Large Random Arrowhead Matrices: Multifractality, Semi-Localization, and Protected Transport in Disordered Quantum Spins Coupled to a Cavity

Abstract

We provide an exact solution of large random arrowhead Hamiltonians with diagonal disorder, a minimal model for inhomogeneously broadened quantum emitters coupled to a cavity mode. We find that the distribution of energy spacing can be continuously tuned between Poisson statistics and a distribution that is very close to semi-Poisson statistics - the latter being usually associated to the critical point of "Anderson" localization-delocalization transitions. We demonstrate that all the eigenstates - including two polaritons and a continuum of dark states - are multifractal, which indicates the existence of a critical "semi-localized" phase for all values of the light-matter coupling strength, where dark states are localized over multiple, arbitrarily-distant sites. By computing the escape probability from an initial site, we find that the system has a peculiar diffusive-like behavior with an escape probability growing linearly with time for any finite coupling strength, and that the escape rate can be controlled by selecting the energy of the initial site. The escape rate averaged over the disorder configurations is found to exhibit a maximum for intermediate coupling strengths, before saturating at a lower value in the collective strong coupling limit - a "cavity protection" effect. Surprisingly, we show that the saturation value increases with the disorder, indicating that the cavity does not only protect transport against disorder but can also turn the latter into an ally improving transport. We finally investigate the system in a two-terminal configuration, and show that the steady-state excitation current exhibits similar features as the escape probability, thereby extending our cavity-protected transport scenario to out-of-equilibrium situations. We finally demonstrate that dark states can provide the major contribution to long-distance transport in disordered systems.

References in corpus (38)

• Random-Matrix Theory of Quantum Transport
• Random Matrix Theories in Quantum Physics: Common Concepts
• Anderson Transitions
• Strong coupling between surface plasmon polaritons and emitters
• Mechanically-Controlled Binary Conductance Switching of a Single-Molecule Junction
• Strong Coupling of a Spin Ensemble to a Superconducting Resonator
• Conductivity in organic semiconductors hybridized with the vacuum field
• Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system
• Theory of the spin bath
• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Extraordinary exciton conductance induced by strong coupling
• Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit QED
• Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa
• Cavity enhanced transport of excitons
• Molecular polaritons for controlling chemistry with quantum optics
• Fluctuations of the inverse participation ratio at the Anderson transition
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Electron spin evolution induced by interaction with nuclei in a quantum dot
• Heat conduction in molecular transport junctions
• Theory of the strong coupling between quantum emitters and propagating surface plasmons
• Exact relations between multifractal exponents at the Anderson transition
• Dark state semilocalization of quantum emitters in a cavity
• Dicke model simulation via cavity-assisted Raman transitions
• Spectroscopic properties of inhomogeneously broadened spin ensembles in a cavity
• Uncoupled dark states can inherit polaritonic properties
• Coherent Coupling of Remote Spin Ensembles via a Cavity Bus
• Disorder-Enhanced and Disorder-Independent Transport with Long-Range Hopping: Application to Molecular Chains in Optical Cavities
• Thermodynamics and Excitations of Condensed Polaritons in Disordered Microcavities
• Cavity-assisted mesoscopic transport of fermions: Coherent and dissipative dynamics
• Algorithmic simulation of far-from-equilibrium dynamics using quantum computer
• Dispersive regime of the Jaynes-Cummings and Rabi lattice
• Accurate eigenvalue decomposition of arrowhead matrices and applications
• Dispersive Response of a Disordered Superconducting Quantum Metamaterial
• Transmission Spectrum of an Optical Cavity Containing N Atoms
• Absorption, Photoluminescence and Resonant Rayleigh Scattering Probes of Condensed Microcavity Polaritons
• Non-interacting central site model: localization and logarithmic entanglement growth
• Single-molecule-mediated heat current between an electronic and a bosonic bath

Cited by in corpus (16)

• Polariton Localization and Dispersion Properties of Disordered Quantum Emitters in Multimode Microcavities
• Disorder enhanced vibrational entanglement and dynamics in polaritonic chemistry
• Engineering random spin models with atoms in a high-finesse cavity
• Generalization of the Tavis-Cummings model for multi-level anharmonic systems: insights on the second excitation manifold
• Disorder-enhanced transport in a chain of lossy dipoles strongly coupled to cavity photons
• Theoretical Analysis of Exciton Wave Packet Dynamics in Polaritonic Wires
• Eliminating radiative losses in long-range exciton transport
• Spectral Engineering of Cavity-Protected Polaritons in an Atomic Ensemble with Controlled Disorder
• Integrability and quench dynamics in the spin-1 central spin XX model
• Multifractality in the interacting disordered Tavis-Cummings model
• Integrability, multifractality, and two-photon dynamics in disordered Tavis-Cummings models
• Theory for polaritonic quantum tunneling
• Multiple Interacting Photonic Modes in Strongly Coupled Organic Microcavities
• Stable interaction-induced Anderson-like localization embedded in standing waves
• Linear level repulsions near exceptional points of non-Hermitian systems
• Strong light-matter interaction effects on molecular ensembles