Lorentz-group Berry phases in squeezed light

R. Y. Chiao, Thomas F. Jordan

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.

Henrik Svensmark, P. Dimon

Berry's phase of the Lorentz group has been measured in a system of connected nonlinear electronic oscillators. Each oscillator was driven so that it was in the vicinity of a period-doubling bifurcation where the response to a small perturbation transforms similarly to a Lorentz boost of a spinor. By connecting the output of one oscillator to the input of the next, it was possible to make a closed loop on a hyperboloid (the invariant surface of the Lorentz group), the enclosed area of which is Berry's phase. Good agreement between theory and experiment is found.