Coherent quantum optics, where the interaction of a photon with an emitter does not scramble phase coherence, lies at the heart of many quantum optical effects and emerging technologies. Solid-state emitters coupled to nanophotonic waveguides are a promising platform for quantum devices, as this combination is scalable. Yet, reaching full coherence in these systems is challenging due to the dynamics of the solid-state environment of the emitters. Here, we review progress towards coherent light-matter interactions with solid-state quantum emitters coupled to nanophotonic waveguides. We first lay down the theoretical foundation for coherent and nonlinear light-matter interactions of a two-level system in a quasi-one-dimensional system, and then benchmark experimental realizations. We then discuss higher-order nonlinearities that arise due to the addition of photons of different frequencies, more complex energy-level schemes of the emitters, and the coupling of multiple emitters via a shared photonic mode. Throughout, we highlight protocols for applications and novel effects that are based on these coherent interactions, the steps taken towards their realization, and the challenges that remain to be overcome.
We propose a deterministic yet fully passive scheme to transfer the quantum state from a frequency-encoded photon to the spin of a quantum-dot mediated by a nanophotonic waveguide. We assess the quality of the state transfer by studying the effects of all relevant experimental imperfections on the state-transfer fidelity. We show that a transfer fidelity exceeding 95% is achievable for experimentally realistic parameters. Our work sets the stage for deterministic solid-state quantum networks tailored to frequency-encoded photonic qubits.
Coherent photon-emitter interfaces offer a way to mediate efficient nonlinear photon-photon interactions, much needed for quantum information processing. Here we experimentally study the case of a two-level emitter, a quantum dot, coupled to a single optical mode in a nanophotonic waveguide. We carry out few-photon transport experiments and record the statistics of the light to reconstruct the scattering matrix elements of 1- and 2-photon components. This provides direct insight to the complex nonlinear photon interaction that contains rich many-body physics.
A lattice of trapped atoms strongly coupled to a one-dimensional nanophotonic waveguide is investigated in exploiting the concept of polariton as the system natural eigenstate. We apply a bosonization procedure, which was presented separately by P. W. Anderson and V. M. Agranovich, to transform excitation spin-half operators into interacting bosons, and which shown here to confirm the hard-core boson model. We derive polariton-polariton kinematic interactions and study them by solving the scattering problem. In using the excitation-photon detuning as a control parameter, we examine the regime …
We theoretically investigate the quantum scattering of a single-photon pulse interacting with an ensemble of $Λ$-type three-level atoms coupled to a one-dimensional waveguide. With an effective non-Hermitian Hamiltonian, we study the collective interaction between the atoms mediated by the waveguide mode. In our scheme, the atoms are randomly placed in the lattice along the axis of the one-dimensional waveguide, which closely corresponds to the practical condition that the atomic positions can not be controlled precisely in experiment. Many interesting optical properties occur in our waveguide…
In the waveguide quantum electrodynamics (QED) system, emitter separation plays an important role for its functionality. Here, we present a method to measure the deep-subwavelength emitter separation in a waveguide-QED system. In this method, we can also determine the number of emitters within one diffraction-limited spot. In addition, we also show that ultrasmall emitter separation change can be detected in this system which may then be used as a waveguide-QED-based sensor to measure tiny local temperature/strain variation.
Atoms coupled to nanophotonic interfaces represent an exciting frontier for the investigation of quantum light-matter interactions. While most work has considered the interaction between statically positioned atoms and light, here we demonstrate that a wealth of phenomena can arise from the self-consistent interaction between atomic internal states, optical scattering, and atomic forces. We consider in detail the case of atoms coupled to a one-dimensional nanophotonic waveguide, and show that this interplay gives rise to self-organization of atomic positions along the waveguide, which can be p…
We extend the input-output formalism of quantum optics to analyze few-photon transport in waveguides with an embedded qubit. We provide explicit analytical derivations for one and two-photon scattering matrix elements based on operator equations in the Heisenberg picture.
We present an overview of the framework of macroscopic quantum electrodynamics from a quantum nanophotonics perspective. Particularly, we focus our attention on three aspects of the theory which are crucial for the description of quantum optical phenomena in nanophotonic structures. First, we review the light-matter interaction Hamiltonian itself, with special emphasis on its gauge independence and the minimal and multipolar coupling schemes. Second, we discuss the treatment of the external pumping of quantum-optical systems by classical electromagnetic fields. Third, we introduce an exact, co…
We propose a scheme in which broadband nanostructures allow to generate squeezed light and entanglement of quantum emitters that are extremely far detuned. It is shown that the reduced fluctuations of the electromagnetic field arising from collective resonance fluorescence provide also a means to detect the entanglement between the emitters. Due to the near-field enhancement in the proposed hybrid systems, these nonclassical effects can be encountered outside both the extremely close separations limiting the observation in free space and narrow frequency bands in high-Q cavities. Our approach …
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 non-identical. 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 literatures, can significantly modify the dyna…
We develop a systematic method for deriving a quantum optical multi-mode Hamiltonian for the interaction of photons and phonons in nanophotonic dielectric materials by applying perturbation theory to the electromagnetic Hamiltonian. The Hamiltonian covers radiation pressure and electrostrictive interactions on equal footing. As a paradigmatic example, we apply our method to a cylindrical nanoscale waveguide, and derive a Hamiltonian description of Brillouin quantum optomechanics. We show analytically that in nanoscale waveguides radiation pressure dominates over electrostriction, in agreement …
Coherent interactions between quantum emitters in tailored photonic structures is a fundamental building block for future quantum technologies, but remains challenging to observe in complex solid-state environments, where the role of decoherence must be considered. Here, we investigate the optical interaction between two quantum emitters mediated by one-dimensional waveguides in a realistic solid-state environment, focusing on the creation, population and detection of a sub-radiant state, in the presence of dephasing. We show that as dephasing increases, the signatures of sub-radiance quickly …
Controlling the flow of light by means of nanophotonic waveguides has the potential of transforming integrated information processing much in the same way that conventional glass fibers have revolutionized global communication. Owing to the strong transverse confinement of the light, such waveguides give rise to a coupling between the internal spin of the guided photons and their orbital angular momentum. Here, we employ this spin-orbit coupling of light to break the mirror symmetry of the scattering of light by a single gold nanoparticle on the surface of a nanophotonic waveguide. We thereby …
We study a system made up of one or two two-level quantum emitters, coupled to a single transverse mode of a closed waveguide, in which photon wavenumbers and frequencies are discretized, and characterize the stable states in which one excitation is steadily shared between the field and the emitters. We unearth finite-size effects in the field-emitter interactions and identify a family of dressed states, that represent the forerunners of bound states in the continuum in the limit of an infinite waveguide. We finally consider the potential interest of such states for applications in the field o…
By coupling a $Λ$-type quantum emitter to a chiral waveguide, in which the polarization of a photon is locked to its propagation direction, we propose a controllable photon-emitter interface for quantum networks. We show that this chiral system enables the SWAP gate and a hybrid-entangling gate between the emitter and a flying single photon. It also allows deterministic storage and retrieval of single-photon states with high fidelities and efficiencies. In short, this chirally coupled emitter-photon interface can be a critical building block toward a large-scale quantum network.
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 non-guided 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 calc…
We study the dynamics of a single photon pulse travels 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 reflectivit…
We review recent advances towards the realization of quantum networks based on atom-like solid-state quantum emitters coupled to nanophotonic devices. Specifically, we focus on experiments involving the negatively charged silicon-vacancy color center in diamond. These emitters combine homogeneous, coherent optical transitions and a long-lived electronic spin quantum memory. We discuss optical and spin properties of this system at cryogenic temperatures and describe experiments where silicon-vacancy centers are coupled to nanophotonic devices. Finally, we discuss experiments demonstrating quant…
We report on quantum, classical, and total correlations in a set of distant quantum emitters coupled via their interaction with the plasmon modes of a one-dimensional waveguide driven by an external laser field. The coupling of the emitters with the plasmonic modes and its influence on the collective decay rate suggest that entanglement does not play a significant role in the qubit dynamics. Rather, discord is the quantity that matters and should be harnessed as a resource.
This Letter shows that chains of optical or microwave emitters coupled to a 1D waveguide support subradiant states with close pairs of excited emitters, which have longer lifetimes than even the most subradiant states with only a single excitation. Exact, analytical expressions for non-radiative excitation dimer states are obtained in the limit of infinite chains. To understand the mechanism underlying these states, we present a formal equivalence between subradiant dimers and single localized excitations around a chain defect (unoccupied site). Our analytical mapping permits extension to emit…
We discuss the scattering of photons from a three-level emitter in a one-dimensional waveguide, where the transport is governed by the interference of spontaneously emitted and directly transmitted waves. The scattering problem is solved in closed form for different level structures. Several possible applications are discussed: The state of the emitter can be switched deterministically by Raman scattering, thus enabling applications in quantum computing such as a single photon transistor. An array of emitters gives rise to a photonic band gap structure, which can be tuned by a classical drivin…
Strong amplification in integrated photonics is one of the most desired optical functionalities for computing, communications, sensing, and quantum information processing. Semiconductor gain and cubic nonlinearities, such as four-wave mixing and stimulated Raman and Brillouin scattering, have been among the most studied amplification mechanisms on chip. Alternatively, material platforms with strong quadratic nonlinearities promise numerous advantages with respect to gain and bandwidth, among which nanophotonic lithium niobate is one of the most promising candidates. Here, we combine quasi-phas…
We report on the analysis of electroabsorption in thin GaAs/Al$_{0.3}$Ga$_{0.7}$As nanophotonic waveguides with an embedded $p$-$i$-$n$ junction. By measuring the transmission through waveguides of different lengths, we derive the propagation loss as a function of electric field, wavelength, and temperature. The results are in good agreement with the Franz-Keldysh model of electroabsorption extending over 200 meV below the GaAs bandgap, i.e. in the 910--970 nm wavelength range. We find a pronounced residual absorption in forward bias, which we attribute to Fermi-level pinning at the waveguide …
The combination of established nanofabrication with attractive material properties makes silicon a promising material for quantum technologies, where implanted dopants serve as qubits with high density and excellent coherence even at elevated temperatures. In order to connect and control these qubits, interfacing them with light in nanophotonic waveguides offers unique promise. Here, we present resonant spectroscopy of implanted erbium dopants in such waveguides. We overcome the requirement of high doping and above-bandgap excitation that limited earlier studies. We thus observe erbium incorpo…
We study theoretically a laser-driven one-dimensional chain of atoms interfaced with the guided optical modes of a nanophotonic waveguide. The period of the chain and the orientation of the laser field can be chosen such that emission occurs predominantly into a single guided mode. We find that the fluorescence excitation line shape changes as the number of atoms is increased, eventually undergoing a splitting that provides evidence for the waveguide-mediated all-to-all interactions. Remarkably, in the regime of strong driving the light emitted into the waveguide is non-classical, with a signi…
We examine the routing scheme of single photons in a one-dimensional periodic chain of two-level quantum emitters (QEs) strongly coupled to two waveguides in a ladder configuration. It is known that for a single-emitter chiral waveguide ladder setting, photons can be redirected from one waveguide to another with a $100\%$ probability (deterministically) provided the resonance condition is met and spontaneous emission is completely ignored. However, when the spontaneous emission is included the routing scheme becomes considerably imperfect. In this paper, we present a solution to this issue by …
We investigate single photon scattering properties in one-dimensional waveguide coupled to quantum emitter's chain with dipole-dipole interaction (DDI). The photon transport is extremely sensitive to the location of the evanescently coupled emitters. The analytical expressions of reflection and transmission amplitudes for the chain containing two emitters with DDI are deduced by using real-space Hamiltonian. Two cases, where the two emitters symmetrically and asymmetrically couple to the waveguide, are discussed in detail. It shows that the reflection and transmission typical spectra split int…
We study the dynamics of a general multi-emitter system coupled to the squeezed vacuum reservoir and derive a master equation for this system based on the Weisskopf-Wigner approximation. In this theory, we include the effect of positions of the squeezing sources which is usually neglected in the previous studies. We apply this theory to a quasi-one-dimensional waveguide case where the squeezing in one dimension is experimentally achievable. We show that while dipole-dipole interaction induced by ordinary vacuum depends on the emitter separation, the two-photon process due to the squeezed vacuu…
Room-temperature (RT), on-chip deterministic generation of indistinguishable photons coupled to photonic integrated circuits is key for quantum photonic applications. Nevertheless, high indistinguishability (I) at RT is difficult to obtain due to the intrinsic dephasing of most deterministic single-photon sources (SPS). Here we present a numerical demonstration of the design and optimization of a hybrid slot-Bragg nanophotonic cavity that achieves theoretical near-unity I and high coupling efficiency (\b{eta}) at RT for a variety of singlephoton emitters. Our numerical simulations predict moda…
Photon-mediated coupling between distant matter qubits may enable secure communication over long distances, the implementation of distributed quantum computing schemes, and the exploration of new regimes of many-body quantum dynamics. Nanophotonic devices coupled to solid-state quantum emitters represent a promising approach towards realization of these goals, as they combine strong light-matter interaction and high photon collection efficiencies. However, the scalability of these approaches is limited by the frequency mismatch between solid-state emitters and the instability of their optical …
We propose a novel quantum electrodynamics (QED) platform where quantum emitters interact with a Hofstadter-ladder waveguide. We demonstrate several intriguing phenomena stemming from the exotic dispersion relation and vacuum mode properties led by the effective spin-orbit coupling, which have no analog in other QED setups. First, by assuming emitter's frequency to be resonant with the lower band, we find that the spontaneous emission is chiral with most photonic field decaying unidirectionally. Both numerical and analytical results indicate that the Hofstadter-ladder waveguide can be engineer…
The fundamental process limiting the coherence of quantum-dot based single-photon sources is the interaction with phonons. We study the effect of phonon decoherence on the indistinguishability of single photons emitted from a quantum dot embedded in a suspended nanobeam waveguide. At low temperatures, the indistinguishability is limited by the coupling between the quantum dot and the fundamental vibrational modes of the waveguide and is sensitive to the quantum-dot position within the nanobeam cross-section. We show that this decoherence channel can be efficiently suppressed by clamping the wa…
Bound states arise in waveguide QED systems with a strong frequency-dependence of the coupling between emitters and photonic modes. While exciting such bound-states with single photon wave-packets is not possible, photon-photon interactions mediated by the emitters can be used to excite them with two-photon states. In this letter, we use scattering theory to provide upper limits on this excitation probability for a general non-Markovian waveguide QED system and show that this limit can be reached by a two-photon wave-packet with vanishing uncertainty in the total photon energy. Furthermore, we…
We show that two-photon transport can be modulated by a two-level emitter coupled to a cavity in a one-dimensional waveguide. In the ordinary case, the transmitted light has a wider frequency spectrum than the situation without the cavity because it is reflected and scattered many times. But when the two photons are resonant with the cavity resonance reflection frequency, the frequency spectrum of the transmitted light becomes narrower than that without the cavity. This means that properly tuning the cavity resonance frequency can improve the photon-photon interaction. In addition, we show tha…
Bimodal non-Gaussian photonic states from a single quantum emitter in a waveguide
Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France（索邦大学、法国国家科学研究中心、巴黎文理研究大学、法兰西公学院）；Weizmann Institute of Science（魏茨曼科学研究所）；Palacký University（帕拉茨基大学）
We theoretically demonstrate dynamically selective bidirectional emission and absorption of a single itinerant microwave photon in a waveguide. The proposed device is an artificial molecule composed of two qubits coupled to a waveguide a quarter-wavelength apart. By using simulations based on the input--output theory, we show that upon preparing an appropriate entangled state of the two qubits, a photon is emitted directionally as a result of the destructive interference occurring either at the right or left of the qubits. Moreover, we demonstrate that this artificial molecule possesses the ca…
Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ansätze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity…
Future scalable photonic quantum information processing relies on the ability of integrating multiple interacting quantum emitters into a single chip. Quantum dots provide ideal on-chip quantum light sources. However, achieving quantum interaction between multiple quantum dots on-a-chip is a challenging task due to the randomness in their frequency and position, requiring local tuning technique and long-range quantum interaction. Here, we demonstrate quantum interactions between distant two quantum dots on a nanophotonic waveguide. We achieve a photon-mediated long-range interaction by integra…
The capability to embed self-assembled quantum dots (QDs) at predefined positions in nanophotonic structures is key to the development of complex quantum photonic architectures. Here, we demonstrate that QDs can be deterministically positioned in nanophotonic waveguides by pre-locating QDs relative to a global reference frame using micro-photoluminescence ($μ$PL) spectroscopy. After nanofabrication, $μ$PL images reveal misalignments between the central axis of the waveguide and the embedded QD of only $(9\pm46$) nm and $(1\pm33$) nm, for QDs embedded in undoped and doped membranes, respectivel…
We establish a general framework for studying the bound states and the photon-emission dynamics of quantum emitters coupled to structured nanophotonic lattices with engineered dissipation (loss). In the single-excitation sector, the system can be described exactly by a non-Hermitian formalism. We have pointed out in the accompanying letter [Gong \emph{et al}., arXiv:2205.05479] that a single emitter coupled to a one-dimensional non-Hermitian lattice may already exhibit anomalous behaviors without Hermitian counterparts. Here we provide further detail on these observations. We also present seve…
Single particle-resolved fluorescence imaging is an enabling technology in cold-atom physics. However, so far, this technique was not available for nanophotonic atom-light interfaces. Here, we image single atoms that are trapped and optically interfaced using an optical nanofiber. Near-resonant light is scattered off the atoms and imaged while counteracting heating mechanisms via degenerate Raman cooling. We detect trapped atoms within 150 ms and record image sequences of given atoms. Building on our technique, we perform two experiments which are conditioned on the number and position of the …
We study the enhancement of cooperativity in the atom-light interface near a nanophotonic waveguide for application to quantum nondemolition (QND) measurement of atomic spins. Here the cooperativity per atom is determined by the ratio between the measurement strength and the decoherence rate. Counterintuitively, we find that by placing the atoms at an azimuthal position where the guided probe mode has the lowest intensity, we increase the cooperativity. This arises because the QND measurement strength depends on the interference between the probe and scattered light guided into an orthogonal p…
We demonstrate a quantum nanophotonics platform based on germanium-vacancy (GeV) color centers in fiber-coupled diamond nanophotonic waveguides. We show that GeV optical transitions have a high quantum efficiency and are nearly lifetime-broadened in such nanophotonic structures. These properties yield an efficient interface between waveguide photons and a single GeV without the use of a cavity or slow-light waveguide. As a result, a single GeV center reduces waveguide transmission by $18 \pm 1\%$ on resonance in a single pass. We use a nanophotonic interferometer to perform homodyne detection …
Entanglement is the fuel of advanced quantum technology. It is for instance consumed in measurement-based quantum computing and allows loss-tolerant encoding of quantum information. In photonics, entanglement has traditionally been generated probabilistically, requiring massive multiplexing for scaling up to many photons. An alternative approach utilizes quantum emitters in nanophotonic devices for deterministic generation of single photons, which an be extended to two- and multi-photon generation on demand. The proposed polarization-entanglement sources are, however, incompatible with spatial…
