Quantum thermo-dynamical construction for driven open quantum systems

Roie Dann and Ronnie Kosloff

The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel

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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.

The theoretical simulation of quantum systems dynamics is a prerequisite for the engineering and realization of quantum devices. Since any quantum device interacts with its environment and is controlled by an external classical agent, the dynamical description is typically described in terms of a time-dependent master equation.

In the present study, we construct a master equation from thermodynamical principles. We start from a fully quantum description of a total system partitioned to a primary system, controller and environment. By employing dynamical symmetry considerations and a semi-classical limit for the controller, we obtain the general dynamical form of the driven open system, consistent with the thermodynamical principles.

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[2] Roie Dann and Ronnie Kosloff, "Open system dynamics from thermodynamic compatibility", Physical Review Research 3 2, 023006 (2021).

[3] Chang-Kang Hu, Roie Dann, Jin-Ming Cui, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo, Alan C. Santos, and Ronnie Kosloff, "Experimental verification of the inertial theorem control protocols", arXiv:1903.00404.

[4] Roie Dann, Nina Megier, and Ronnie Kosloff, "Non-Markovian dynamics under time-translation symmetry", arXiv:2106.05295.

[5] Shimshon Kallush, Roie Dann, and Ronnie Kosloff, "Controlling the uncontrollable: Quantum control of open system dynamics", arXiv:2107.11767.

[6] Patrick P. Potts, Alex Arash Sand Kalaee, and Andreas Wacker, "A thermodynamically consistent Markovian master equation beyond the secular approximation", arXiv:2108.07528.

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