Geometric Floquet Condition for Quantum Adiabaticity

TL;DR

This paper establishes a geometric Floquet-based criterion for quantum adiabaticity in periodically driven systems, offering a rigorous, single-cycle measure that improves upon traditional gap conditions.

Contribution

It introduces a novel, geometric Floquet formalism-derived sufficient condition for quantum adiabaticity applicable to finite-dimensional systems.

Findings

The criterion depends only on single-cycle Floquet information.

It provides a certification method for periodic protocols.

The approach is demonstrated through three example systems.

Abstract

Quantum adiabaticity is the evolution of a quantum system that remains close to an instantaneous eigenstate of a time-dependent Hamiltonian. Using Floquet formalism, we derive a rigorous sufficient condition for adiabaticity in closed, finite-dimensional periodically driven systems that is valid for arbitrarily many driving periods. The condition is stroboscopic and geometric, depending only on single-cycle information: the Fubini--Study length of the instantaneous eigenray and a quasienergy-separation measure extracted from the Floquet operator. We also formulate a state-targeted refinement that reduces conservativeness when only one adiabatic branch is relevant. Rather than synthesizing control pulses, the result provides a certification criterion for a given periodic protocol. We illustrate the criterion and contrast it with conventional instantaneous-gap conditions in three representative examples.