483 research outputs found
Fast-forward scaling in a finite-dimensional Hilbert space
Time evolution of quantum systems is accelerated by the fast-forward scaling.
We reformulate the method to study systems in a finite-dimensional Hilbert
space. For several simple systems, we explicitly construct the acceleration
potential. We also use our formulation to accelerate the adiabatic dynamics.
Applying the method to the transitionless quantum driving, we find that the
fast-forward potential can be understood as a counterdiabatic term.Comment: 7 pages, 5 figures, revise
Unitary deformations of counterdiabatic driving
We study a deformation of the counterdiabatic-driving Hamiltonian as a
systematic strategy for an adiabatic control of quantum states. Using a unitary
transformation, we design a convenient form of the driver Hamiltonian. We apply
the method to a particle in a confining potential and discrete systems to find
explicit forms of the Hamiltonian and discuss the general properties. The
method is derived by using the quantum brachistochrone equation, which shows
the existence of a nontrivial dynamical invariant in the deformed system.Comment: 10 pages, 3 figures; revise
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