Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model

Abstract

The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of the critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point that allows one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.

2 figures, 5 pages

References in corpus (14)

• An Open-System Quantum Simulator with Trapped Ions
• Shortcut to adiabatic passage in two and three level atoms
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Universal adiabatic dynamics across a quantum critical point
• Defect production in non-linear quench across a quantum critical point
• Exact results for quench dynamics and defect production in a two-dimensional model
• Ground state fidelity from tensor network representations
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Optimal non-linear passage through a quantum critical point
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Phase Transition in Space: How Far Does a Symmetry Bend Before It Breaks?
• Optimal control for unitary preparation of many-body states: application to Luttinger liquids
• Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent

Cited by in corpus (33)

• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
• Adiabatic tracking of quantum many-body dynamics
• Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
• Fast preparation of W states with superconducting quantum interference devices by using dressed states
• Focus on Shortcuts to Adiabaticity
• High-fidelity rapid ground-state loading of an ultracold gas into an optical lattice
• Shortcuts to adiabaticity using flow fields
• Criticality revealed through quench dynamics the Lipkin-Meshkov-Glick model
• Shortcuts to adiabaticity for quantum annealing
• Fast quantum state engineering via universal SU(2) transformation
• Counterdiabatic driving of the quantum Ising model
• Superadiabatic quantum heat engine with a multiferroic working medium
• Controlling quantum critical dynamics of isolated systems
• Complete Bell-state analysis for superconducting-quantum-interference-device qubits with transitionless tracking algorithm
• Non-Abelian holonomic transformation in the presence of classical noise
• Shortcuts to adiabatic cat-state generation in bosonic Josephson junctions
• Fast-forward scaling in a finite-dimensional Hilbert space
• Constraints on scattering amplitudes in multistate Landau-Zener theory
• Exact results for models of multichannel quantum nonadiabatic transitions
• Optimal suppression of defect generation during a passage across a quantum critical point
• Resonant shortcuts for adiabatic rapid passage with only $z$-field control
• Multistate Landau-Zener models with all levels crossing at one point
• Shortcuts to adiabaticity in the infinite-range Ising model by mean-field counter-diabatic driving
• Shortcuts to adiabaticity applied to nonequilibrium entropy production: An information geometry viewpoint
• Unitary deformations of counterdiabatic driving
• Fast-forward approach to adiabatic quantum dynamics of regular spin clusters: nature of geometry-dependent driving interactions
• Invariant-based pulse design for three-level systems without the rotating-wave approximation
• Improving shortcuts to non-Hermitian adiabaticity for fast population transfer in open quantum systems
• Dynamics of a two-state system through a real level crossing
• Optimal control of many-body quantum dynamics: chaos and complexity
• Counter-diabatic vortex pump in spinor Bose-Einstein condensates
• Optimal protocols for finite-duration quantum quenches in the Luttinger model
• Selective Vibrational Population Transfer using Combined STIRAP and Counter-Diabatic Fields