Effects of Modal Dispersion on Few Photon - Qubit Scattering in One-Dimensional Waveguides
arXiv:1510.03069 · doi:10.1103/PhysRevA.93.033829
Abstract
We study one- and two-photon scattering from a qubit embedded in a one-dimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersion leads to atom-photon bound states which necessitate the use of multichannel scattering theory. We present multichannel scattering matrix elements in terms of the solution of a Fredholm integral equation of the second kind. Through the use of the Lippmann-Schwinger equation, we derive an infinite series of Feynman diagrams that represent the solution to the integral equation. We use the Feynman diagrams as vertex correction terms to come up with closed form formulas that successfully predict the trapping rate of a photon in the atom-photon bound state. We verify our formalism through Krylov-subspace based numerical studies with pulsed excitations. Our results provide the tools to calculate the complex correlations between scattered photons in a dispersive environment.
19 pages, 10 figures, published version with updated introduction, discussion, figures and references, supplementary files include data files for figures and the TeX code to generate all of the figures
References in corpus (17)
- Controllable scattering of photons inside a one-dimensional resonator waveguide
- Input-Output Formalism For Few-Photon Transport in One-Dimensional Nanophotonic Waveguides Coupled to a Qubit
- Strongly-correlated multi-particle transport in one-dimension through a quantum impurity: an outline of exact and complete solutions
- Waveguide QED: Power Spectra and Correlations of Two Photons Scattered Off Multiple Distant Qubits and a Mirror
- Scattering in the ultrastrong regime: nonlinear optics with one photon
- Bound states in the continuum in a single-level Fano-Anderson model
- Input-Output Formalism for Few-Photon Transport: A Systematic Treatment Beyond Two Photons
- Scattering of two photons from two distant qubits: Exact solution
- Scattering of massless particles in one-dimensional chiral channel
- Scattering of two photons on a quantum emitter in a one-dimensional waveguide: Exact dynamics and induced correlations
- Chains with loops - synthetic magnetic fluxes and topological order in one-dimensional spin systems
- Quantum dynamics in photonic crystals
- Green's Function Formalism for Waveguide QED Applications
- Strong non-linearity-induced correlations for counter-propagating photons scattering on a two-level emitter
- Photon distribution function for propagation of two-photon pulses in waveguide-qubit systems
- Lattice mapping for many-body open quantum systems and its application to atoms in photonic cystals
- Ken Wilson: Solving the Strong Interactions
Cited by in corpus (19)
- Microwave photonics with superconducting quantum circuits
- Exciting a Bound State in the Continuum through Multi-Photon Scattering plus Delayed Quantum Feedback
- The SLH framework for modeling quantum input-output networks
- Bound states in boson impurity models
- Inelastic scattering of photon pairs in qubit arrays with subradiant states
- Non-Markovian Dynamics of a Qubit Due to Single-Photon Scattering in a Waveguide
- Nonperturbative Waveguide Quantum Electrodynamics
- Bound state in the continuum by spatially separated ensembles of atoms in a coupled-cavity array
- General structure of two-photon S matrix in waveguide quantum electrodynamics systems containing a local quantum system with multiple ground states
- Bound state and non-Markovian dynamics of a quantum emitter around a surface plasmonic nanostructure
- Diagrammatic Approach to Multiphoton Scattering
- Few-photon Fock-state wave packet interacting with a cavity-atom system in a waveguide: Exact quantum state dynamics
- Fano Interference in Two-Photon Transport
- Few-Photon Scattering in Dispersive Waveguides with Multiple Qubits
- One- and two-photon scattering from generalized V-type atoms
- Diagrammatic Approach to Scattering of Multi-Photon States in Waveguide QED
- FDTD: solving 1+1D delay PDE in parallel
- Emergent Causality and the N-photon Scattering Matrix in Waveguide QED
- Two-Photon Scattering in USC regime