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Optics and Spectroscopy

Broadband radiation of a degenerate optical parametric oscillator operating above threshold in information applications

Valentin Averchenko, T. Yu. Golubeva, Yu. M. Golubev, Claude Fabre

Published Nov 1, 2008• 4 citations
Publisher

Abstract

Information applications of the essentially multimode (in time) radiation of a degenerate optical parametric oscillator operating above the oscillation threshold, such as protocols of quantum parallel dense coding and multimode quantum teleportation, have been considered. The stream of Shannon mutual information as a function of the spectral width of Alice’s signal and the spectral fidelity of transmission of a multimode quantum signal are evaluated from the estimates of the achievable radiation squeezing that occurs as the oscillation threshold is approached. The advantages of the multimode scheme over the single-mode scheme are discussed.

DOI
10.1134/s0030400x08110192

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We have developed a full multimode theory of a synchronously pumped type-I optical parametric oscillator. We calculate the output quantum fluctuations of the device and find that, in the degenerate case (coincident signal and idler set of frequencies), significant squeezing is obtained when one approaches threshold from below for a set of well-defined ``supermodes,'' or frequency combs, consisting of a coherent linear superposition of signal modes of different frequencies which are resonant in the cavity.
Dynamical restrictions to the squeezing achievable by means of a degenerate optical parametric oscillator (OPO) are considered by quantum-statistical diagram techniques. We determine optimal pumping conditions which maximize the degree of squeezing in the output signal of the OPO. The maximal spectral squeezing in the OPO's output radiation is found to scale as ${\mathit{N}}_{2}^{\mathrm{\ensuremath{-}}2/3}$ where N2{\mathit{N}}_{2}N2​ is the number of photons in the pump mode.
The quantum features of ultrashort-pulse optical parametric oscillators (OPOs) are investigated theoretically in the nonlinear regime near and above threshold. Viewing the pulsed OPO as a multimode open quantum system, we rigorously derive a general input-output model that features nonlinear coupling among many cavity (i.e., system) signal modes and a broadband single-pass (i.e., reservoir) pump field. Under appropriate assumptions, our model produces a Lindblad master equation with multimode nonlinear Lindblad operators describing two-photon dissipation and a multimode four-wave-mixing Hamiltonian describing a broadband, dispersive optical cascade, which we show is required to preserve causality. To simplify the multimode complexity of the model, we employ a supermode decomposition to perform numerical simulations in the regime where the pulsed supermodes experience strong single-photon nonlinearity. We find that the quantum nonlinear dynamics induces pump depletion as well as corrections to the below-threshold squeezing spectrum predicted by linearized models. We also observe the formation of non-Gaussian states with Wigner-function negativity and show that the multimode interactions with the pump, both dissipative and dispersive, can act as effective decoherence channels. Finally, we briefly discuss some experimental considerations for potentially observing such quantum nonlinear phenomena with ultrashort-pulse OPOs on nonlinear nanophotonic platforms.
The optical parametric oscillator is one of the most well-characterized devices in nonlinear optics, with many useful applications, especially as a frequency converter and as a wide-band amplifier. Novel discoveries made with these devices in the quantum domain include demonstrations of large amounts of both single-mode and two-mode squeezing, and, in the two-mode case, significant quantum intensity correlations between the two modes and quadrature correlations, which provided the first experimental demonstration of the original Einstein–Podolsky–Rosen (EPR) paradox. In this chapter, a systematic theory is developed of quantum fluctuations in the degenerate parametric oscillator. The quantum statistical effects produced by the degenerate parametric amplifier and oscillator have been intensely studied. As we have seen, the amount of transient squeezing produced in an ideal lossless parametric amplifier was calculated using asymptotic methods by Crouch and Braunstein. It was found to scale inversely with the square root of the initial pump photon number. When the system is put into a cavity, and driving and dissipation are introduced, we find that the steady state of a driven degenerate parametric oscillator bifurcates. There is a single steady state at low driving strengths, but, as the driving field increases, a threshold value is reached and the single state splits and forms two stable states. Below the threshold, a linearized analysis of squeezing in the quantum quadratures is possible; while above this threshold, or critical point, the tunneling time between the two states due to quantum fluctuations can be calculated.