Based on concepts from quantum thermodynamics, the two-level system coupled to a single electromagnetic mode is analyzed. Focusing on the case of detuning, where the mode frequency does not match the transition frequency, effective energies are derived for the levels and the photon energy. It is shown that these should be used for energy exchange with fermionic and bosonic reservoirs in the steady state to achieve a thermodynamically consistent description. While recovering known features such as frequency pulling or Bloch gain, this sheds light on their thermodynamic background and allows for a coherent understanding.

• Received 27 September 2021
• Revised 11 November 2021
• Accepted 11 January 2022

DOI:https://doi.org/10.1103/PhysRevA.105.012214

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Published by the American Physical Society