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Physical Review Applied

Single-Photon Transport in a Topological Waveguide from a Dynamically Modulated Photonic System

Luojia Wang, Luqi Yuan, Xianfeng Chen, Shanhui Fan

Published Jul 21, 2020• 13 citations
Publisher

Abstract

The topologically protected one-way edge modes for light show a way to manipulate the interaction between a single photon and a quantum emitter. We systematically study single-photon quantum optics in a topological waveguide supporting the frequency-dependent one-way edge mode at the boundary of a dynamically modulated photonic system, and compare the results of the single-photon interacting dynamics with the quantum emitter in a unidirectional waveguide. As a major difference, a photon in a topological waveguide propagates around the resonant site coupled to the quantum emitter due to the topological protection. Our results show that, despite different subtleties, photon-emitter interactions for one photon at the edge mode and for one photon propagating in a unidirectional waveguide hold similar features. In addition, we consider the interaction between the photon and a $\mathrm{\ensuremath{\Lambda}}$-type three-level quantum emitter in the topological waveguide, where we show the nonlocal correlated photon-state generation as well as the single-photon reflection with the frequency conversion. Our work provides insight for understanding the interaction between the topologically protected unidirectional-propagating photon and the quantum emitter, which holds promise for potential applications in quantum-information processing.

DOI
10.1103/physrevapplied.14.014063

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The topologically protected one-way edge modes for light show a way to manipulate the interaction between a single photon and a quantum emitter. We systematically study single-photon quantum optics in a topological waveguide supporting the frequency-dependent one-way edge mode at the boundary of a dynamically modulated photonic system, and compare the results of the single-photon interacting dynamics with the quantum emitter in a unidirectional waveguide. As a major difference, a photon in a topological waveguide propagates around the resonant site coupled to the quantum emitter due to the topological protection. Our results show that, despite different subtleties, photon-emitter interactions for one photon at the edge mode and for one photon propagating in a unidirectional waveguide hold similar features. In addition, we consider the interaction between the photon and a \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ-type three-level quantum emitter in the topological waveguide, where we show the nonlocal correlated photon-state generation as well as the single-photon reflection with the frequency conversion. Our work provides insight for understanding the interaction between the topologically protected unidirectional-propagating photon and the quantum emitter, which holds promise for potential applications in quantum-information processing.
We develop a general dynamical theory for studying a single-photon transport in a one-dimensional (1D) waveguide coupled to multiple emitters which can be either identical or nonidentical. In this theory, both the effects of the waveguide and non-waveguide vacuum modes are included. This theory enables us to investigate the propagation of an emitter excitation or an arbitrary single-photon pulse along an array of emitters coupled to a 1D waveguide. The dipole-dipole interaction induced by the non-waveguide modes, which is usually neglected in the literature, can significantly modify the dynamics of the emitter system as well as the characteristics of the output field if the emitter separation is much smaller than the resonance wavelength. Nonidentical emitters can also strongly couple to each other if their energy difference is less than or of the order of the dipole-dipole energy shift. Interestingly, if their energy difference is close but nonzero, a very narrow transparency window around the resonance frequency can appear which does not occur for identical emitters. This phenomenon may find important applications in quantum waveguide devices such as optical switches and ultranarrow single-photon frequency comb generator.
We explore special features of quantum light-matter interactions inside structured waveguides due to their finite bandwidth, band edges, and nontrivial topological properties. We model the waveguides as either a tight-binding (TB) chain or a Su-Schrieffer-Heeger (SSH) chain. For unstructured waveguides with infinite bandwidth, the transmission and reflection coefficients of a side-coupled two-level emitter (2LE) are the same as the reflection and transmission coefficients of a direct-coupled 2LE. We show that this analogy breaks down for structured waveguides with finite bandwidth due to the appearance of Lamb shift only for the direct-coupled 2LE. We further predict a robust light-emitter coupling at zero collective decay width of a single giant 2LE (with two couplings at different points) near the band edges of the structured waveguides where topological features can be beneficial. Finally, we study single-photon dynamics in a heterojunction of a long TB and short SSH waveguide connected to a 2LE at the SSH end. We show the propagation of a photon from the excited emitter to the TB waveguide only when the SSH waveguide is in the topological phase. Thus, the heterojunction acts as a conditional propagation channel.
All-optical manipulation of a single-photon quantum transport is of fundamental importance in quantum nanophotonics. Here, a system consisting of a single-mode waveguide coupling with a V-type three-level atom is proposed, where two excited states of the atom are strongly driven by the external coherent field. Transmission and reflection spectra for the output photon at different frequency components, including virtual transitions induced by the ultrastrong driving, are calculated. The interaction between the waveguide photon and the driven atom experiences quantum interferences, which leads to a variety of capabilities for manipulating the single-photon transport in the spectral domain. We perform simulations to demonstrate the possibilities of achieving desired frequency conversions as well as generating different correlated single-photon states by using external drive field at chosen strength. Our work therefore studies the single-photon transport in a strongly driven atom–waveguide system and shows applications for all-optically manipulating the single photon in the field of quantum information processing.
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.
We investigate the coherent single-photon scattering process in a topological waveguide coupled to a driven three-level atom in the $\mathrm{\ensuremath{\Lambda}}$ configuration, where two ground states are optically connected to a common excited state. We derive an analytical expression for transmittance by using the scattering formalism for three distinct sublattice sites (A, B, and AB) of the waveguide, which couple to the $\mathrm{\ensuremath{\Lambda}}$ system. We have demonstrated that the system's response is topology independent for A and B sublattice-site coupling and becomes topology dependent for AB sublattice-site coupling. In a weak-control-field regime, the system behaves as a perfect mirror in all of these configurations. Upon control field strength enhancement, the transmission spectrum evolves from Electromagnetically Induced Transparency to Autler-Townes splitting in A and B sublattice-site coupling. The manipulation of transmission from opaque to transparent holds the key mechanism of a single-photon switching. Furthermore, the topology-dependent AB sublattice configuration allows multiple-path-induced quantum interference, resulting in the sharper Fano line shape. This topological Fano resonance is not only tunable via the control field and coupling strength but also robust against structural imperfections due to the topological nature of the waveguide. These combined features such as tunability and topological protection make our system a promising platform for next-generation quantum technologies, including single-photon switches, high-resolution sensors, and communication devices.