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Journal of the Optical Society of America B

Statistically driven model for efficient analysis of few-photon transport in waveguide quantum electrodynamics

Ruiqi Cui, Dian Tan, Yuecheng Shen

Published Dec 23, 2019• 1 citation
Publisher

Abstract

Understanding transport properties in quantum nanophotonics plays a central role in designing few-photon devices, yet it suffers from a longstanding extensive computational burden. In this work, we propose a statistically driven model with a tremendously eased computational burden, which is based on the deep understanding of the few-photon spontaneous emission process. By utilizing phenomenological, statistically driven inter-photon offset parameters, the proposed model expedites the transport calculation with a three-order-of-magnitude enhancement of speed in contrast to conventional numerical approaches. We showcase the two-photon transport computation benchmarked by the rigorous analytical approach. Our work provides an efficient tool for designing few-photon nano-devices, and it significantly deepens the understanding of correlated quantum many-body physics.

DOI
10.1364/josab.380142

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•Jan 1, 2020•0 citations
Understanding transport properties in quantum nanophotonics plays a central role in designing few-photon devices, yet it suffers from a longstanding extensive computational burden. In this work, we propose a statistically driven model with a tremendously eased computational burden, which is based on the deep understanding of the few-photon spontaneous emission process. By utilizing phenomenological, statistically driven inter-photon offset parameters, the proposed model expedites the transport calculation with a three-order-of-magnitude enhancement of speed in contrast to conventional numerical approaches. We showcase the two-photon transport computation benchmarked by the rigorous analytical approach. Our work provides an efficient tool for designing few-photon nano-devices, and it significantly deepens the understanding of correlated quantum many-body physics.
We propose an exact analytical approach to study the single-photon spontaneous emissions in waveguide quantum electrodynamic (QED) systems. Using the ab initio evolution technique, our approach provides a universal framework to investigate the full spatiotemporal dynamics of the atomic response, the cavity response, and the emitted photonic wave functions. The validity of the analytical approach is numerically confirmed. Our rigorous approach can be extensively applied to more complicated waveguide QED architectures. Moreover, such an approach can readily incorporate the effects of dissipations and has the potential to tremendously facilitate the design of spontaneous emission-driven quantum nanophotonic devices in the dissipative regime.
Understanding multi-photon interactions in non-equilibrium quantum systems is an outstanding challenge in quantum optics. In this work, we develop an analytical and diagrammatic framework to explore three-photon interactions in atomic ensembles weakly coupled to a one-dimensional waveguide. Taking advantage of the weak coupling, we use our diagrammatic framework to perform perturbation theory and calculate the leading-order contributions to the three-photon wavefunction, which would otherwise be intractable. We then compute the outgoing photon wavefunction of a resonantly driven atomic ensemble, with photon-photon interactions truncated up to three photons. Our formulation not only captures the individual transmission of photons but also isolates the connected S-matrix elements that embody genuine photon-photon correlations. Through detailed analysis, we obtain the analytic expressions of the connected third-order correlation function and the third-order electric-field-quadrature cumulant, which reveal non-Gaussian signatures emerging from the interplay of two- and three-photon processes. We also calculate the optical depth where non-Gaussian photon states can be observed. Numerical simulations based on a cascaded master equation validate our analytical predictions on a small-scale system. These results provide a formalism to further explore non-equilibrium quantum optics in atomic ensembles and extend this to the regime of non-Gaussian photon transport.
A promising way to scale up superconducting quantum computers is to link different devices together using propagating photons. Correspondingly, accurately modeling the quantum information transfer in such quantum interconnects is critical to advancing this emerging technology. To accomplish this, a full-wave quantum numerical model is essential for describing the few-photon transport characteristics of various components. Unfortunately, validating the accuracy of such numerical models remains a difficult challenge due to the lack of appropriate analytical solutions for standard component types. Recently, progress has been made on creating the first-ever analytical quantum full-wave solutions for a superconducting circuit quantum device. These efforts considered the case of two-photon transport through an empty rectangular waveguide cavity and the interactions of photons inside a closed rectangular waveguide cavity with a transmon qubit formed by a Josephson junction connected across the terminals of a small wire dipole antenna. Here, we advance these efforts by considering the one- and two-photon transport properties through a rectangular waveguide cavity containing a qubit in this form when the cavity is interfaced with via two coaxial ports. Such devices can be used in various ways for quantum interconnects, such as to form parts of a quantum memory or a photon source. We perform this analysis leveraging a quantum input-output theory formalism to derive the relevant single- and two-photon transport characteristics of interest. We then examine the signatures of the nonlinear quantum scattering effects in the good and bad cavity regimes of cavity quantum electrodynamics. In the future, these analytical results can be used to validate numerical full-wave quantum solvers for modeling quantum interconnects.
Engineering strong photon–photon interactions at the quantum level have been crucial in various areas of research, notably in quantum information processing and quantum simulation. It is often done by coupling matter strongly to light. A promising way to achieve this is via waveguide quantum electrodynamics (QED). Motivated by these advancements, we study few-photon transport in waveguide QED setups. First, we present a diagrammatic technique to systematically study multiphoton scattering based on the scattering formalism and Green’s function approach. We demonstrate our proposal through physically relevant examples involving scattering of few-photon states from two-level emitters as well as from arrays of correlated Kerr nonlinear resonators described by the Bose–Hubbard model. In the second part, we apply the diagrammatic technique that was developed to perform a comprehensive study on a Bose–Hubbard lattice with a quasi-periodic potential. This model exhibits many-body localisation. We compute the two-photon transmission probability and show that it carries signatures of the underlying localisation transition with close agreement to the participation ratio of the eigenstates. The systematic scattering approach provided in this paper provides a foundation for future works at the interface between quantum optics and condensed matter.
Strong light-matter coupling between a guided electromagnetic mode and an excitonic semiconductor transition gives rise to exciton-polaritons with optical nonlinearities far exceeding those of conventional photonic platforms. Utilizing these nonlinearities in the few-particle regime, where quantum signatures such as photon antibunching, sub-Poissonian statistics and non-trivial inter-mode correlations become accessible, is a central goal of integrated quantum photonics. Yet, a quantitative theoretical framework connecting realistic waveguide parameters to measurable non-classical photonic output is absent. Here, we present a comprehensive framework for predicting and benchmarking quantum photon statistics in polaritonic integrated circuits, using state-of-the-art experimentally achieved device parameters for (Al)GaAs waveguide platforms. By mapping the pulsed nonlinear waveguide dynamics onto a bosonic quantum circuit representation that explicitly incorporates dissipation, we identify experimentally accessible quantum signatures across two circuit configurations: a single waveguide in a free-space interferometric configuration and a fully integrated multimode coupled-waveguide circuit. We further show that slow-light engineering of the polariton dispersion offers a practical route to amplifying the effective nonlinearity, pushing quantum signatures beyond Gaussian statistics.
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.