Modelling the ultra-strongly coupled spin-boson model with unphysical modes

Area of Science:

• Quantum Dynamics
• Open Quantum Systems
• Strong Coupling Physics

Background:

• Weakly coupled quantum systems relax to their ground-state via spontaneous emission.
• Ultra-strong coupling to a zero-temperature environment leads to ground-state dressing with virtual excitations.
• Traditional methods struggle with the exponential increase in Matsubara frequencies in this regime.

Purpose of the Study:

• To develop and generalize methods capable of accurately describing quantum systems in the ultra-strong coupling regime.
• To investigate the role of Matsubara terms in maintaining detailed balance and preventing unphysical emissions.
• To provide a theoretical framework for understanding ground-state dressing via virtual excitations.

Main Methods:

• Generalization of the hierarchical equations of motion (HEOM) method.
• Adaptation of the pseudomode method to handle the exponential terms.
• Utilizing a biexponential fitting function to manage the explosion of Matsubara frequencies.
• Comparison with the reaction coordinate mapping method.

Main Results:

• The generalized HEOM and pseudomode methods successfully capture the ultra-strong coupling regime.
• Biexponential fitting effectively manages the computational complexity arising from Matsubara frequencies.
• Demonstrated the importance of Matsubara terms in regulating detailed balance and preventing unphysical virtual excitation emission.
• Provided a general proof for the validity of using superficially unphysical Matsubara-modes in the pseudomode method.

Conclusions:

• The developed methods offer a robust approach to studying quantum systems under ultra-strong environmental coupling.
• Accurate treatment of Matsubara terms is crucial for preserving the physical consistency of quantum dynamics simulations.
• The findings advance the understanding of ground-state properties and dynamics in strongly driven quantum systems.