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arXiv:1902.10855 · Physical Review A

Multiple Fano interferences due to waveguide-mediated phase coupling between atoms

Debsuvra Mukhopadhyay, G. S. Agarwal

Published Jul 8, 2019• 43 citations
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Abstract

We examine quantum interference effects due to absorption and emission from multiple atoms coupled to a waveguide and highlight the modifications they entail with regard to single-photon transport properties. A prominent upshot of these interference phenomena is the resonant suppression of the reflection amplitude, which leads to the observation of multiple Fano minima in the reflection spectrum. Such minima determine the points at which transparency is induced in the system. By taking recourse to the real-space Hamiltonian framework, we calculate analytically the reflectivity and transmissivity for a one-dimensional waveguide that evanescently couples to a chain of equally spaced quantum emitters. The interemitter spacing relative to the wavelength of the propagating photon, leading to a waveguide-mediated ``phase coupling'' between the atoms, is found to fundamentally affect the existence of Fano minima. For a chain of $N$ atoms, the number of minima can be at most $N\ensuremath{-}1$. However, suitable choices of the phase can suppress the discernibility of the full range of roots in the reflection spectrum. A principal observation for the case of multiple emitters is the emergence of super-Gaussian characteristics close to zero detuning and, consequently, a plateau-shaped broadband spectrum in the region of high reflectivity. For a large chain size, the plateau gets transformed into a flat-topped quasirectangular profile in the frequency domain.

DOI
10.1103/physreva.100.013812

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We examine quantum interference effects due to absorption and emission from multiple atoms coupled to a waveguide and highlight the modifications they entail with regard to single-photon transport properties. A prominent upshot of these interference phenomena is the resonant suppression of the reflection amplitude, which leads to the observation of multiple Fano minima in the reflection spectrum. Such minima determine the points at which transparency is induced in the system. By taking recourse to the real-space Hamiltonian framework, we calculate analytically the reflectivity and transmissivity for a one-dimensional waveguide that evanescently couples to a chain of equally spaced quantum emitters. The interemitter spacing relative to the wavelength of the propagating photon, leading to a waveguide-mediated ``phase coupling'' between the atoms, is found to fundamentally affect the existence of Fano minima. For a chain of NNN atoms, the number of minima can be at most N\ensuremath−1N\ensuremath{-}1N\ensuremath−1. However, suitable choices of the phase can suppress the discernibility of the full range of roots in the reflection spectrum. A principal observation for the case of multiple emitters is the emergence of super-Gaussian characteristics close to zero detuning and, consequently, a plateau-shaped broadband spectrum in the region of high reflectivity. For a large chain size, the plateau gets transformed into a flat-topped quasirectangular profile in the frequency domain.
We investigate single-photon scattering properties in a one-dimensional waveguide coupled to a quantum emitter's chain with dipole-dipole interaction (DDI). The photon transport is extremely sensitive to the location of the evanescently coupled atoms. The analytical expressions of reflection and transmission amplitudes for the chain containing two emitters with DDI are deduced by using a real-space Hamiltonian. Two cases, where the two emitters symmetrically or asymmetrically couple to the waveguide, are discussed in detail. It shows that the reflection and transmission typical spectra split into two peaks due to the DDI. The Fano minimum in the spectra can be used to estimate the strength of the DDI. Furthermore, the DDI makes spectra strongly asymmetric and creates a transmission window in the region where there was zero transmission. The scattering spectra for the chain consisting of multiple emitters are also given. Our key finding is that DDI can broaden the frequency bandwidth for high reflection when the chain consists of many emitters.
We demonstrate the emergence of transparent behavior in a chain of periodically spaced nonidentical quantum emitters coupled to a waveguide, in the special case when the nearest neighbor separation is a half-integral multiple of the resonant wavelength, i.e., kLkLkL is an integral multiple of $\ensuremath{\pi}$, with kkk being the wave number and LLL the spatial periodicity. When equal but opposite frequency detunings are assigned in pairs to a system of even number of atoms, perfect transmission ensues. When the chain size is odd, a similar assignment leads to the disappearance of collective effects as the odd atom determines the spectral behavior. We also manifest the robustness of these features against dissipative effects and show how the spectral behavior hinges significantly on the relative detunings between the atoms as compared to the decay rate. A key distinction from the phenomenon of electromagnetically induced transparency is that in the waveguide case, the presence of an intrinsic waveguide-mediated phase coupling between the atoms strongly affects the transport properties. Furthermore, while reciprocity in single-photon transport does not generally hold due to the phase coupling, we observe an interesting exception for $kL=n\ensuremath{\pi}$ at which the waveguide demonstrates reciprocal behavior with regard to both the transmission and reflection coefficients.
We investigate photon transport in a waveguide coupled to two-level quantum emitters with long-range interactions. We derive an exact solution for transmission and reflection amplitudes in the framwork of real-space Hamiltonian. Our explicit formula allows for a complete description of photon transport in the presence of N quantum emitters with arbitrary non-local interactions. We apply this approach to single-photon transport in an one-dimensional waveguide coupled to two atoms with dipole-dipole interaction (DDI). Our numerical results confirm the Fano spectrum line shapes as a result of strong DDI, and demonstrate how the split of perfect reflection spectrum and the resonance transmission can be achieved by tuning the photon-atom and the atom-atom interactions.
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 lineshapes. When the atom couples to the waveguide via multiple resonators, we show numerically how the destructive interference effect leads to a complete single-photon reflection. We also find a phase-transition phenomena for the multiresonator coupling case, which reveals that the upper bound state only exists when the atom-waveguide coupling strength is above a critical value.
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 line shape, 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 wave packets 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 SSS 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.
Efficient single-photon frequency conversion is investigated in a two-giant-atom waveguide-QED system, where a two-level giant atom and a ΛΛΛ-type three-level giant atom couple to a common one-dimensional waveguide. While the ΛΛΛ-type atom provides the inelastic channel, the two-level atom induces secondary coherent coupling, creating multi-path interference for the converted photon. Using the real-space approach and within the Markovian approximation, we derive analytical four-channel scattering amplitudes and reveal that the inelastic transmission spectrum, governed by three complex resonance poles, exhibits a multi-peak interference pattern. By introducing a local single-pole approximation, we reduce this complex spectrum to a local Fano lineshape, decomposing it into a coherent superposition of a local background term and a single-pole resonant term. The interplay between these two terms-controlled by the photon propagation phase between the giant atoms' coupling points-determines the conversion efficiency, with the background suppression condition leading to a Lorentzian reduction. Based on the single-pole resonance weight, we formulate a phase-selection criterion for highly efficient conversion. Compared with both the small-atom and single ΛΛΛ-type giant-atom models, the two-giant-atom scheme achieves substantially enhanced inelastic transmission over a broader frequency-conversion range. This work reveals how phase-controlled local Fano resonance enables high-efficiency frequency conversion, establishing a general paradigm for engineering resonant light-matter interactions in structured quantum systems.