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Annual Meeting Optical Society of America

Spatial effects in traveling-wave squeezed-state generation and detection

Chonghoon Kim, Ruo-Ding Li, Prem Kumar

Published Jan 1, 1993• 0 citations
Publisher

Abstract

Recent experiments that have demonstrated the generation of quadrature-squeezed light in the traveling-wave configuration of an optical parametric amplifier (OPA) indicate that the observable squeezing is largely limited by the effects of diffraction in the parametric process1 and by the spatio-temporal mismatch between the generated squeezed mode and the local-oscillator (LO) mode employed in homodyne detection of squeezing.2

DOI
10.1364/oam.1993.wii.3

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Recent experiments that have demonstrated the generation of quadrature-squeezed light in the traveling-wave configuration of an optical parametric amplifier (OPA) indicate that the observable squeezing is largely limited by the effects of diffraction in the parametric process1 and by the spatio-temporal mismatch between the generated squeezed mode and the local-oscillator (LO) mode employed in homodyne detection of squeezing.2
We investigate temporal effects in pulsed squeezing by parametric amplification, including effects of group-velocity dispersion. Our calculations show that the local oscillator pulse used to detect the squeezed field cannot be made shorter than the inverse phase-matching bandwidth of the generation process without degrading the amount of squeezing detected. This result generalizes an earlier result that showed that in the absence of dispersion, the local oscillator pulse duration should approach zero for optimum squeezing detection. We further show that by using local oscillator amplitude and phase pulse shaping it should be possible to achieve more than 40 dB of detectable quadrature squeezing. This is applicable where it is possible to neglect transverse spatial dimensions and diffraction, such as in a waveguide. We derive the s-parametrized quasiprobability evolution equation for the traveling-wave parametric amplifier. As the Wigner representation results in third-order derivatives, we also use the positive-P representation as an exact representation with equivalent Ito stochastic differential equations. This allows us to compare approximate --- but easily simulated --- Wigner representation results with those using the positive-P representation.
Nowadays, the realization of quantum computations and communications based on continuous variables has attracted a significant attention due to a substantial expansion of the system dimensionality. The main progress in this area is attributed to the implementation of multimode systems based on squeezed states of light. One of the simplest ways to generate such states relies upon their producing in a single-pass optical parametric amplifier (OPA) using ultrafast pumping. However, for homodyne detection of such multimode states, the profile of the local oscillator (LO) must perfectly match the profile of the measured mode. Usually, this is not the case; therefore a proper treatment of multimode squeezing is required. In this work, we study both theoretically and experimentally the multimode squeezed light generated in type-0 and type-II OPA. We characterize such sources and investigate the degree of squeezing in dependence on the LO spectral profile, employing a pulse shaping technique. The theoretical analysis is performed using the Schmidt-mode theory. This work might have a significant impact on the realization of multimode quantum protocols
A local oscillator (LO) which can correctly decode the spatiotemporally distorted quadrature-squeezed light generated by means of single-pass traveling-wave optical parametric amplification is experimentally demonstrated. Such a matched LO is automatically produced in our squeezed-light generation scheme. With the matched LO 5.8 \ifmmode\pm\else\textpm\fi{} 0.2 dB [(74 \ifmmode\pm\else\textpm\fi{} 1)%] of quadrature squeezing is observed which, to the best of the authors' knowledge, is the highest observed in any traveling-wave squeezing experiment to date.
This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.
Optical parametric amplifiers (OPAs) in traveling-wave configuration can generate localized spatial quantum correlations between a signal and an idler beam, a useful resource for quantum imaging. To characterize the spatial correspondence between the optical modes of the signal and those of the idler, we look at the classical transverse dynamics of these beams when they propagate in a generic thick OPA at a nominally small angle. In these conditions, the beams tend to copropagate while maintaining a fixed separation, a phenomenon that we term hitching. We develop a model for hitching, validated by a numerical simulation, and provide an experimental demonstration using four-wave mixing in a hot atomic vapor. They show that the OPA gain is the primary influence on the final hitching distance. These results have implications for the generation of multi-spatial-mode squeezed light for quantum imaging applications, where the exact spatial correlations between the quantum fluctuations of the signal and the idler are of prime importance.