Lindblad Equation for the Inelastic Loss of Ultracold Atoms

TL;DR

This paper derives a Lindblad equation framework for describing inelastic atom loss in ultracold systems, providing universal loss rate relations for fermions and bosons, advancing the theoretical understanding of inelastic processes.

Contribution

It introduces a Lindblad equation approach for multi-atom ultracold systems with inelastic loss, extending previous effective field theories by incorporating local Lindblad operators.

Findings

Derived a Lindblad equation for ultracold atom loss.

Established universal loss rate relations for fermions and bosons.

Connected inelastic loss rates to local anti-Hermitian terms.

Abstract

The loss of ultracold trapped atoms due to deeply inelastic reactions has previously been taken into account in effective field theories for low-energy atoms by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-atom systems are considered, an additional modification is required in the equation governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum atoms produced by deeply inelastic reactions. We show that it satisfies a Lindblad equation, with local Lindblad operators determined by the local anti-Hermitian terms in the effective Hamiltonian. We use the Lindblad equation to derive the universal relation for the two-atom inelastic loss rate for fermions with two spin states and the universal relation for the three-atom inelastic loss rate for identical bosons.