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Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of a self-phase-locked nondegenerate optical parametric oscillator with nonsymmetric feedback loops

Robert Olkiewicz, Mariusz Żaba

Published Oct 7, 2009• 2 citations
Publisher

Abstract

We discuss the evolution of two-mode states of a self-phase-locked type-II nondegenerate optical parametric oscillator with homodyne-mediated quantum feedback. It is shown that different strengths of the feedback loops can simulate the effect of a squeezed thermal environment and lead additionally to the process of the parametric-down conversion for each mode. In the steady state regime all initial density matrices evolve towards a Gaussian equilibrium state. It is shown that the nonsymmetric feedback can further increase entanglement of the equilibrium state. Dynamical behaviour of intracavity entanglement for a number of initial states is investigated, and entanglement sudden death and birth phenomena, and a delay birth of entanglement are reported.

DOI
10.1088/0953-4075/42/20/205504

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We discuss the evolution of two-mode states of a self-phase-locked type-II nondegenerate optical parametric oscillator with homodyne-mediated quantum feedback. It is shown that different strengths of the feedback loops can simulate the effect of a squeezed thermal environment and lead additionally to the process of the parametric-down conversion for each mode. In the steady state regime all initial density matrices evolve towards a Gaussian equilibrium state. It is shown that the nonsymmetric feedback can further increase entanglement of the equilibrium state. Dynamical behaviour of intracavity entanglement for a number of initial states is investigated, and entanglement sudden death and birth phenomena, and a delay birth of entanglement are reported.
We investigate the enhancement of the intracavity entanglement of a self-phase-locked type-II nondegenerate optical parameter oscillator (SPL NOPO) via homodyne-mediated quantum feedback. It is found that the feedback can effectively enhance the squeezing, entanglement, and purity of the two-mode field in the SPL NOPO. Especially for an ordinary NOPO, our feedback scheme can simulate a standard two-mode squeezed vacuum environment and a pure steady two-mode squeezed vacuum cavity field can be generated, different from the scheme proposed by Mancini [Phys. Rev. A 73, 010304(R) (2006)] in which only a mixed two-mode entangled state is generated.
We explore in detail the possibility of generation of continuous-variable (CV) entangled states of light fields with well-localized phases. We show that such quantum states, called entangled self-phase locked states, can be generated in nondegenerate optical parametric oscillator (NOPO) based on a type-II phase-matched down-conversion combined with polarization mixer in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both sub-threshold and above-threshold operational regimes. We show that the system providing relative phase coherence between two generated modes also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the entanglement as two-mode squeezing and show that CV entanglement is realized for both unitary, non-dissipative dynamics and for dissipative NOPO in the entire range of pump field intensities.
A study of an open nondegenerate parametric oscillator is presented below threshold in the undepleted pump regime with time-delayed coherent feedback. The figure of merit is the two-mode squeezing spectrum measuring the strength of continuous-variable Einstein-Podolsky-Rosen-type entanglement between the down-converted modes in the output field as a function of frequency. Exploring different areas of the parameter space reveals the possibility of significantly enhanced entanglement with tunable characteristic frequency. This is a result of the emerging dynamical features that are only accessible due to delayed feedback. The system is very sensitive to phase matching, which can be adjusted by various parameters of the system and the feedback loop. In this way, sharp, resonancelike features are obtained that show a level of robustness against extraneous losses.
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.
We investigate quantum properties of phase-locked light beams generated in a nondegenerate optical parametric oscillator (NOPO) with an intracavity waveplate. This investigation continues our previous analysis presented in Phys. Rev. A 69, 053814 (2004), and involves problems of continuous-variable quadrature entanglement in the spectral domain, photon-number correlations as well as the signatures of phase-locking in the Wigner function. We study the role of phase-localizing processes on the quantum correlation effects. The peculiarities of phase-locked NOPO in the self-pulsing instability operational regime are also cleared up. The results are obtained in the PPP-representation as a quantum-mechanical calculation in the framework of stochastic equations of motion, as well as by numerical simulation based on the method of quantum state diffusion.