Exactly soluble model of a quantum system in external field with periodic time dependence

Boyan T. Torosov, Nikolay V. Vitanov

A class of exact analytic solutions of the time-dependent Schrödinger equation is presented for a two-state quantum system coherently driven by a nonresonant external field. The coupling is a linear function of time with a finite duration and the detuning is constant. Four special models are considered in detail, namely the shark, double-shark, tent and zigzag models. The exact solution is derived by rotation of the Landau–Zener propagator at an angle of π/4 and is expressed in terms of Weber's parabolic cylinder function. Approximations for the transition probabilities are derived for all four models by using the asymptotics of the Weber function; these approximations demonstrate various effects of physical interest for each model.

Giulio Casati, Italo Guarneri

J. D. Morales‐Guzmán, Virginia González‐Vélez

Hiroshi Kuratsuji

We investigate a semiclassical quantization of time-dependent classical field for an exact soluble one-dimensional boson systems. The classical field equation admits the analytic solution of soliton type, by which the semiclassical bound state spectrum is evaluated which reproduces the exact quantum mechanical spectrum in good accuracy.

A. A. Suzko, Grigori Karlovich Giorgadze

A time-dependent periodic Hamiltonian admitting exact solutions is applied to construct a set of universal gates for a quantum computer. The time evolution matrices are obtained in an explicit form and used to construct logic gates for computation. A way of obtaining an entanglement operator is discussed, too. The method is based on transformation of soluble time-independent equations into time-dependent ones by employing a set of special time-dependent transformation operators.

David R. Dion