Geometric Effects on Tunneling in Driven Quantum Systems

Abstract

We review quantum tunneling provoked by external field driving, focusing on the role of geometric effects. The discussion begins with an overview of tunneling phenomena, including the Landau-Zener model and the Schwinger effect, both of which are essential frameworks to describe the generation of elementary excitation of the system. We also refer to the relation between the modern theory of polarization and the geometry of the system, and introduce the shift vector via adiabatic perturbation theory. Then we introduce the twisted Landau-Zener model and shown how the shift vector modulates tunneling probability, followed by several illustrative applications of this model. We also explain the Keldysh crossover, which is the crossover from a quantum tunneling regime to photon absorption regime in driven systems.

9 pages, 4 figures

References in corpus (58)

• Topological Insulators
• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides
• Experimental realisation of the topological Haldane model
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Valley filter and valley valve in graphene
• Photovoltaic Hall effect in graphene
• Entanglement spectrum of a topological phase in one dimension
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Observation of Floquet-Bloch states on the surface of a topological insulator
• Valley Dependent Optoelectronics from Inversion Symmetry Breaking
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Shortcuts to adiabaticity: concepts, methods, and applications
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Floquet Engineering of Quantum Materials
• Light-induced anomalous Hall effect in graphene
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Shortcuts to adiabaticity
• Topological Thouless Pumping of Ultracold Fermions
• Topological nature of nonlinear optical effects in solids
• Shortcuts to adiabaticity by counter-diabatic driving
• The simplest quantum model supporting the Kibble-Zurek mechanism of topological defect production: Landau-Zener transitions from a new perspective
• Dynamically assisted Schwinger mechanism
• Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators
• Topological charge pumping in a one-dimensional optical lattice
• When chiral photons meet chiral fermions - Photoinduced anomalous Hall effects in Weyl semimetals
• Breakdown of a Mott insulator -- non-adiabatic tunneling mechanism
• Ground-State Decay Rate for the Zener Breakdown in Band and Mott Insulators
• Floquet Weyl Semimetal Induced by Off-Resonant Light
• Non-linear doublon production in a Mott insulator --- Landau-Dykhne method applied to an integrable model
• Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains
• Chiral pumping effect induced by rotating electric fields
• Dielectric Breakdown in a Mott Insulator: Many-body Schwinger-Landau-Zener Mechanism studied with a Generalized Bethe Ansatz
• Sufficient Conditions for Topological Order in Insulators
• Tunneling Breakdown of a Strongly Correlated Insulating State in VO${}_2$ Induced by Intense Multi-Terahertz Excitation
• Magnetization and phase transition induced by circularly polarized laser in quantum magnets
• Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension
• Emergent Weyl nodes and Fermi arcs in a Floquet Weyl semimetal
• Laser-induced magnetization curve
• Nonreciprocal Landau-Zener tunneling
• Quantum Spin Pump in S=1/2 antiferromagnetic chains -Holonomy of phase operators in sine-Gordon theory-
• Adiabatic Condition and Quantum Geometric Potential
• Holographic Floquet states: (I) A strongly coupled Weyl semimetal
• Keldysh space control of charge dynamics in a strongly driven Mott insulator
• Rectification of Spin Current in Inversion-Asymmetric Magnets with Linearly-Polarized Electromagnetic Waves
• Temporal Interferometry: A Mechanism for Controlling Qubit Transitions During Twisted Rapid Passage with Possible Application to Quantum Computing
• Holographic Floquet states II: Floquet condensation of vector mesons in nonequilibrium phase diagram
• Nonadiabatic Nonlinear Optics and Quantum Geometry -- Application to the Twisted Schwinger Effect
• Shift current from electromagnon excitations in multiferroics
• A Quantized Inter-level Character in Quantum Systems
• Lefschetz-thimble inspired analysis of the Dykhne-Davis-Pechukas method and an application for the Schwinger Mechanism
• Unexpected linear conductivity in Landau-Zener model: limitations and improvements of the relaxation time approximation in the quantum master equation
• Robust high-fidelity universal set of quantum gates through non-adiabatic rapid passage
• Demonstration of geometric diabatic control of quantum states
• Multi-tunneling effect of nonreciprocal Landau-Zener tunneling: Insights from DC field responses
• Problem of nonlinear conductivity within relaxation time approximation in noncentrosymmetric insulators