Input-output theory for fermions in an atom cavity

TL;DR

This paper extends quantum optical input-output theory to ultracold fermionic atoms in an atom cavity, deriving Langevin equations and boundary conditions to analyze fermion transport and cavity interactions.

Contribution

It introduces a generalized input-output framework for fermions in atom cavities, accounting for Pauli exclusion and cavity mode coupling, which was not previously developed.

Findings

Derived quantum Langevin equations for fermionic cavity modes

Established boundary conditions relating input, output, and cavity fields

Calculated fermion occupation numbers and currents after cavity interaction

Abstract

We generalize the quantum optical input-output theory developed for optical cavities to ultracold fermionic atoms confined in a trapping potential, which forms an "atom cavity". In order to account for the Pauli exclusion principle, quantum Langevin equations for all cavity modes are derived. The dissipative part of these multi-mode Langevin equations includes a coupling between cavity modes. We also derive a set of boundary conditions for the Fermi field that relate the output fields to the input fields and the field radiated by the cavity. Starting from a constant uniform current of fermions incident on one side of the cavity, we use the boundary conditions to calculate the occupation numbers and current density for the fermions that are reflected and transmitted by the cavity.