First order dipolar phase transition in the Dicke model with infinitely coordinated frustrating interaction

Abstract

We found analytically a first order quantum phase transition in the Cooper pair box array of $N$ low-capacitance Josephson junctions capacitively coupled to a resonant photon in a microwave cavity. The Hamiltonian of the system maps on the extended Dicke Hamiltonian of $N$ spins one-half with infinitely coordinated antiferromagnetic (frustrating) interaction. This interaction arises from the gauge-invariant coupling of the Josephson junctions phases to the vector potential of the resonant photon field. In $N\gg 1$ semiclassical limit, we found a critical coupling at which ground state of the system switches to the one with a net collective electric dipole moment of the Cooper pair boxes coupled to superradiant equilibrium photonic condensate. This phase transition changes from the first to second order if the frustrating interaction is switched off. A self-consistently `rotating' Holstein-Primakoff representation for the Cartesian components of the total superspin is proposed, that enables to trace both the first and the second order quantum phase transitions in the extended and standard Dicke models respectively.

12 pages, 10 figures

References in corpus (10)

• Ultra-Strong Light-Matter Coupling Regime with Polariton Dots
• Is there a no-go theorem for superradiant quantum phase transitions in cavity and circuit QED ?
• Single artificial-atom lasing
• Ultrastrong coupling phenomena beyond the Dicke model
• Demonstration of an ac Josephson junction laser
• Super-radiant phase transition in superconducting circuit in thermal equilibrium
• Single-artificial-atom lasing using a voltage-biased superconducting charge qubit
• Time-delayed feedback control of the Dicke-Hepp-Lieb superradiant quantum phase transition
• Effects of lasing in a one-dimensional quantum metamaterial
• Double resonance response of a superconducting quantum metamaterial: manifestation of non-classical states of photons

Cited by in corpus (5)

• Quantum Dicke battery supercharging in the "bound luminocity" state
• Dicke model semiclassical dynamics in superradiant dipolar phase in the 'bound luminosity' state
• Correspondence between Dicke-model semiclasscial dynamics in the superradiant dipolar phase and the Euler heavy top
• "Bound luminosity" state in the extended Dicke model
• Spontaneous symmetry breaking and Husimi Q-functions in extended Dicke model