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arXiv:1609.03090 · Physical Review A

Dynamical theory of single-photon transport in a one-dimensional waveguide coupled to identical and nonidentical emitters

Zeyang Liao, Hyunchul Nha, Muhammad Suhail Zubairy

Published Nov 21, 2016• 69 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.94.053842

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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 derive a generalized master equation for multiphoton pulses interacting with multiple emitters in a waveguide-quantum electrodynamics system where the emitter frequency can be modulated and the effects of nonguided modes can also be considered. Based on this theory, we can calculate the real-time dynamics of an array of interacting emitters driven by an incident photon pulse which can be vacuum, a coherent state, a Fock state, or their superpositions. Moreover, we also derive generalized input-output relations to calculate the reflectivity and transmissivity of this system. We can also calculate the output photon pulse shapes. Our theory can find important applications in the study of waveguide-based quantum systems.
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.
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.
Abstract The waveguide quantum electrodynamics (QED) system may have important applications in quantum device and quantum information technology. In this article we review the methods being proposed to calculate photon transport in a one-dimensional (1D) waveguide coupled to quantum emitters. We first introduce the Bethe ansatz approach and the input–output formalism to calculate the stationary results of a single photon transport. Then we present a dynamical time-dependent theory to calculate the real-time evolution of the waveguide QED system. In the longtime limit, both the stationary theory and the dynamical calculation give the same results. Finally, we also briefly discuss the calculations of the multiphoton transport problems.
We study the dynamics of a single-photon pulse travelling through a linear qubit chain coupled to continuum modes in a one-dimensional (1D) photonic waveguide. We derive a time-dependent dynamical theory for qubit amplitudes and for transmitted and reflected spectra. We show that the requirement for the photon-qubit coupling to exist only for positive frequencies can significantly change the dynamics of the system. First, it leads to an additional photon-mediated dipole-dipole interaction between qubits which results in the violation of the phase coherence between them. Second, the spectral lines of transmitted and reflected spectra crucially depend on the shape of the incident pulse and the initial distance between the pulse center and the first qubit in the chain. We apply our theory to one-qubit and two-qubit systems. For these two cases, we obtain the explicit expressions for the qubits' amplitudes and the photon radiation spectra as time tends to infinity. For the incident Gaussian wave packet we calculate the line shapes of transmitted and reflected photons.