From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity

Abstract

Using shortcuts to adiabaticity, we solve the time-dependent Schroedinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic XY spin chains from the Toda equations are studied in detail.

6+6pages, 5 figures, title changed, substantially revised

References in corpus (12)

• Shortcut to adiabatic passage in two and three level atoms
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Shortcut to adiabaticity for an interacting Bose-Einstein condensate
• Realizable Hamiltonians for Universal Adiabatic Quantum Computers
• Fast optimal transition between two equilibrium states
• Adiabatic tracking of quantum many-body dynamics
• Shortcuts to adiabaticity in three-level systems using Lie transforms
• Fast and robust spin manipulation in a quantum dot by electric fields
• Shortcuts to nonabelian braiding
• Fast generation of spin-squeezed states in bosonic Josephson junctions
• Counterdiabatic driving of the quantum Ising model
• Unitary deformations of counterdiabatic driving

Cited by in corpus (27)

• Shortcuts to adiabaticity: concepts, methods, and applications
• Floquet-engineering counterdiabatic protocols in quantum many-body systems
• Focus on Shortcuts to Adiabaticity
• Shortcuts to adiabaticity using flow fields
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Shortcuts to adiabaticity for quantum annealing
• Controlling and exploring quantum systems by algebraic expression of adiabatic gauge potential
• Shortcuts to adiabaticity in the strongly-coupled regime: nonadiabatic control of a unitary Fermi gas
• Shortcuts to Adiabaticity in Krylov Space
• Performance Evaluation of Adiabatic Quantum Computation via Quantum Speed Limits and Possible Applications to Many-Body Systems
• Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
• Superadiabatic thermalization of a quantum oscillator by engineered dephasing
• Shortcuts to adiabaticity in Fermi gases
• Shortcut to adiabatic control of soliton matter waves by tunable interaction
• Hamiltonian engineering for adiabatic quantum computation: Lessons from shortcuts to adiabaticity
• Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations
• Shortcuts to adiabaticity in non-Hermitian quantum systems without rotating-wave approximation
• Shortcuts to adiabaticity applied to nonequilibrium entropy production: An information geometry viewpoint
• Quantum-Classical Correspondence of Shortcuts to Adiabaticity
• Shortcuts to Adiabaticity Assisted by Counterdiabatic Born-Oppenheimer Dynamics
• Counterdiabatic Formalism of Shortcuts to Adiabaticity
• Counter-diabatic driving in the classical $\beta$-Fermi-Pasta-Ulam-Tsingou chain
• Transitionless intra-cavity quantum state transfer in optomechanical systems
• Dynamical invariant formalism of shortcuts to adiabaticity
• Shortcuts to adiabaticity in open quantum critical systems
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows