Diffusive Stochastic Master Equation (SME) with dispersive qubit/cavity coupling
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Abstract
A detailed analysis of the quantum diffusive Stochastic Master Equation (SME) for qubit/cavity systems with dispersive coupling is provided. This analysis incorporates classical input signals and output signals (measurement outcomes through homodyne/heterodyne detection). The dynamics of the qubit/cavity density operator is shown to converge exponentially towards a slow invariant manifold. This invariant manifold is parameterized by the density operator of a fictitious qubit governed by a quantum SME incorporating the classical input/output signals preserving complete-positivity and trace. The reduced cavity (resp. qubit) operator obtained by partial trace of the qubit (resp. cavity) is then given by a time-varying deterministic quantum channel from the density operator of this fictitious qubit. This formulation avoids non-Markovian descriptions where negative dephasing rates and detection efficiency exceeding temporary one are present in several publications. Extensions are considered where the qubit is replaced by any qudit dispersively coupled to an arbitrary set of cavity modes with collective input/output classical signals.