Eur. Phys. J. D (2016) 70: 213
https://doi.org/10.1140/epjd/e2016-70492-x

Regular Article

Quantum Monte Carlo study of the Rabi-Hubbard model

¹ UCA, CNRS, INLN, 1361 route des Lucioles, 06560 Valbonne, France
² Physics Department, Loyola University New Orleans, 6363 Saint Charles Ave., New Orleans, LA 70118, USA
³ Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁴ MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit UMI 3654, Singapore, Singapore
⁵ Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore

^a e-mail: frederic.hebert@unice.fr

Received: 2 August 2016
Received in final form: 30 August 2016
Published online: 18 October 2016

Abstract

We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of a one dimensional Rabi-Hubbard model. The model consists of a lattice of Rabi systems coupled by a photon hopping term between near neighbor sites. For large enough coupling between photons and atoms, the phase diagram generally consists of only two phases: a coherent phase and a compressible incoherent one separated by a quantum phase transition (QPT). We show that, as one goes deeper in the coherent phase, the system becomes unstable exhibiting a divergence of the number of photons. The Mott phases which are present in the Jaynes-Cummings-Hubbard model are not observed in these cases due to the presence of non-negligible counter-rotating terms. We show that these two models become equivalent only when the detuning is negative and large enough, or if the counter-rotating terms are small enough