Energy Transfer in Random-Matrix ensembles of Floquet Hamiltonians

Abstract

We explore the statistical properties of energy transfer in ensembles of doubly-driven Random- Matrix Floquet Hamiltonians, based on universal symmetry arguments. The energy pumping efficiency distribution P(E) is associated with the Hamiltonian parameter ensemble and the eigenvalue statistics of the Floquet operator. For specific Hamiltonian ensembles, P(E) undergoes a transition that cannot be associated with a symmetry breaking of the instantaneous Hamiltonian. The Floquet eigenvalue spacing distribution indicates the considered ensembles constitute generic nonintegrable Hamiltonian families. As a step towards Hamiltonian engineering, we develop a machine-learning classifier to understand the relative parameter importance in resulting high conversion efficiency. We propose Random Floquet Hamiltonians as a general framework to investigate frequency conversion effects in a new class of generic dynamical processes beyond adiabatic pumps.

arXiv comment10 pages, 15 figures

References in corpus (34)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Berry Phase Effects on Electronic Properties
• Random-Matrix Theory of Quantum Transport
• Random Matrix Theories in Quantum Physics: Common Concepts
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Topological characterization of periodically-driven quantum systems
• Atomic quantum gases in periodically driven optical lattices
• The Magnus expansion and some of its applications
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
• The Statistical Theory of Quantum Dots
• Topological Thouless Pumping of Ultracold Fermions
• An Adiabatic Quantum Electron Pump
• Quantum critical scaling of the geometric tensors
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
• Quantum Transduction of Telecommunications-band Single Photons from a Quantum Dot by Frequency Upconversion
• Classification of Interacting Topological Floquet Phases in One Dimension
• Classification of topological phases in periodically driven interacting systems
• Non-adiabatic breaking of topological pumping
• Experimental Observation of a Generalized Thouless Pump with a Single Spin
• Adiabatic quantum motors
• Topological Floquet-Thouless energy pump
• Topological classification of quasi-periodically driven quantum systems
• Floquet Thermalization: Symmetries and Random Matrix Ensembles
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit
• Topological energy conversion through bulk or boundary of driven systems
• Learning the Ising Model with Generative Neural Networks
• Topological Frequency Conversion in a Driven Dissipative Quantum Cavity
• Topological two-dimensional Floquet lattice on a single superconducting qubit
• Machine Learning Application to Two-Dimensional Dzyaloshinskii-Moriya Ferromagnets
• Stability of Periodically Driven Topological Phases against Disorder
• Hilbert-space geometry of random-matrix eigenstates
• A learning algorithm with emergent scaling behavior for classifying phase transitions

Cited by in corpus (3)

• Bosonic Entanglement and Quantum Sensing from Energy Transfer in two-tone Floquet Systems
• Non-abelian Geometric Quantum Energy Pump
• Topological energy pumping in a quasi-periodically driven four-level system