Abstract We study two-photon scattering by a two-level giant atom in a waveguide. We first study the case that the giant atom is coupled to the waveguide via two coupling points, and obtain Bethe ansatz (BA) eigenstates and eigenvalues in the Hilbert space of two-excitation. Then we derive bound states by subtracting the states corresponding to BA solutions from the entire two-excitation Hilbert space, and construct the two-photon scattering matrix ( S -matrix) by using BA eigenstates and bound states. We further study the properties of output states, which include both the scattering and bound states, for arbitrarily incident two-photon states by using a concrete example. We find that the oscillation period of the scattering states and decay rates of the bound states strongly depend on the distance between two coupling points. Moreover, we find that the two-photon correlation in the bound states can be enhanced by changing such distance when the total energy of two incident photons equals to two times of single photon resonance energy. We also generalize our study to the case that the giant atom is coupled to the waveguide via N coupling points. We obtain all the eigenstates and eigenvalues of the S -matrix and construct the S -matrix. Comparing with the case of the two coupling points, we find the photon correlation can be further enhanced by increasing the number of the coupling points for the same incident states when the distance of any two nearest neighbor coupling points is half of the wavelength.
Abstract We study two-photon scattering by a two-level giant atom in a waveguide. We first study the case that the giant atom is coupled to the waveguide via two coupling points, and obtain Bethe ansatz (BA) eigenstates and eigenvalues in the Hilbert space of two-excitation. Then we derive bound states by subtracting the states corresponding to BA solutions from the entire two-excitation Hilbert space, and construct the two-photon scattering matrix ( S -matrix) by using BA eigenstates and bound states. We further study the properties of output states, which include both the scattering and bound states, for arbitrarily incident two-photon states by using a concrete example. We find that the oscillation period of the scattering states and decay rates of the bound states strongly depend on the distance between two coupling points. Moreover, we find that the two-photon correlation in the bound states can be enhanced by changing such distance when the total energy of two incident photons equals to two times of single photon resonance energy. We also generalize our study to the case that the giant atom is coupled to the waveguide via N coupling points. We obtain all the eigenstates and eigenvalues of the S -matrix and construct the S -matrix. Comparing with the case of the two coupling points, we find the photon correlation can be further enhanced by increasing the number of the coupling points for the same incident states when the distance of any two nearest neighbor coupling points is half of the wavelength.
We investigate the two-photon scattering processes in a one-dimensional waveguide coupled to either a two-level or three-level giant atom. By manipulating the accumulated phase shift between the two coupling points, we are able to effectively modify the characteristics of these scattering processes. Utilizing the Lippmann-Schwinger formalism, we obtain the exact two-photon interacting scattering wave functions of these two systems. Additionally, analytical expressions for the incoherent power spectra and second-order correlations are derived. The incoherent spectrum, which is defined by the correlation of the bound state, provides valuable insights into photon-photon correlations. It serves as a useful indicator of the degree of photon-photon correlation between scattered photons. Furthermore, the second-order correlation function gives a direct measure of the photon-photon correlation. For photons scattered by the two-level giant atom, manipulating the accumulated phase shift allows for improvement of the photon-photon correlation and adjustment of the evolution of the second-order correlation. In the case of the three-level giant atom, the photon-photon correlation can be substantially increased. The photon-photon interaction and correlation distance of the scattered photons can be further enhanced by tuning the accumulated phase shift. Moreover, the statistical properties can be adjusted by the control field.
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.
Abstract The giant atom, which means the nonlocal atom-waveguide coupling, gives lots of newfangled physics. In this paper, we study the single- and two-photon scattering in the waveguide quantum electrodynamics on a two-level giant atom. For single-photon scattering, we find that the transmission rate is dependent on the atomic size. For the two-photon scattering, using a reasonable wave function hypothesis, we can get the two-photon scattering state, which consists of the symmetric and anti-symmetric plane wave functions. The other eigenstate is the two-photon bound state, which is orthogonal to the two-photon scattering state. We find that the spatial extent of the two-photon bound state is related to the detuning between waveguide and atom, which is distinguished from the character of the general atom. Our study is beneficial to photon control and the fundamental research of the two-photon scattering.
This work investigates single-photon scattering in a one-dimensional coupled-resonator waveguide coupled to a giant atom with a complex on-site energy. Within the generalized projection operator formalism, we derive analytical expressions for the scattering coefficients. We find that a lossy giant atom absorbs the incident wave, whereas a gain giant atom not only amplifies the incident wave but also leads to scattering divergence at certain energies, corresponding to spectral singularities. We explore the critical scattering dynamics associated with these singularities, and attribute the persistent wave emission to the existence of a stationary bound state in the continuum. Due to the presence of this bound state, the conventional time-independent scattering theory proves inadequate for such a non-Hermitian system. Furthermore, we show that the system with gain always features at least one time-growing bound state, which dominates the long-time dynamics, and we verify our time-dependent theoretical predictions via numerical simulations of Gaussian wave packet scattering.
The giant-atom topological-waveguide-QED systems have recently emerged as a promising platform for manipulating light-matter interactions. The combination of the multiple-point couplings and topological phase effect could lead to rich physical phenomena and effects. Here, we study single-photon scattering in a Su-Schrieffer-Heeger (SSH) waveguide coupled to either one or two two-level giant atoms. We assume that each giant atom is coupled to the waveguide via two coupling points and hence there exist four and sixteen coupling configurations for the single-giant-atom case and two-giant-atom separate coupling case, respectively. By solving the single-photon scattering problem in the real space, we obtain the exact expressions of the single-photon scattering amplitudes. It is found that a single photon in the SSH waveguide can be completely reflected or transmitted by choosing proper coupling configurations, coupling-point distances, atomic resonance frequency, and dimerization parameter. In addition, under proper parameter conditions, the scattering spectra are periodically modulated by the coupling-point distances. We also find that the collective behavior of the two giant atoms can be adjusted by quantum interference effect and topological effect and that the single-photon scattering spectra can exhibit the Lorentzian, super-Gaussian, electromagnetically induced transparencylike, and asymmetric Fano line shapes for some coupling configurations. This work will inspire the development of controllable single-photon devices based on the giant-atom topological-waveguide-QED systems.
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.