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

TL;DR

This paper develops a mesoscopic mean-field and spin-wave theoretical framework for spin-boson chains in quantum optical systems, analyzing deviations from mean-field predictions influenced by size-dependent cooperative effects.

Contribution

It introduces a spin-wave theory for spin-boson chains, extending mean-field analysis to include mesoscopic fluctuations relevant for quantum optical experiments.

Findings

Deviations from mean-field are governed by magnetic order and cooperativity.

Size-dependent effects significantly influence the system's behavior.

Theoretical framework applicable to experimental setups like trapped ions and cavity QED.

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$\otimes$$\beta$) 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.