# Coalescence of two branch points in complex time marks the end of rapid adiabatic passage and the start of Rabi oscillations

## TL;DR

This paper explores how the coalescence of two branch points in complex time signals the transition from rapid adiabatic passage to Rabi oscillations in laser-driven two-level atoms, linking non-Hermitian singularities to atomic dynamics.

## Contribution

It reveals that the transition between RAP and Rabi oscillations is governed by the coalescence of branch points and an exceptional point in the complex time plane, providing new insights into non-Hermitian quantum dynamics.

## Key findings

- Critical phenomenon emanates from an exceptional point in non-Hermitian system.
- Switch between RAP and Rabi oscillations is triggered by branch point coalescence.
- Complex time analysis uncovers non-adiabatic dynamics in laser-driven atoms.

## Abstract

We study theoretically the population transfer in two-level atoms driven by chirped lasers. It is known that in the Hermitian case, the rapid adiabatic passage (RAP) is stable for an above-critical chirp below which the final populations of states Rabi oscillate with varying laser power. We show that if the excited state is represented by a resonance, the separatrix marking this critical phenomenon in the space of the laser pulse parameters emanates from an exceptional point (EP) -- a non-Hermitian singularity formed in the atomic system by the fast laser field oscillations and encircled due to slow variations of the laser pulse envelope and instantaneous frequency. This critical phenomenon is neatly understood via extending the "slow" time variable into the complex plane, uncovering a set of branch points which encode non-adiabatic dynamics, where the switch between RAP and Rabi oscillations is triggered by a coalescence of two such branch points. We assert that the intriguing interrelation between the two different singularities -- the EP and the branch point coalescence in complex time plane -- can motivate feasible experiments involving laser driven atoms.