Explicit closed-form propagators for time-dependent gain-loss master equations

Abstract:Time ordering is a central obstacle in driven open-system dynamics governed by master equations with time-dependent rates. We derive explicit closed-form factorizations of the chronological and antichronological propagators for a time-dependent generator of the form $\mathcal{L}(t)=\alpha(t)A+\beta(t)B$, when the commutator $[A,B]$ is a simultaneous eigenoperator of the adjoint actions of $A$ and $B$, namely $[A,[A,B]]=\lambda_{A}[A,B]$ and $[B,[A,B]]=\lambda_{B}[A,B]$. In contrast to the disentangling procedure known as the Wei-Norman decomposition, our construction determines the factorization coefficients directly, without solving a coupled system of nonlinear differential equations. Applying this result to the bosonic gain-loss Lindblad equation, we obtain the exact dynamical map for arbitrary time-dependent gain and loss rates. The gain-loss master equation provides a canonical description of a driven harmonic oscillator coupled to a thermal bath. We benchmark the construction by deriving the time evolution of the Wigner function of an initial Fock state and comparing it with independent phase-space results. We further apply the resulting dynamical map to evaluate the code-space survival probability of a binomial bosonic code under driven gain-loss dynamics.

arXiv:2609.24617 [quant-ph]

(or arXiv:2609.24617v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.24617 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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