Two emitters coupled to a bath with Kerr-like non-linearity: Exponential decay, fractional populations, and Rabi oscillations

Abstract

We consider two non-interacting two-level emitters that are coupled weakly to a one-dimensional non-linear wave guide. Due to the Kerr-like non-linearity, the wave guide considered supports -- in addition to the scattering continuum -- a two-body bound state. As such, the wave guide models a bath with non-trivial mode structure. Solving the time-dependent Schrödinger equation, the radiation dynamics of the two emitters, initially prepared in their excited states, is presented. Changing the emitter frequency such that the two-emitter energy is in resonance with one of the two-body bound states, radiation dynamics ranging from exponential decay to fractional populations to Rabi oscillations is observed. Along with the detuning, the dependence on the separation of the two emitters is investigated. Approximate reduced Hilbert space formulations, which result in effective emitter-separation and momentum dependent interactions, elucidate the underlying physical mechanisms and provide an avenue to showcase the features that would be absent if the one-dimensional wave guide did not contain a non-linearity. Our theoretical findings apply to a number of experimental platforms and the predictions can be tested with state-of-the-art technology. In addition, the weak-coupling Schrödinger equation based results provide critical guidance for the development of master equation approaches.

arXiv comment13 figures

References in corpus (41)

• Ultrastrong coupling between light and matter
• Decoherence, the measurement problem, and interpretations of quantum mechanics
• An Open-System Quantum Simulator with Trapped Ions
• Ultrastrong coupling regimes of light-matter interaction
• Repulsively bound atom pairs in an optical lattice
• Topology by Dissipation in Atomic Quantum Wires
• Quantum many-body models with cold atoms coupled to photonic crystals
• Quantum Phase Transition and Universal Dynamics in the Rabi model
• Topology by dissipation
• A review of progress in the physics of open quantum systems: theory and experiment
• Simulation methods for open quantum many-body systems
• Atom-field dressed states in slow-light waveguide QED
• Programmable Interactions and Emergent Geometry in an Atomic Array
• Two-particle states in the Hubbard model
• Markovian and Non-Markovian Dynamics of Quantum Emitters coupled to Two-dimensional Structured Reservoirs
• Bound states in boson impurity models
• Nonequilibrium Phase Diagram of a Driven-Dissipative Many-Body System
• Interacting Qubit-Photon Bound States with Superconducting Circuits
• Steady-state coherences by composite system-bath interactions
• Quantum liquid of repulsively bound pairs of particles in a lattice
• Correlated dynamics in a synthetic lattice of momentum states
• Interacting atomic quantum fluids on momentum-space lattices
• Dynamical signatures of bound states in waveguide QED
• Exact real-time dynamics of the quantum Rabi model
• Super-correlated radiance in nonlinear photonic waveguides
• Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
• Dynamical polaron ansatz: a theoretical tool for the ultra-strong coupling regime of circuit QED
• Tunnelling couplings in discrete lattices, single particle band structure and eigenstates of interacting atom pairs
• Quantum Dynamics of the Driven and Dissipative Rabi Model
• Two-channel Feshbach physics in a structured continuum
• Dissipative binding of atoms by non-conservative forces
• Dissipative dynamics of quantum correlations in the strong-coupling regime
• Photon-mediated qubit interactions in 1D discrete and continous models
• Reservoir engineering with localized dissipation: dynamics and pre-thermalization
• Stabilization of multi-mode Schrodinger cat states via normal-mode dissipation engineering
• Analytic Few Photon Scattering in Waveguide QED
• Chiral Light--Matter Interaction Beyond the Rotating-Wave Approximation
• Engineering infinite-range SU($n$) interactions with spin-orbit-coupled fermions in an optical lattice
• Photon pair condensation by engineered dissipation
• Diagrammatic approach for analytical non-Markovian time-evolution: Fermi's two atom problem and causality in waveguide quantum electrodynamics
• Diagrammatic Approach to Scattering of Multi-Photon States in Waveguide QED

Cited by in corpus (6)

• Undamped Rabi oscillations due to polaron-emitter hybrid states in non-linear photonic wave guide coupled to emitters
• Long-Range Four-body Interactions in Structured Nonlinear Photonic Waveguides
• Electromagnetically induced transparency in many-emitter waveguide quantum electrodynamics: linear versus nonlinear waveguide dispersions
• Photon-induced droplet-like bound states in one-dimensional qubit array
• Nonlinear cascaded quantum network with giant emitters
• Supercorrelated decay in a quasiperiodic nonlinear waveguide: From Markovian to non-Markovian transitions