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Measurement-based quantum computing offers a promising route towards scalable, universal photonic quantum computation. This approach relies on the deterministic and efficient generation of photonic graph states in which many photons are mutually entangled with various topologies. Recently, deterministic sources of graph states have been demonstrated with quantum emitters in both the optical and microwave domains. In this work, we demonstrate deterministic and reconfigurable graph state generation with optical solid-state integrated quantum emitters. Specifically, we use a single semiconductor quantum dot in a cavity to generate caterpillar graph states, the most general type of graph state that can be produced with a single emitter. By using fast detuned optical pulses, we achieve full control over the spin state, enabling us to vary the entanglement topology at will. We perform quantum state tomography of two successive photons, measuring Bell state fidelities up to 0.80$\pm$0.04 and concurrences up to 0.69$\pm$0.09, while maintaining high photon indistinguishability. This simple optical scheme, compatible with commercially available quantum dot-based single photon sources, brings us a step closer to fault-tolerant quantum computing with spins and photons.

The frequency or color of photons is an attractive degree of freedom to encode and distribute the quantum information over long distances. However, the generation of frequency-encoded photonic qubits has so far relied on probabilistic non-linear single-photon sources and inefficient gates. Here, we demonstrate the deterministic generation of photonic qubits hyper-encoded in frequency and polarization based on a semiconductor quantum dot in a cavity. We exploit the double dipole structure of a neutral exciton and demonstrate the generation of any quantum superposition in amplitude and phase, controlled by the polarization of the pump laser pulse. The source generates frequency-polarization single-photon qubits at a rate of 4 MHz corresponding to a generation probability at the first lens of 28 $\pm$ 2%, with a photon number purity > 98%. The photons show an indistinguishability > 91% for each dipole and 88% for a balanced quantum superposition of both. The density matrix of the hyper-encoded photonic state is measured by time-resolved polarization tomography, evidencing a fidelity to the target state of 94 $\pm$ 8% and concurrence of 77 $\pm$ 2%, here limited by frequency overlap in our device. Our approach brings the advantages of quantum dot sources to the field of quantum information processing based on frequency encoding.

Photonic graph states, quantum light states where multiple photons are mutually entangled, are key resources for optical quantum technologies. They are notably at the core of error-corrected measurement-based optical quantum computing and all-optical quantum networks. In the discrete variable framework, these applications require high efficiency generation of cluster-states whose nodes are indistinguishable photons. Such photonic cluster states can be generated with heralded single photon sources and probabilistic quantum gates, yet with challenging efficiency and scalability. Spin-photon entanglement has been proposed to deterministically generate linear cluster states. First demonstrations have been obtained with semiconductor spins achieving high photon indistinguishablity, and most recently with atomic systems at high collection efficiency and record length. Here we report on the efficient generation of three partite cluster states made of one semiconductor spin and two indistinguishable photons. We harness a semiconductor quantum dot inserted in an optical cavity for efficient photon collection and electrically controlled for high indistinguishability. We demonstrate two and three particle entanglement with fidelities of 80 % and 63 % respectively, with photon indistinguishability of 88%. The spin-photon and spin-photon-photon entanglement rates exceed by three and two orders of magnitude respectively the previous state of the art. Our system and experimental scheme, a monolithic solid-state device controlled with a resource efficient simple experimental configuration, are very promising for future scalable applications.

Spins in semiconductor quantum dots are promising local quantum memories to generate polarization-encoded photonic cluster states, as proposed in the pioneering Rudolph-Lindner scheme [1]. However, harnessing the polarization degree of freedom of the optical transitions is hindered by resonant excitation schemes that are widely used to obtain high photon indistinguishability. Here we show that acoustic phonon-assisted excitation, a scheme that preserves high indistinguishability, also allows to fully exploit the polarization selective optical transitions to initialise and measure single spin states. We access the coherence of hole spin systems in a low transverse magnetic field and directly monitor the spin Larmor precession both during the radiative emission process of an excited state or in the quantum dot ground state. We report a spin state detection fidelity of $94.7 \pm 0.2 \%$ granted by the optical selection rules and a $20\pm5$~ns hole spin coherence time, demonstrating the potential of this scheme and system to generate linear cluster states with a dozen of photons, Comment: 3 figures

The excitonic fine structure plays a key role for the quantum light generated by semiconductor quantum dots, both for entangled photon pairs and single photons. Controlling the excitonic fine structure has been demonstrated using electric, magnetic, or strain fields, but not for quantum dots in optical cavities, a key requirement to obtain high source efficiency and near-unity photon indistinguishability. Here, we demonstrate the control of the fine structure splitting for quantum dots embedded in micropillar cavities. We propose a scheme based on remote electrical contacts connected to the pillar cavity through narrow ridges. Numerical simulations show that such a geometry allows for a three-dimensional control of the electrical field. We experimentally demonstrate tuning and reproducible canceling of the fine structure, a crucial step for the reproducibility of quantum light source technology., Comment: 9 pages, 7 figures

Entanglement and spontaneous emission are fundamental quantum phenomena that drive many applications of quantum physics. During the spontaneous emission of light from an excited two-level atom, the atom briefly becomes entangled with the photonic field. Here, we show that this natural process can be used to produce photon-number entangled states of light distributed in time. By exciting a quantum dot -- an artificial two-level atom -- with two sequential $\pi$ pulses, we generate a photon-number Bell state. We characterise this state using time-resolved intensity and phase correlation measurements. Furthermore, we theoretically show that applying longer sequences of pulses to a two-level atom can produce a series of multi-temporal mode entangled states with properties intrinsically related to the Fibonacci sequence. Our results on photon-number entanglement can be further exploited to generate new states of quantum light with applications in quantum technologies., Comment: Main: 7 pages, 3 figures; Supplementary: 15 pages, 7 figures

We theoretically describe the quantum Zeno effect in a spin-photon interface represented by a charged quantum dot in a micropillar cavity. The electron spin in this system entangles with the polarization of the transmitted photons, and their continuous detection leads to the slowing of the electron spin precession in external magnetic field and induces the spin relaxation. We obtain a microscopic expression for the spin measurement rate and calculate the second and fourth order correlation functions of the spin noise, which evidence the change of the spin statistics due to the quantum Zeno effect. We demonstrate, that the quantum limit for the spin measurement can be reached for any probe frequency using the homodyne nondemolition spin measurement, which maximizes the rate of the quantum information gain., Comment: 14 pages, 9 figures

Semiconductor quantum dots in cavities are promising single-photon sources. Here, we present a path to deterministic operation, by harnessing the intrinsic linear dipole in a neutral quantum dot via phonon-assisted excitation. This enables emission of fully polarized single photons, with a measured degree of linear polarization up to 0.994 $\pm$ 0.007, and high population inversion -- 85\% as high as resonant excitation. We demonstrate a single-photon source with a polarized first lens brightness of 0.50 $\pm $ 0.01, a single-photon purity of 0.954 $\pm$ 0.001 and single-photon indistinguishability of 0.909 $\pm$ 0.004., Comment: 5 pages, 4 figures, plus supplementary material

Hong-Ou-Mandel interference is a cornerstone of optical quantum technologies. We explore both theoretically and experimentally how the nature of unwanted multi-photon components of single photon sources affect the interference visibility. We apply our approach to quantum dot single photon sources in order to access the mean wavepacket overlap of the single-photon component - an important metric to understand the limitations of current sources. We find that the impact of multi-photon events has thus far been underestimated, and that the effect of pure dephasing is even milder than previously expected., Comment: 9 pages, 5 figures

Light states composed of multiple entangled photons - such as cluster states - are essential for developing and scaling-up quantum computing networks. Photonic cluster states with discrete variables can be obtained from single-photon sources and entangling gates, but so far this has only been done with probabilistic sources constrained to intrinsically-low efficiencies, and an increasing hardware overhead. Here, we report the resource-efficient generation of polarization-encoded, individually-addressable, photons in linear cluster states occupying a single spatial mode. We employ a single entangling-gate in a fiber loop configuration to sequentially entangle an ever-growing stream of photons originating from the currently most efficient single-photon source technology - a semiconductor quantum dot. With this apparatus, we demonstrate the generation of linear cluster states up to four photons in a single-mode fiber. The reported architecture can be programmed to generate linear-cluster states of any number of photons with record scaling ratios, potentially enabling practical implementation of photonic quantum computing schemes., Comment: 7 pages, 4 figures. Supp. info: 7 pages, 3 figures

Developing future quantum communication may rely on the ability to engineer cavity-mediated interactions between photons and solid-state artificial atoms, in a deterministic way. Here, we report a set of technological and experimental developments for the deterministic coupling between the optical mode of a micropillar cavity and a quantum dot trion transition. We first identify a charged transition through in-plane magnetic field spectroscopy, and then tune the optical cavity mode to its energy via in-situ lithography. In addition, we design an asymmetric tunneling barrier to allow the optical trapping of the charge, assisted by a quasi-resonant pumping scheme, in order to control its occupation probability. We evaluate the generation of a positively-charged quantum dot through second order auto-correlation measurements of its resonance fluorescence, and the quality of light-matter interaction for these spin-photon interfaces is assessed by measuring the performance of the device as a single-photon source., Comment: 9 pages, 7 figures

Scaling-up optical quantum technologies requires to combine highly efficient multi-photon sources and integrated waveguide components. Here, we interface these scalable platforms: a quantum dot based multi-photon source and a reconfigurable photonic chip on glass are combined to demonstrate high-rate three-photon interference. The temporal train of single-photons obtained from a quantum emitter is actively demultiplexed to generate a 3.8 kHz three-photon source, which is then sent to the input of a tuneable tritter circuit, demonstrating the on-chip quantum interference of three indistinguishable single-photons. Pseudo number-resolving photon detection characterising the output distribution shows that this first combination of scalable sources and reconfigurable photonic circuits compares favourably in performance with respect to previous implementations. A detailed loss-budget shows that merging solid-state based multi-photon sources and reconfigurable photonic chips could allow ten-photon experiments on chip at ${\sim}40$ Hz rate in a foreseeable future., Comment: 7 pages, 4 figures, 2 tables

We introduce a monolithic Brillouin generator based on a semiconductor micropillar cavity embedding a high frequency nanoacoustic resonator operating in the hundreds of GHz range. The concept of two nested resonators allows an independent design of the ultrahigh frequency Brillouin spectrum and of the optical device. We develop an optical free-space technique to characterize spontaneous Brillouin scattering in this monolithic device and propose a measurement protocol that maximizes the Brillouin generation efficiency in the presence of optically induced thermal effects. The compact and versatile Brillouin generator studied here could be readily integrated into fibered and on-chip architectures., Comment: 9 pages, 4 figures

The ability to generate light in a pure quantum state is essential for advances in optical quantum technologies. However, obtaining quantum states with control in the photon-number has remained elusive. Optical light fields with zero and one photon can be produced by single atoms, but so far it has been limited to generating incoherent mixtures, or coherent superpositions with a very small one-photon term. Here, we report on the on-demand generation of quantum superpositions of zero, one, and even two photons, via pulsed coherent control of a single artificial atom. Driving the system up to full atomic inversion leads to the generation of quantum superpositions of vacuum and one photon, with their relative populations controlled by the driving laser intensity. A stronger driving of the system, with $2\pi$-pulses, results in a coherent superposition of vacuum, one and two photons, with the two-photon term exceeding the one-photon component, a state allowing phase super-resolving interferometry. Our results open new paths for optical quantum technologies with access to the photon-number degree-of-freedom., Comment: Main text: 8 pages, 3 figures. Supp. info: 5 pages, 4 figures

Pillar microcavities are excellent light-matter interfaces providing an electromagnetic confinement in small mode volumes with high quality factors. They also allow the efficient injection and extraction of photons, into and from the cavity, with potentially near-unity input and output-coupling efficiencies. Optimizing the input and output coupling is essential, in particular, in the development of solid-state quantum networks where artificial atoms are manipulated with single incoming photons. Here we propose a technique to accurately measure input and output coupling efficiencies using polarization tomography of the light reflected by the cavity. We use the residual birefringence of pillar microcavities to distinguish the light coupled to the cavity from the uncoupled light: the former participates to rotating the polarization of the reflected beam, while the latter decreases the polarization purity. Applying this technique to a micropillar cavity, we measure a $53 \pm2 \% $ output coupling and a $96 \pm 1\%$ input coupling with unprecedented precision., Comment: 6 pages, 3 figures

We propose a novel acoustic cavity design where we confine a mechanical mode by adiabatically changing the acoustic properties of a GaAs/AlAs superlattice. By means of high resolution Raman scattering measurements, we experimentally demonstrate the presence of a confined acoustic mode at a resonance frequency around 350 GHz. We observe an excellent agreement between the experimental data and numerical simulations based on a photoelastic model. We demonstrate that the spatial profile of the confined mode can be tuned by changing the magnitude of the adiabatic deformation, leading to strong variations of its mechanical quality factor and Raman scattering cross section. The reported alternative confinement method could lead to the development of a novel generation of nanophononic and optomechanical systems.

We study theoretically the spin-induced and photon-induced fluctuations of optical signals from a singly-charged quantum dot-microcavity structure. We identify the respective contributions of the photon-polariton interactions, in the strong light-matter coupling regime, and of the quantum back-action induced by photon detection on the spin system. Strong spin projection by a single photon is shown to be achievable, allowing the initialization and measurement of a fully-polarized Larmor precession. The spectrum of second-order correlations is deduced, displaying information on both spin and quantum dot-cavity dynamics. The presented theory thus bridges the gap between the fields of spin noise spectroscopy and quantum optics., Comment: 12 pages, 8 figures

Recent experiments demonstrated that GaAs-AlAs based micropillar cavities are promising systems for quantum optomechanics, allowing the simultaneous three-dimensional confinement of near-infrared photons and acoustic phonons in the 18-100 GHz range. Here, we investigate through numerical simulations the optomechanical properties of this new platform. We evidence how the Poisson's ratio and semiconductor-vacuum boundary conditions lead to very distinct features in the mechanical and optical three dimensional confinement. We find a strong dependence of the mechanical quality factor and strain distribution on the micropillar radius, in great contrast to what is predicted and observed in the optical domain. The derived optomechanical coupling constants g_0 reach ultra-large values in the 10^6 rad/s range.

Path-entangled N-photon states can be obtained through the coalescence of indistinguishable photons inside linear networks. They are key resources for quantum enhanced metrology, quantum imaging, as well as quantum computation based on quantum walks. However, the quantum tomography of path-entangled indistinguishable photons is still in its infancy as it requires multiple phase estimations increasing rapidly with N. Here, we propose and implement a method to measure the quantum tomography of path-entangled two-photon states. A two-photon state is generated through the Hong-Ou-Mandel interference of highly indistinguishable single photons emitted by a semiconductor quantum dot-cavity device. To access both the populations and the coherences of the path-encoded density matrix, we introduce an ancilla spatial mode and perform photon correlations as a function of a single phase in a split Mach-Zehnder interferometer. We discuss the accuracy of standard quantum tomography techniques and show that an overcomplete data set can reveal spatial coherences that could be otherwise hidden due to limited or noisy statistics. Finally, we extend our analysis to extract the truly indistinguishable part of the density matrix, which allows us to identify the main origin for the imperfect fidelity to the maximally entangled state., Comment: 7 pages, 5 figures

We introduce a tomography approach to describe the optical response of a cavity quantum electrodynamics device, beyond the semiclassical image of polarization rotation, by analyzing the polarization density matrix of the reflected photons in the Poincar\'e sphere. Applying this approach to an electrically-controlled quantum dot-cavity device, we show that a single resonantly-excited quantum dot induces a large optical polarization rotation by $20^\circ$ in latitude and longitude in the Poincar\'e sphere, with a polarization purity remaining above $84\%$. The quantum dot resonance fluorescence is shown to contribute to the polarization rotation via its coherent part, whereas its incoherent part contributes to degrading the polarization purity., Comment: Main text: 6 pages, 4 figures Supplementary material: 4 pages, 1 figure

Applications of cavity optomechanics span from gravitational wave detection to the study of quantum motion states in mesoscopic mechanical systems. The engineering of resonators supporting strongly interacting mechanical and optical modes is central to these developments. However, current technological and experimental approaches limit the accessible mechanical frequencies to a few GHz, imposing hard constraints on quantum mechanical studies. Here we demonstrate the optical control of 20-100~GHz mechanical modes confined in the three dimensions within semiconductor nano-optomechanical pillar cavities. We use a time-resolved transient optical reflectivity technique and access both the energy spectrum and dynamics of the mechanical modes at the picosecond timescale. A strong increase of the optomechanical coupling upon reducing the pillar size is observed together with unprecedent room temperature Q-frequency products above $10^{14}$. The measurements also reveal sideband generation in the optomechanical response. Such resonators can naturally integrate quantum wells and quantum dots, enabling novel applications in cavity quantum electrodynamics and high frequency nanomechanics.

A strong limitation of linear optical quantum computing is the probabilistic operation of two-quantum bit gates based on the coalescence of indistinguishable photons. A route to deterministic operation is to exploit the single-photon nonlinearity of an atomic transition. Through engineering of the atom-photon interaction, phase shifters, photon filters and photon- photon gates have been demonstrated with natural atoms. Proofs of concept have been reported with semiconductor quantum dots, yet limited by inefficient atom-photon interfaces and dephasing. Here we report on a highly efficient single-photon filter based on a large optical non-linearity at the single photon level, in a near-optimal quantum-dot cavity interface. When probed with coherent light wavepackets, the device shows a record nonlinearity threshold around $0.3 \pm 0.1$ incident photons. We demonstrate that directly reflected pulses consist of 80% single-photon Fock state and that the two- and three-photon components are strongly suppressed compared to the single-photon one.

Single photons are the natural link between the nodes of a quantum network: they coherently propagate and interact with many types of quantum bits including natural and artificial atoms. Ideally, one atom should deterministically control the state of a photon and vice-versa. The interaction between free space photons and an atom is however intrinsically weak and many efforts have been dedicated to develop an efficient interface. Recently, it was shown that the propagation of light can be controlled by an atomic resonance coupled to a cavity or a single mode waveguide. Here we demonstrate that the state of a single artificial atom in a cavity can be efficiently controlled by a few-photon pulse. We study a quantum dot optimally coupled to an electrically-controlled cavity device, acting as a near optimal one-dimensional atom. By monitoring the exciton population through resonant fluorescence, we demonstrate Rabi oscillations with a $\pi$-pulse of only 3.8 photons on average. The probability to flip the exciton quantum bit with a single photon Fock state is calculated to reach 55% in the same device.

Single-photons are key elements of many future quantum technologies, be it for the realisation of large-scale quantum communication networks for quantum simulation of chemical and physical processes or for connecting quantum memories in a quantum computer. Scaling quantum technologies will thus require efficient, on-demand, sources of highly indistinguishable single-photons. Semiconductor quantum dots inserted in photonic structures are ultrabright single photon sources, but the photon indistinguishability is limited by charge noise induced by nearby surfaces. The current state of the art for indistinguishability are parametric down conversion single-photon sources, but they intrinsically generate multiphoton events and hence must be operated at very low brightness to maintain high single photon purity. To date, no technology has proven to be capable of providing a source that simultaneously generates near-unity indistinguishability and pure single photons with high brightness. Here, we report on such devices made of quantum dots in electrically controlled cavity structures. We demonstrate on-demand, bright and ultra-pure single photon generation. Application of an electrical bias on deterministically fabricated devices is shown to fully cancel charge noise effects. Under resonant excitation, an indistinguishability of $0.9956\pm0.0045$ is evidenced with a $g^{2}(0)=0.0028\pm0.0012$. The photon extraction of $65%$ and measured brightness of $0.154\pm0.015$ make this source $20$ times brighter than any source of equal quality. This new generation of sources open the way to a new level of complexity and scalability in optical quantum manipulation.

We present a microscopic theory of optical initialization, control and detection for a single electron spin in a quantum dot embedded into a zero-dimensional microcavity. The strong coupling regime of the trion and the cavity mode is addressed. We demonstrate that efficient spin orientation by a single circularly polarized pulse is possible in relatively weak transverse magnetic fields. The possibilities for spin control by additional circularly polarized pulse are analyzed. Under optimal conditions the Kerr and Faraday rotation angles induced by the spin polarized electron may reach tens of degrees., Comment: 14 pages, 7 figures, v2 contains minor revisions

Quantum dots in cavities have been shown to be very bright sources of indistinguishable single photons. Yet the quantum interference between two bright quantum dot sources, a critical step for photon based quantum computation, has never been investigated. Here we report on such a measurement, taking advantage of a deterministic fabrication of the devices. We show that cavity quantum electrodynamics can efficiently improve the quantum interference between remote quantum dot sources: poorly indistinguishable photons can still interfere with good contrast with high quality photons emitted by a source in the strong Purcell regime. Our measurements and calculations show that cavity quantum electrodynamics is a powerful tool for interconnecting several devices., Comment: 5 pages, 4 figures (Supp. Mat. attached)

The origin of the emission within the optical mode of a coupled quantum dot-micropillar system is investigated. Time-resolved photoluminescence is performed on a large number of deterministically coupled devices in a wide range of temperature and detuning. The emission within the cavity mode is found to exhibit the same dynamics as the spectrally closest quantum dot state. Our observations indicate that fast dephasing of the quantum dot state is responsible for the emission within the cavity mode. An explanation for recent photon correlation measurements reported on similar systems is proposed., Comment: 4 pages, 4 figures

Using far field optical lithography, a single quantum dot is positioned within a pillar microcavity with a 50 nm accuracy. The lithography is performed in-situ at 10 K while measuring the quantum dot emission. Deterministic spectral and spatial matching of the cavity-dot system is achieved in a single step process and evidenced by the observation of strong Purcell effect. Deterministic coupling of two quantum dots to the same optical mode is achieved, a milestone for quantum computing., Comment: Modified version: new title, additional experimental data in figure 3