Physical Review A

Analytical results for a monochromatically driven two-level system

Qiongtao Xie, Wenhua Hai

Published Sep 22, 2010• 53 citations

Abstract

We show that the frequently encountered physical model of a monochromatically driven two-level system is exactly solvable. We present an analytical exact solution to this driven system in terms of two known special functions. Our analytical solution is valid for all parameter regimes and may find applications in current solid-state experiments.

DOI: 10.1103/physreva.82.032117

Related papers

Exactly solvable model for Landau-Zener-Stückelberg-Majorana interferometry

Qiongtao Xie

A periodically driven multiple-parametric two-level model is introduced. Under certain special parameter conditions, an exact analytical solution to this model can be obtained in an explicit form. This gives an exact analytical demonstration of the well-known Landau-Zener-St\"uckelberg-Majorana resonances.

Physical Review AFeb 21, 20187 citations

Analytical Solution of Weak-Coupling Periodically Driven Two-Level System

Qingping Zhou, Mao-Fa Fang

We present an approximate analytical solution to periodically driven two-level system in the weak-coupling regime. The analytical solution is in good agreement with the exact numerical solution in resonance and near resonance cases when Ω ≤ 0.3 ω a with Ω and ω a denoting the Rabi and transition frequencies respectively.

Communications in Theoretical PhysicsApr 1, 20081 citation

Analytically Solvable Driven Time-Dependent Two-Level Quantum Systems

Edwin Barnes, S. Das Sarma

Analytical solutions to the time-dependent Schrödinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm that generates an unlimited number of exact analytical solutions. We show that a general single-axis driving term and its corresponding evolution operator are determined by a single real function which is constrained only by a certain inequality and initial conditions. Any function satisfying these constraints yields an exact analytical solution. We demonstrate this method by presenting several new exact solutions to the time-dependent Schrödinger equation. Our general method and many of the new solutions we present are particularly relevant to qubit control in quantum computing applications.

arXiv:1206.0297Physical Review LettersAug 7, 2012159 citations

Analytical solutions for a two-level system driven by a class of chirped pulses

Pankaj K. Jha, Yuri V. Rostovtsev

We present analytical solutions for the problem of a two-level atom driven by a class of chirped pulses. The solutions are given in terms of Heun functions. By use of the appropriate chirping parameters, an enhancement of four orders of magnitude in the population transfer is obtained.

arXiv:1005.4555Physical Review AJul 6, 201027 citations

Efficient approach to seek exact analytical solutions of periodically driven two-level systems

Xiaoxue Yang, Ying Wu

By developing an efficient approach, we are able to obtain a large number of exact analytical solutions for various periodically driven two-level systems. The approach should be able to be generalized to certain situations of periodically driven multi-level systems as well.

Journal of Physics B Atomic Molecular and Optical PhysicsApr 24, 200616 citations

Weak-Coupling Theory for Semiclassical Periodically Driven Two-Level Systems: Beyond Rotating-Wave Approximation

Xiaoxue Yang, Ying Wu

We present a weak-coupling theory of semiclassical periodically driven two-level systems. The explicit analytical approximating solution is shown to reproduce highly accurately the exact results well beyond the regime of the rotating-wave approximation.

Communications in Theoretical PhysicsAug 1, 20073 citations