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Journal of Optics A Pure and Applied Optics

Dynamics of photon transport through quantum impurities in dispersion-engineered one-dimensional systems

Paolo Longo, Peter Schmitteckert, Kurt Busch

Published Sep 16, 2009• 37 citations
Publisher

Abstract

We provide a theoretical and computational framework for fully quantum mechanical studies of few-photon transport phenomena in arbitrary waveguiding structures in the presence of coherent interaction with optically active emitters. The reduced dimensionality of such systems leads to pronounced quantum interference effects that may be exploited for a number of applications and we apply our framework to the case of single-photon transport through a two-level atom. In this system, the atom's emission dynamics leads to strong interference effects that can be used for the realization of nanomirrors.

DOI
10.1088/1464-4258/11/11/114009

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We provide a theoretical and computational framework for fully quantum mechanical studies of few-photon transport phenomena in arbitrary waveguiding structures in the presence of coherent interaction with optically active emitters. The reduced dimensionality of such systems leads to pronounced quantum interference effects that may be exploited for a number of applications and we apply our framework to the case of single-photon transport through a two-level atom. In this system, the atom's emission dynamics leads to strong interference effects that can be used for the realization of nanomirrors.
We analyze the role of quantum interference effects induced by an embedded two-level system on the photon transport properties in waveguiding structures that exhibit cutoffs (band edges) in their dispersion relation. In particular, we demonstrate that these systems invariably exhibit single-particle photon-atom bound states and strong effective nonlinear responses on the few-photon level. Based on this, we find that the properties of these photon-atom bound states may be tuned via the underlying dispersion relation and that their occupation can be controlled via multiparticle scattering processes. This opens an interesting route for controlling photon transport properties in a number of solid-state-based quantum optical systems and the realization of corresponding functional elements and devices.
We present a detailed analysis of the dynamics of photon transport in waveguiding systems in the presence of a two-level system. In these systems, quantum interference effects generate a strong effective optical nonlinearity on the few-photon level. We clarify the relevant physical mechanisms through an appropriate quantum many-body approach. Based on this, we demonstrate that a single-particle photon-atom bound state with an energy outside the band can be excited via multiparticle scattering processes. We further show that these trapping effects are robust and, therefore, will be useful for the control of photon entanglement in solid-state based quantum-optical systems.
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 dynamics of a single-photon pulse traveling 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 reflectivity of a photon can be tuned by changing the ratio of coupling strength and the photon linewidth or by changing the number of atoms in the chain. The reflectivity of a single-photon pulse with finite bandwidth can even approach 100100%100. The spectrum of the reflected and transmitted photon can also be significantly different from the single-atom case. Many interesting physical phenomena can occur in this system such as the photonic band-gap effects, quantum entanglement generation, Fano-like interference, and superradiant effects. For engineering, this system may serve as a single-photon frequency filter, single-photon modulation, and may find important applications in quantum information.
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 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.