Generation of Squeezed Light in Nonlinear Media
Two different nonlinear optical processes are studied and are shown to produce squeezed light. In Chapter 2 the photon statistics at the output of the degenerate four-wave mixer are studied. The formalism developed also applies to the degenerate parametric amplifier. The statistics are examined in terms of the matrix representation of the process which belongs to the SU(1,1) group of second-order unimodular matrices. The connection between this group and that of proper Lorentz transformations in two space dimensions and one time dimension permits the field density operators at the input and output ports of the device to be related by means of unitary transformations. This, in turn, provides the joint output photon-number distribution for any joint input state. The case where the inputs to both ports are restricted to be pure number states is studied in detail. The marginal output distributions are expressed in terms of a recursion relation. For number state inputs within a certain range, the output modes will be marginally photon-number-squeezed, or sub-Poisson, when the interaction is sufficiently weak. Quadrature-squeezed light can be generated for arbitrary input states by using a suitable combination of the output beams, when the interaction is sufficiently strong. In Chapter 3 the time-dependent Hartree approximation is used to obtain solutions to a quantized higher-order nonlinear Schroedinger equation. This equation describes femtosecond pulses propagating in nonlinear optical fibers and under certain conditions has soliton solutions. These solitons travel at velocities that differ from the picosecond solitons obtained from the standard quantum nonlinear Schroedinger equation. It is found that quadruple-clad fibers are required for the propagation of these solitons; unlike the solitons of the standard nonlinear Schroedinger equation which can propagate in graded-index optical fibers. From the quantum solution, it is found that the soliton experiences phase -spreading and self-squeezing as it propagates.
- Pub Date:
- QUANTUM OPTICS;
- Physics: Optics