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arXiv:quant-ph/9907090

Nonclassical correlations in damped N-solitons

Eduard Schmidt, L. Knöll, Dirk‐Gunnar Welsch

Published Jul 27, 1999• 0 citations
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Abstract

The quantum statistics of damped higher-order optical solitons are analyzed numerically, using cumulant-expansion techniques in Gaussian approximation. A detailed analysis of nonclassical properties in both the time and the frequency domain is given, with special emphasis on the role of absorption. Highly nonclassical broadband spectral correlation is predicted.

DOI
10.48550/arxiv.quant-ph/9907090

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The quantum statistics of damped higher-order optical solitons are analyzed numerically, using cumulant-expansion techniques in Gaussian approximation. A detailed analysis of nonclassical properties in both the time and the frequency domain is given, with special emphasis on the role of absorption. Highly nonclassical broadband spectral correlation is predicted.
Using cumulant expansion in Gaussian approximation, the internal quantum statistics of damped soliton-like pulses in Kerr media are studied numerically, considering both narrow and finite bandwidth spectral pulse components. It is shown that the sub-Poissonian statistics can be enhanced, under certain circumstances, by absorption, which damps out some destructive interferences. Further, it is shown that both the photon-number correlation and the correlation of the photon-number variance between different pulse components can be highly nonclassical even for an absorbing fiber. Optimum frequency windows are determined in order to realize strong nonclassical behavior, which offers novel possibilities of using solitons in optical fibers as a source of nonclassically correlated light beams.
Using cumulant expansion in Gaussian approximation, the internal quantum statistics of damped soliton-like pulses in Kerr media are studied numerically, considering both narrow and finite bandwidth spectral pulse components. It is shown that the sub-Poissonian statistics can be enhanced, under certain circumstances, by absorption, which damps out some destructive interferences. Further, it is shown that both the photon-number correlation and the correlation of the photon-number variance between different pulse components can be highly nonclassical even for an absorbing fiber. Optimum frequency windows are determined in order to realize strong nonclassical behavior, which offers novel possibilities of using solitons in optical fibers as a source of nonclassically correlated light beams.
The quantum statistics of damped optical solitons is studied using cumulant-expansion techniques. The effect of absorption is described in terms of ordinary Markovian relaxation theory, by coupling the optical field to a continuum of reservoir modes. After introduction of local bosonic field operators and spatial discretization, pseudo-Fokker-Planck equations for multidimensional s-parametrized phase-space functions are derived. These partial differential equations are equivalent to an infinite set of ordinary differential equations for the cumulants of the phase-space functions. Introducing an appropriate truncation condition, the resulting finite set of cumulant evolution equations can be solved numerically. Solutions are presented in a Gaussian approximation and the quantum noise is calculated, with special emphasis on squeezing and the recently measured spectral photon-number correlations [Sp\"alter et al., Phys. Rev. Lett. 81, 786 (1998)].
Quantum effects in N-bound solitons can be drastically enhanced compared to the fundamental soliton. In particular, the spectral photon-number correlations are much stronger. The formation of spectral domains of almost perfect positive and negative correlations is predicted. Criteria that are based on the Cauchy-Schwarz inequality are used for studying nonclassical correlations. Interferences between different soliton components of the N-bound solution being responsible for the strong changes in the coherent amplitude may also be a mechanism for the strong correlations. The results offer novel possibilities of producing light with highly nonclassical properties.
Based on the measurement of quantum correlation functions, the quantum statistical properties of spectral measurements are studied for broadband radiation fields. The spectral filtering of light before its detection is compared with the direct detection followed by the spectral analysis of the recorded photocurrents. As an example, the squeezing spectra of the atomic resonance fluorescence are studied for both types of filtering procedures. The conditions for which the detection of the nonclassical signatures of the radiation is possible are analyzed. For the considered example, photocurrent filtering appears to be the superior option to detect nonclassicality due to the vacuum-noise effects in the optical filtering.
Statistical properties of light generated in nonlinear optical couplers are discussed. Methods suitable for the description of non-classical properties of light are mentioned; special attention is paid to generalized superposition of coherent fields and noise. Regimes suitable for non-classical light generation in various types of nonlinear couplers based on second-harmonic and second- subharmonic generation, optical parametric processes, Kerr effect as well as Raman and Brillouin processes are analyzed. Special attention is devoted to the generation of light with sub-Poissonian statistics, squeezed light, and light in purely quantum states. Role of real effects like damping of optical fields and phase mismatches is also discussed.