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Physical Review A

Two-color continuous-variable quantum entanglement in a singly resonant optical parametric oscillator

Domenico Cuozzo, Gian‐Luca Oppo

Published Oct 5, 2011• 6 citations
Publisher

Abstract

We apply the input-output theory of optical cavities to formulate a quantum treatment of a continuous-wave singly resonant optical parametric oscillator. This case is mainly relevant to highly nondegenerate signal and idler modes. We show that both intensity and quadrature squeezing are present and that the maximum noise reduction below the standard quantum limit is the same at the signal and idler frequencies as in the doubly resonant case. As the threshold of oscillation is approached, however, the intensity-difference and quadrature spectra display a progressive line narrowing which is absent in the balanced doubly resonant case. By use of the separability criterion for continuous variables, the signal-idler state is found to be entangled over wide ranges of the parameters. We show that attainable levels of squeezing and entanglement make singly resonant configurations ideal candidates for two-color quantum information processes, because of their ease of tuning in experimental realizations.

DOI
10.1103/physreva.84.043810

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We apply the input-output theory of optical cavities to formulate a quantum treatment of a continuous-wave singly resonant optical parametric oscillator. This case is mainly relevant to highly nondegenerate signal and idler modes. We show that both intensity and quadrature squeezing are present and that the maximum noise reduction below the standard quantum limit is the same at the signal and idler frequencies as in the doubly resonant case. As the threshold of oscillation is approached, however, the intensity-difference and quadrature spectra display a progressive line narrowing which is absent in the balanced doubly resonant case. By use of the separability criterion for continuous variables, the signal-idler state is found to be entangled over wide ranges of the parameters. We show that attainable levels of squeezing and entanglement make singly resonant configurations ideal candidates for two-color quantum information processes, because of their ease of tuning in experimental realizations.
Following the analytical work of Ref. [1], a numerical analysis of squeezing and quantum entanglement in a continuous wave singly-resonant optical parametric oscillator approaching threshold is provided. The singly resonant case is mainly relevant to largely non-degenerate signal and idler modes (two-colour output). As the threshold of oscillation is approached the numerical spectra of the intensity difference confirm squeezing of quantum fluctuations and a progressive line-narrowing in the linear case. In the nonlinear case entanglement is confirmed although progressively reduced when approaching threshold with the squeezing spectra still displaying a narrowing of the spectral line. Modification of quantum entanglement approaching threshold is also evaluated via the condition of state inseparability.
We calculate the quantum correlations existing among the three output fields (pump, signal, and idler) of a triply resonant nondegenerate optical parametric oscillator operating above threshold. By applying the standard criteria [P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003)], we show that strong tripartite continuous-variable entanglement is present in this well-known and simple system. Furthermore, since the entanglement is generated directly from a nonlinear process, the three entangled fields can have very different frequencies, opening the way for multicolored quantum information networks.
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We report the observation of nonclassical quantum correlations of continuous light variables from an altogether different type of source. It is a frequency nondegenerate optical parametric oscillator below threshold, where signal and idler fields are separated by 740 MHz corresponding to two free spectrum ranges of the parametric oscillator cavity. The degree of entanglement observed, $\ensuremath{-}3.8\mathrm{dB},$ is the highest to date for a narrow-band tunable source suitable for atomic quantum memory and other applications in atomic physics. Finally we use the latter to visualize the Einstein-Podolsky-Rosen paradox.
We explore in detail the possibility of intracavity generation of continuous-variable (CV) entangled states of light beams under mode phase-locked conditions. We show that such quantum states can be generated in a self-phase-locked nondegenerate optical parametric oscillator (NOPO) based on type II phase-matched down-conversion combined with a linear mixer of two orthogonally polarized modes of the subharmonics in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both subthreshold and above-threshold operational regimes. We show that the system providing high-level phase coherence between two generated modes, unlike the ordinary NOPO, also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the CV entanglement as two-mode squeezing and show that the maximal degree of the integral two-mode squeezing (which is 5050%50 relative to the level of vacuum fluctuations) is achieved at the pump field intensity close to the generation threshold of a self-phase-locked NOPO, provided that the constant of linear coupling between the two polarizations is much less than the mode detunings. The peculiarities of CV entanglement for the case of unitary, nondissipative dynamics of the system under consideration are also cleared up.
The quantum correlations between the output signal, the output idler and the reflected pump fields generated by non-degenerate optical parametric oscillator operating above the oscillation threshold are theoretically calculated with the semi-classical formulae. According to the multipartite entanglement criteria for the continuous variables, proposed by P. van Loock and A. Furusawa, the calculated results prove the existence of the quantum correlations between the amplitude and the phase quadrature for the three optical fields, i. e. they form a tripartite entangled state. We numerically calculate the dependence of the entanglement on the physical parameters of the optical oscillator and find the optimum operating conditions of the oscillator to produce the three-color tripartite entangled state, which provide the direct references for the design of the continuous variable multipartite entanglement generation systems.