We investigate one- and two-photon scattering in a one-dimensional waveguide coupled to a giant atom within the non-Markovian regime using the resolvent approach. The non-Markovian behavior gives rise to an atom-photon bound state that cannot be excited by a single incident photon. However, the bound state can be excited via the two-photon scattering process described by multichannel scattering theory, from which an analytical trapping probability of a photon in the bound state can be achieved. Additionally, we analyze the two-photon scattering process, obtaining the analytical expressions for scattered states. As non-Markovian effects strengthen, two peaks appear in the incoherent power spectrum, attributed to the system behaving as a leaky cavity formed by the giant atom's coupling points. Through the analysis of second-order correlation functions, we observe the bunching behavior for transmitted photons, antibunching behavior for reflected photons, and the distinctive retrieval behavior at the coupling points' separation.
We investigate one- and two-photon scattering in a one-dimensional waveguide coupled to a giant atom within the non-Markovian regime using the resolvent approach. The non-Markovian behavior gives rise to an atom-photon bound state that cannot be excited by a single incident photon. However, the bound state can be excited via the two-photon scattering process described by multichannel scattering theory, from which an analytical trapping probability of a photon in the bound state can be achieved. Additionally, we analyze the two-photon scattering process, obtaining the analytical expressions for scattered states. As non-Markovian effects strengthen, two peaks appear in the incoherent power spectrum, attributed to the system behaving as a leaky cavity formed by the giant atom's coupling points. Through the analysis of second-order correlation functions, we observe the bunching behavior for transmitted photons, antibunching behavior for reflected photons, and the distinctive retrieval behavior at the coupling points' separation.
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.
We investigate the single-photon scattering spectra of a giant atom coupled to a one-dimensional waveguide via multiple connection points or a continuous coupling region. Using a full quantum mechanical method, we obtain the general analytic expressions for the single-photon scattering coefficients, which are valid in both the Markovian and the non-Markovian regimes. We summarize the influences of the nondipole effects, mainly caused by the phases accumulated by photons traveling between coupling points, on the scattering spectra. We find that under the Markovian limit, the phase decay is detuning independent, resulting in Lorentzian line shapes characterized by the Lamb shifts and the effective decay rates, while in the non-Markovian regime, the accumulated phases become detuning dependent, giving rise to non-Lorentzian line shapes, characterized by multiple side peaks and total transmission points. Another interesting phenomenon in the non-Markovian regime is the generation of a broad photonic band gap by a single giant atom. We further generalize the case of discrete coupling points to the continuum limit with atom coupling to the waveguide via a continuous area, and analyze the scattering spectra for some typical distributions of coupling strength.
We investigate the single-photon scattering spectra in a giant-molecule waveguide quantum electrodynamics system, where a giant molecule consisting of two coupled giant atoms is connected to two waveguides via two separate sites, respectively. The phases of coupling strengths between the giant molecule and waveguides are considered. Using a real-space method, we obtain the exact analytical expressions for the single-photon scattering coefficients, which are valid both in the Markovian and non-Markovian regimes. It is shown that the transmission spectra strongly depend on phases, including the phases accumulated by photons traveling between coupling points and the phase difference between two coupled channels of the giant-molecule upper (lower) waveguide. Under the Markovian limit, we find that by selecting appropriate accumulated phases and local phase difference, targeted routing and asymmetrical scattering of photons can be achieved without breaking the symmetry in the coupling configuration between the giant molecule and waveguides. Moreover, all the optimal phase combinations for implementing single-photon routing have been summarized. In the non-Markovian regime, the scattering spectra show more complicated line shapes with multiple staggered peaks and dips. More interestingly, the scattering spectrum exhibits periodic changes during the transition from the Markovian to the non-Markovian regime, which makes one obtain a means to control photon routing in addition to phases. Our results may be useful in controlling and manipulating light-matter interactions involving giant atoms at the single-photon level.
We investigate the scattering processes of two photons in a one-dimensional waveguide coupled to two giant atoms. By adjusting the accumulated phase shifts between the coupling points, we are able to effectively manipulate the characteristics of these scattering photons. Utilizing the Lippmann-Schwinger formalism, we derive analytical expressions for the wave functions describing two-photon interaction in separate, braided, and nested configurations. Based on these wave functions, we also obtain analytical expressions for the incoherent power spectra and second-order correlation functions. In contrast to small atoms, the incoherent spectrum, which is defined by the correlation of the bound state, can exhibit more tunability due to the phase shifts. Additionally, the second-order correlation functions in the transmission and reflection fields could be tuned to exhibit either bunching or antibunching upon resonant driving. These unique features offered by the giant atoms in waveguide QED could benefit the generation of nonclassical itinerant photons in quantum networks.
We study the generation of quantum entanglement between two giant atoms coupled to a common one-dimensional waveguide. Here each giant atom interacts with the waveguide at two separate coupling points. Within the Wigner-Weisskopf framework for single coupling points, we obtain the time-delayed quantum master equations governing the evolution of the two giant atoms for three different coupling configurations: separated, braided, and nested couplings. For each coupling configuration, we consider both the Markovian and non-Markovian entanglement dynamics of the giant atoms, which are initially in two different separable states: single- and double-excitation states. Our results show that the generated entanglement depends on the phase shift, time delay, atomic initial state, and the coupling configuration. For the single-excitation initial state, there exists the steady-state entanglement for each coupling in both the Markovian and non-Markovian regimes due to the appearance of the dark state. For the double-excitation initial state, we observe entanglement sudden birth via adjusting the phase shift in both regimes. In particular, the maximally achievable entanglement for the nested coupling is about one order of magnitude larger than those of separate and braided couplings. We also find that the maximal entanglement for these three coupling configurations can be enhanced in the case of small time delays. This work can be utilized for the generation and control of entanglement in quantum networks based on giant-atom waveguide-QED systems, which have wide potential applications in quantum information processing.
Describing systems of superconducting atoms coupled to a continuum of photonic modes at multiple separated locations in a waveguide, waveguide quantum electrodynamics (QED) with giant atoms has emerged as a promising platform for realizing quantum interconnect. Such systems have been reported to exhibit rich phenomena that differ from those of natural atoms. Going beyond the widely used Born-Markov and Wigner-Weisskopf approximations, we investigate the non-Markovian dynamics of one and two giant atoms interacting with a waveguide formed by an array of coupled resonators. We discover that the diverse dynamical behaviors of the giant atoms are intrinsically determined by the energy spectrum of the composite system consisting of the giant atoms and the photonic modes in the waveguide. As long as one and more bound states are present in the energy spectrum, their excited-state probabilities, respectively, tend to stable finite values and lossless Rabi-like oscillations with frequencies proportional to the differences of the bound-state eigenenergies. Our result provides an insightful guideline for suppressing the decoherence of giant atoms and facilitates the development of quantum interconnect devices using giant-atom waveguide QED.