Fluctuations and photon statistics in quantum metamaterial near the superradiant transition
arXiv:1812.04915 · doi:10.1103/PhysRevA.99.063821
Abstract
The analysis of single-mode photon fluctuations and their counting statistics at the superradiant phase transition is presented. The study concerns the equilibrium Dicke model in a regime where the Rabi frequency, related to a coupling of the photon mode with a finite-number qubit environment, plays a role of the transition's control parameter. We use the effective Matsubara action formalism based on the representation of Pauli operators as bilinear forms with complex and Majorana fermions. Then, we address fluctuations of superradiant order parameter and quasiparticles. The average photon number, the fluctuational Ginzburg-Levanyuk region of the phase transition and Fano factor are evaluated. We determine the cumulant generating function which describes a full counting statistics of equilibrium photon number. Exact numerical simulation of the superradiant transition demonstrates quantitative agreement with analytical calculations.
arXiv comment16 pages, 3 figures; revised version
References in corpus (32)
- Chaos and the Quantum Phase Transition in the Dicke Model
- Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime
- Qubit architecture with high coherence and fast tunable coupling
- Coherent and Collective Quantum Optical Effects in Mesoscopic Systems
- Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa
- Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
- Bose condensation of cavity polaritons beyond the linear regime: the thermal equilibrium of a model microcavity
- Progress in Superconducting Metamaterials
- Tunable coupling in circuit quantum electrodynamics with a superconducting V-system
- Analog quantum simulation of the Rabi model in the ultra-strong coupling regime
- Superradiant Hybrid Quantum Devices
- Implementation of a Quantum Metamaterial
- Protecting a Spin Ensemble against Decoherence in the Strong-Coupling Regime of Cavity QED
- Microwave-Induced Amplitude and Phase Tunable Qubit-Resonator Coupling in Circuit Quantum Electrodynamics
- Strong magnetic coupling of an inhomogeneous NV ensemble to a cavity
- Observation of collective coupling between an engineered ensemble of macroscopic artificial atoms and a superconducting resonator
- Dicke phase transition without total spin conservation
- Coherent Control of a Superconducting Qubit with Dynamically Tunable Qubit-cavity Coupling
- Scrambling in the Dicke model
- Dynamical Lamb Effect in a Tunable Superconducting Qubit-Cavity System
- Ultrastrong coupling dynamics with a transmon qubit
- Schwinger-Keldysh semionic approach for quantum spin systems
- Majorana representation for dissipative spin systems
- Quantum metamaterials in the microwave and optical ranges
- Kondo Impurities Coupled to Helical Luttinger Liquid: RKKY-Kondo Physics Revisited
- Approaching ultra-strong coupling in Transmon circuit-QED using a high-impedance resonator
- Josephson Metamaterial with a widely tunable positive/negative Kerr constant
- Dispersive Response of a Disordered Superconducting Quantum Metamaterial
- Finite-size fluctuations and photon statistics near the polariton condensation transition in a single-mode microcavity
- Using Majorana spin-1/2 representation for the spin-boson model
- Exact solution for the inhomogeneous Dicke model in the canonical ensemble: thermodynamical limit and finite-size corrections
- Influence of Impurity on the Rate of Single Photon Superradiance in Disordered N Qubit Chain