Quantum phase transition in a three-level atom-molecule system

TL;DR

This paper investigates a quantum phase transition in a three-level atom-molecule system using a bosonic model, identifying a second-order transition characterized by changes in energy structure, fidelity, and geometric phase.

Contribution

It introduces a detailed analysis of a three-level atom-molecule system, revealing a second-order phase transition with explicit critical point and unique geometric phase behavior.

Findings

Second-order phase transition confirmed between atom-molecule mixture and pure molecule phases

Critical point explicitly derived and characterized by scaling laws

Ground-state geometric phase exhibits a jump from zero to pi/3 at the transition

Abstract

We adopt a three-level bosonic model to investigate the quantum phase transition in an ultracold atom-molecule conversion system which includes one atomic mode and two molecular modes. Through thoroughly exploring the properties of energy level structure, fidelity, and adiabatical geometric phase, we confirm that the system exists a second-order phase transition from an atommolecule mixture phase to a pure molecule phase. We give the explicit expression of the critical point and obtain two scaling laws to characterize this transition. In particular we find that both the critical exponents and the behaviors of ground-state geometric phase change obviously in contrast to a similar two-level model. Our analytical calculations show that the ground-state geometric phase jumps from zero to ?pi/3 at the critical point. This discontinuous behavior has been checked by numerical simulations and it can be used to identify the phase transition in the system.