amplifier (NOPA) can be enhanced and manipulated phase sensitively by means of another NOPA. When both NOPAs operate at deamplification, the entanglement degree is increased at the cavity resonance of the second NOPA. When the first NOPA operates at deamplification and the second one at amplification, the spectral features of the correlation variances are significantly changed. The experimental results are in good agreement with the theoretical expectation.
The solution of the time-dependent periodic pumping non-degenerate optical parametric amplifier (NOPA) is derived when the pump depletion is considered both above and below thresholds. Based on this solution, the quantum fluctuation calculated shows that a high entanglement and a good squeezing degree of the parametric light beams are achieved near and above thresholds. We adopt two kinds of pump fields: (i) a continuously modulated pump with a sinusoidal envelope; (ii) a sequence of laser pulses with Gaussian envelopes. We analyse the time evolution of continuous variable entanglement by analytical and numerical calculations, and show that the periodic driven pumping also improves the degree of entanglement. The squeezing and Einstein–Podolsky–Rosen (EPR) entanglement by using the two pumping driven functions are investigated from below to above the threshold regions, the tendencies are nearly the same, and the Gaussian driven function is superior to that of the sine driven function, when the maximum squeezing and the minimum variance of quantum fluctuation are considered. In the meantime, the generalization of frequency degenerate OPA to frequency non-degenerated OPA problem is investigated.
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.
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.