Geometry and Adiabatic Control of Periodically Driven Quantum Systems

Paul Manuel Schindler

AutorIn

Paul Manuel Schindler

Titel

Geometry and Adiabatic Control of Periodically Driven Quantum Systems

Zitierfähige Url:

https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-1054756

Erstveröffentlichung

2026

Datum der Einreichung

31.03.2026

Datum der Verteidigung

18.06.2026

Abstract (EN)

Periodically driven quantum systems have emerged as one of the most versatile tools for quantum simulation, enabling the engineering of eﬀective Hamiltonians, topological phases, and inherently nonequilibrium phenomena such as discrete time crystals. Yet fundamental challenges persist: from a spectral ambiguity that precludes a unique Floquet ground state to an inability to manipulate Floquet eigenstates beyond the adiabatic regime. This thesis demonstrates that counterdiabatic driving—a technique from adiabatic quantum control—provides a unifying framework to address these challenges. We first show that the periodic lab-frame Hamiltonian generates counterdiabatic driving for the Floquet eigenstates, revealing Floquet theory as an inverse counterdiabatic driving problem. Exploiting this equivalence, we develop geometric Floquet theory: a reformulation based on the parallel-transport gauge, which uniquely decomposes Floquet dynamics into a geometric contribution, encoded in Berry phases, and a dynamical contribution, generated by the average-energy operator. The average-energy operator provides an unambiguous sorting of the quasienergy spectrum, identifies a unique Floquet ground state at all drive frequencies, and serves as a sensitive diagnostic for heating and symmetry-breaking transitions. Inherently nonequilibrium phenomena—the 𝜋-quasienergy splitting of discrete time crystals and the anomalous edge modes of Floquet topological insulators—are traced to geometric phases. On the practical side, we exploit the intrinsic robustness of prethermal discrete time crystals for a highly frequency-selective DTC-based AC magnetic field sensing scheme and demonstrate it experimentally on a nuclear spin quantum simulator. We then generalize counterdiabatic driving to periodically driven systems. In particular, we derive a non-perturbative variational principle for the Floquet adiabatic gauge potential; this yields local, experimentally feasible control protocols for transitionless manipulation of Floquet states. We demonstrate this formalism on Floquet state preparation in an ultracold atom quantum simulator and many-body state transfer across a quantum phase transition, with significant improvements over unassisted protocols in both cases.

Freie Schlagwörter (EN)

Physics, Quantum Physics, Nonequilibrium Physics, Floquet Engineering, Quantum Dynamics

Klassifikation (DDC)

530

Klassifikation (RVK)

UK 1000

GutachterIn