Periodically driven Quantum Ratchets: Symmetries and Resonances

Abstract

We study the quantum version of a tilting and flashing Hamiltonian ratchets, consisting of a periodic potential and a time-periodic driving field. The system dynamics is governed by a Floquet evolution matrix bearing the symmetry of the corresponding Hamiltonian. The dc-current appears due to the desymmetrization of Floquet eigenstates, which become transporting when all the relevant symmetries are violated. Those eigenstates which mostly contribute to a directed transport reside in phase space regions corresponding to classical resonances. Quantum dynamics leads to the dependence of the average velocity on the initial phase of the ac-field. A resonant enhancement (or suppression) of the dc-current, due to avoided crossings between different Floquet states takes place upon tuning some control parameters. Our studies are predominantly aimed at experimental realizations of ac-driven quantum ratchets with cold atoms.

10 pages, 10 figures

References in corpus (22)

• Brownian motors: noisy transport far from equilibrium
• Brownian motors
• Directed current due to broken time-space symmetry
• Classical and Quantum Hamiltonian Ratchets
• Phase-control of directed diffusion in a symmetric optical lattice
• Molecular Wires Acting as Coherent Quantum Ratchets
• Quasiperiodically driven ratchets for cold atoms
• Dissipation-induced symmetry breaking in a driven optical lattice
• Broken space-time symmetries and mechanisms of rectification of ac fields by nonlinear (non)adiabatic response
• Fourier synthesis of optical potentials for atomic quantum gases
• Directed Chaotic Transport in Hamiltonian Ratchets
• Rectifying fluctuations in an optical lattice
• Tunneling And The Onset Of Chaos In A Driven Bistable System
• Rectification of current in ac-driven nonlinear systems and symmetry properties of the Boltzmann equation
• Dynamical mechanisms of DC current generation in driven Hamiltonian systems
• Generic Quantum Ratchet Accelerator with Full Classical Chaos
• Directed anomalous diffusion without a biased field: A ratchet accelerator
• Multi-band quantum ratchets
• Demonstration of a controllable three-dimensional Brownian motor in symmetric potentials
• Dissipationless Directed Transport in Rocked Single-Band Quantum Dynamics
• Quantum diffusion in the quasiperiodic kicked rotor
• Tunneling of quantum rotobreathers

Cited by in corpus (69)

• Artificial Brownian motors: Controlling transport on the nanoscale
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Atomic quantum gases in periodically driven optical lattices
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Directed Transport of Atoms in a Hamiltonian Quantum Ratchet
• Tunable transport with broken space-time symmetries
• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Atomic Landau-Zener tunneling in Fourier-synthesized optical lattices
• Skyrmions Driven by Intrinsic Magnons
• Controlling the Ratchet Effect for Cold Atoms
• Experimental control of transport resonances in a coherent quantum rocking ratchet
• Quantum Ratchets for Quantum Communication with Optical Superlattices
• ac-driven atomic quantum motor
• Three-dimensional localized-delocalized Anderson transition in the time domain
• Quantum Suppression of Ratchet Rectification in a Brownian System Driven by a Biharmonic Force
• Quantum Ratchet Accelerator without a Bichromatic Lattice Potential
• Mechanism of Molecular Orientation by Single-cycle Pulses
• Periodically-driven facilitated high-efficiency dissipative entanglement with Rydberg atoms
• Coherent ratchets in driven Bose-Einstein condensates
• Steering Bose-Einstein condensates despite time symmetry
• Coherent ground-state transport of neutral atoms
• Time-dependent Landauer-Büttiker approach to charge pumping in AC-driven graphene nanoribbons
• Hamiltonian ratchets with ultra-cold atoms
• Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands
• Effective Josephson dynamics in resonantly driven Bose-Einstein condensates
• Interaction-induced current-reversals in driven lattices
• Slowly rocking symmetric, spatially periodic Hamiltonians: The role of escape and the emergence of giant transient directed transport
• Perturbative analysis of coherent quantum ratchets in cold atom systems
• Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays
• Orbital Josephson effect and interactions in driven atom condensates on a ring
• Rectification of light refraction in curved waveguide arrays
• Directed transport and localization in phase-modulated driven lattices
• Underdamped quantum ratchets
• A regular Hamiltonian halting ratchet for matter wave transport
• Quantum ratchet transport with minimal dispersion rate
• Transport and dynamical properties of inertial ratchets
• Net motion induced by nonantiperiodic vibratory or electrophoretic excitations with zero time average
• Asymptotic theory of quasiperiodically driven quantum systems
• Chaos and Correspondence in Classical and Quantum Hamiltonian Ratchets: A Heisenberg Approach
• Exposing local symmetries in distorted driven lattices via time-averaged invariants
• Patterned Deposition of Particles in Spatio-temporally Driven Lattices
• On the environmental stability of quantum chaotic ratchets
• Accurate control of a Bose-Einstein condensate by managing the atomic interaction
• Statistical Approach to Quantum Chaotic Ratchets
• Bichromatically driven double well: parametric perspective of the strong-field control landscape reveals the influence of chaotic states
• Quantum many-body spin ratchets
• Optimal driving waveform for overdamped, adiabatic rocking ratchets
• Freezing, accelerating and slowing directed currents in real time with superimposed driven lattices
• Comment on "Coherent Ratchets in Driven Bose-Einstein Condensates"
• Quantum ratchet control - harvesting on Landau-Zener transitions
• Weak-Chaos Ratchet Accelerator
• Dynamical Control in a Quasi-periodically Modulated Optical Lattice
• Dissipation engineered directional filter for quantum ratchets
• Asymptotic population imbalance of an ultracold bosonic ensemble in a driven double-well
• Directed motion of doublons and holes in periodically driven Mott insulators
• Superexponential Self-Interacting Oscillator
• Quantum ratchet driven by broadband perturbation
• Quantum transport in a driven disordered potential: onset of directed current and noise-induced current reversal
• Symmetries and transport in site-dependently driven quantum lattices
• Avoided crossing and sub-Fourier sensitivity in driven quantum systems
• Tailored particle current in an optical lattice by a weak time-symmetric harmonic potential
• Behavior of the current in the asymmetric quantum multibaker map
• Thermal effects on chaotic directed transport
• Spectral Magnetization Ratchets with Discrete Time Quantum Walks
• Synthetic fractional flux quanta in a ring of superconducting qubits
• A multiple-timing analysis of temporal ratcheting
• Experimental demonstration of photonic quantum ratchet
• Quantum ratchet with Lindblad rate equations