Coherence time of a Bose-Einstein condensate

TL;DR

This paper predicts the intrinsic coherence time of a Bose-Einstein condensate using quantum kinetic theory, highlighting how interactions with non-condensed modes cause phase spreading and setting fundamental limits for interferometry applications.

Contribution

The study provides a quantitative prediction of the condensate phase variance growth over time and identifies the diffusive phase motion as the ultimate coherence limit.

Findings

Phase variance grows as A t^2 + B t + C at long times.

Coefficient A vanishes with zero initial energy fluctuations.

Coefficient B indicates diffusive phase spreading limiting coherence time.

Abstract

Temporal coherence is a fundamental property of macroscopic quantum systems, such as lasers in optics and Bose-Einstein condensates in atomic gases and it is a crucial issue for interferometry applications with light or matter waves. Whereas the laser is an "open" quantum system, ultracold atomic gases are weakly coupled to the environment and may be considered as isolated. The coherence time of a condensate is then intrinsic to the system and its derivation is out of the frame of laser theory. Using quantum kinetic theory, we predict that the interaction with non-condensed modes gradually smears out the condensate phase, with a variance growing as A t^2+B t+C at long times t, and we give a quantitative prediction for A, B and C. Whereas the coefficient A vanishes for vanishing energy fluctuations in the initial state, the coefficients B and C are remarkably insensitive to these fluctuations. The coefficient B describes a diffusive motion of the condensate phase that sets the ultimate limit to the condensate coherence time. We briefly discuss the possibility to observe the predicted phase spreading, also including the effect of particle losses.