Waveguide QED: Multiple Qubits, Inelastic Scattering, and Non-Markovianity

Rahul Trivedi, Daniel Malz, Shuo Sun +2 more

Bound states arise in waveguide QED systems with a strong frequency-dependence of the coupling between emitters and photonic modes. While exciting such bound-states with single-photon wave-packets is not possible, photon-photon interactions mediated by the emitters can be used to excite them with two-photon states. In this Letter, we use scattering theory to provide upper limits on this excitation probability for a general non-Markovian waveguide QED system and show that this limit can be reached by a two-photon wave packet with vanishing uncertainty in the total photon energy. Furthermore, we also analyze multi-emitter waveguide QED systems with multiple bound states and provide a systematic construction of two-photon wave packets that can excite a given superposition of these bound states. As specific examples, we study bound-state trapping in waveguide QED systems with single and multiple emitters and a time-delayed feedback.

Rempe

Neill Lambert, Yi-Te Huang, Yueh-Nan Chen +2 more

We consider the problem of modeling a single qubit in contact with a one-dimensional waveguide beyond the standard perturbative and Markovian approximations. Using the recently developed input-output hierarchical equations of motion (io-HEOM), we investigate multiple examples of such waveguides, characterized by different spectral densities. Our examples highlight that the io-HEOM method can accurately capture non-Markovianity in waveguide QED from two distinct origins. The first source of non-Markovianity is spatially non-local coupling between the qubit and the waveguide. By examining two examples with non-local coupling, we show how the coupling function affects the steady-state bound photons, and demonstrate the release of these photons when the qubit energy is quenched. The second source of non-Markovianity is non-linear dispersion. We illustrate this scenario using the example of a cavity array with point-like coupling, where the non-linear dispersion leads to persistent oscillations due to Van Hove singularities in the spectral density.

Andrés Rosario Hamann

Xian-Li Yin, Yu-Hong Liu, Jin-Feng Huang +1 more

We study the coherent single-photon scattering in a one-dimensional waveguide coupled to a giant artificial molecule consisting of two coupled giant atoms. Since each giant atom couples to the waveguide via two coupling points, the couplings of the molecule with the waveguide have three different coupling configurations: the separated-, braided-, and nested-coupling cases. We obtain the exact expressions of the single-photon transmission and reflection amplitudes with the real-space approach. It is found that the behavior of the scattering spectra depends on the phase shift between two neighboring coupling points, the coupling configuration, and the coupling between the two giant atoms. Concretely, we study the photon scattering in both the Markovian and non-Markovian regimes, in which the photon propagating time between two neighboring coupling points is neglected and considered, respectively. Under the Markovian limit, the asymmetric Fano line shapes in different coupling configurations of the giant-molecule waveguide-QED system can be obtained by choosing proper phase shift, and the transmission window can be adjusted by the coupling strength between the two giant atoms in these three coupling configurations. In particular, multiple reflection peaks and dips in these configurations are revived in the non-Markovian regime. This paper will pave the way for the study of controllable single-photon devices based on the giant-molecule waveguide-QED systems.

Maximilian Zanner, Christian Schneider, Mathieu L. Juan +4 more