Stochastic excitation during the decay of a two-level emitter subject to homodyne and heterodyne detection

TL;DR

This paper investigates the stochastic dynamics of a two-level atom during decay under continuous homodyne and heterodyne detection, revealing measurement-dependent excitation behaviors using Ito calculus.

Contribution

It introduces a detailed stochastic analysis of atomic decay under different continuous measurement schemes, highlighting measurement-induced excitation phenomena.

Findings

Homodyne detection can fully excite the atom during decay.

Heterodyne detection does not fully excite the atom.

The atom always decays to the ground state in the long term.

Abstract

We study the dynamics of an atomic two-level system decaying by spontaneous emission of light. Subject to continuous detection of the radiated field, the system tends with certainty to the ground state in the long time limit, but at initial times the excited state population exhibits non-trivial stochastic behavior. Employing methods from Ito calculus, we characterize this behavior, and we show, for example, that the emitter, as a result of in-phase homodyne measurements, may become fully excited during the decay process while heterodyne and out of phase homodyne measurements do not drive the atom completely into the excited state.