Abstract
This chapter discusses the quantum statistics of dissipative nonlinear oscillators. Among the nonlinear optical phenomena, the effects that are connected with the dependence of the complex dielectric constant on the light intensity are called “self-action” effects of strong light beams. The nonlinear properties of fibers cancel the fiber dispersion so that pulses behave as if they were travelling through a linear nondispersive medium. The spreadless pulses are known as “optical solitons.” Optical bistability has been observed in a number of materials that exhibit the optical Kerr effect. Quantum nondemolition measurement of photon number based on the optical Kerr effect has been proposed. In quantum optics, a Kerr medium is modeled as the one-mode quantum third-order nonlinear oscillator. A Kerr medium is capable of producing quadrature squeezed states and number-phase squeezed states. Modeling dissipation by coupling the third-order nonlinear oscillator to a reservoir of oscillators helps formulate the Hamiltonian of the compound optical system.
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