Abstract
We consider Markovian dynamics of a finitely dimensional open quantum system featuring a weak unitary symmetry, i.e., when the action of a unitary symmetry on the space of density matrices commutes with the master operator governing the dynamics. We show how to encode the weak symmetry in quantum stochastic dynamics of the system by constructing a weakly symmetric representation of the master operator: a symmetric Hamiltonian, and jump operators connecting only the symmetry eigenspaces with a fixed eigenvalue ratio. In turn, this representation simplifies both the construction of the master operator as well as quantum jump Monte Carlo simulations, where, for a symmetric initial state, stochastic trajectories of the system state are supported within a single symmetry eigenspace at a time, which is changed only by the action of an asymmetric jump operator. Our results generalize directly to the case of multiple Abelian weak symmetries.
Highlights
Markovian open quantum systems describe a broad class of systems interacting weakly with environments whose dynamics are much faster than those of the system itself, as relevant, e.g., for atomic, molecular, and optical physics [1], as well as optomechanics [2]
We show how to encode the weak symmetry in quantum stochastic dynamics of the system by constructing a weakly symmetric representation of the master operator: a symmetric Hamiltonian, and jump operators connecting only the symmetry eigenspaces with a fixed eigenvalue ratio
In this work we show how a weak symmetry of the master equation can be encoded in the corresponding stochastic dynamics of an open quantum system: via a symmetric Hamiltonian and jump operators connecting only the symmetry eigenspaces with a fixed eigenvalue ratio, which we refer as a weakly symmetric representation of a master operator
Summary
Markovian open quantum systems describe a broad class of systems interacting weakly with environments whose dynamics are much faster than those of the system itself, as relevant, e.g., for atomic, molecular, and optical physics [1], as well as optomechanics [2] This leads to system dynamics efficiently described by a local-in-time master equations [3,4], so that both the dynamics and stationary states can be found by its numerical integration or diagonalization. In this work we show how a weak symmetry of the master equation can be encoded in the corresponding stochastic dynamics of an open quantum system: via a symmetric Hamiltonian and jump operators connecting only the symmetry eigenspaces with a fixed eigenvalue ratio, which we refer as a weakly symmetric representation of a master operator This has direct consequences for the numerics: QJMC simulations are simplified, for symmetric initial states, which remain symmetric and confined to a single symmetry eigenspace at a time.
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