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arXiv:1209.0399 · Scientific Reports

Cascaded two-photon nonlinearity in a one-dimensional waveguide with multiple two-level emitters

Dibyendu Roy

Published Aug 16, 2013• 42 citations
arXivHTMLPDF

Abstract

We propose and theoretically investigate a model to realize cascaded optical nonlinearity with few atoms and photons in one-dimension (1D). The optical nonlinearity in our system is mediated by resonant interactions of photons with two-level emitters, such as atoms or quantum dots in a 1D photonic waveguide. Multi-photon transmission in the waveguide is nonreciprocal when the emitters have different transition energies. Our theory provides a clear physical understanding of the origin of nonreciprocity in the presence of cascaded nonlinearity. We show how various two-photon nonlinear effects including spatial attraction and repulsion between photons, background fluorescence can be tuned by changing the number of emitters and the coupling between emitters (controlled by the separation).

DOI
10.1038/srep02337

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We propose and theoretically investigate a model to realize cascaded optical nonlinearity with few atoms and photons in one-dimension (1D). The optical nonlinearity in our system is mediated by resonant interactions of photons with two-level emitters, such as atoms or quantum dots in a 1D photonic waveguide. Multi-photon transmission in the waveguide is nonreciprocal when the emitters have different transition energies. Our theory provides a clear physical understanding of the origin of nonreciprocity in the presence of cascaded nonlinearity. We show how various two-photon nonlinear effects including spatial attraction and repulsion between photons, background fluorescence can be tuned by changing the number of emitters and the coupling between emitters (controlled by the separation).
We investigate interference and correlation effects when several detuned emitters are placed along a one-dimensional photonic waveguide. Such a setup allows multiple interactions between the photons and the strongly coupled emitters, and underlies proposed devices for quantum information processing. We show, first, that a pair of detuned two-level systems (2LS) separated by a half wavelength mimic a driven $\mathrm{\ensuremath{\Lambda}}$-type three-level system (3LS) in both the single- and two-photon sectors. There is an interference-induced transparency peak at which the fluorescence is quenched, leaving the transmitted photons completely uncorrelated. Slightly away from this separation, we find that the inelastic scattering (fluorescence) is large, leading to nonlinear effects such as nonreciprocity (rectification). We connect this nonreciprocity to inelastic scattering caused by driving a dark pole and so derive a condition for maximum rectification. Finally, by placing a true 3LS midway between the two 2LS, we show that elastic scattering produces only transmission, but inelastic scattering nevertheless occurs (the fluorescence is not quenched) causing substantial photon correlations.
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.
Transmission and correlation properties of a two-photon pulse are studied in a one-dimensional waveguide (1DW) in the presence of three types of quantum emitters: two-level atom (TLA), side optical cavity (SOC), and Jaynes-Cummings model (JCM). Since there are many plane-wave components for a two-photon pulse, a nonlinear waveguide dispersion is used instead of the linearized one. The two-photon transmission spectra become flatter with decreasing the pulse width. With respect to the $\ensuremath{\delta}$ coupling between the 1DW and quantum emitter the transmission dips show a blueshift for the non-$\ensuremath{\delta}$ one and the blueshift first increases and then decreases with increasing the width of the coupling. The TLA and JCM can induce an effective photon-photon interaction that depends on the distance between the two photons, while the SOC cannot. We show that the 1DW coupled with the TLA or JCM is able to evaluate the overlap of the two photons and that the non-$\ensuremath{\delta}$ coupling has potential for controlling the two-photon correlation.
The generation of indistinguishable single photons and control of photon-photon interactions are key requirements for photonic quantum networks. Nano-photonic waveguide-based architectures, in which few-level solid state systems provide both single photon generation and the nonlinearity through which two or more photons interact, offer a scalable route to such networks. However, it is a challenge to maintain the optical quality of the embedded photon sources whilst also providing fine-tuning of the emission frequency and optical nonlinearity in a waveguide geometry. We demonstrate a tunable solid-state platform for scalable photonic quantum networks which allows local electrical control of both single photon generation and optical nonlinearity at the single photon level. Electrical tuning and switching of coherent photon scattering from a quantum dot embedded in a nano-photonic waveguide is demonstrated, with a transmission extinction as large as 40±2% measured on resonance. Observation of a clear, voltage-controlled bunching signal in the photon statistics of the transmitted light demonstrates the single photon character of the nonlinearity. The deterministic nature of the nonlinearity is particularly attractive for the future realization of photonic gates for scalable nano-photonic waveguide-based quantum information processing.
We study the controllable single-photon scattering via a one-dimensional waveguide which is coupled to a two-level emitter and a single-mode cavity simultaneously. The emitter and the cavity are also coupled to each other and form a three-level system with cyclic transitions within the zero- and single-excitation subspaces. As a result, the phase of emitter-cavity coupling strength serves as a sensitive control parameter. When the emitter and cavity locate at the same point of the waveguide, we demonstrate the Rabi splitting and quasidark-state-induced perfect transmission for the incident photons. More interestingly, when they locate at different points of the waveguide, a controllable nonreciprocal transmission can be realized and the nonreciprocity is robust to the weak coupling between the system and environment. Furthermore, we demonstrate that our theoretical model is experimentally feasible with currently available technologies.
We study controllable single-photon transport in a one-dimensional waveguide with a nonlinear dispersion relation coupled to a three-level emitter in a cascade configuration. An extra cavity field is introduced to drive one of the level transitions of the emitter. In the resonance case, when the extra cavity does not contain photons, the input single photon will be reflected; when the cavity contains one photon, the full transmission of the input single photon can be obtained. In the off-resonance case, the single-photon transport can also be controlled by the parameters of the cavity. Therefore, we show that single-photon transport can be controlled by an extra cavity field.