Critical fluctuations in an optical parametric oscillator: when light behaves like magnetism

We study the nondegenerate optical parametric oscillator in a planar interferometer near threshold, where critical phenomena are expected. These phenomena are associated with nonequilibrium quantum dynamics that are known to lead to quadrature entanglement and squeezing in the oscillator field modes. We obtain a universal form for the equation describing this system, which allows a comparison with other phase transitions. We find that the unsqueezed quadratures of this system correspond to a two-dimensional XY-type model with a tricritical Lifshitz point. This leaves open the possibility of a controlled experimental investigation into this unusual class of statistical models. We evaluate the correlations of the unsqueezed quadrature using both an exact numerical simulation and a Gaussian approximation, and obtain an accurate numerical calculation of the non-Gaussian correlations.Comment: Title changed. New figures adde

Universality of Quantum Critical Dynamics in a Planar Optical Parametric Oscillator

We analyze the critical quantum fluctuations in a coherently driven planar optical parametric oscillator. We show that the presence of transverse modes combined with quantum fluctuations changes the behavior of the ''quantum image'' critical point. This zero-temperature nonequilibrium quantum system has the same universality class as a finite-temperature magnetic Lifshitz transition. DOI: 10.1103/PhysRevLett.95.083601 PACS numbers: 42.50.2p, 64.60.Ht The nonequilibrium system consisting of a nonlinear crystal inside a laser driven Fabry-Perot interferometer, that couples subharmonic intracavity modes to a harmonic pump When extended to an interferometer with multiple transverse modes, more complex dynamical effects occur due to diffraction of the down-converted light, which are governed by the Swift-Hohenberg equation near threshold In this Letter we apply the theory of finite size scaling to solve for the critical quantum dynamical properties, and obtain the universality class this phase-transition corresponds to. We provide a full quantum description of this nonequilibrium system using the positive P representation, focusing on the nature of the critical point and critical fluctuations. This allows us to obtain an analytic solution for the functional distribution of the large critical fluctuations caused by quantum noise in the down-conversion process. There is an unexpected universality property in the solutions. Even though this is a nonequilibrium quantum system of coupled boson fields, we find that in one quadrature, the quantum fluctuations have exactly the same behavior as a classical thermal system of fields at a twodimensional Lifshitz point, which is a model commonly used to describe the phase transition to a modulated magnetic phase; in the complementary quadrature there is strong entanglement. The unitary evolution of the OPO system can be described by the Hamiltonia

Entanglement in the above-threshold optical parametric oscillator

We investigate entanglement in the above-threshold Optical Parametric Oscillator, both theoretically and experimentally, and discuss its potential applications to quantum information. The fluctuations measured in the subtraction of signal and idler amplitude quadratures are $\Delta^2 \hat p_-=0.50(1)$, or $-3.01(9)$ dB, and in the sum of phase quadratures are \Delta^2 \hatq_+=0.73(1), or $-1.37(6)$ dB. A detailed experimental study of the noise behavior as a function of pump power is presented, and discrepancies with theory are discussed.Comment: 9 pages, 6 figs. Important reference for readers of quant-ph/0610197. J. Opt. Soc. Am. B, Feature Issue on Optical Quantum-Information Science, doc. ID 70938 (posted 5 September 2006, in press

Zero Point Electromagnetic Fluctuations, Radiation Reaction, and the Coherent States of the Oscillator

A eletrodinâmica clássica estocástica pode ser entendida como sendo a teoria clássica de Maxwell, onde se inclui um novo elemento da realidade física: As flutuações eletromagnéticas de ponto zero. Sob esse enfoque, estudamos a interação de um \"ensemble\", de osciladores harmônicos carregados com a radiação térmica e de ponto zero (atérmica). Incluímos os efeitos de dissipação através da força de reação da radiação. Além disso estudamos também a excitação do oscilador por uma força determinística com dependência temporal arbitrária. Nossa análise estatística do sistema físico é baseada na solução exata da equação de Fokker-Planck adequada ao problema. Obtém-se a evolução temporal, no espaço de fase, para uma dada distribuição inicial que caracteriza um \"ensemble\" de osciladores forçados que apresentam estados excitados na forma de estados coerentes e estados coerentes comprimidos e pulsantes. A comparação direta com a formulação quântica do mesmo problema nos faz reconhecer que é possível obter da física clássica alguns resultados antes só obtidos pela teoria quântica. Identificamos na radiação de ponto zero o ingrediente que torna possível entender a estabilidade do estado fundamental e o princípio de incerteza.Classical stochastic electrodynamics may be understood as classical electrodynamics theory, when a new element of physical reality is included: The zero point electrodynamics fluctuations. Under this approach, we study the interaction of a charged harmonic oscillator with the thermal radiation and zero point radiation. We include the effect of dissipation by the radiation reaction force. We also study the excitation of this oscillator by a deterministic force with arbitrary temporal dependence. Our statistical analysis of the physical system is based on the exact solution of the appropriate Fokker-Planck equation. We get the temporal evolution in phase space for a given initial distribution that characterizes one \"ensemble\" of forced oscillators that presents excited states in the coherent and squeezed states form. A direct comparison with the quantum formulation of the same problem make us recognize that it is possible to get some results from classical physics which were accomplished previously only by quantum theory. We identify in the zero point radiation the ingredient that makes it possible to understand the stability of the fundamental state and the uncertainty principle

The stochastic electrodynamics and classical aspects of quantum theory

Apresentamos uma tentativa de estender o alcance da teoria clássica na previsão de fenômenos microscópicos. Baseamos nosso enfoque na hipótese de que a mecânica quântica é uma teoria estocástica cujas origens são as flutuações eletromagnéticas de ponto zero. Discutimos uma abordagem nova para a descrição do movimento browniano, clássico e quântico, através de uma equação clássica estocástica do tipo Schröedinger eficiência dessa equação é testada para sistemas lineares em contato com diferentes reservatórios de ruídos. Ambientes diferentes do espaço vazio levam naturalmente a interações do tipo força de Casimir. Para a descrição de rotações intrínsecas introduzimos na teoria clássica a representação espinorial e obtemos uma equação do tipo Pauli-Schrödinger, com flutuação e dissipação, que nos permite gerar distribuições no espaço de fase para partículas com spin arbitrário. Concluímos que a eletrodinâmica estocástica é uma teoria clássica apta a descrever os processos quânticos que se originam das autuações do vácuo.We present an attempt to extend the range of the classical theory in the description of microscopic phenomena. We base our point of view in the hypothesis that quantum mechanics is a stochastic theory whose origin is in the electromagnetic zero-point fluctuations. We discuss a new approach for the description of Brownian motion, both classical and quantum with a stochastic Schrödinger type equation. The effectiveness of this equation is tested for linear systems in contact with different noise reservoirs. Environments different from the vacuum lead naturally to the Casimir force interaction. For the description of particles with spin we introduce in the classical theory a spinorial representation for rotations and obtain a Pauli-Schrödinger type equation, with fluctuation and dissipation, that allows us to generate phase space distributions for particles with arbitrary spin. We conclude that stochastic electrodynamics is a classical theory that is able to describe those quantum processes whose origins are in the vacuum fluctuations