Quantum theory of soliton propagation in an optical fiber using the Hartree approximation

The quantum theory of pulse propagation in a nonlinear optical fiber is presented using the time-dependent Hartree approximation. This formulation clarifies the connections between the quantum theory of soliton propagation and single-mode theories that have been used to describe the effects of self-phase modulation. An approximate solution is obtained for coherent-state soliton pulses that gives excellent agreement with numerical calculations for the quadrature phase amplitudes of the field. These amplitudes are found to undergo a series of collapses and revivals with propagation; the first collapse is related to the appearance of interference fringes in the field Q function.