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arXiv:1603.02920 · Optics Letters

Few-photon scattering in dispersive waveguides with multiple qubits

Şükrü Ekin Kocabaş

Published May 20, 2016• 11 citations
arXivHTMLPDF

Abstract

We extend the Krylov-subspace-based time-dependent numerical simulation technique for a qubit interacting with photons in a waveguide to the multiple qubit case. We analyze photon scattering from two qubits and derive expressions for the bound states in the continuum (BICs). We show how the BIC can be excited. We use the BIC in a recent Pauli-Z gate proposal involving decoherence free subspaces and obtain the gate fidelity as a function of the gate parameters. The techniques presented in this Letter are useful for investigating the time evolution of quantum gates and other many-body systems with multiple quenches in the Hamiltonian.

DOI
10.1364/ol.41.002533

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We extend the Krylov-subspace-based time-dependent numerical simulation technique for a qubit interacting with photons in a waveguide to the multiple qubit case. We analyze photon scattering from two qubits and derive expressions for the bound states in the continuum (BICs). We show how the BIC can be excited. We use the BIC in a recent Pauli-Z gate proposal involving decoherence free subspaces and obtain the gate fidelity as a function of the gate parameters. The techniques presented in this Letter are useful for investigating the time evolution of quantum gates and other many-body systems with multiple quenches in the Hamiltonian.
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.
We consider a semi-infinite waveguide with linear dispersion coupled to a qubit, in which a dressed bound state in the continuum (BIC) is known to exist. We predict that this BIC can be excited with significant probability via multi-photon scattering in the non-Markovian regime where the photon delay time (corresponding to the qubit-mirror distance) is of the order of the qubit’s decay time. A similar process excites the BIC existing in an infinite waveguide coupled to a pair of qubits, yielding stationary entanglement between them. This shows, in particular, that photon trapping via scattering can occur without band-edge effects or cavities, the essential resource being instead the delayed quantum feedback due to the mirror.
The excitation of bound states in the continuum (BICs) in two- or multiqubit systems lies at the heart of entanglement generation and harnessing in waveguide quantum electrodynamics platforms. However, the generation of qubit pair BICs through single-photon scattering is hindered by the fact that these states are effectively decoupled from propagating photons. We prove that scattering of a parity-invariant single photon on a qubit pair, combined with a properly engineered time variation of the qubit detuning, is not only feasible, but also more effective than strategies based on the relaxation of the excited states of the qubits when the distance between the qubits gives rise to non-negligible photon delays (non-Markovian regime). The use of tensor network methods to simulate the proposed scheme enables us to include such photon delays in collision models, thus opening the possibility to follow the time evolution of the full quantum system, including qubits and field, and to efficiently implement and characterize the dynamics, hence identifying optimal working points for the BIC generation.
Excitation of a bound state in the continuum (BIC) through scattering is problematic since it is by definition uncoupled. Here, we consider a type of dressed BIC and show that it can be excited in a nonlinear system through multiphoton scattering and delayed quantum feedback. The system is a semi-infinite waveguide with linear dispersion coupled to a qubit, in which a single-photon, dressed BIC is known to exist. We show that this BIC can be populated via multiphoton scattering in the non-Markovian regime, where the photon delay time (due to the qubit-mirror distance) is comparable with the qubit's decay. A similar process excites the BIC existing in an infinite waveguide coupled to two distant qubits, thus yielding stationary entanglement between the qubits. This shows, in particular, that single-photon trapping via multiphoton scattering can occur without band edge effects or cavities, the essential resource being instead the delayed quantum feedback provided by a single mirror or the emitters themselves.
Bound states in the continuum (BICs) have been extensively exploited to enhance light--matter interactions in metamaterials, yet their emergence and utility in multi-atom waveguide platforms remain far less explored. Here we study atom--waveguide-dressed BICs in a one-dimensional coupled-resonator waveguide, where two spatially separated atomic arrays couple to distinct resonators with time-dependent strengths. We show that these BICs support a standing-wave photonic mode and enable the transfer of an arbitrary unknown quantum state between the two arrays with fidelities exceeding 99%99\%99%. The protocol remains robust against both disorder and intrinsic dissipation. Our results establish BICs as long-lived resources for high-fidelity quantum information processing in waveguide-QED architectures.
Bound states in the continuum (BICs) have been extensively exploited to enhance light-matter interactions in metamaterials, yet their emergence and utility in multiatom waveguide platforms remain far less explored. Here we study atom-waveguide-dressed BICs in a one-dimensional coupled-resonator waveguide, where two spatially separated atomic arrays couple to distinct resonators with time-dependent strengths. We show that these BICs host standing-wave photonic components and enable the transfer of unknown atomic quantum states encoded in the single-excitation subspace between the two arrays, with fidelities exceeding 99%. Going beyond traditional cascaded-quantum-network protocols, our scheme leverages BIC-assisted interference to remain robust against both disorder and intrinsic dissipation. Our results establish BICs as long-lived resources for high-fidelity quantum information processing in waveguide-QED architectures.