We present a theoretical study of Fano interference effects in few-photon transport. Under appropriate conditions, a local defect in an optical waveguide induces a highly asymmetric transmission lineshape, characteristic of Fano interference. For a two-level emitter placed adjacent to such a defect, here modeled as a partially transmitting element, we find an analytical expression for the full time evolution of single-photon wavepackets and the emitter excitation probability. We show how the partially transmitting element affects the emitter lifetime and shifts the spectral position of the effective system resonances. Using input-output formalism, we determine the single and two-photon $ S $-matrices for both a two-level emitter and a cavity-emitter system coupled to a waveguide with a partially transmitting element. We show how the Fano interference effect can be exploited for the implementation of a Hong-Ou-Mandel switch in analogy with a tunable linear or nonlinear beam splitter.
A strong optical nonlinearity arises when coherent light is scattered by a semiconductor quantumdot (QD) coupled to a nano-photonic waveguide. We exploit the Fano effect in such a waveguide to control the phase of the quantum interference underpinning the nonlinearity, experimentally demonstrating a tunable quantum optical filter which converts a coherent input state into either a bunched, or antibunched non-classical output state. We show theoretically that the generation of non-classical light is predicated on the formation of a two-photon bound state due to the interaction of the input cohe…
A route toward lineshape engineering of Fano resonances in photonic structures is theoretically proposed, which uses dynamic modulation of the refractive index of a microcavity. The method is exemplified by considering coupled-resonator optical waveguide systems. An exact Floquet analysis, based on coupled-mode theory, is presented. Two distinct kinds of resonances can be dynamically created, depending on whether the static structure sustains a localized mode or not. In the former case a single Fano resonance arises, which can be tuned in both frequency and line width by varying the refractive…
Phase-Selected Efficient Single-Photon Frequency Conversion via Local Fano Resonance in a Two-Giant-Atom Waveguide-QED System
Key Laboratory of Opto-electronic Control and Detection Technology of University of Hunan Province, and College of Physics and Electronic Engineering, Hengyang Normal University（衡阳师范学院光电控制与检测技术湖南省重点实验室及物理与电子工程学院）；Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education，Hunan Normal University（湖南师范大学教育部低维量子结构与量子控制重点实验室）
We present a general input-output formalism for the few-photon transport in multiple waveguide channels coupled to a local cavity. Using this formalism, we study the effect of Fano interference in two-photon quantum transport. We show that the physics of Fano interference can manifest as an asymmetric spectral line shape in the frequency dependence of the two-photon correlation function. The two-photon fluorescence spectrum, on the other hand, does not exhibit the physics of Fano interference.
We investigate coherent single-photon transport in a waveguide-QED structure containing two giant atoms. The unified analytical expressions of the single-photon scattering amplitudes applicable for different topological configurations are derived. The spectroscopic characteristics in different parameter regimes, especially the asymmetric Fano line shapes and the electromagnetically induced transparency (EIT)-like spectra, are analyzed in detail. Specifically, we find that the appearance of Fano line shapes is influenced by not only the phase delays between coupling points but also the topologi…
Finite projective geometries, especially the Fano plane, have been observed to arise in the context of certain quantum gate operators. We use Clifford algebras to explain why these geometries, both planar and higher dimensional, appear in the context of multi-qubit composite systems.
Fano profiles, with their asymmetric character, have many potential applications in technology. The design of Fano profiles into optical systems may create new nonlinear and switchable metamaterials, high-quality optical waveguides, ultrasensitive media for chemical or biosensing etc. In this paper, we consider an external field-driven double Fano model, in which, instead of one autoionizing state, there are two discrete states embedded in one continuum. We assume further that the external electromagnetic field can be decomposed into two parts: a deterministic (or coherent) part and a randomly…
In this paper, we investigate the single-photon scattering and bound states in a one-dimensional coupled-resonator waveguide which couples to a single artificial giant atom with two or more coupling points. When the atom couples to the waveguide via two resonators, the single-photon reflection rate is characterized by either Breit-Wigner or Fano line shapes. When the atom couples to the waveguide via multiple resonators, we numerically show how the destructive interference effect leads to a complete single-photon reflection. We also find a phase transition phenomena for the multi-resonator cou…
We study the effect of PT-symmetric complex potentials on the transport properties of non-Hermitian systems, which consist of an infinite linear chain and two side-coupled defect points with PT-symmetric complex on-site potentials. By analytically solving the scattering problem of two typical models, which display standard Fano resonances in the absence of non-Hermitian terms, we find that the PT-symmetric imaginary potentials can lead to some pronounced effects on transport properties of our systems, including changes from the perfect reflection to perfect transmission, and rich behaviors for…
We study a waveguide QED system with a rectangular waveguide and a two-level system (TLS) inside, where the transverse modes TMmn define the quantum channels of guided photons. It is discovered that the loss of photons in the TM11 channel into the others can be overcome by replacing it with a certain coherent superposition of TMmn channels, which is named as the controllable channel (CC) as the photons in CC can be perfectly reflected or transmitted by the TLS, and never lost into the other channels. The dark state emerges when the photon is incident from one of the scattering-free channels (S…
Non-zero curvature in a waveguide leads to the appearance of an attractive quantum potential which crucially affects the dynamics in matter-wave circuits. Using methods of supersymmetric quantum mechanics, pairs of bent waveguides are found whose geometry-induced potentials share the same scattering properties. As a result, reflectionless waveguides, dual to the straight waveguide, are identified. Strictly isospectral waveguides are also found by modulating the depth of the trapping potential. Numerical simulations are used to demonstrate the efficiency of these approaches in tailoring and con…
We introduce a three qubit waveguide QED system to mimic the cavity-QED strong coupling regime of a probe qubit embedded in atom-like mirrors, which was realized in recent experiments. We then extend this system into the deep non-Markovian regime and demonstrate the profound role that retardation plays on the dressed resonances, allowing one to significantly improve the polariton lifetimes (by many orders of magnitude), tune the resonances, as well as realize Fano-like resonances and simultaneous coupling to multiple cavity modes. Exact Green function solutions are presented for the spectral r…
This is a theory for the effect of localization on the super-Poissonian noise of radiation propagating through an absorbing disordered waveguide. Localization suppresses both the mean photon current I and the noise power P, but the Fano factor P/I is found to remain unaffected. For strong absorption the Fano factor has the universal value 1+3f/2 (with f the Bose-Einstein function), regardless of whether the waveguide is long or short compared to the localization length.
We investigate single photon scattering properties in one-dimensional waveguide coupled to quantum emitter's chain with dipole-dipole interaction (DDI). The photon transport is extremely sensitive to the location of the evanescently coupled emitters. The analytical expressions of reflection and transmission amplitudes for the chain containing two emitters with DDI are deduced by using real-space Hamiltonian. Two cases, where the two emitters symmetrically and asymmetrically couple to the waveguide, are discussed in detail. It shows that the reflection and transmission typical spectra split int…
Quantum routing of single photons in a system with two waveguides coupled to two whispering-gallery resonators (WGRs) are investigated theoretically. With a real-space full quantum theory, photonic scattering amplitudes along four ports of the waveguide network are analytically obtained. It is shown that, by adjusting the geometric and physical parameters of the two-WGR configuration, the quantum routing properties of single photons along the present waveguide network can be controlled effectively. For example, the routing capability from input waveguide to another one can significantly exceed…
We present a semiconductor master equation technique to study the input/output characteristics of coherent photon transport in a semiconductor waveguide-cavity system containing a single quantum dot. We use this approach to investigate the effects of photon propagation and anharmonic cavity-QED for various dot-cavity interaction strengths, including weakly-coupled, intermediately-coupled, and strongly-coupled regimes. We demonstrate that for mean photon numbers much less than 0.1, the commonly adopted weak excitation (single quantum) approximation breaks down, even in the weak coupling regime.…
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 neighbo…
We show that two-photon transport can be modulated by a two-level emitter coupled to a cavity in a one-dimensional waveguide. In the ordinary case, the transmitted light has a wider frequency spectrum than the situation without the cavity because it is reflected and scattered many times. But when the two photons are resonant with the cavity resonance reflection frequency, the frequency spectrum of the transmitted light becomes narrower than that without the cavity. This means that properly tuning the cavity resonance frequency can improve the photon-photon interaction. In addition, we show tha…
We study the photon-photon correlation properties of two-photon transport in a one-dimensional waveguide coupled to a nonlinear cavity via a real-space approach. It is shown that the intrinsic dissipation of the nonlinear cavity has an important effect upon the correlation of the transported photons. More importantly, strongly correlated photons can be obtained in the transmitted photons even when the nonlinear interaction strength is weak in the cavity. The strong photon-photon correlation is induced by the Fano resonance involving destructive interference between the plane wave and bound sta…
We analyze d-wave resonances in atom-atom scattering in the presence of harmonic confinement by employing a higher partial wave pseudopotential. Analytical results for the scattering amplitude and transmission are obtained and compared to corresponding numerical ones, which employ the Lennard-Jones potential. Qualitative agreement is observed for weak confinement. For strong confinement the pseudopotential does not capture the s- and d-wave interference phenomena yielding an asymmetric Fano profile for the transmission resonance.
We consider the problem of motion-induced photon creation from quantum vacuum inside closed, perfectly conducting cavities with time-dependent geometries. These include one dimensional Fabry-Perrot resonators with Dirichlet or Neumann boundary conditions, three dimensional cylindrical waveguides, and a spherical shell. The number of Casimir TE, TM and TEM photons is computed. We also present a classical mechanical analogue of the one dimensional dynamical Casimir effect.
We study the dynamics of a single photon pulse travels through a linear atomic chain coupled to a one-dimensional (1D) single mode photonic waveguide. We derive a time-dependent dynamical theory for this collective many-body system which allows us to study the real time evolution of the photon transport and the atomic excitations. Our analytical result is consistent with previous numerical calculations when there is only one atom. For an atomic chain, the collective interaction between the atoms mediated by the waveguide mode can significantly change the dynamics of the system. The reflectivit…
We present a study of light-induced forces between two coupled plasmonic nano-particles above various slab geometries including a metallic half-space and a 280-nm thick negative index material (NIM) slab waveguide. We investigate optical forces by non-perturbatively calculating the scattered electric field via a Green function technique which includes the particle interactions to all orders. For excitation frequencies near the surface plasmon polariton and slow-light waveguide modes of the metal and NIM, respectively, we find rich light-induced forces and significant dynamical back-action effe…
The single-photon scattering in a rectangular waveguide by a V-type three-level emitter is studied for large range of input-photon energy beyond the single-mode region. By using Lippmann-Schwinger formalism, the necessary and sufficient conditions of complete transmission and complete reflection are derived analytically. In the single-mode region, the complete transmission caused by electromagnetically induced transparency (EIT) and the complete reflection due to Fano resonance can both be achieved by adjusting the emitter's parameters. But in the multi-mode region, except that the input-state…
We study the self interference effect of a resonator coupled with a bent waveguide at two separated ports. Such interference effects are shown to be similar for the cases of standing-wave and traveling-wave resonators, while in the system of two separated resonators indirectly coupled via a waveguide, the coupling forms and the related interference effects depend on which kind of resonators is chosen. Due to the self interference, controllable optical responses including tunable linewidth and frequency shift, and optical dark state can be achieved. Moreover, we consider a self-interference pho…
In this article, we developed a generalized coupled-mode theory for mixing an isolated state with the gapped continuum to unify the engineering mechanism of gap-protected zero modes, Fano resonance and Tamm surface states, even though those phenomena are diverse in numerous branches of physics and optics. By tuning the on-site potential and coupling strength of/with the isolated state, we found the operating characteristics from zero modes, Fano resonance and to Tamm modes, with explicitly demonstrating their localization, transmission spectra and distinct evolution dynamics of the 'bound stat…
We study the cooperative optical coupling between regularly spaced atoms in a one-dimensional waveguide using decompositions to subradiant and superradiant collective excitation eigenmodes, direct numerical solutions, and analytical transfer-matrix methods. We illustrate how the spectrum of transmitted light through the waveguide including the emergence of narrow Fano resonances can be understood by the resonance features of the eigenmodes. We describe a method based on superradiant and subradiant modes to engineer the optical response of the waveguide and to store light. The stopping of light…
Quantum transmission spectra of a twisted electron waveguide expose the coupling between traveling and quasi-bound states. Through a direct numerical solution of the open-boundary Schrödinger equation we single out the effects of the twist and show how the presence of a localized state leads to a Breit-Wigner or a Fano resonance in the transmission. We also find that the energy of quasi-bound states is increased by the twist, in spite of the constant section area along the waveguide. While the mixing of different transmission channels is expected to reduce the conductance, the shift of localiz…
We present a quantum-field-theoretical framework based on path integrals and Feynman diagrams for the investigation of the quantum-optical properties of one-dimensional waveguiding structures with embedded quantum impurities. In particular, we obtain the Green's functions for a waveguide with an embedded two-level system in the single- and two-excitation sector for arbitrary dispersion relations. In the single excitation sector, we show how to sum the diagrammatic perturbation series to all orders and thus obtain explicit expressions for physical quantities such as the spectral density and the…
