How to describe collective decay of uncoupled modes in the input–output formalism

We extend the input-output formalism to study the behavior of uncoupled discrete modes (bosonic cavity modes and fermionic qubits) when they decay to the same Markovian continuum. When the continuum interacts with only a single mode, this decay is irreversible. However, when multiple modes decay to the same Markovian continuum they develop correlations and decay collectively. In the input-output formalism these correlations manifest in additional terms in the quantum Langevin equation. For two modes this collective decay can dramatically extend the lifetimes of both modes (Dicke subradiance) and, within the single-mode subsystem, induces non-Markovian memory effects including energy back flow.