We provide the first classification of three-photon eigenstates in a finite periodic array of two-level atoms coupled to a waveguide. We focus on the strongly subwavelength limit and show the hierarchical structure of the eigenstates in the complex plane. The main characteristic eigenstates are explored using entanglement entropy as a distinguishing feature. We show that the rich interplay of effects from order, chaos to localisation found in two-photon systems extends naturally to three-photon systems. There also exist interaction-induced localised states unique to three-photon systems such as bound trimers, corner states and trimer edge states.
We consider the quantum electrodynamics of a binary array of chiral waveguides, each containing many atoms. We show that the one-photon amplitude of a single-excitation state obeys a two-dimensional Dirac equation. Using this result, we develop the scattering theory for the Dirac equation in this setting and illustrate our results with numerical simulations.
This review describes the emerging field of waveguide quantum electrodynamics (WQED) concerned with the interaction of photons propagating in a waveguide with localized quantum emitters. The collective emitter-photon interactions can lead to both enhanced and suppressed coupling compared to the case of independent emitters. Here, we focus on guided photons and ordered arrays, leading to super- and sub-radiant states, bound photon states and quantum correlations with promising quantum information applications. We highlight recent groundbreaking experiments performed with different quantum platf…
We study theoretically driven quantum dynamics in periodic arrays of two-level qubits coupled to the waveguide. We demonstrate, that strongly subradiant eigenstates of the master equation for the density matrix emerge under strong coherent driving for arrays with the anti-Bragg periods $d=λ/4,3λ/4$... This happens even though are no such states at low driving powers. Thus, our findings show that in the quantum nonlinear regime the domain of existence of subradiant states expands beyond conventional subwavelength structures. These driven states are directly manifested in long-living quantum cor…
We study theoretically subradiant states in the array of atoms coupled to photons propagating in a one-dimensional waveguide focusing on the strongly interacting many-body regime with large excitation fill factor $f$. We introduce a generalized many-body entropy of entanglement based on exact numerical diagonalization followed by a high-order singular value decomposition. This approach has allowed us to visualize and understand the structure of a many-body quantum state. We reveal the breakdown of fermionized subradiant states with increase of $f$ with emergence of short-ranged dimerized antif…
Architectures based on waveguide quantum electrodynamics have emerged as promising candidates for quantum networks. In this paper, we analyze the propagation of single-photons in disordered many-atom waveguides. We pay special attention to the influence of chirality (directionality of photon transport) on the formation of localized photonic states, considering separately the cases of the disorder in the atomic positions and in the atomic transition frequencies.
Quantum correlations between distant particles remain enigmatic since the birth of quantum mechanics. Here we predict a novel kind of bound quantum state in the simplest one-dimensional setup of two interacting particles in a box. Paradoxically, two entangled particles become localized at the opposite edges of the box even though their interactions at large distance should seemingly play no role. Such states could be realized in the waveguide quantum electrodynamics platform, where an array of superconducting qubits or cold atoms is coupled to a waveguide. We demonstrate how long-range wavegui…
We identify a general connection between the physics of exceptional points in non-Hermitian systems and the few-photon bound states in waveguide quantum electrodynamics (QED) systems. We show that, in waveguide QED systems where the local quantum system exhibits an exceptional point, the tightest-bound few-photon bound state occurs at the exceptional point. We illustrate this connection with an explicit computation on a waveguide QED system in which a waveguide is coupled to a Jaynes-Cummings system. Our result provides a quantum signature of the exceptional point physics and indicates that th…
While the theoretical studies in waveguide quantum electrodynamics predominate with single-photon and two-photon Fock state (photon number states) input, the experiments are primarily carried out using a faint coherent light. We create a theoretical toolbox to compare and contrast linear and nonlinear light scattering by a two-level or a three-level emitter embedded in an open waveguide carrying Fock state or coherent state inputs. We identify rules to compare light transport properties, the Kerr, and cross-Kerr nonlinearities of the medium for the two types of inputs. A generalized descriptio…
Unidirectional reflectionlessness is investigated in a waveguide quantum electrodynamics system that consists of a cavity and a $Λ$-type three-level quantum dot coupled to a one-dimensional plasmonic waveguide. Analytical expressions of transmission and reflection coefficients are derived and discussed for both resonant and off-resonant couplings. By appropriately modulating the coupling strength, phase shift and Rabi frequency, unidirectional reflectionlessness is observed at the exceptional points. And unidirectional coherent perfect absorption is exhibited at the vicinity of exceptional poi…
We study single photon transport in a one-dimensional disordered lattice of three-level atoms coupled to an optical waveguide. In particular, we study atoms of Λ-type that are capable of exhibiting electromagnetically induced transparency (EIT) and separately consider disorder in the atomic positions and transition frequencies. We mainly address the question of how preferential emission into waveguide modes (chirality) can influence the formation of spatially localized states. Our work has relevance to experimental studies of cold atoms coupled to nanoscale waveguides and has possible applicat…
We consider a two-dimensional extension of the 1D waveguide quantum electrodynamics and investigate the nature of linear excitations in two-dimensional arrays of qubits coupled to networks of chiral waveguides. We show that the combined effects of chirality and long-range photon mediated qubit-qubit interactions lead to the emergence of the two-dimensional flat bands in the polaritonic spectrum, corresponding to slow strongly correlated light.
We present the general structure of two-photon S matrix for a waveguide coupled to a local quantum system that supports multiple ground states. The presence of the multiple ground states results in a non-commutative aspect of the system with respect to the exchange of the orders of photons. Consequently, the two-photon S matrix significantly differs from the standard form as described by the cluster decomposition principle in the quantum field theory.
We theoretically predict the formation of two-photon bound states in a two-dimensional waveguide network hosting a lattice of two-level atoms. The properties of these bound pairs and the exclusive domains of the parameter space where they emerge due to the interplay between the on-site photon blockade and peculiar shape of polariton dispersion resulting from the long-range radiative couplings between the qubits are investigated in detail. In addition, we analyze the effect of the finite-size system on localization characteristics of these excitations.
Quantum information is typically encoded in the state of a qubit that is decoupled from the environment. In contrast, waveguide quantum electrodynamics studies qubits coupled to a mode continuum, exposing them to a loss channel and causing quantum information to be lost before coherent operations can be performed. Here we restore coherence by realizing a dark state that exploits symmetry properties and interactions between four qubits. Dark states decouple from the waveguide and are thus a valuable resource for quantum information but also come with a challenge: they cannot be controlled by th…
We examine the propagation of single photons in periodic and disordered dimer chains coupled to one-dimensional chiral and bidirectional waveguides. Each dimer is composed of two dipole-coupled atoms. In the disordered setting, we separately treat two types of position disorder, namely in dimer length and in dimer separation. The focus of this study is to understand in what ways the interplay between dipole-dipole interactions and directionality of photon emission can impact the transport of single photons. Cold atoms trapped near optical fibers can serve as an experimentally realizable platfo…
Realizing a fully connected network of quantum processors requires the ability to distribute quantum entanglement. For distant processing nodes, this can be achieved by generating, routing, and capturing spatially entangled itinerant photons. In this work, we demonstrate the deterministic generation of such photons using superconducting transmon qubits that are directly coupled to a waveguide. In particular, we generate two-photon N00N states and show that the state and spatial entanglement of the emitted photons are tunable via the qubit frequencies. Using quadrature amplitude detection, we r…
We study the collective decay rates of multi-dimensional quantum networks in which one-dimensional waveguides form an intersecting hyper-rectangular lattice, with qubits located at the lattice points. We introduce and motivate the \emph{dimensional reduction of poles} (DRoP) conjecture, which identifies all collective decay rates of such networks via a connection to waveguides with a one-dimensional topology (e.g. a linear chain of qubits). Using DRoP, we consider many-body effects such as superradiance, subradiance, and bound-states in continuum in multi-dimensional quantum networks. We find …
While designing the energy-momentum relation of photons is key to many linear, non-linear, and quantum optical phenomena, a new set of light-matter properties may be realized by employing the topology of the photonic bath itself. In this work we investigate the properties of superconducting qubits coupled to a metamaterial waveguide based on a photonic analog of the Su-Schrieffer-Heeger model. We explore topologically-induced properties of qubits coupled to such a waveguide, ranging from the formation of directional qubit-photon bound states to topology-dependent cooperative radiation effects.…
We investigate the behavior of two quantum emitters (two-level atoms) embedded in a linear waveguide, in a quasi-one-dimensional configuration. Since the atoms can emit, absorb and reflect radiation, the pair can spontaneously relax towards an entangled bound state, under conditions in which a single atom would instead decay. We analyze the properties of these bound states, which occur for resonant values of the interatomic distance, and discuss their relevance with respect to entanglement generation. The stability of such states close to the resonance is studied, as well as the properties of …
Atom arrays are a new type of quantum light-matter interface. Here, we propose to employ one-dimensional ordered arrays as atomic waveguides. These arrays support optical guided modes that do not decay into free space. We show that these modes can be harnessed to mediate tunable, long-range interactions between additional "impurity qubits" coupled to the chain, without need for photonic structures. The efficient coupling between qubits and atomic waveguides enables the realization of tunable qubit-qubit interactions, which can be short- or long-range, dissipative or coherent, as well as chiral…
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…
Dark state spectroscopy in nonlinear waveguide quantum electrodynamics
Andrew and Erna Viterbi Department of Electrical & Computer Engineering, Technion - Israel Institute of Technology（安德鲁和埃尔纳·维特比电气与计算机工程系，以色列理工学院）；Helen Diller Quantum Center, Technion - Israel Institute of Technology（海伦·迪勒量子中心，以色列理工学院）
Non-Markovian time-evolution of quantum systems is a challenging problem, often mitigated by employing numerical methods or making simplifying assumptions. In this work, we address this problem in waveguide QED by developing a diagrammatic approach, which performs fully analytical non-Markovian time evolution of single-photon states. By revisiting Fermi's two atom problem, we tackle the impeding question of whether rotating-wave approximation violates causality in single-photon waveguide QED. Afterward, we introduce and prove the \emph{no upper half-plane poles (no-UHP) theorem}, which connect…
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…
We explore amplification and cross-Kerr nonlinearity by a three-level emitter (3LE) embedded in a waveguide and driven by two light beams. The coherent amplification and cross-Kerr nonlinearity were demonstrated in recent experiments, respectively, with a V and a ladder-type 3LE coupled to an open superconducting transmission line carrying two microwave fields. Here, we consider $Λ$, V, and ladder-type 3LE, and compare the efficiency of coherent and incoherent amplification as well as the magnitude of the cross-Kerr phase shift in all three emitters. We apply the Heisenberg-Langevin equations …
The embedding of tunable quantum emitters in a photonic bandgap structure enables the control of dissipative and dispersive interactions between emitters and their photonic bath. Operation in the transmission band, outside the gap, allows for studying waveguide quantum electrodynamics in the slow-light regime. Alternatively, tuning the emitter into the bandgap results in finite range emitter-emitter interactions via bound photonic states. Here we couple a transmon qubit to a superconducting metamaterial with a deep sub-wavelength lattice constant ($λ/60$). The metamaterial is formed by periodi…
Loss resilience of driven-dissipative remote entanglement in chiral waveguide quantum electrodynamics
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Department of Physics, University of Chicago（芝加哥大学物理系）
We propose an on-chip source of entangled photon pairs that uses an arrayed-waveguide grating (AWG) with multiple nonlinear input waveguides as correlated photon pair sources. The AWG wavelength-demultiplexes photon pairs created in input waveguides and simultaneously produces a high-dimensional entangled state encoded in the optical path. We implemented the device with a monolithic silicon-silica waveguide integration platform and demonstrated the entanglement of two dimensions in a proof-of-principle experiment.
We demonstrate the generation of quantum-correlated photon pairs from a Si photonic-crystal coupled-resonator optical waveguide. A slow-light supermode realized by the collective resonance of high-Q and small-mode-volume photonic-crystal cavities successfully enhanced the efficiency of the spontaneous four-wave mixing process. The generation rate of photon pairs was improved by two orders of magnitude compared with that of a photonic-crystal line defect waveguide without a slow-light effect.
Quantum photonic integration circuits are a promising approach to scalable quantum processing with photons. Waveguide single-photon-detectors (WSPDs) based on superconducting nanowires have been recently shown to be compatible with single-photon sources for a monolithic integration. While standard WSPDs offer single-photon sensitivity, more complex superconducting nanowire structures can be configured to have photon-number-resolving capability. In this work, we present waveguide photon-number-resolving detectors (WPNRDs) on GaAs/Al0.75Ga0.25As ridge waveguides based on a series connection of n…
Routing quantum information between non-local computational nodes is a foundation for extensible networks of quantum processors. Quantum information transfer between arbitrary nodes is generally mediated either by photons that propagate between them, or by resonantly coupling nearby nodes. The utility is determined by the type of emitter, propagation channel, and receiver. Conventional approaches involving propagating microwave photons have limited fidelity due to photon loss and are often unidirectional, whereas architectures that use direct resonant coupling are bidirectional in principle, b…
We demonstrate experimentally the frequency time entanglement of photon pairs produced in a CW pumped quasi phased matched AlGaAs superlattice waveguide. A visibility of 96.0+-0.7% without background subtraction has been achieved, which corresponds the violation of Bell inequality by 52 standard deviations.
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.
Interfacing solid-state emitters with photonic structures is a key strategy for developing highly efficient photonic quantum technologies. Such structures are often organised into two distinct categories: nanocavities and waveguides. However, any realistic nanocavity structure simultaneously has characteristics of both a cavity and waveguide, which is particularly pronounced when the cavity is constructed using low-reflectivity mirrors in a waveguide structure with good transverse light confinement. In this regime, standard cavity quantum optics theory breaks down, as the waveguide character o…
We describe theoretically the process of spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays in the presence of linear loss. We derive a set of discrete Schrodinger-type equations for the biphoton wave function, and the wave function of one photon when the other photon in a pair is lost. We demonstrate effects arising from loss-affected interference between the generated photon pairs and show that nonlinear waveguide arrays can serve as a robust loss-tolerant integrated platform for the generation of entangled photon states with non-classical spatial correlations.
A major challenge in quantum optics and quantum information technology is to enhance the interaction between single photons and single quantum emitters. Highly engineered optical cavities are generally implemented requiring nanoscale fabrication precision. We demonstrate a fundamentally different approach in which disorder is used as a resource rather than a nuisance. We generate strongly confined Anderson-localized cavity modes by deliberately adding disorder to photonic crystal waveguides. The emission rate of a semiconductor quantum dot embedded in the waveguide is enhanced by a factor of 1…
We suggest a method for trapping photons in quasi one-dimensional waveguide or coupled-resonator lattices, which is based on an optical analogue of the Aharonov-Bohm cages for charged particles. Light trapping results from a destructive interference of Aharonov-Bohm type induced by a synthetic magnetic field, which is realized by periodic modulation of the waveguide/resonator propagation constants/resonances.
We report on the demonstration of correlated photon pair generation in quasi-phase-matched superlattice AlGaAs waveguides with a high coincidence-to-accidental ratio (CAR); with a continuous (CW) pump, the observed CAR (>100) is more than two order of magnitudes improvement over previously reported spontaneous down conversion (SPDC) schemes in AlGaAs waveguides with a pulsed pump.
On-chip chiral quantum light-matter interfaces, which support directional interactions, provide a promising platform for efficient spin-photon coupling, non-reciprocal photonic elements, and quantum logic architectures. We present full-wave three-dimensional calculations to quantify the performance of conventional and topological photonic crystal waveguides as chiral emitter-photon interfaces. Specifically, the ability of these structures to support and enhance directional interactions while suppressing subsequent backscattering losses is quantified. Broken symmetry waveguides, such as the non…
