Time rescaling of nonadiabatic transitions

Applying time-dependent driving is a basic way of quantum control. Driven systems show various dynamics as its time scale is changed due to the different amount of nonadiabatic transitions. The fast-forward scaling theory enables us to observe slow (or fast) time-scale dynamics during moderate time by applying additional driving. Here we discuss its application to nonadiabatic transitions. We derive mathematical expression of additional driving and also find a formula for calculating it. Moreover, we point out relation between the fast-forward scaling theory for nonadiabatic transitions and shortcuts to adiabaticity by counterdiabatic driving.Comment: Submission to SciPos

The first-order Trotter decomposition in the dynamical-invariant basis

The Trotter decomposition is a basic approach to Hamiltonian simulation (digital quantum simulation). The first-order Trotter decomposition is the simplest one, whose deviations from target dynamics are of the first order of a small coefficient in terms of the infidelity. In this paper, we consider the first-order Trotter decomposition in the dynamical-invariant basis. By using a state-dependent inequality, we point out that deviations of this decomposition are of the second order of a small coefficient. Moreover, we also show that this decomposition includes a useful example, i.e., digital implementation of shortcuts to adiabaticity by counterdiabatic driving.Comment: Extended abstract, poster presentation, AQIS'2

Distribution of eigenstate populations and dissipative beating dynamics in uniaxial single-spin magnets

Numerical simulations of magnetization reversal of a quantum uniaxial magnet under a swept magnetic field [Hatomura, \textit{et al}., \textit{Quantum Stoner-Wohlfarth Model}, Phys. Rev. Lett. \textbf{116}, 037203 (2016)] are extended. In particular, how the "wave packet" describing the time-evolution of the system is scattered in the successive avoided level crossings is investigated from the viewpoint of the distribution of the eigenstate populations. It is found that the peak of the distribution as a function of the magnetic field does not depend on spin-size $S$, which indicates that the delay of magnetization reversal due to the finite sweeping rate is the same in both the quantum and classical cases. The peculiar synchronized oscillations of all the spin components result in the beating of the spin-length. Here, dissipative effects on this beating are studied by making use of the generalized Lindblad-type master equation. The corresponding experimental situations are also discussed in order to find conditions for experimental observations

Quantum Stoner-Wohlfarth model

The quantum mechanical counterpart of the famous Stoner-Wohlfarth model -- an easy-axis magnet in a tilted magnetic field -- is studied theoretically and through simulations, as a function of the spin-size $S$ in a sweeping longitudinal field. Beyond the classical Stoner-Wohlfarth transition, the sweeping field-induced adiabatic change of states slows down as $S$ increases, leading to a dynamical quantum phase transition. This result is described as a critical phenomenon associated with Landau-Zener tunneling gaps at metastable quasi-avoided crossings. Furthermore, a beating of the magnetization is discovered after the Stoner-Wohlfarth transition. The period of the beating, obtained analytically, arises from a new type of quantum phase factor.Comment: 4 pages, 6 figure