On the Phase-Space Approach to Squeezed Phenomena in Quantum Optics

Sascha Wallentowitz, W. Vogel

Raman-type laser excitation of a trapped atom allows one to realize the quantum-mechanical counterpart of phenomena of nonlinear optics, such as Kerr-type nonlinearities, parametric amplification, and multimode mixing. Additionally, huge nonlinearities emerge from the interference of the atomic wave function with the laser waves. They lead to a partitioning of the phase space accompanied by a significantly different action of the time evolution in neighboring phase-space zones. For example, a nonlinearly modified coherent 'displacement' of the motional quantum state may induce strong amplitude squeezing and quantum interferences.

A. D. Jannussis, Vasileios Bartzis

Xiang‐Bin Wang, Keiji, Matsumoto, Tomita Akihisa

Almost all novel observable phenomena in quantum optics are related to the quantum coherence. The coherence here is determined by the relative phase inside a state. Unfortunately, so far all the relevant experimental results in quantum optics are insensitive to the phase information of the coherent state. Lack of phase information may cause serious consequences in many problems in quantum optics. For example, an ensemble of two mode squeezed states is a classical ensemble if the phase in each state is totally random; but it is a non-classical ensemble if the phase in each state is fixed. As a timly application, verification of this type of phase information in an ensemble of two mode squeezed states from the conventional laser is crucial to the validity of the continuous variavable quantum teleportation(CVQT) experiment. Here we give a simple scheme to distinguish two different ensemble of states: the Rudolph-Sanders ensemble, by which each squeezed states emitted has a uniform distribution from $0-2π$ on the phase value; and the van Enk-Fuchs ensemble, which emmits identical states with a fixed(but unknown) phase for every state. We believe our proposal can help to give a clear picture on whether the existing two mode squeezed states so far are indeed non-classical states which can be used as the entanglement resource.

Carlton M. Caves

Leehwa Yeh

The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite-mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena.

S. Olivares