Quantum Fluctuations in Nonlinear Optics

Hermann Haken

Min Xiao

L. A. Lugiato, A. Gatti, Helmut Wiedemann

Asian Selvakumaran, Anna Minguzzi, Iacopo Carusotto +1 more

We theoretically investigate the response of a coherently-driven nonlinear optical cavity to an additional incident single photon. Using a quantum description of the nonlinear dynamics that fully accounts for the quantum fluctuations of the cavity field and for the discrete nature of the incident photon, we characterize the quantum dynamics of single-photon-stimulated jumps from the low-photon-number to the high-photon-number state of the optical bistability loop. We find that the system can exhibit a giant response to this single quantum of excitation, rooted in the phase-transition picture of optical bistability. In addition to shedding light on the role of quantum fluctuations in the non-equilibrium dynamics of a nonlinear optical cavity, our results suggest a strategy for an all-optical single-photon avalanche detector.

Christopher J. Mertens, T. A. B. Kennedy, S. Swain

Quantum properties of intracavity nonlinear optical processes such as parametric oscillation and second harmonic generation are limited to a linearized analytical treatment except for certain special cases. Perfect squeezing in one quadrature and the divergence in fluctuations of the conjugate quadrature predicted at threshold in parametric oscillation are a consequence of the approximate linearized analysis. We investigate nonlinear quantum fluctuation corrections by using nonequilibrium Green’s function methods1,2 in concert with quantum master equations, to assess when these system-size effects may be observable in the laboratory.

Chao Zhao, W. H. Tan

An analytical solution of the Fokker–Planck equation for the nonlinear degenerate optical parametric amplifier (DOPA) is presented, taking into account the influence of pump depletion on the generation of squeezed light. Results conform to those obtained using perturbation series expansion theory near threshold, and also apply to the whole region far away from threshold. When the nonlinear term(η → 0) is neglected, the solution transitions naturally to the linear approximation solution; when the nonlinear term is retained (∞ η), in the case μ → 0, the quantum fluctuations are close to vacuum fluctuations; in the case μ ≫ 1, squeezing increases, and tends to the result obtained using linear theory, 1/(1 + μ).