Abstract
Quantum dynamics of driven open systems should be compatible with both quantum mechanic and thermodynamic principles. By formulating the thermodynamic principles in terms of a set of postulates we obtain a thermodynamically consistent master equation. Following an axiomatic approach, we base the analysis on an autonomous description, incorporating the drive as a large transient control quantum system. In the appropriate physical limit, we derive the semi-classical description, where the control is incorporated as a time-dependent term in the system Hamiltonian. The transition to the semi-classical description reflects the conservation of global coherence and highlights the crucial role of coherence in the initial control state. We demonstrate the theory by analyzing a qubit controlled by a single bosonic mode in a coherent state.
Highlights
Any realizable quantum system interacts with its environment to some extent
Such a constraint is a manifestation of an additional symmetry which implies that the dynamical map is covariant with respect to the free propagation [27]. This restriction leads to the general structure of the master equation which complies with the basic laws of thermodynamics [14]. We extend this methodology to obtain the dynamical equation for a driven open quantum system
This is manifested by the fact that in this limit the Lindblad jump operators, which are the eigenoperators of the free dynamics, coincide
Summary
Any realizable quantum system interacts with its environment to some extent. As a consequence, accurate modeling and simulation of quantum dynamics requires equations of motion which incorporate the environmental influence. Based on this embedding principle and the thematic approach, the seminal work of Gorini, Kossakowski, Lindblad and Sudarshan (GKLS) obtained the general form of the Markovian master equation [26, 41] This construction guarantees consistency with the probability interpretation of quantum mechanics, in certain cases it can violate thermodynamic principles [33, 37]. The explicit time dependence is replaced by an initial non-stationary state of the control This procedure can be viewed as an additional embedding of the driven system within a larger Hilbert space, with dynamics generated by a static Hamiltonian. The axiomatic construction serves as a bridge between a dynamical description and ideas from quantum thermodynamic resource theory [7, 29, 30]
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