Eur. Phys. J. Special Topics 217, 29-41 (2013)
https://doi.org/10.1140/epjst/e2013-01751-1

Regular Article

Mesoscopic mean-field theory for spin-boson chains in quantum optical systems

Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain

^a e-mail: pnevado@estumail.ucm.es
^b e-mail: diego.porras@fis.ucm.es

Received: 19 September 2012
Revised: 15 January 2013
Published online: 11 March 2013

Abstract

We present a theoretical description of a system of many spins strongly coupled to a bosonic chain. We rely on the use of a spin-wave theory describing the Gaussian fluctuations around the mean-field solution, and focus on spin-boson chains arising as a generalization of the Dicke Hamiltonian. Our model is motivated by experimental setups such as trapped ions, or atoms/qubits coupled to cavity arrays. This situation corresponds to the cooperative (E⊗β) Jahn-Teller distortion studied in solid-state physics. However, the ability to tune the parameters of the model in quantum optical setups opens up a variety of novel intriguing situations. The main focus of this paper is to review the spin-wave theoretical description of this problem as well as to test the validity of mean-field theory. Our main result is that deviations from mean-field effects are determined by the interplay between magnetic order and mesoscopic cooperativity effects, being the latter strongly size-dependent.