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Journal of Optics B Quantum and Semiclassical Optics

Kerr noise reduction and squeezing

Andrew G. White, Ping Koy Lam, David E. McClelland, Hans‐A. Bachor, William J. Munro

Published Aug 1, 2000• 18 citations
Publisher

Abstract

We introduce a model of squeezing and noise reduction in the Kerr effect that accounts for noise in all quadratures of the driving field. Consequently we show that Kerr squeezing is much more sensitive to driving noise than squeezing produced by second harmonic generation (SHG). We experimentally demonstrate this sensitivity using a nonlinear system that tunes between strong classical SHG and Kerr behaviours. Whilst the system experiences strong squeezing in the SHG limit, it experiences no squeezing in the Kerr limit, although it does experience strong classical noise reduction, or `classical squeezing'.

DOI
10.1088/1464-4266/2/4/315

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We introduce a model of squeezing and noise reduction in the Kerr effect that accounts for noise in all quadratures of the driving field. Consequently we show that Kerr squeezing is much more sensitive to driving noise than squeezing produced by second harmonic generation (SHG). We experimentally demonstrate this sensitivity using a nonlinear system that tunes between strong classical SHG and Kerr behaviours. Whilst the system experiences strong squeezing in the SHG limit, it experiences no squeezing in the Kerr limit, although it does experience strong classical noise reduction, or `classical squeezing'.
We analyze squeezing of both the fundamental and harmonic fields undergoing traveling-wave, second-harmonic generation (SHG) in second-order (${\mathrm{\ensuremath{\chi}}}^{(2)}$) nonlinear media. We take into account depletion of the fundamental field as well as the phase mismatch between the fundamental and harmonic fields. The behavior of the quantum noises on the propagating fields is studied by linearizing the nonlinear operator equations around the mean-field values. We first consider the degenerate case that is applicable to type-I phase-matching geometries, obtaining expressions for squeezing in both the fundamental and harmonic fields under the conditions of perfect phase matching and large phase mismatch. We show that in the case of a large phase mismatch, the intensity-dependent self-phase shift of the fundamental field, arising due to cascading of the ${\mathrm{\ensuremath{\chi}}}^{(2)}$ nonlinearity, is responsible for the squeezing generation. We also numerically solve the linearized quadrature-operator equations together with the nonlinear mean-field equations. We find that in the case of a finite phase mismatch the harmonic field can be highly squeezed. This is in contrast to the perfectly phase-matched case where the maximum squeezing is limited to 50%. Finally, we analyze the nondegenerate case that applies to type-II phase-matching geometries. Here we show that the commonly used type-II phase-matched SHG process with the input harmonic field in the vacuum state is equivalent to a type-I SHG process in parallel with a degenerate optical-parametric process. The latter causes squeezing in the mode that is polarized orthogonal to the fundamental beam. In the perfect phase-matching case, the squeezing in the orthogonally polarized mode follows the simple expression S=1-\ensuremath{\gamma}, where \ensuremath{\gamma} is the harmonic conversion frequency.
Quantum noise in a model of singly resonant frequency doubling, including phase mismatch and driving in the harmonic mode, is analyzed. The use of a nonlinear normalization allows us to disentangle in the spectra the squeezing induced by the system dynamics from the deleterious effect of the noise coming from the various inputs. The physical insight gained permits the elaboration of general criteria to optimize noise-suppression performance. The subsequent application to the specific system here addressed reveals excellent squeezing behavior. In particular, unlimited degrees of squeezing in the harmonic mode are possible by means of an adequate phase mismatch or driving in the harmonic mode. This is in contrast with the standard phase-matched second-harmonic generation in which the squeezing is limited to 1/9. The applicability of the model, as well as possible experimental implementations, is extensively discussed.
The competition between the ${\ensuremath{\chi}}^{(2)}$ nonlinearity of a resonant second-harmonic-generation (SHG) system and an added ${\ensuremath{\chi}}^{(3)}$ nonlinearity shifts the Hopf bifurcation of the standard SHG towards higher photon numbers eventually completely stabilizing the system. Remarkably, perfect squeezing survives the stabilization. Two important consequences are discussed, namely, efficient bright squeezing generation and strong suppression of the excess noise which, for parameters corresponding to an experiment reported in the literature, can be reduced by two orders of magnitude without diminishing the squeezing. Possible experimental implementations are finally discussed.
Quantum noise in a model of a singly resonant frequency doubler including phase mismatch and a driving in the harmonic mode is analyzed. The squeezing spectra calculated inside the linear approximation are given. For squeezing in the fundamental mode, the optimum working point corresponds to turning points of dispersive bistability induced by cascading of the second order nonlinear response. In the case of the harmonic mode phase mismatch as well as a finite driving in the harmonic allows for surpass the 1/9 limit of the standard SHG scheme. The squeezing improvement when the driving is included is substantial for parameter values corresponding to reported experiments. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Kerr microresonators are integrated nonlinear devices widely used to generate classical optical frequency combs and nonclassical states of light. In particular, they provide a promising platform for squeezed light sources, which are important elements of emerging quantum sensing, communication, and computing technologies. Designing such sources requires numerical tools that efficiently incorporate realistic device physics and noise processes. Here, we show that established semi-classical frameworks based on the Lugiato-Lefever equation and the Ikeda map, instrumental in the development of classical light sources, can also predict the quadrature-noise properties of squeezed light when vacuum fluctuations are properly included. We consider three canonical configurations producing two-mode quadrature squeezing, single-mode quadrature squeezing, and intensity difference squeezing. In each case, the semi-classical simulations produce quadrature variances and noise spectra in close agreement with the quantum theoretical predictions. These frameworks therefore provide practical tools for designing squeezed light sources, with the capability to incorporate additional noise mechanisms, nonlinear effects, and complex resonator arrangements. More fundamentally, our results show that key experimental signatures of squeezing can be modeled as phase-sensitive amplification of properly normalized vacuum fluctuations within stochastic semi-classical field equations. This observation helps distinguish squeezing properties accessible through semi-classical field evolution from those intrinsically requiring a full quantum description.
The characteristics of squeezed light generated by both passive (occurring in a cavity external to a laser) and active (occurring within a laser cavity) second-harmonic generation (SHG) are investigated and contrasted. Squeezing of both the fundamental and the second harmonic is discussed, and the issue of doubly versus singly resonant behavior is addressed. We examine passive squeezing by explicitly modeling the intrinsically noisy output of the pump laser and coupling it to a passive, multiport, lossy SHG cavity. Low-frequency degradation of the squeezing caused by the laser pump noise is predicted and provides a probable explanation for previous discrepancies between theory and experiment. Active squeezing is quantitatively modeled by a three-level laser model that retains all laser dynamics. Previously disparate predictions are reconciled. For one parameter set two regimes of squeezing are predicted: 50% squeezing at frequencies lower than the laser relaxation oscillation, and near-perfect squeezing at frequencies above. A particular problem of active squeezing is highlighted: The fast dephasing of the laser coherence introduces considerable excess noise likely to mask squeezing in experimental situations. We conclude that, although passive SHG is a practical source of squeezing, active SHG is unlikely to be so in the foreseeable future.