Time-dependent adiabatic elimination in matter-wave optics

TL;DR

This paper introduces a time-dependent adiabatic elimination formalism for matter-wave optics, enabling the separation of specific state dynamics from the total quantum state without assuming commuting Hamiltonian elements.

Contribution

It develops a novel formalism for adiabatic elimination that handles explicit time dependence and non-commuting Hamiltonians in matter-wave systems.

Findings

Formalism accommodates non-commuting Hamiltonians.

Allows adiabatic elimination with explicit time dependence.

Applicable to matter-wave optics with center-of-mass degrees of freedom.

Abstract

We show how the dynamics of a specific subset of states can be separated from the dynamic of the total quantum state via a time-dependent projector-based formalism of adiabatic elimination. Within our formalism, we assume explicit time dependency in the coupling between both subsystems. Additionally, we do not assume that the elements of the Hamiltonian commute, as in matter-wave optics this not given in general. Here the center-of-mass degrees of freedom frequently need to be taken into account. Our formalism allows to perform the adiabatic elimination in such a setting.