Ensemble master equation for a trapped-atom clock with one- and two-body losses

TL;DR

This paper develops a comprehensive ensemble density matrix model for trapped-atom clocks that incorporates one- and two-body losses, providing insights into population decay behaviors and coherence times relevant for experimental setups.

Contribution

The paper introduces a novel ensemble master equation model including one- and two-body losses, enhancing the predictive accuracy for trapped-atom clock dynamics.

Findings

Population decay is nonexponential due to two-body losses.

One-body losses are crucial for population trapping behavior.

The model can be experimentally verified immediately.

Abstract

An ensemble density matrix model that includes one- and two-body losses is derived for a trapped-atom clock. A trapped-atom clock is mainly affected by one- and two-body losses, generally giving nonexponential decays of populations; nevertheless, three-body recombination is also quantitatively analyzed to demonstrate the boundaries of its practical relevance. The importance of one-body losses is highlighted without which population trapping behavior would be observed. The model is written with decay constants expressed through experimental parameters. It can complement, e.g., the ISRE (identical spin rotation effect) model to improve its predictions: ISRE dramatically increases the ensemble coherence time, hence it enables one to observe the influence of two-body losses on the interferometry contrast envelope. The presented model is useful for Ramsey interferometry and is ready for immediate experimental verification in existing systems.