Atom state evolution and collapse in ultracold gases during light scattering into a cavity

TL;DR

This paper models the quantum evolution and collapse of atom-light states in ultracold gases within a cavity, revealing phase-dependent dynamics and rapid atom number squeezing during measurement.

Contribution

It introduces a fully quantum mechanical treatment of light and atomic motion, highlighting the exponential atom number squeezing during state collapse, a novel insight.

Findings

Quantum state evolution shows phase dependence quadratic in atom number.

Collapse leads to exponential atom number squeezing.

Fast squeezing rate surpasses initial square root time dependence.

Abstract

We consider the light scattering from ultracold atoms trapped in an optical lattice inside a cavity. In such a system, both the light and atomic motion should be treated in a fully quantum mechanical way. The unitary evolution of the light-matter quantum state is shown to demonstrate the non-trivial phase dependence, quadratic in the atom number. This is essentially due to the dynamical self-consistent nature of the light modes assumed in our model. The collapse of the quantum state during the photocounting process is analyzed as well. It corresponds to the measurement-induced atom number squeezing. We show that, at the final stage of the state collapse, the shrinking of the width of the atom number distribution behaves exponentially in time. This is much faster than the square root time dependence, obtained for the initial stage of the state collapse. The exponentially fast squeezing appears due to the discrete nature of the atom number distribution.