Theory of nonlinear Landau-Zener tunneling

Abstract

A nonlinear Landau-Zener model was proposed recently to describe, among a number of applications, the nonadiabatic transition of a Bose-Einstein condensate between Bloch bands. Numerical analysis revealed a striking phenomenon that tunneling occurs even in the adiabatic limit as the nonlinear parameter $C$ is above a critical value equal to the gap $V$ of avoided crossing of the two levels. In this paper, we present analytical results that give quantitative account of the breakdown of adiabaticity by mapping this quantum nonlinear model into a classical Josephson Hamiltonian. In the critical region, we find a power-law scaling of the nonadiabatic transition probability as a function of $C/V-1$ and $\alpha$, the crossing rate of the energy levels. In the subcritical regime, the transition probability still follows an exponential law but with the exponent changed by the nonlinear effect. For $C/V>>1$, we find a near unit probability for the transition between the adiabatic levels for all values of the crossing rate.

9 figures

References in corpus (1)

• Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1-D optical lattices

Cited by in corpus (134)

• Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
• Adiabatic Theory of Nonlinear Evolution of Quantum States
• Cold Bosons in Optical Lattices
• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Asymmetric Landau-Zener tunneling in a periodic potential
• Principal problems in Bose-Einstein condensation of dilute gases
• Many-body Landau-Zener dynamics in coupled 1D Bose liquids
• Superfluidity and Swallowtails; Hysteretic Behavior in Bose Condensates
• Non-adiabatic dynamics of two strongly coupled nanomechanical resonator modes
• Periodic Modulation Effect on Self-Trapping of Two weakly coupled Bose-Einstein Condensates
• Collective modes, chaotic behavior and self-trapping in the dynamics of three coupled Bose-Einstein condensates
• Josephson Oscillation and Transition to Self-Trapping for Bose-Einstein-Condensates in a Triple-Well Trap
• Adiabatic Condition for Nonlinear Systems
• Quantum Entanglement Manifestation of Transition to Nonlinear Self-trapping for Bose-Einstein Condensates in a Symmetric Double-Well
• Non-adiabacity and large flucutations in a many particle Landau Zener problem
• Transition to Instability in a Kicked Bose-Einstein Condensate
• Towards a Landau-Zener formula for an interacting Bose-Einstein condensate
• Nonlinear quantum interferometry with Bose condensed atoms
• Landau-Zener Tunnelling in a Nonlinear Three-level System
• Commutability between Semiclassical Limit and Adiabatic Limit
• Fast noise in the Landau-Zener theory
• Rosen-Zener Transition in a Nonlinear Two-Level System
• $\eta$-pairing superfluid in periodically-driven fermionic Hubbard model with strong attraction
• Spin-orbit coupled Bose-Einstein condensate in a tilted optical lattice
• Many-body effects on adiabatic passage through Feshbach resonances
• Nonreciprocal Landau-Zener tunneling
• Two-mode Bose-Einstein condensate in a high-frequency driving field that directly couples the two modes
• Resonant Generation of Topological Modes in Trapped Bose Gases
• Phase-Dependent Spontaneous Spin Polarization and Bifurcation Delay in Coupled Two-Component Bose-Einstein Condensates
• Nonlinear Ramsey interferometry with the Rosen-Zener pulses on a two-component Bose-Einstein condensate
• Dynamics of a many-particle Landau-Zener model: inverse sweep
• Interaction-Enhanced Group Velocity of Bosons in the Flat Band of an Optical Kagome Lattice
• Nonlinear adiabatic passage from fermion atoms to boson molecules
• Landau-Zener Tunneling of Bose-Einstein Condensates in an Optical Lattice
• Axion cloud evaporation during inspiral of black hole binaries -- the effects of backreaction and radiation
• Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances
• Nonlinear dynamics of a spin-orbit-coupled Bose-Einstein condensate
• Nonlinear Landau-Zener tunneling in quantum phase space
• Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains
• Nonlinear resonant tunneling of Bose-Einstein condensates in tilted optical lattices
• Universality in nonadiabatic behaviour of classical actions in nonlinear models with separatrix crossings
• Occupation Statistics of a BEC for a Driven Landau-Zener Crossing
• Nonlinear Landau-Zener Processes in a Periodic Driving Field
• Many-Body Effects on Nonadiabatic Feshbach Conversion in Bosonic Systems
• Wave interactions in localizing media - a coin with many faces
• Adiabaticity in nonreciprocal Landau-Zener tunneling
• Kinetic simulations of ladder climbing by electron plasma waves
• Optical lattice influenced geometry of quasi-2D binary condensates and quasiparticle spectra
• The role of particle interactions in a many-body model of Feshbach molecular formation in bosonic systems
• Nonlinear Landau-Zener Tunnelling in Coupled Waveguide Arrays
• Time-dependent self-trapping of Bose-Einstein Condensates in a double-well potential
• Reverse engineering protocols for controlling spin dynamics
• Landau-Zener-Stueckelberg effect in a model of interacting tunneling systems
• Dynamics of a Magnetic Needle Magnetometer: Sensitivity to Landau-Lifshitz-Gilbert Damping
• Quantum dynamics of Bose-Einstein condensates in tilted and driven bichromatic optical lattices
• Dynamics of Rogue Wave Excitation Pattern on Stripe Phase Backgrounds in a Two-component Bose-Einstein Condensate
• Non-exponential tunneling due to mean-field induced swallowtails
• Macroscopic superposition states of ultracold bosons in a double-well potential
• Observation of quantum dynamical oscillations of ultracold atoms in the F and D bands of an optical lattice
• WKB approach and quantum corrections to classical dynamics in the Josephson problem
• Nonlinear energy transfer in classical and quantum systems
• Adiabatic passage through chaos
• Role of Particle Interactions in the Feshbach Conversion of Fermion Atoms to Bosonic Molecules
• Rosen-Zener interferometry with Ultracold Atoms
• Nonlinear Non-Hermitian Landau-Zener-Stückelberg-Majorana interferometry
• Nonlinearity-assisted quantum tunneling in a matter-wave interferometer
• Hysteresis from nonlinear dynamics of Majorana modes in topological Josephson junctions
• Breakdown of quantization in nonlinear Thouless pumping
• Nonlinearly driven Landau-Zener transition with telegraph noise
• Adiabatic transport of Bose-Einstein condensate in double-well trap
• Adiabatic state preparation of interacting two-level systems
• Variational ansatz for the nonlinear Landau-Zener problem for cold atom association
• Singularity of Berry Connections Inhibits the Accuracy of Adiabatic Approximation
• Phase diagram of Landau-Zener phenomena in coupled one-dimensional Bose quantum fluids
• Cluster Gutzwiller study of Bose-Hubbard ladder: ground-state phase diagram and many-body Landau-Zener dynamics
• Nonlinear Landau-Zener-Stückelberg-Majorana problem
• Loop Structure Stability of a Double-Well-Lattice BEC
• Nonlinear dynamics of Rydberg-dressed Bose-Einstein condensates in a triple-well potential
• Many-body Landau-Zener Transition in Cold Atom Double Well Optical Lattices
• Feshbach molecule production in fermionic atomic gases
• Autoresonant excitation of Bose-Einstein condensates
• Topology hidden behind the breakdown of adiabaticity
• Interaction induced Landau-Zener transitions
• Dynamical evolutions in non-Hermitian triple-well system with complex potential
• Generalized formula for the Landau-Zener transition in interacting Bose-Einstein condensates
• Quantum dynamics of hard-core bosons in tilted bichromatic optical lattices
• Semiclassical Spectrum of Small Bose-Hubbard Chains: A Normal Form Approach
• Tunneling Time in the Landau-Zener Model
• Current response of nonequilibrium steady states in Landau-Zener problem: Nonequilibrium Green's function approach
• Many-body adiabatic passage: Quantum detours around chaos
• Quantum Speed Limit under Brachistochrone Evolution
• Quantum Nonlinear Switching Model
• Rabi oscillations and Ramsey-type pulses in ultracold bosons: Role of interactions
• Efficient choice of coloured noises in stochastic dynamics of open quantum systems
• Floquet eigenspectra of a nonlinear two-mode system under periodic driving: the emergence of "ring" structures
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential
• Josephson radiation from nonlinear dynamics of Majorana zero modes
• Photon-induced sideband transitions in a many-body Landau-Zener process
• Parametric tuning of quantum phase transitions in ultracold reactions
• Driving Spin-Boson Models From Equilibrium Using Exact Quantum Dynamics
• Landau-Zener tunneling problem for Bloch states
• Landau-Zener Tunneling of Solitons
• Probabilistic Hysteresis in an Isolated Quantum System: The Microscopic Onset of Irreversibility from a Quantum Perspective
• Hyperchaos in a Bose-Hubbard chain with Rydberg-dressed interactions
• Nonlinear multi-state tunneling dynamics in a spinor Bose-Einstein condensate
• The Adiabatic Transport of Bose-Einstein Condensates in a Double-Well Trap: Case a Small Nonlinearity
• Nonlinear Bloch-Zener oscillations for Bose-Einstein condensates in a Lieb optical lattice
• Quantum resonance and anti-resonance for a periodically kicked Bose-Einstein Condensate in a one dimensional Box
• Cyclotron dynamics of a Bose-Einstein condensate in a quadruple-well potential with synthetic gauge fields
• Stability and chaotic behavior of Bose-Einstein condensates in optical lattices with two- and three-body interactions
• The Dynamics of an Electric Dipole Moment in a Stochastic Electric Field
• Exactly Thermalised Quantum Dynamics of the Spin-Boson Model coupled to a Dissipative Environment
• Intrinsic Dynamical Fluctuation Assisted Symmetry Breaking in Adiabatic Following
• A nonlinear Landau-Zener formula
• Many-body adiabatic passage: Instability, chaos, and quantum classical correspondence
• How to probe the microscopic onset of irreversibility with ultracold atoms
• Molecules with an Induced Dipole Moment in a Stochastic Electric Field
• Quantum irreversibility of quasistatic protocols for finite-size quantized systems
• Symmetry-protected Landau-Zener-Stückelberg-Majorana interference and non-adiabatic topological transport of edge states
• Tunable nonlinear Landau-Zener tunnelings in a spin-orbit-coupled spinor Bose-Einstein condensate
• Composite polaron formed on surface of two-dimensional lattice system in weak coupling regime
• Generating nonequilibrium stationary state from ground state condensate through an almost-adiabatic cycle
• Nonadiabatic transitions during a passage near a critical point
• Quantum Hamiltonian daemons: unitary analogs of combustion engines
• Stabilizing period-doubled density waves by spin-orbit coupling in Bose-Einstein condensates in optical lattices
• Demkov-Kunike model in cold molecule formation
• Multiple-time-scale Landau-Zener transitions in many-body systems
• Probabilistic Hysteresis from a Quantum Phase Space Perspective
• Electric circuit analog of Landau-Zener tunneling using time-varying elements
• On the quantization of AB phase in nonlinear systems
• Theory of anomalous Landau-Zener tunneling induced by nonlinear coupling
• Nonlinear Dirac Points and topological invariant in coupled hexagonal lattices
• Dynamical Phase Transition of two-component Bose-Einstein condensate with nonlinear tunneling in an optomechanical cavity-mediated double-well system
• The effect of the second nearest neighbor interaction on the population transfer in a four-particle Landau-Zener system