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Acta Physica Sinica

QUANTUM TREATMENT OF OPTICAL SOLITON PROPAGATION

WEN YANG-JING, FENG YU, FU CHUAN-HONG, 江西师范大学物理系,南昌330027

Published Jan 1, 1993• 0 citations
Publisher

Abstract

In this paper, we treat optical soliton propagation with quantum method. We derive the quantum nonlinear Schrodinger equation (QNSE) with corrections by using the micro model of a Kerr-like medium and dispersion relation. We also find the perturbation solution of thisequation and study the influence of corrections on squeezing. The result indicates that thethird-order dispersion has no influence on squeezing and the term in ?/(?τ)(φ+φ2) makes theamount of squeezing decrease.

DOI
10.7498/aps.42.1942

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In this paper, we treat optical soliton propagation with quantum method. We derive the quantum nonlinear Schrodinger equation (QNSE) with corrections by using the micro model of a Kerr-like medium and dispersion relation. We also find the perturbation solution of thisequation and study the influence of corrections on squeezing. The result indicates that thethird-order dispersion has no influence on squeezing and the term in ?/(?τ)(φ+φ2) makes theamount of squeezing decrease.
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We investigate the quantum squeezing of slow-light solitons generated in a $\mathrm{\ensuremath{\Lambda}}$-shaped three-level atomic system working under condition of electromagnetically induced transparency (EIT). Starting from the Heisenberg-Langevin and Maxwell equations governing the quantum dynamics of atoms and probe laser field, we derive a quantum nonlinear Schr\"odinger equation controlling the evolution of the probe-field envelope. By using a direct perturbation approach to diagonalize the effective Hamiltonian (where the atomic variables have been eliminated), we carry out a detailed calculation on the quantum fluctuations of a slow-light soliton, expanded as a superposition of the complete and orthonormalized set of eigenfunctions obtained by solving the Bogoliubov-de Gennes (BdG) equations describing the quantum fluctuations. We show that due to the giant Kerr nonlinearity contributed from the EIT effect, significant quantum squeezing of the slow-light soliton can be realized within a short propagation distance. The results reported here are helpful for understanding the quantum property of slow-light solitons and for realizing light squeezing via EIT in cold atomic gases experimentally.
Generation of light with nonclassical properties, such as squeezed light, has gathered a lot of attention because of possible uses in such areas as quantum state engineering, quantum imaging, continuous variable quantum computing, and detection of gravitational waves. Squeezed light is generally produced by transporting light through a nonlinear medium. One such media is Kerr-nonlinear optical fibres. We aim to find the parameters for a fibre polarization squeezing setup by studying the dependencies of quantum noise suppression on the duration of the pulse and the input power. This is performed by modeling the light field propagation using the split-step Fourier method to numerically solve the stochastic nonlinear Schrödinger equation obtained by using the Wigner representation. This equation includes such physical effects as damping, quantum loss noise, dispersion, Kerr and Raman nonlinearities, and stochastic Raman noise.
A first-order perturbation calculation is performed on a generalized nonlinear Schr\"odinger equation in order to investigate the degree of squeezing that can be obtained for a medium described by such a field theory. Expressions for the amount of squeezing in the normal and anomalous dispersion regimes are obtained. In particular, it is found that the amount of squeezing is greater in the anomalous dispersion region than in the normal dispersion region. By keeping fourth-order derivatives in the field, the squeezing when the pump is located at the zero-dispersion wavelength is also investigated.