Polariton spectrum of the Dicke-Ising model

Abstract

The Dicke-Ising model describes cavity quantum electrodynamics setups in which dipoles couple not only with the photonic cavity field but also to each other through dipole-dipole interaction. In this work we diagonalise such a model in terms of bosonic polaritonic operators for arbitrarily large values of the light-matter coupling and for values of the dipole-dipole interaction until the onset of the ferromagnetic Ising phase transition. In order to accomplish this task we exploit higher order terms of the Holstein-Primakoff transformation, developing a general method which allows to solve the normal phase of the Ising model in term of bosonic excitations for large values of the dipole-dipole interaction. Our results shed light on the interplay between the dipole-dipole and the light-matter coupling strengths, and their effect on the virtual excitations which populate the ground-state when the interactions become comparable with the bare transition frequency.

13 pages, 6 figures

References in corpus (9)

• Coupling Superconducting Qubits via a Cavity Bus
• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Time-reversal symmetry breaking in circuit-QED based photon lattices
• Is there a no-go theorem for superradiant quantum phase transitions in cavity and circuit QED ?
• Stability of polarizable materials against superradiant phase transition
• Vacuum Rabi oscillation induced by virtual photons in the ultrastrong coupling regime
• Interacting spins in a cavity: finite size effects and symmetry-breaking dynamics
• Quantum phase transition of nonlocal Ising chain with transverse field in a resonator