Analytic estimation of transition between instantaneous eigenstates of quantum two-level system

TL;DR

This paper provides an analytical method to estimate transition amplitudes between eigenstates in a quantum two-level system, confirming the adiabatic theorem and clarifying conditions for no transitions.

Contribution

It introduces a new parametrization of the evolution operator to analytically evaluate transition amplitudes, enhancing understanding of adiabatic processes in quantum systems.

Findings

Confirmed the adiabatic theorem in the adiabatic limit

Provided an analytic estimation of the adiabatic approximation

Clarified conditions for no transition between eigenstates

Abstract

Transition amplitudes between instantaneous eigenstates of quantum two-level system are evaluated analytically on the basis of a new parametrization of its evolution operator, which has recently been proposed to construct exact solutions. In particular, they are estimated when the Hamiltonian varies infinitesimally slowly. The results, not only confirm the adiabatic theorem in the adiabatic limit, but also bring us with an analytic estimation of the adiabatic approximation. The condition under which no transition between different instantaneous eigenstates is allowed is also clarified.