Thermalization of open quantum systems with pseudomodes

This paper investigates the thermodynamic consistency of pseudomode models, a popular technique for describing open quantum systems that interact strongly with their environment. The authors examine whether these models, which replace a complex environment with a simpler 'pseudomode' (a damped auxiliary system), correctly drive the system toward its Gibbs state. The study focuses on identifying the conditions under which these models satisfy the detailed balance condition—a prerequisite for thermalization—and explores how parameter choices can be used to force 'weak' detailed balance over limited frequency ranges.

The researchers demonstrate that pseudomode models do not naturally thermalize to the system's Gibbs state. Unlike standard environments characterized by a frequency-dependent spectral density, pseudomodes impose a fixed effective temperature based on the pseudomode's own frequency. This leads to a mismatch between the environment's temperature and the system's transition frequencies. The authors show that while one can engineer specific combinations of Hermitian and non-Hermitian pseudomodes to achieve a flat effective-temperature profile, this is a deliberate design choice rather than an inherent property of the method. They further validate these findings using an analytically solvable harmonic oscillator model, extending the analysis into the strong-coupling regime where deviations from thermal behavior are even more pronounced.

Pseudomode approaches are widely used in quantum optics, energy transfer studies, and quantum heat engines. This paper provides a necessary cautionary framework for researchers using these models. By clarifying that pseudomodes do not automatically guarantee thermodynamic consistency, the authors provide a rigorous foundation for constructing models that are physically accurate in contexts where thermalization is a central concern, such as in quantum reservoir engineering and analog quantum simulation.