arXiv:2302.03918 · Physical Review A

Geometric Floquet condition for quantum adiabaticity

Jie Gu, X.-G. Zhang

Published Apr 27, 2026• 1 citation

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.

DOI: 10.1103/h2xc-hjk2

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