Generalized Adiabatic Theorems: Quantum Systems Driven by Modulated Time-Varying Fields

TL;DR

This paper develops generalized adiabatic theorems for quantum systems under slow modulations of rapidly varying fields, enabling better understanding of their dynamics and steady states in complex optical and biological scenarios.

Contribution

It introduces a unified framework for adiabatic theorems applicable to arbitrary time-dependent fields, including oscillatory and incoherent light, extending previous results.

Findings

Predicts dynamics of frequency-modulated two-level systems beyond earlier models

Shows open quantum systems driven by slow incoherent light can only sustain steady-state coherences

Recovers standard adiabatic theorems in the static field limit

Abstract

We present generalized adiabatic theorems for closed and open quantum systems that can be applied to slow modulations of rapidly varying fields, such as oscillatory fields that occur in optical experiments and light induced processes. The generalized adiabatic theorems show that a sufficiently slow modulation conserves the dynamical modes of time dependent reference Hamiltonians. In the limiting case of modulations of static fields, the standard adiabatic theorems are recovered. Applying these results to periodic fields shows that they remain in Floquet states rather than in energy eigenstates. More generally, these adiabatic theorems can be applied to transformations of arbitrary time-dependent fields, by accounting for the rapidly varying part of the field through the dynamical normal modes, and treating the slow modulation adiabatically. As examples, we apply the generalized theorem to (a) predict the dynamics of a two level system driven by a frequency modulated resonant oscillation, a pathological situation beyond the applicability of earlier results, and (b) to show that open quantum systems driven by slowly turned-on incoherent light, such as biomolecules under natural illumination conditions, can only display coherences that survive in the steady state.