Interaction of radiation with simple quantum systems : multiwave-mixing and squeezing

Sunghyuck An, Murray Sargent

Murray Sargent

David A. Holm

Sunghyuck An, Murray Sargent

A quantum theory of multiwave mixing based on a combination of a Langevin quantum regression method and a density operator technique is outlined. The approach is simple, yet general, and is particularly valuable for analyzing complicated media such as semiconductors. We apply it to find the quantum multiwave mixing equations in a squeezed vacuum. Comparing squeezing spectra in squeezed and ordinary vacua, we find significantly enhanced squeezing for the appropriate pump-vacuum relative phase.

Sunghyuck An

This dissertation presents theories of multiwave mixing in two- and three-level media. The first part of the dissertation treats the semiclassical theories in two-level media. Chapter 2 gives the simple semiclassical theory of four-wave mixing when the two pump frequences differ by more than the reciprocal of the population-difference lifetime. This difference washes out the pump spatial holes as well as one of the two reflection gratings. We compare the results to the degenerate treatment of Abrams and Lind and find significant differences in the reflection coefficient spectra. Chapter 3 presents the semiclassical theory of multiwave in a squeezed vacuum characterized by unequal in-phase and in-quadrature dipole decay times. For a highly squeezed vacuum, we find sharp resonances in both probe absorption and reflection coefficients, which provide sensitive ways to measure the amount of squeezing in the vacuum. The second part of the dissertation treats the quantum theories in two- and three-level media. Chapter 4 develops the fourth-order quantum theory of multiwave mixing to describe the effects of sidemode saturation in two-level media. We derive explicit formulas for the fourth-order quantum coefficients and show that the fourth-order quantum theory reproduces the third-order semiclassical coefficient obtained by truncating a continued fraction. We apply the results to cavity problems and find significant differences in the sideband spectra given by the second- and fourth-order treatments, particularly as the sidemode approaches the laser threshold. The final chapter presents a quantum theory of multiwave mixing in three-level cascades with a two-photon pump. The explicit formulas for the resonance fluorescence spectrum and the quantum combination-tone source term are derived. The theory is applied to the generation of squeezed states of light. We find almost perfect squeezing for some strong pump intensities and good broad-band squeezing for low pump intensities.

Tengfei Jiao, Xuemei Cheng, Qian Zhang +2 more

The traditional multiwave mixing setups are always complicated because multiple laser beams are involved, and they are required to be aligned into certain spatial configurations to get the phase-matching condition satisfied. Here, we report on a multiwave mixing method using a single vector optical field. The spatially separated phase-matching beams are obtained after the vector light passes through a polarizer. Filtering out part(s) of them and focusing the remaining ones into the Rb vapor cell, we detected degenerate four-wave mixing, degenerate six-wave mixing, and coexisting degenerate four-wave mixing signals under different circumstances. As the beams participating in the multiwave mixing processes originate from the same phase plane of the vector laser beam, their relative positions are fixed for the setup so that this method has the potential to resist for turbulence compared with the traditional methods. Besides, the entire system is simple and easy to align because the complicated optical setup is avoided. This work provides a convenient tool for multiwave mixing generation and has great potential in spectroscopy, light squeezing, nonlinear optics, and so on.