ABSTRACT:
We study the effects of squeezed pump fluctuations in the degenerate
parametric amplifier on signal squeezing. We find, both through semiclassical
calculations and through several detailed analytic methods, that pump
squeezing is responsible for two competing processes: Reduced pump phase
fluctuations improve limitations to squeezing; at the same time, increased
pump intensity fluctuations can lead to a ``spill-over'' of pump
fluctuations onto negative pump phases and a consequent reduction in
signal squeezing.
The degenerate parametric amplifier (DPA) is a nonlinear device: It converts pump photons of frequency omega_p to pairs of correlated signal photons centered around frequency omega=omega_p/2. One interesting and useful property of the DPA is its ability to generate a squeezed signal. In this thesis, we are interested in the limitations to signal-squeezing due to the pump's quantum mechanical fluctuations. We develop analytic methods for calculating the long-time evolution of nonlinear devices and apply these tools to the degenerate parametric amplifier. The analytic results obtained are (essentially) independent of the initial signal and pump states. Thus, the evolution of the system for various initial states can be obtained directly. In particular, the results are presented for an initially squeezed-coherent pump and a signal initially in vacuum.
In this thesis, we present two methods for approaching this problem and the results obtained for coherent- and squeezed-pump DPA's (with signal initially in vacuum) for weak as well as intense pumps. Both of these methods employ perturbation theoretic techniques. Thus, finite order (truncated) perturbation theory serves as the starting point of this work. One way of improving these truncated results is by applying the method of Padé approximants. In the second method, dominant terms are selected and summed to all orders of the expansion parameter (1/alpha where alpha is the pump amplitude). Both methods yield analytic expressions for the time-evolved operators. The dynamics of the system is studied by calculating all quadratic matrix elements of the signal and pump quadrature operators (i.e., quadrature variances, correlations and commutators). In addition, these matrix elements are used in a ``commutator test'' which is applied to determine the range of validity of our results. We find that the long-time behavior of the system with an initially coherent pump is described as accurately by our analytic approaches as the best numerical methods available to date. The evolution of squeezing in a squeezed-pump DPA has never been studied, except in the limit of a weak pump (and strong squeezing). Moreover, our treatment helps provide an intuitive understanding of previously obtained results for a DPA with a weak, squeezed pump.