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Physical Review A

Few-photon transport in low-dimensional systems

Paolo Longo, Peter Schmitteckert, Kurt Busch

Published Jun 22, 2011• 102 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.83.063828

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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.
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.
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 address correlated few-photon transport in one-dimensional waveguides coupled to a two-level system (TLS), such as an atom or a quantum dot. We derive exactly the single-photon and two-photon current (transmission) for linear and nonlinear (tight-binding sinusoidal) energy-momentum dispersion relations of photons in the waveguides and compare the results for the different dispersions. A large enhancement of the two-photon current for the sinusoidal dispersion has been seen at a certain transition energy of the TLS away from the single-photon resonances.
We give exact solutions for correlated two-photon transport in one-dimensional waveguide coupled to a two-level system, using a Bethe-Ansatz-like approach. The S-matrix is explicitly constructed to account for the transport properties of the photons. We show that the scattering eigenstates of this system include a two-photon bound state that passes through the two-level system as a composite single particle. Also, the two-level system can induce effective attractive or repulsive interactions in space for photons. This general procedure can be applied to the Anderson model as well.
We study the coherent scattering process of photons in two waveguides chiral coupling to a Λ-type three-level system (3LS). The 3LS acts as a few-photon router that can direct photons with unity. By adjusting the classical field applied to the 3LS, the tunneling paths between two waveguides can be turned off and on, but two photons can not be routed simultaneously from one port of the incident waveguide to an arbitrarily selected port of the other waveguide. Moreover, driven field controls the number of the bi-photon bound states and the interference pattern of the bi-photon bound states.