Stability of polarizable materials against superradiant phase transition

Abstract

The possibility of the superradiant phase transition in polarizable materials described by the minimal-coupling Hamiltonian with the longitudinal dipole-dipole interaction is examined. We try to reduce the Hamiltonian into the Dicke one in homogeneous and infinite case, and discuss the stability of normal ground state by the formalism of Green function in spatially inhomogeneous case. The presence of the longitudinal dipole-dipole interaction does not enable the superradiant phase transition, if the transverse and longitudinal fields are decoupled. Although the full dipole-dipole interaction can be eliminated in the electric-dipole gauge in the absence of overlap between individual atomic dipoles, we cannot reduce the Hamiltonian to the Dicke one, because the elimination is justified only if all the transverse and longitudinal fields remain. Even if the transverse and longitudinal fields are mixed in spatially inhomogeneous systems, the normal ground state is still stable if the system does not show the superradiant phase transition in the homogeneous case.

9 pages, no figure

References in corpus (8)

• 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
• 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 ?
• Strong Coupling of a Quantum Oscillator to a Flux Qubit at its Symmetry Point
• Intersubband Polaritons in the Electrical Dipole Gauge
• Drude weight, cyclotron resonance, and the Dicke model of graphene cavity QED
• QED of excitons with nonlocal susceptibility in arbitrary-structured dielectrics

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• Cavity magnonics with easy-axis ferromagnet: Critically enhanced magnon squeezing and light-matter interaction
• Superradiant Quantum Phase transition for Landau Polaritons with Rashba and Zeeman couplings
• Quantum Phase Transitions in Many-Dipole Light-Matter Systems
• Theory of lifetime of exciton incoherently created below its resonance frequency by inelastic scattering
• Light-matter interactions in the vacuum of ultra-strongly coupled systems
• Terahertz Strong-Field Physics without a Strong External Terahertz Field