title: Analytically solvable driven time-dependent two-level quantum systems.
abstract: 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.
authors.affiliation: Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA.
authors.forename: Edwin
authors.initials: E
authors.lastname: Barnes
authors.forename: S
authors.initials: S
authors.lastname: Das Sarma