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Bulletin of the Russian Academy of Sciences Physics

Formation of entangled states of light in an optical parametric oscillator with partially coherent pumping

V. O. Martynov, Vyacheslav A. Mironov, Lev A. Smirnov

Published Jan 1, 2018• 0 citations
Publisher

Abstract

The quantum dynamics of an optical parametric oscillator under conditions of partially coherent pumping is considered. It is shown that if the pumping amplitude strongly exceeds a threshold value, the average number of emitted photons coincides with the estimate of the classical approximation, but the quantum state of light turns out to be entangled. Even though pumping noises reduce the magnitude of this entanglement, quantum correlations are not completely eliminated.

DOI
10.3103/s1062873818010148

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The quantum dynamics of an optical parametric oscillator under conditions of partially coherent pumping is considered. It is shown that if the pumping amplitude strongly exceeds a threshold value, the average number of emitted photons coincides with the estimate of the classical approximation, but the quantum state of light turns out to be entangled. Even though pumping noises reduce the magnitude of this entanglement, quantum correlations are not completely eliminated.
Abstract A study of ‘high temperature’ entangled states in a system of two parametrically coupled quantum oscillators placed into independent thermal baths is performed taking into account partially coherent parametric pump. Processes in an open system are considered based on the Heisenberg–Langevin formalism. We obtain a closed system of equations for the averaged quadratic correlation functions in quantum stochastic problem as a result of Markov processes approximation. On the basis of numerical calculations the dynamics of the logarithmic negativity, which is the measure of entanglement in the system, is investigated. It is shown that the partial coherence of the parametric pump makes the lifetime of the entangled states finite. The threshold characteristics of the formation and existence of these states are specified.
We theoretically and numerically study the quantum dynamics of two degenerate optical parametric oscillators with mutual injections. The cavity mode in the optical coupling path between the two oscillator facets is explicitly considered. Stochastic equations for the oscillators and mutual injection path based on the positive PPP representation are derived. The system of two gradually pumped oscillators with out-of-phase mutual injections is simulated, and its quantum state is investigated. When the incoherent loss of the oscillators other than the mutual injections is small, the squeezed quadratic amplitudes $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{p}$ in the oscillators are positively correlated near the oscillation threshold. It indicates finite quantum correlation, estimated via Gaussian quantum discord, and the entanglement between the intracavity subharmonic fields. When the loss in the injection path is low, each oscillator around the phase transition point forms macroscopic superposition even under a small pump noise. It suggests that the squeezed field stored in the low-loss injection path weakens the decoherence in the oscillators.
We show theoretically that multipartite entanglement is generated on a massive scale in the spectrum, or optical frequency comb, of a single optical parametric oscillator (OPO) emitting well above threshold. In this system, the quantum dynamics of the strongly depleted pump field are responsible for the onset of the entanglement by correlating the two-mode squeezed, bipartite-entangled pairs of OPO signal fields. (Such pairs are independent of one another in the undepleted, classical pump approximation.) We verify the multipartite nature of the entanglement by evaluating the van Loock-Furusawa criterion for a particular set of entanglement witnesses deduced from physical considerations.
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