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Journal of Contemporary Physics (Armenian Academy of Sciences)

Entanglement of states and quantum distributions in pulsed optical parametric oscillator

N. H. Adamyan, Gagik Yu. Kryuchkyan

Published Apr 1, 2008• 1 citation
Publisher

Abstract

The time-domain properties of Einstein-Podolsky-Rosen (EPR) entangled states of light are studied by means of analysis of both the Wigner functions and variance of quadrature amplitudes of generated modes. As a source of EPR states a non-degenerate optical parametric oscillator is considered driven by a sequence of laser pulses with a Gaussian time envelope.

DOI
10.3103/s1068337208020023

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The time-domain properties of Einstein-Podolsky-Rosen (EPR) entangled states of light are studied by means of analysis of both the Wigner functions and variance of quadrature amplitudes of generated modes. As a source of EPR states a non-degenerate optical parametric oscillator is considered driven by a sequence of laser pulses with a Gaussian time envelope.
We investigate time-dependent properties of Einstein-Podolsky-Rosen (EPR) light beams generated in a nondegenerate optical parametric oscillator (NOPO) driven by a sequence of laser pulses with Gaussian time-dependent envelopes. This investigation continues our previous analysis [H. H. Adamyan and G. Yu. Kryuchkyan, Phys. Rev. A 74, 023810 (2006)] and involves problems of two-mode quadrature squeezing as well as intensity-difference squeezing in the time domain. The peculiarities of EPR beams are also discussed in the framework of phase-space quantum distributions. Two kinds of non-Gaussian Wigner functions, for the reduced one-mode state of periodically pulsed NOPO and for EPR beams which are combined on a one-half beam splitter are calculated numerically. We also investigate the Wigner functions of intensity-correlated twin beams following the conditional photon state-preparation scheme. It is demonstrated that the Wigner functions involve negative values in parts of the phase space for the schemes with one, two, and three photons.
We investigate time-dependent properties of Einstein-Podolsky-Rosen (EPR) light beams generated in nondegenerate optical parametric oscillator (NOPO) driven by a sequence of laser pulses with Gaussian time-dependent envelops. The peculiarities of EPR beams are discussed on the base of quadrature squeezing and also in the framework of phase-space Wigner functions for EPR beams which are combined on a half beam splitter. We also investigate the Wigner functions of intensity-correlated twin beams following the conditional photon state-preparation scheme. It is demonstrated that the Wigner functions involve negative values in parts of the phase space for the schemes with one-, two-, and three-photons.
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.
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.
We experimentally demonstrate the creation and characterization of Einstein-Podolsky-Rosen (EPR) correlation between optical beams in a time-gated fashion. The correlated beams are created with two independent continuous-wave optical parametric oscillators and a half beam splitter. We define the temporal modes using a square temporal filter with duration TTT and make time-resolved measurements on the generated state. We observe correlations between the relevant conjugate variables in the temporal mode which correspond to EPR correlation. Our scheme is extendable to continuous-variable quantum teleportation of a non-Gaussian state defined in the time domain such as a superposition of coherent states.
We study theoretically and experimentally the quantum properties of a type-II frequency-degenerate optical parametric oscillator below threshold with a quarter-wave plate inserted inside the cavity which induces a linear coupling between the orthogonally polarized signal and idler fields. This original device provides a good insight into general properties of two-mode Gaussian states, illustrated in terms of the covariance matrix. We report on the experimental generation of a two-mode squeezed vacuum on nonorthogonal quadratures depending on the plate angle. After a simple operation, the entanglement is maximized and put into standard form, i.e., quantum correlations and anticorrelations on orthogonal quadratures. A half sum of squeezed variances as low as $0.33\ifmmode\pm\else\textpm\fi{}0.02$, well below the unit limit for inseparability, is obtained and the entanglement measured by the entropy of formation.