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arXiv:1603.08595 · Physical Review A

Fano interference in two-photon transport

Shanshan Xu, Shanhui Fan

Published Oct 17, 2016• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.94.043826

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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 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.
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 $N\ensuremath{-}1$. 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 theoretically single photon transport in one-dimensional waveguide coupled to a pair of cavities, which are denoted by the first cavity and the auxiliary cavity. Two cases with no atom and one atom embedded in the first cavity are discussed. The Fano dips in the transmission spectrum and locations of transparency window are calculated. When no atom is embedded in the first cavity, there exists a transparency window under the condition that the first cavity and the auxiliary cavity are not resonant. The locations of the transparency window and Fano line type depend strongly on the eigen frequency of the auxiliary cavity and the coupling strength between the auxiliary cavity and the waveguide. When one atom is embedded in the first cavity, we show that the transparency window exists even though the first cavity, the atom and the auxiliary cavity are resonant. The Fano line type is strongly dependent on the eigen frequency of the auxiliary cavity and the coupling strength. Our results have potential applications in design of quantum devices at the level of single photon, such as single photon switch and single photon routers.
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 state for two-photon transport.
Realising a platform for efficiently guiding and manipulating light at the singlephoton level lies at the heart of optical quantum information processing. In this thesis we aid in the pursuit of this goal by analysing few-photon transport properties in photonic devices while keeping in mind possible applications and experimental challenges. We especially focus on single and two-photon transport properties in one-dimensional waveguides coupled to (artificial) atoms modelled as two and three-level emitters. We begin by introducing key concepts relevant for this thesis and then explain how to model such waveguide geometries. We show how directional-dependent coupling between a waveguide and a localized quantum system can be modelled from a chain of harmonic oscillators by allowing the system to couple to more than one site. Using the input-output formalism and scattering matrix theory we determine a general form for the single and two-photon S-matrices for a waveguide coupled to a two-level system. We also explain how to engineer a quantum optical Fanoresonance waveguide geometry and calculate how this modifies the S-matrices, the few-photon scattering probabilities, and the scattered output spectra. We show that the nonlinear effects in such a system generates highly correlated directional scattering probabilities. We device a protocol that can generate maximal entanglement between two spectrally distinct solid-state emitters by the use of multi-photon scattering. The results also reveal a rich structure for multi-photon states interacting with non-identical emitters. As a final investigation, we quantify how spectral diffusion in quantum dots affects finite-width single and two-photon scattering. Single-photon scattering probabilities are described by a simple convolution but this is not the case for a two-photon state scattering off a two-level emitter. We show that the effect of spectral wandering depletes the nonlinear scattering properties, but that it affects co and counter-propagating output probabilities differently.
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 topologies of system. We also summarize the general conditions for appearance of EIT-like spectra by analyzing the master equation and verify these conditions by checking the corresponding analytical expressions of the scattering spectra. These phenomena may provide powerful tools for controlling and manipulating photon transport in future quantum networks.