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

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.

To appear in EPJ ST issue on "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases"

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Cited by in corpus (7)

• Analog Quantum Simulation of (1+1)D Lattice QED with Trapped Ions
• Hybrid quantum magnetism in circuit-QED: from spin-photon waves to many-body spectroscopy
• Adiabatic quantum metrology with strongly correlated quantum optical systems
• Lieb-Robinson bounds for spin-boson lattice models and trapped ions
• Hidden Frustrated Interactions and Quantum Annealing in Trapped Ion Spin-Phonon Chains
• Simulation of Jahn-Teller-Dicke Magnetic Structural Phase Transition with Trapped Ions
• The Interspersed Spin Boson Lattice Model