AGREEMENT OF STOCHASTIC SOLITON FORMALISM WITH 2ND-QUANTIZED AND CONFIGURATION-SPACE MODELS

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