We devise a mathematical framework for assessing the fidelity of multi-photon entangled states generated by a single solid-state quantum emitter, such as a quantum dot or a nitrogen-vacancy center. Within this formalism, we theoretically study the role of imperfections present in real systems on the generation of time-bin encoded Greenberger-Horne-Zeilinger and one-dimensional cluster states. We consider both fundamental limitations, such as the effect of phonon-induced dephasing, interaction with the nuclear spin bath, and second-order emissions, as well as technological imperfections, such as branching effects, non-perfect filtering, and photon losses. In a companion paper, we consider a particular physical implementation based on a quantum dot emitter embedded in a photonic crystal waveguide and apply our theoretical formalism to assess the fidelities achievable with current technologies.
Entangled photons are crucial for quantum technologies, but generating arbitrary entangled photon states deterministically, efficiently, and with high fidelity remains a challenge. Here, we demonstrate how hybridization and dipole-dipole interactions -- potentially simultaneously available in colloidal quantum dots and molecular aggregates -- leveraged in conjunction can couple simple, well understood emitters into composite emitters with flexible control over the level structure. We show that cascade decay through carefully designed level structures can result in emission of frequency-entangl…
We study single-photon emission of a classically pumped three-level $Λ$-type emitter in a high-$Q$ cavity. In particular, generation of single-photon time-bin double-peak wave packets is shown.
Entangled photon pairs are key to many novel applications in quantum technologies. Semiconductor quantum dots can be used as sources of on-demand, highly entangled photons. The fidelity to a fixed maximally entangled state is limited by the excitonic fine-structure splitting. This work demonstrates that, even if this splitting is absent, the degree of entanglement cannot reach unity when the excitation pulse in a two-photon resonance scheme has a finite duration. The degradation of the entanglement has its origin in a dynamically induced splitting of the exciton states caused by the laser puls…
The controlled interaction between a single, trapped, laser-driven atom and the mode of a high-finesse optical cavity allows for the generation of temporally separated, entangled light pulses. Entanglement between the photon-number fluctuations of the pulses is created and mediated via the atomic center-of-mass motion, which is interfaced with light through the mechanical effect of atom-photon interaction. By means of a quantum noise analysis we determine the correlation matrix which characterizes the entanglement, as a function of the system parameters. The scheme is feasible in experimentall…
Localized radiation sources are analyzed with respect to the relation of nonclassicality and quantum entanglement of the emitted light. The source field parts of the radiation emitted in different directions are closely related to each other. As a consequence, nonclassicality of the light fields in one direction directly implies entanglement of the field modes in different directions. This implication can be extended to multipartite-entanglement and multi-time quantum correlations. Given that a nonclassical effect is observed, our approach explicitly yields the multipartite entanglement witnes…
We consider the radiative properties of a system of two identical correlated atoms interacting with the electromagnetic field in its vacuum state in the presence of a generic dielectric environment. We suppose that the two emitters are prepared in a symmetric or antisymmetric superposition of one ground state and one excited state and we evaluate the transition rate to the collective ground state, showing distinctive cooperative radiative features. Using a macroscopic quantum electrodynamics approach to describe the electromagnetic field, we first obtain an analytical expression for the decay …
Within the matrix product state framework, we study the non-Markovian feedback dynamics of a two-level system interacting with the electromagnetic field inside a semi-infinite waveguide where the excitation of an atom-photon bound state is possible. Taking the steady-state excitation of the emitter as a figure of merit, we compare the trapped excitation for an initially excited quantum emitter and an emitter prepared via quantized pulses containing up to four photons. In the latter case, we find that for large feedback delay times, multi-photon pulses can yield a significantly higher steady-st…
We show that with a new family of pyramidal site-controlled InGaAsN quantum dots it is possible to obtain areas containing as much as 15% of polarization-entangled photon emitters - a major improvement if compared to the small fraction achievable by other quantum dot systems. Entanglement is attested by a two-photon polarization state density matrix and the parameters obtained from it. Emitters showing fidelities up to 0.721+-0.043 were found.
The ability to create large highly entangled `cluster' states is crucial for measurement-based quantum computing. We show that deterministic multi-photon entanglement can be created from coupled solid state quantum emitters without the need for any two-qubit gates and regardless of whether the emitters are identical. In particular, we present a general method for controlled entanglement creation by making direct use of the always-on exchange interaction, in combination with single-qubit operations. This is used to provide a recipe for the generation of two-dimensional, cluster-state entangled …
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 …
When a single emitter is excited by two phase-coherent pulses with a time delay, each of the pulses can lead to the emission of a photon pair, thus creating a ``time-bin entangled'' state. Double pair emission can be avoided by initially preparing the emitter in a metastable state. We show how photons from separate emissions can be made indistinguishable, permitting their use for multi-photon interference. Possible realizations are discussed. The method might also allow the direct creation of n-photon entangled states (n>2).
Inherent binary or collective interactions in ensembles of quantum emitters induce a spread in the energy and lifetime of their eigenstates. While this typically causes fast decay and dephasing, in many cases certain special entangled collective states with minimal decay can be found, which possess ideal properties for spectroscopy, precision measurements or information storage. We show that for a specific choice of laser frequency, power and geometry or a suitable configuration of control fields one can efficiently prepare these states. We demonstrate this by studying preparation schemes for …
To generate entangled photon pairs via quantum dots (QDs), the exciton fine structure splitting (FSS) must be comparable to the exciton homogeneous line width. Yet in the (In,Ga)As/GaAs QD, the intrinsic FSS is about a few tens $μ$eV. To achieve photon entanglement, it is necessary to Cherry-pick a sample with extremely small FSS from a large number of samples, or to apply strong in-plane magnetic field. Using theoretical modeling of the fundamental causes of FSS in QDs, we predict that the intrinsic FSS of InAs/InP QDs is an order of magnitude smaller than that of InAs/GaAs dots, and better y…
Generation of polarization-entangled photon pairs from two interacting quantum emitters
Centro de Física de Materiales (CMF-MPC), CSIC-UPV/EHU（材料物理中心（CMF-MPC），CSIC-巴斯克国立大学联盟）；Department of Electricity and Electronics, University of the Basque Country (UPV/EHU)（巴斯克国立大学（UPV/EHU）电力与电子工程系）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心（DIPC））；Ikerbasque, Basque Foundation for Science（伊克尔巴斯科，巴斯克科学基金会）
The cascaded decay in a four-level quantum emitter is a well established mechanism to generate polarization entangled photon pairs, the building blocks of many applications in quantum technologies. The four most prominent maximally entangled photon pair states are the Bell states. In a typical experiment based on an undriven emitter only one type of Bell state entanglement can be observed in a given polarization basis. Other types of Bell state entanglement in the same basis can be created by continuously driving the system by an external laser. In this work we propose a protocol for time-depe…
We examine the dissipative dynamics of N00N states with an arbitrary photon number N in two architectures of fiber-coupled optical ring resonators (RRs) interacting with two-level quantum emitters. One architecture consists of a two-way cascaded array of emitter-cavity systems, while in the other architecture we consider two fiber-coupled RRs each coupled to multiple dipole-dipole interacting (DDI) quantum emitters (QEs). Our focus in this paper is to study how am initially prepared multiple excitation atomic N00N states transfers to the RRs and then how rapidly it decays in these open cavity …
We investigate the distribution of errors on a computationally useful entangled state generated via the repeated emission from an emitter undergoing strongly non-Markovian evolution. For emitter-environment coupling of pure-dephasing form, we show that the probability that a particular patten of errors occurs has a bound of Markovian form, and thus accuracy threshold theorems based on Markovian models should be just as effective. This is the case, for example, for a charged quantum dot emitter in a moderate to strong magnetic field. Beyond the pure-dephasing assumption, though complicated erro…
Parallel distributed quantum gates for dual-species quantum emitters
MIIT Key Laboratory of Semiconductor Microstructure and Quantum Sensing, School of Physics, Nanjing University of Science and Technology（南京理工大学物理学院）；Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University（亚当·密茨凯维奇大学物理学院自旋电子学与量子信息研究所）；Center for Quantum Computing, RIKEN（理化学研究中心量子计算中心）；Engineering Research Center of Semiconductor Device Optoelectronic Hybrid Integration in Jiangsu Province（江苏省半导体器件光电混合集成工程研究中心）；Physics Department, The University of Michigan（密歇根大学物理系）
Several semiconductor quantum dot techniques have been investigated for the generation of entangled photon pairs. Among the other techniques, droplet epitaxy enables the control of the shape, size, density, and emission wavelength of the quantum emitters. However, the fraction of the entanglement-ready quantum dots that can be fabricated with this method is still limited to around 5%, and matching the energy of the entangled photons to atomic transitions (a promising route towards quantum networking) remains an outstanding challenge. Here, we overcome these obstacles by introducing a modified …
A photonic cluster state with a tree-type entanglement structure constitutes an efficient resource for quantum error correction of photon loss. But the generation of a tree cluster state with an arbitrary size is notoriously difficult. Here, we propose a protocol to deterministically generate photonic tree states of arbitrary size by using only a single quantum emitter. Photonic entanglement is established through both emission and re-scattering from the same emitter, enabling fast and resource-efficient entanglement generation. The same protocol can also be extended to generate more general t…
Entanglement constitutes a main feature that distinguishes quantum from classical physics and is a key resource of quantum technologies. Here we show, however, that entanglement may also serve as the essential ingredient for the emergence of classical behavior in a composite nonlinear radiating system. We consider the radiation from a macroscopic spin emitter, such as the collective radiation from an atomic ensemble. We introduce a new class of macroscopic spin states, the coherently radiating spin states (CRSS), defined as the asymptotic eigenstates of the SU(2) lowering operator. We find tha…
We present protocols to generate arbitrary photonic graph states from quantum emitters that are in principle deterministic. We focus primarily on two-dimensional cluster states of arbitrary size due to their importance for measurement-based quantum computing. Our protocols for these and many other types of two-dimensional graph states require a linear array of emitters in which each emitter can be controllably pumped, rotated about certain axes, and entangled with its nearest neighbors. We show that an error on one emitter produces a localized region of errors in the resulting graph state, whe…
Multi-photon entangled graph states are a fundamental resource in quantum communication networks, distributed quantum computing, and sensing. These states can in principle be created deterministically from quantum emitters such as optically active quantum dots or defects, atomic systems, or superconducting qubits. However, finding efficient schemes to produce such states has been a long-standing challenge. Here, we present an algorithm that, given a desired multi-photon graph state, determines the minimum number of quantum emitters and precise operation sequences that can produce it. The algor…
We present a physical setup with which it is possible to produce arbitrary symmetric long-lived multiqubit entangled states in the internal ground levels of photon emitters, including the paradigmatic GHZ and W states. In the case of three emitters, where each tripartite entangled state belongs to one of two well-defined entanglement classes, we prove a one-to-one correspondence between well-defined sets of experimental parameters, i.e., locally tunable polarizer orientations, and multiqubit entanglement classes inside the symmetric subspace.
Quantifying Pauli Errors in Single-Photon Resource-State Generation
Centre for Engineered Quantum Systems, School of Physics, The University of Sydney（悉尼大学物理学院量子工程系统中心）；Sydney Quantum Academy（悉尼量子学院）；Institute for Photonics and Optical Sciences (IPOS), School of Physics, The University of Sydney（悉尼大学物理学院光子与光学科学研究所）
A scheme to utilize atom-like emitters coupled to nanophotonic waveguides is proposed for the generation of many-body entangled states and for the reversible mapping of these states of matter to photonic states of an optical pulse in the waveguide. Our protocol makes use of decoherence-free subspaces (DFS) for the atomic emitters with coherent evolution within the DFS enforced by strong dissipative coupling to the waveguide. By switching from subradiant to superradiant states, entangled atomic states are mapped to photonic states with high fidelity. An implementation using ultracold atoms coup…
Quantum repeaters are nodes in a quantum communication network that allow reliable transmission of entanglement over large distances. It was recently shown that highly entangled photons in so-called graph states can be used for all-photonic quantum repeaters, which require substantially fewer resources compared to atomic-memory based repeaters. However, standard approaches to building multi-photon entangled states through pairwise probabilistic entanglement generation severely limit the size of the state that can be created. Here, we present a protocol for the deterministic generation of large…
The control and manipulation of quantum-entangled non-local states is a crucial step for the development of quantum information processing. A promising route to achieve such states on a wide scale is to couple solid-state quantum emitters through their coherent dipole-dipole interactions. Entanglement in itself is challenging, as it requires both nanometric distances between emitters and nearly degenerate electronic transitions. Implementing hyperspectral imaging to identify pairs of coupled organic molecules trapped in a low temperature matrix, we reach distinctive spectral signatures of maxi…
Bell states are the most prominent maximally entangled photon states. In a typical four-level emitter, like a semiconductor quantum dot, the photon states exhibit only one type of Bell state entanglement. By adding an external driving to the emitter system, also other types of Bell state entanglement are reachable without changing the polarization basis. In this paper, we show under which conditions the different types of entanglement occur and give analytical equations to explain these findings. We further identify special points, where the concurrence, being a measure for the degree of entan…
We present an input/output analysis of photon-correlation experiments whereby a quantum mechanically entangled bi-photon state interacts with a material sample placed in one arm of a Hong-Ou-Mandel (HOM) apparatus. We show that the output signal contains detailed information about subsequent entanglement with the microscopic quantum states in the sample. In particular, we apply the method to an ensemble of emitters interacting with a common photon mode within the open-system Dicke Model. Our results indicate considerable dynamical information concerning spontaneous symmetry breaking can be rev…
When multiple quantum emitters radiate, their emission rate may be enhanced or suppressed due to collective interference in a process known as super- or subradiance. Such processes are well-known to occur also in light emission by free charged particles. To date, all experimental and theoretical studies of super- and subradiance in these systems involved the classical correlations between the emitters. However, dependence on quantum correlations, such as entanglement between different emitting particles, has not been studied. Recent advances in coherent-shaping of free-electron wavefunctions m…
We propose a novel approach for efficient generation of entangled photons, based on Cooper-pair luminescence in semiconductors, which does not require isolated emitters such as single atoms or quantum dots. We show that in bulk materials, electron-spin entanglement in Cooper pairs should not be expected to be translated into pure entangled photons despite the selection rules, due to mixing introduced by light-hole heavy-hole degeneracy. Semiconductor quantum wells, however, remove this degeneracy, allowing efficient photon entanglement generation in simple electrically-driven structures, takin…
The general concept of entangled photon holes is based on a correlated absence of photon pairs in an otherwise constant optical background. Here we consider the specialized case when this background is confined to two well-defined time bins, which allows the formation of time-bin entangled photon holes. We show that when the typical coherent state background is replaced by a true single-photon (Fock state) background, the basic time-bin entangled photon-hole state becomes equivalent to one of the time-bin entangled photon-pair states. We experimentally demonstrate these ideas using a parametri…
Purdue University（普渡大学）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与工程中心）；Virginia Tech（弗吉尼亚理工大学）；Northwestern University（西北大学）；University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）；Stanford University（斯坦福大学）
Successful generation of photonic cluster states is the key step in the realization of measurement-based quantum computation and quantum network protocols. Several proposals for the generation of such entangled states from different solid-state emitters have been put forward. Each of these protocols come with their own challenges in terms of both conception and implementation. In this work we propose deterministic generation of these photonic cluster states from a spin-photon interface based on a hole spin qubit hosted in a quantum dot molecule. Our protocol resolves many of the difficulties o…
We report progress in the theory of photoluminescence and light scattering by two closely spaced particles. This study is based on our original method to derive the master equation for a system of coupled quantum emitters driven by a cw laser. We emphasise on the case when the emitters are two-level systems but notably different in their transition frequencies and transition moments. The master equation is shown to describe the dipole-dipole coupling and the cooperative entanglement between the particles naturally. It is provided by the use of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hi…
We analyze optical binary communication assisted by entanglement and show that: i) ideal entangled channels have smaller error probability than ideal single-mode coherent channels if the photon number of the channel is larger than one; ii) realistic entangled channels with heterodyne receivers have smaller error probability than ideal single-mode coherent channels if the photon number of the channel is larger than a threshold of about five photons.
We develop the analytic theory describing the formation and evolution of entangled quantum states for a fermionic quantum emitter coupled to a quantized electromagnetic field in a nanocavity and quantized phonon or mechanical vibrational modes. The theory is applicable to a broad range of cavity quantum optomechanics problems and emerging research on plasmonic nanocavities coupled to single molecules and other quantum emitters. The optimal conditions for a tri-state entanglement are realized near the parametric resonances in a coupled system. The model includes decoherence effects due to coupl…
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 consider entangled two-photon generalized binomial states of the electromagnetic field in two separate cavities. The nonlocal properties of this entangled field state are analyzed by studying the electric field correlations between the two cavities. A Bell's inequality violation is obtained using an appropriate dichotomic cavity operator, that is in principle measurable.
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…
Generation of polarization-entangled photons from quantum dots via the biexciton-exciton recombination cascade is complicated by the presence of an energy spitting between the intermediate excitonic levels, which severely degrades the quality of the entangled photon source. In this paper we present a novel, conceptually simple and straightforward proposal for restoring the entanglement of said source by applying a cascade of time-dependent operations on the emitted photons. This is in striking contrast with the techniques usually employed, that act on the quantum emitter itself in order to rem…
