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arXiv:0907.3825 · Physical Review A

Non-Gaussian states produced by close-to-threshold optical parametric oscillators: Role of classical and quantum fluctuations

Virginia D’Auria, Corrado de Lisio, A. Porzio, S. Solimeno, Javaid Anwar, Matteo G. A. Paris

Published Mar 29, 2010• 27 citations
arXivHTMLPDF

Abstract

Quantum states with non-Gaussian statistics generated by optical parametric oscillators (OPO) with fluctuating parameters are studied by means of the kurtosis excess of the external field quadratures. The field generated is viewed as the response of a nonlinear device to the fluctuations of pump laser amplitude and frequency, crystal temperature, and cavity detuning, in addition to quantum noise sources. The kurtosis excess has been evaluated perturbatively up to the third order in the strength of the crystal nonlinear coupling factor and the second order in the classical fluctuating parameters. Applied to the device described in Opt. Expr. 13, 948 (2005), the model has given values of the kurtosis excess in good agreement with the measured ones.

DOI
10.1103/physreva.81.033846

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Quantum states with non-Gaussian statistics generated by optical parametric oscillators (OPO) with fluctuating parameters are studied by means of the kurtosis excess of the external field quadratures. The field generated is viewed as the response of a nonlinear device to the fluctuations of pump laser amplitude and frequency, crystal temperature, and cavity detuning, in addition to quantum noise sources. The kurtosis excess has been evaluated perturbatively up to the third order in the strength of the crystal nonlinear coupling factor and the second order in the classical fluctuating parameters. Applied to the device described in Opt. Expr. 13, 948 (2005), the model has given values of the kurtosis excess in good agreement with the measured ones.
Coherence properties of light beams generated by optical parametric oscillators (OPOs) are discussed in the region of threshold. Analytic expressions, that are valid throughout the threshold region, for experimentally measurable quantities such as the mean and variance of photon number fluctuations, squeezing of field quadratures, and photon counting distributions are derived. These expressions describe non-Gaussian fluctuations of light in the region of threshold and reproduce Gaussian fluctuations below and above threshold, thus providing a bridge between below and above threshold regimes of operation. They are used to study the transformation of fluctuation properties of light as the OPOs make a transition from below to above threshold. The results for the OPOs are compared to those for the single-mode and two-mode lasers and their similarities and differences are discussed.
Systems of coupled optical parametric oscillators (OPOs) forming an Ising machine are emerging as large-scale simulators of the Ising model. The advances in computer science and nonlinear optics have triggered not only the physical realization of hybrid (electrooptical) or all-optical Ising machines, but also the demonstration of quantum-inspired algorithms boosting their performances. To date, the use of the quantum nature of parametrically generated light as a further resource for computation represents a major open issue. A key quantum feature is the non-Gaussian character of the system state across the oscillation threshold. In this paper, we perform an ab initio analysis of the emergence of non-Gaussianity in the single quantum OPO with an applied external field. We model the OPO by a Lindblad master equation, which is numerically solved by a first-principles method based on exact diagonalization. Non-Gaussianity is quantified by means of three different metrics: the Hilbert-Schmidt distance, quantum relative entropy, and photon distribution. Our findings reveal a nontrivial interplay between parametric drive and applied field: (i) the increasing pump monotonically enhances non-Gaussianity and (ii) the increasing field first sharpens non-Gaussianity, and then restores the Gaussian character of the state when above a threshold value. We also report a first-principles computation in the Fock space of the distance from the mixture of coherent states, a strongly nonclassical behavior that can play a significant role in the quantum parallel search for optimization.
A semi-classical analysis of the noise characteristics of a non degenerate, above threshold, optical parametric oscillator is presented, yielding expressions for the quantum fluctuations of the output field intensities and phases. Particular emphasis is given to the study of the noise on the intensity difference between the two generated fields. The effect of losses, unbalance, detunings and excess pump noise is investigated. A significant quantum noise reduction is found over a broad domain of the parameter space.
The redistribution of intrinsic quantum noise in the quadratures of the field generated in a sub-threshold degenerate optical parametric oscillator exhibits interesting dependences on the individual output mirror transmittances, when they are included exactly. We present a physical picture of this problem, based on mirror boundary conditions, which is valid for arbitrary transmittances. Hence, our picture applies uniformly to all values of the cavity Q factor representing, in the opposite extremes, both perfect oscillator and amplifier configurations. Beginning with a classical second-harmonic pump, we shall generalize our analysis to the finite amplitude and phase fluctuations of the pump.
We have constructed a mode-locked optical parametric oscillator (OPO), synchronously pumped by the second harmonic of a continuously mode-locked Nd:YAG laser and based on type II phase matching in a KTP crystal. The two subharmonics (signal and idler waves) are nearly degenerate in frequency but are distinct orthogonal polarization states, and the oscillator is thus a nondegenerate OPO. Above threshold, the intensities of the signal and idler output beams should be highly correlated, as recently demonstrated for a similar single-frequency OPO.1 Ideally, the quantum noise on the corresponding photocurrent difference signal is completely suppressed for frequencies that are small compared to the OPO cavity bandwidth. Since this configuration produces intense light beams with potentially very good noise suppression, it is an important prototype for possible applications, e.g., to spectroscopy. Initial results with our OPO show an excess uncorrelated polarization noise, possibly due to depolarized light scattering in the KTP crystal. When the OPO cavity is stabilized with the signal and idler degenerate in frequency, they can be mixed to form a superposition by manipulating their polarization. When the oscillator is pumped below threshold, a pulsed squeezed vacuum state is produced in two such mixtures.2 When the polarizations are mixed inside the OPO cavity by a Faraday rotator, the backaction evasion necessary for a quantum nondemolition (QND) measurement of one of the field quadratures of an externally injected beam is obtained.3 The pulsed local oscillator used in observing the squeezing or QND effects is derived from the fundamental output of the pump laser. Progress in implementing these experiments with our mode-locked OPO is described as well as possible applications to time-domain measurements with noise below the shot-noise limit.
A Langevin model is introduced to study quantum fluctuations below the threshold of pattern formation for optical parametric oscillators (OPO's). In particular we compare analytical and numerical results for the OPO with one and two transverse spatial dimensions and in the presence of either plane or spherical cavity mirrors. The far-field structure and the correlation functions of the fluctuating signal field anticipate the onset of a transverse spatial pattern which arises classically even in the presence of Gaussian input beams. Correlation functions also reveal the squeezed nature of the OPO field. Numerical simulations of the Langevin model describe the result of short time measurements and show that close to threshold the near-field signal is a noisy spot pattern evolving on a time scale longer than the inverse decay rate of the resonator. This and other far-field features should be experimentally accessible.