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Physical Review A

Bright three-color entangled state produced by cascaded optical parametric oscillators

Aihong Tan, Changde Xie, Kunchi Peng

Published Jan 17, 2012• 16 citations
Publisher

Abstract

We propose a generation system of continuous-variable (CV) three-color entangled state of bright optical beams based on two cascaded standard nondegenerate optical parametric oscillators (NOPOs) above the threshold. One of signal and idler beams produced by the first NOPO is used for the pump light of the second NOPO. The three-color entanglement among signal and idler beams produced by the second NOPO and the retained another beam of the first NOPO is theoretically demonstrated. The symplectic eigenvalues of the partial transposition covariance matrix of the generated optical entangled state are numerically calculated in terms of experimentally reachable system parameters. The optimal operation conditions of the cascaded NOPOs system for obtaining high entanglement are found. The calculated results explicitly demonstrate that the OPO action can transfer entanglement. Due to that the cavity parameters and the nonlinear crystals of the two NOPOs can be freely chosen, the flexibility of the proposed protocol is relatively good and the system can be also extended to prepare entangled states with more parts easily.

DOI
10.1103/physreva.85.013819

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We propose a generation system of continuous-variable (CV) three-color entangled state of bright optical beams based on two cascaded standard nondegenerate optical parametric oscillators (NOPOs) above the threshold. One of signal and idler beams produced by the first NOPO is used for the pump light of the second NOPO. The three-color entanglement among signal and idler beams produced by the second NOPO and the retained another beam of the first NOPO is theoretically demonstrated. The symplectic eigenvalues of the partial transposition covariance matrix of the generated optical entangled state are numerically calculated in terms of experimentally reachable system parameters. The optimal operation conditions of the cascaded NOPOs system for obtaining high entanglement are found. The calculated results explicitly demonstrate that the OPO action can transfer entanglement. Due to that the cavity parameters and the nonlinear crystals of the two NOPOs can be freely chosen, the flexibility of the proposed protocol is relatively good and the system can be also extended to prepare entangled states with more parts easily.
Entangled states of light including low-loss optical fiber transmission and atomic resonance frequencies are essential resources for future quantum information networks. We present the experimental achievement on the three-color entanglement generation at 852, 1550, and 1440 nm wavelengths for optical continuous variables. The entanglement generation system consists of two cascaded nondegenerated optical parametric oscillators (NOPOs). The flexible selectivity of nonlinear crystals in the two NOPOs and the tunable property of NOPO provide large freedom for the frequency selection of three entangled optical beams. The presented system will hopefully be developed as a practical entangled source to be used in quantum-information networks with atomic storage units and long fiber transmission lines.
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 show that scalable multipartite entanglement among light fields may be generated by optical parametric oscillators (OPOs). The tripartite entanglement existent among the three bright beams produced by a single OPO---pump, signal, and idler---is scalable to a system of many OPOs by pumping them in cascade with the same optical field. This latter serves as an entanglement distributor. The special case of two OPOs is studied, as it is shown that the resulting five bright beams share genuine multipartite entanglement. In addition, the structure of entanglement distribution among the fields can be manipulated to some degree by tuning the incident pump power. The scalability to many fields is straightforward, allowing an alternative implementation of a multipartite quantum information network with continuous variables.
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.
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.
We investigate semiclassical dynamics and quantum properties of light beams generated in time-modulated nondegenerate optical parametric oscillator (NOPO). Having in view production of continuous-variable (CV) entangled states of light beams we propose two experimentally feasible schemes of NOPO: (i) driven by continuously modulated pump field; (ii) under action of a periodic sequence of identical laser pulses. It is shown that the time modulation of pump field amplitude essentially improves the degree of CV entanglement in NOPO. On the whole the level of integral two-mode squeezing, which characterizes the degree of CV entanglement, goes below the standard limit established in an ordinary NOPO with monochromatic pumping. We develop semiclassical and quantum theories of these devices for both below- and above-threshold regimes of generation. Properties of CV entanglement for various operational regimes of the devices are discussed in the time domain in application to time-resolved quantum information technologies. Our analytical results are in well agreement with the results of numerical simulation and support a concept of CV entangled states of time-modulated light beams.