Landau-Zener Lindblad equation and work extraction from coherences

Area of Science:

• Quantum Dynamics
• Quantum Thermodynamics
• Open Quantum Systems

Background:

• Understanding the dynamics of driven quantum systems interacting with finite reservoirs is crucial for quantum technologies.
• Previous models often simplified reservoir interactions or assumed infinite reservoirs, limiting applicability.
• The role of coherence in energy exchange with thermal reservoirs remains an active area of research.

Purpose of the Study:

• To develop an approximate model for driven quantum systems weakly coupled to finite reservoirs.
• To derive a quantum master equation describing the system's evolution.
• To investigate the possibility of work extraction from a thermal reservoir and the role of coherence.

Main Methods:

• Approximation of system dynamics using a sequence of Landau-Zener transitions.
• Formulation of repeated interaction dynamics.
• Derivation of a Lindblad-form quantum master equation.
• Validation through comparison with numerically exact dynamics of the full system.
• Proposal of a model system to study work extraction and coherence.

Main Results:

• The dynamics of a driven quantum system coupled to a finite reservoir can be accurately approximated by Landau-Zener transitions under specific conditions (large reservoir level spacing).
• This approximation yields a Lindblad-form quantum master equation for the driven system.
• The derived master equation correctly describes the system's dynamics when compared to exact numerical simulations.
• A model system demonstrates that coherence is essential for extracting work from a thermal reservoir; its absence prevents work extraction.

Conclusions:

• Landau-Zener transitions provide a powerful approximation for driven quantum systems interacting with finite reservoirs.
• The derived quantum master equation offers a computationally tractable method for studying such systems.
• Quantum coherence plays a vital role in enabling work extraction from thermal environments, with implications for quantum thermodynamics and engine design.