Lorentz-group Berry phases in squeezed light

R. Y. Chiao

Ulf Leonhardt

Masao Kitano, T. Yabuzaki

E. V. Damaskinski

R. Y. Chiao, Paul G. Kwiat, William A. Vareka +1 more

The Berry phases most often observed in experiments are produced by rotations. Berry phases produced by Lorentz transformations are almost as simple mathematically. They have been discussed at length, but there has been no suggestion of observing them in an experiment. Indeed, it has been shown that in one context they can be removed by a canonical transformation; thus they appear to be a property of the mathematical description that could not be observed physically. Here we show that the essential element of these Berry phases could be observed as a change of phase of the electromagnetic field in squeezed states of light or microwaves, as could be produced by degenerate parametric amplifiers. It could be seen as a fringe shift in interference experiments. In this way, a physical effect of the squeezing could be measured without measuring anything like photon statistics or noise.

Sibel Baskal, Marilyn E. Noz

This paper starts with the transition from classical physics to quantum mechanics which was greatly aided by the concept of phase space. The role of canonical transformations in quantum mechanics is addressed. The Wigner phase-space distribution function is then defined which arises from the formulation of the density matrix, followed by the harmonic oscillator in phase space. Coherent and one- and two-mode squeezed states of light as well as the squeezed vacuum are discussed in the phase-space picture. Attention is also drawn to the fact that squeezed states naturally generate entanglement between the two-modes. Coupled harmonic oscillators are also elucidated in connection with the Wigner phase space. It will be noted that the phase-space picture of quantum mechanics has become an important scientific language for the rapidly expanding field of quantum optics. Here, we mainly focus on the simplest form of the Wigner function, which finds application in many branches of quantum mechanics. We make use of several symmetry groups such as Lorentz groups, the symplectic group in two and four dimensions, and the Euclidean group. The decoherence problem of an optical field is examined through a reformulation of the Poincaré sphere as a further illustration of the density matrix.