Inertial Theorem: Overcoming the quantum adiabatic limit

TL;DR

The paper introduces the inertial theorem, a new framework for stable solutions in fast-driven quantum systems, surpassing adiabatic methods and applicable to open systems with geometric phase implications.

Contribution

The inertial theorem provides a novel approach for analyzing strongly driven quantum systems, extending the Markovian master equation and revealing new geometric phases.

Findings

Inertial solutions outperform adiabatic approximations.

The theorem applies to harmonic, two-level, and three-level systems.

New geometric phases are identified in driven quantum dynamics.

Abstract

We present a new theorem describing stable solutions for a driven quantum system. The theorem, coined `inertial theorem', is applicable for fast driving, provided the acceleration rate is small. The theorem states that in the inertial limit eigenoperators of the propagator remain invariant throughout the dynamics, accumulating dynamical and geometric phases. The proof of the theorem utilizes the structure of Liouville space and a closed Lie algebra of operators. We demonstrate applications of the theorem by studying three explicit solutions of a harmonic oscillator, a two-level and three-level system models. These examples demonstrate that the inertial solution is superior to that obtained with the adiabatic approximation. Inertial protocols can be combined to generate a new family of solutions. The inertial theorem is then employed to extend the validity of the Markovian Master equation to strongly driven open quantum systems. In addition, we explore the consequence of new geometric phases associated with the driving parameters.