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arXiv:2001.05773 · Physical Review A

Few-photon transport in Fano-resonance waveguide geometries

Kristoffer B. Joanesarson, Jake Iles-Smith, Mikkel Heuck, Jesper Mørk

Published Jun 3, 2020• 12 citations
arXivHTMLPDF

Abstract

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 $S$ 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.

DOI
10.1103/physreva.101.063809

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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.
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 study the probe-field transmission in cavity quantum electrodynamics (cavity-QED) systems with a partially transmitting element (PTE), where the PTE is used to control and tune the amplitude of the weak probe field propagating along a single waveguide channel in the structure. We derive analytic formulas utilized to determine the transmission coefficient of the probe field within the framework of quantum optics. Using experimentally accessible parameters, it is clearly shown that the asymmetric Fano-resonance line shape can be formed and manipulated by means of the added PTE. Furthermore, we reveal that there exists superluminal light with large intensity transmission in the transport spectrum of the waveguide-coupled cavity-QED system. This superluminal-light propagation effect, which exhibits the anomalous phase shift and is characterized by the negative group delay, can be enhanced by properly choosing the system parameters. The obtained results may be used for designing switching, modulation, and sensing for nanophotonic applications and ultrafast on-chip signal processing in telecom applications.
An analysis of some aspects of photon transport through cavities and emitters embedded in a one-dimensional geometries is presented. The concept of photon blockade is defined for few-photon states interacting with a single two-level atom and the strength of achievable blockade is calculated in this setting. A brief review of some promising schemes for achieving photon blockade from the literature is also provided. The conflict between linear and nonlinear optical processes is studied for a novel version of the famous Hong-Ou-Mandel effect in a photonic waveguide with a side-coupled two-level emitter.
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.
The single-photon scattering by a V-type three-level emitter in a rectangular waveguide is studied. Here the frequency value of input photons can be large beyond the single-transverse-mode region. By using Green's function formalism, the necessary and sufficient conditions of complete transmission as well as complete reflection are derived analytically. In the region of single transverse mode, the physical mechanisms of complete transmission and complete reflection are electromagnetically induced transparency (EIT) and Fano resonance, respectively. In the region of multiple transverse modes, which are induced by the finite cross section, the quantum interference between multiple scattering pathways with different transverse modes can be used to manipulate the single-photon transport. We find that the emitter becomes transparent when the superposition of waveguide modes has zero amplitude at the position of emitter. And the perfect reflection is absent even under Fano resonance unless the input-state is in a coherent superposition state. These results may promote the development of single-photon devices with wide applicable frequency region.