Counterdiabatic Driving for Periodically Driven Systems
arXiv:2310.02728 · doi:10.1103/PhysRevLett.133.123402
Abstract
Periodically driven systems have emerged as a useful technique to engineer the properties of quantum systems, and are in the process of being developed into a standard toolbox for quantum simulation. An outstanding challenge that leaves this toolbox incomplete is the manipulation of the states dressed by strong periodic drives. The state-of-the-art in Floquet control is the adiabatic change of parameters. Yet, this requires long protocols conflicting with the limited coherence times in experiments. To achieve fast control of nonequilibrium quantum matter, we generalize the notion of variational counterdiabatic driving away from equilibrium focusing on Floquet systems. We derive a nonperturbative variational principle to find local approximations to the adiabatic gauge potential for the effective Floquet Hamiltonian. It enables transitionless driving of Floquet eigenstates far away from the adiabatic regime. We discuss applications to two-level, Floquet band, and interacting periodically driven models. The developed technique allows us to capture nonperturbative photon resonances and obtain high-fidelity protocols that respect experimental limitations like the locality of the accessible control terms.
5 + 18 pages; 3 + 10 figures
References in corpus (86)
- Quantum Computing in the NISQ era and beyond
- Many-Body Physics with Ultracold Gases
- Quantum Annealing in the Transverse Ising Model
- Experimental realisation of the topological Haldane model
- Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- Atomic quantum gases in periodically driven optical lattices
- The Magnus expansion and some of its applications
- Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
- Shortcuts to adiabaticity: concepts, methods, and applications
- Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
- Floquet Engineering of Quantum Materials
- Floquet Time Crystals
- Topological Bands for Ultracold Atoms
- On the phase structure of driven quantum systems
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
- Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates
- Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
- Topological Quantum Matter with Ultracold Gases in Optical Lattices
- High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
- Quantum Annealing and Analog Quantum Computation
- Dynamical control of matter-wave tunneling in periodic potentials
- Shortcut to adiabatic passage in two and three level atoms
- Tunable gauge potential for neutral and spinless particles in driven lattices
- Synthetic gauge fields in synthetic dimensions
- Equilibrium states of generic quantum systems subject to periodic driving
- Shortcuts to adiabaticity by counter-diabatic driving
- QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
- Exponentially slow heating in periodically driven many-body systems
- Floquet-Bloch theory and topology in periodically driven lattices
- Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
- Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems
- Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
- Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators
- Engineering Ising-XY spin models in a triangular lattice via tunable artificial gauge fields
- Quantum simulation of an extra dimension
- QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
- Geometry and non-adiabatic response in quantum and classical systems
- Realization of an anomalous Floquet topological system with ultracold atoms
- Topological singularities and the general classification of Floquet-Bloch systems
- Coherent control of dressed matter waves
- Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
- A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
- Equilibration and Order in Quantum Floquet Matter
- Artificial gauge fields in materials and engineered systems
- Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms
- Exploring dynamic localization with a Bose-Einstein condensate
- Floquet-engineering counterdiabatic protocols in quantum many-body systems
- Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
- Tailoring quantum gases by Floquet engineering
- Colloquium: Quantum and Classical Discrete Time Crystals
- Experimental band structure spectroscopy along a synthetic dimension
- Adiabatic tracking of quantum many-body dynamics
- Realization of a fractional quantum Hall state with ultracold atoms
- Periodically-driven quantum matter: the case of resonant modulations
- Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
- Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
- Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
- Shortcuts to adiabaticity for non-Hermitian systems
- Heating and many-body resonances in a periodically driven two-band system
- Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin Chains
- Superadiabatic dynamics in open quantum systems
- Shortcuts to Adiabaticity in Driven Open Quantum Systems: Balanced Gain and Loss and Non-Markovian Evolution
- Counterdiabatic Optimised Local Driving
- Adiabatic Theorem for Quantum Spin Systems
- Random multipolar driving: tunably slow heating through spectral engineering
- Floquet analysis of a quantum system with modulated periodic driving
- Tuning anomalous Floquet topological bands with ultracold atoms
- Fast adiabatic evolution by oscillating initial Hamiltonians
- Avoided level crossing spectroscopy with dressed matter waves
- Variational principle for optimal quantum controls in quantum metrology
- Realizing discontinuous quantum phase transitions in a strongly-correlated driven optical lattice
- Is there a Floquet Lindbladian?
- Driving protocol for a Floquet topological phase without static counterpart
- Shortcuts to Adiabaticity in Krylov Space
- Floquet engineering to exotic topological phases in systems of cold atoms
- Generalized Shortcuts to Adiabaticity and Enhanced Robustness Against Decoherence
- Experimental Implementation of Generalized Transitionless Quantum Driving
- Floquet-engineered quantum state manipulation in a noisy qubit
- Accelerating adiabatic protocols for entangling two qubits in circuit QED
- Optimal quantum annealing: A variational shortcut to adiabaticity approach
- Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain
- General bound on the performance of counter-diabatic driving acting on dissipative spin systems
- Efficient Paths for Local Counterdiabatic Driving
- Shortcut-to-Adiabatic Controlled-Phase Gate in Rydberg Atoms
Cited by in corpus (14)
- Realization of strongly-interacting Meissner phases in large bosonic flux ladders
- Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
- Geometric Floquet theory
- Universal Counterdiabatic Driving
- Counterdiabatic Route to Entanglement Steering and Dynamical Freezing in the Floquet Lipkin-Meshkov-Glick Model
- Counterdiabatic Driving with Performance Guarantees
- Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics
- Quantum control without quantum states
- Walsh-Floquet Theory of Periodic Kick Drives
- Impact of Boundary Conditions on the Double-Kicked Quantum Rotor
- Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra
- Geometric Quantum Gates of Non-closed Paths Under Counterdiabatic Driving
- Shortcuts to Analog Preparation of Non-Equilibrium Quantum Lakes
- Detuning the Floquet anomalous chiral spin liquid