Scaling of Berry's phase close to the Dicke quantum phase transitionF. Plastina1, G. Liberti1 and A. Carollo2
1 Dipartimento di Fisica, Università della Calabria and Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza I-87036 Arcavacata di Rende, Cosenza, Italy
2 Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences - A-6020 Innsbruck, Austria
received 26 June 2006; accepted in final form 31 August 2006
published online 20 September 2006
We discuss the thermodynamic and finite-size scaling properties of the geometric phase in the adiabatic Dicke model, describing a quantum phase transition for an N qubit register coupled to a slow oscillator mode. We show that, in the thermodynamic limit, a non-zero Berry phase is obtained only if a path in parameter space is followed that encircles the critical point. Furthermore, we investigate the precursors of this critical behavior for a system with finite size and obtain the leading orders in the 1/N expansion of the Berry phase and its critical exponent.
03.65.Vf - Phases: geometric; dynamic or topological.
42.50.Fx - Cooperative phenomena in quantum optical systems.
© EDP Sciences 2006