Time Averaged Quantum Dynamics and the Validity of the Effective Hamiltonian Model

TL;DR

This paper introduces a technique to analyze the time evolution of averaged quantum states, incorporating an effective Hamiltonian and decoherence, and applies it to specific quantum systems to validate and extend existing models.

Contribution

It develops a general method for deriving the evolution of averaged quantum states, including decoherence effects, and applies it to confirm and extend the effective Hamiltonian approach.

Findings

Confirmed a formula for the effective Hamiltonian in harmonic systems.

Identified a new decoherence term affecting the effective Hamiltonian validity.

Discovered a new decoherence effect in Three-Level Raman Transitions.

Abstract

We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the general equation to harmonic Hamiltonians, we confirm a previous formula for the Effective Hamiltonian together with a new decoherence term which should in general be included, and whose vanishing provides the criteria for validity of the Effective Hamiltonian approach. Finally, we apply the theory to examples of the AC Stark Shift and Three- Level Raman Transitions, recovering a new decoherence effect in the latter.