Counterintuitive transitions between crossing energy levels

TL;DR

This paper analytically investigates the probabilities of both intuitive and counterintuitive transitions in a three-state quantum system with crossing energies, revealing how these probabilities depend on coupling strength, interaction duration, energy splitting, and tilt rate.

Contribution

It provides a novel analytical framework for understanding counterintuitive transitions in a three-state system with crossing energies, applicable to atomic and optical physics.

Findings

Counterintuitive transition probability increases with the square of the coupling.

Transition probability decreases with longer interaction durations and higher energy splitting.

Model has applications in atomic excitation and optical shielding in cold collisions.

Abstract

We calculate analytically the probabilities for intuitive and counterintuitive transitions in a three-state system, in which two parallel energies are crossed by a third, tilted energy. The state with the tilted energy is coupled to the other two states in a chainwise linkage pattern with constant couplings of finite duration. The probability for a counterintuitive transition is found to increase with the square of the coupling and decrease with the squares of the interaction duration, the energy splitting between the parallel energies, and the tilt (chirp) rate. Physical examples of this model can be found in coherent atomic excitation and optical shielding in cold atomic collisions.