Configuration space methods and quantum optical solitons

Lai Yinchien

John M. Fini, H. A. Haus

Summary form only given. The term configuration space applies to any approach which treats a quantum system in terms of particle coordinates, as opposed to a second-quantized or field operator approach. Any physical system can be described in terms these two exactly equivalent formulations. Configuration space methods are a natural approach to certain propagation problems, providing simplified calculations and new physical insight. One motivation is the potential to design devices that manipulate wave functions for the collective coordinates of optical pulses. Some examples are discussed.

A. S. Chirkin

Peter L. Hagelstein

Lai and Haus [Phys. Rev. A 40, 854 (1989)] recently introduced the use of a photon configuration-space wave function to analyze optical soliton propagation in a fiber. This is of interest as photon wave functions have long been the source of controversy; the work of Lai and Haus was the first to demonstrate that they could be of use in quantum optics. The systematic reduction of photon configuration-space wave functions directly from QED was recently carried out, which puts the general approach on solid ground. Here we apply the photon configuration-space approach systematically to the dynamics of the soliton center of mass and phase spread, and to squeezing in optical fibers. The predictions of the configuration-space model agree with results from the quantum field theory linearization models, which provide an important benchmark for the new approach. The configuration-space model leads ultimately to a description of the soliton as a quantum object that obeys free particle dynamics in relative position and phase. Phase squeezing appears in the configuration-space model as a consequence of free particle dynamics following initial phase localization due to the use of an initial classical soliton state. \textcopyright{} 1996 The American Physical Society.

John M. Fini, Peter L. Hagelstein, H. A. Haus

The stochastic theory presented by Drummond, Gardiner, and Walls [Phys. Rev. A 24, 914 (1981)] is an interesting approach to problems in quantum optics. In this theory, an exact, quantum evolution is written in terms of classical functions (not operators) driven by explicit, quantum noise. We examine the origin of uncertainty in the formalism through the simple example of a single, nonlinear oscillator. We then test the stochastic theory applied to the problem of soliton propagation. We extend the linearized stochastic model by computing analytically quantum uncertainties in the four basic soliton parameters: photon number, momentum, phase, and position. Agreement with second-quantized and configuration-space soliton theories verifies the stochastic formalism.

F. Kh. Abdullaev, Sergei Darmanyan, Pulat K. Khabibullaev