Coarse-grained dynamics of ac-driven two-state systems

TL;DR

This paper applies Magnus expansion to a two-level system driven by an AC field, deriving effective Hamiltonians and shifts in energy levels due to coarse-graining, enhancing understanding of driven quantum systems.

Contribution

It introduces a method to derive effective Hamiltonians for ac-driven two-state systems using Magnus expansion, highlighting coarse-grained dynamics and energy shifts.

Findings

Derived Stark and Bloch-Siegert shifts for the Hamiltonian

Demonstrated coarse-grained effective Hamiltonian formulation

Provided insights into driven two-level quantum systems

Abstract

Magnus expansion is used to identify effective Hamiltonians describing the coarse-grained dynamics of more complex problems. Here, we apply this method to a two-level system driven by an and AC field. We derive Stark and Bloch-Siegert shifs of both diagonal and off-diagonal entries of the Hamiltonian as a result of coarse-graining only.