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We experimentally investigate a solid-state quantum emitter - a B center in hexagonal boron nitride (hBN) - that has lifetime-limited coherence at short times, and experiences inhomogeneous broadening due to spectral diffusion at longer times. By making use of power broadening in resonant laser excitation, we explore the crossover between the inhomogeneous and the homogeneous broadening regimes. With the support of numerical simulations, we show that the lineshape, count rate, second-order correlations and long-time photon statistics evolve from a regime where they are dictated by spectral diffusion to a regime where they are simply given by the homogeneous response of the emitter, yielding restored Lorentzian shape and Poissonian photon statistics. Saturation of the count rate and line broadening occur not at the onset of the Rabi oscillations, but when the power-broadened homogeneous response becomes comparable with the inhomogeneous linewidth. Moreover, we identify specific signatures in both the second-order correlations and long-time photon statistics that are well explained by a microscopic spectral diffusion model based on discrete jumps at timescales of micro- to milliseconds. Our work provides an extensive description of the photophysics of B-centers under resonant excitation, and can be readily extended to a wide variety of solid-state quantum emitters.

High-dimensional quantum units of information, or qudits, can carry more than one quantum bit of information in a single degree of freedom, and can therefore be used to boost the performance of quantum communication and quantum computation protocols. A photon in a superposition of $2^N$ time bins - a time-bin qudit - contains as much information as N qubits. Here, we show that N-qubit states encoded in a single time-bin qudit can be arbitrarily and deterministically generated, manipulated and measured using a number of linear optics elements that scales linearly with N, as opposed with prior proposals of single-qudit implementation of N-qubit logic, which typically requires $O(2^N)$ elements. The simple and cost-effective implementation we propose can be used as a small-scale quantum processor. We then demonstrate a path towards scalability by interfacing distinct qudit processors to a matter qubit (atom or quantum dot spin) in an optical resonator. Such a cavity QED system allows for more advanced functionalities, such as single-qubit nondemolition measurement and two-qubit gates between distinct qudits. It could also enable quantum interfaces with other matter quantum nodes in the context of quantum networks and distributed quantum computing.

Color centers in hexagonal boron nitride (hBN) advantageously combine excellent photophysical properties with a potential for integration in highly compact devices. Progress towards scalable integration necessitates a high quantum efficiency and an efficient photon collection. In this context, we compare the optical characteristics of individual hBN color centers generated by electron irradiation, in two different electromagnetic environments. We keep track of well-identified emitters that we characterize before and after dry transfer of exfoliated crystals. This comparison provides information about their quantum efficiency - which we find close to unity - as well as their vertical position in the crystal with nanometric precision, which we find away from the flake surfaces. Our work suggests hybrid dielectric-metal planar structures as an efficient tool for characterizing quantum emitters in addition to improving the count rate, and can be generalized to other emitters in 2D materials or in planar photonic structures.

In the solid state, a large variety of single-photon emitters present high quality photophysical properties together with a potential for integration. However, in many cases, the host matrix induces fluctuations of the emission wavelength in time, limiting the potential applications based on indistinguishable photons. A deep understanding of the underlying spectral diffusion processes is therefore of high importance for improving the stability of the light emission. Here, we theoretically investigate the photon statistics of an emitter driven by a resonant laser, and subject to either of two qualitatively different stationary spectral diffusion processes - a continuous diffusion process and a process based on discrete spectral jumps, both of which being known to model the spectral diffusion of various solid-state emitters. We show that the statistics of light emission carries several experimentally accessible signatures that allow to discriminate between the two classes of models, both at short times in the intensity correlation function, and at long times in the fluctuations of the integrated intensity. These results establish that resonant excitation combined with photon statistics offers a rich access to the spectral diffusion processes, yielding information that goes beyond the bare characterization of the inhomogeneous shape and noise correlation time. Incidentally, our findings shed a new light on recent experimental results of spectral diffusion of B centers in hexagonal boron nitride, providing more insight in their spectral diffusion mechanisms.

Integrated quantum photonics, with potential applications in quantum information processing, relies on the integration of quantum emitters into on-chip photonic circuits. Hexagonal boron nitride (hBN) is recognized as a material that is compatible with such implementations, owing to its relatively high refractive index and low losses in the visible range, together with advantageous fabrication techniques. Here, we combine hBN waveguide nanofabrication with the recently demonstrated local generation of quantum emitters using electron irradiation to realize a fully top-down elementary quantum photonic circuit in this material, operating at room temperature. This proof of principle constitutes a first step towards deterministic quantum photonic circuits in hBN.

The ability to identify and characterize homogeneous and inhomogeneous dephasing processes is crucial in solid-state quantum optics. In particular, spectral diffusion leading to line broadening is difficult to evidence when the associated timescale is shorter than the inverse of the photon detection rate. Here, we show that a combination of resonant laser excitation and second-order photon correlations allows to access such fast dynamics. The resonant laser drive converts spectral diffusion into intensity fluctuations, leaving a signature in the second-order coherence function $g^{(2)}(\tau)$ of the scattered light that can be characterized using two-photon coincidences -- which simultaneously provides the homogeneous dephasing time. We experimentally implement this method to investigate the fast spectral diffusion of a color center generated by an electron beam in the two-dimensional material hexagonal boron nitride. The $g^{(2)}(\tau)$ function of the quantum emitter measured over more than ten orders of magnitude of delay times, at various laser powers, establishes that the color center experiences spectral diffusion at a characteristic timescale of a few tens of microseconds, while emitting Fourier-limited single photons ($T_2/2T_1 \sim 1$) between spectral jumps.

Recently discovered quantum emitters in two-dimensional (2D) materials have opened new perspectives of integrated photonic devices for quantum information. Most of these applications require the emitted photons to be indistinguishable, which has remained elusive in 2D materials. Here, we investigate two-photon interference of a quantum emitter generated in hexagonal boron nitride (hBN) using an electron beam. We measure the correlations of zero-phonon-line photons in a Hong-Ou-Mandel (HOM) interferometer under non-resonant excitation. We find that the emitted photons exhibit a partial indistinguishability of $0.44 \pm 0.11$ in a 3 ns time window, which corresponds to a corrected value of $0.56 \pm 0.11$ after accounting for imperfect emitter purity. The dependence of the HOM visibility on the width of the post-selection time window allows us to estimate the dephasing time of the emitter to be $\sim 1.5$ ns, about half the limit set by spontaneous emission. A visibility above 90 % is under reach using Purcell effect with up-to-date 2D material photonics.

The ability to locally activate or generate quantum emitters in two-dimensional materials is of major interest for the realization of integrated quantum photonic devices. In particular, hexagonal boron nitride (hBN) has recently been shown to allow a variety of techniques for obtaining quantum emitters at desired locations. Here, we use cathodoluminescence (CL) to monitor in situ the local activation of color centers by an electron beam in hBN. We observe that the CL signal saturates at a given surface dose, independently of the electron current density. Based on photoluminescence and photon correlations, we show that the number of photoactive color centers is proportional to the CL signal, and we estimate the maximum density of quantum emitters that can be generated by our technique. Our results provide insights about the activation mechanism and could help to optimize the controlled generation of single photon sources in hexagonal boron nitride.

Inhomogeneous broadening is well known to hinder individual characteristics of emitters, supplanting the single-particle properties by their broader probability distribution. Here, we present an analysis of the emission spectra of mesoscopic ensembles of inhomogeneously distributed emitters below the thermodynamic limit (10 - 10^4 emitters). Based on a simple analytical model and an extensive numerical analysis, we show that the number and individual linewidths of the emitters can be directly estimated from the ensemble autocorrelation function in spite of an inhomogeneously broadened emission. As an application, we analyze the photoluminescence of colloidal nanocrystal aggregates embedded in a gold shell. Our general method can be applied to a wide range of mesoscopic many-body systems and could provide new insights into their first-order coherence properties.

Single photon emitters (SPEs) in low-dimensional layered materials have recently gained a large interest owing to the auspicious perspectives of integration and extreme miniaturization offered by this class of materials. However, accurate control of both the spatial location and the emission wavelength of the quantum emitters is essentially lacking to date, thus hindering further technological steps towards scalable quantum photonic devices. Here, we evidence SPEs in high purity synthetic hexagonal boron nitride (hBN) that can be activated by an electron beam at chosen locations. SPE ensembles are generated with a spatial accuracy better than the cubed emission wavelength, thus opening the way to integration in optical microstructures. Stable and bright single photon emission is subsequently observed in the visible range up to room temperature upon non-resonant laser excitation. Moreover, the low-temperature emission wavelength is reproducible, with an ensemble distribution of width 3 meV, a statistical dispersion that is more than one order of magnitude lower than the narrowest wavelength spreads obtained in epitaxial hBN samples. Our findings constitute an essential step towards the realization of top-down integrated devices based on identical quantum emitters in 2D materials., Comment: Main text and supplementary information: 22 pages, 11 figures

The second-order correlation function of light $g^{(2)}(\tau)$ constitutes a pivotal tool to quantify the quantum behavior of an emitter and in turn its potential for quantum information applications. The experimentally accessible time resolution of $g^{(2)}(\tau)$ is usually limited by the jitter of available single photon detectors. Here, we present a versatile technique allowing to measure $g^{(2)}(\tau)$ from a large variety of light signals with a time resolution given by the pulse length of a mode-locked laser. The technique is based on frequency upconversion in a nonlinear waveguide, and we analyze its properties and limitations by modeling the pulse propagation and the frequency conversion process .We measure $g^{(2)}(\tau)$ from various signals including light from a quantum emitter - a confined exciton-polariton structure - revealing its quantum signatures at a scale of a few picoseconds and demonstrating the capability of the technique.

Cavity-polaritons in semiconductor microstructures have emerged as a promising system for exploring nonequilibrium dynamics of many-body systems. Key advances in this field, including the observation of polariton condensation, superfluidity, realization of topological photonic bands, and dissipative phase transitions, generically allow for a description based on a mean-field Gross-Pitaevskii formalism. While observation of polariton intensity squeezing and decoherence of a polarization entangled photon pair by a polariton condensate provide counter-examples, quantum effects in these experiments show up at high polariton occupancy. Going beyond into the regime of strongly correlated polaritons requires the observation of a photon blockade effect where interactions are strong enough to suppress double occupancy of a photonic lattice site. Here, we report the observation of quantum correlations between polaritons in a fiber cavity which spatially confines polaritons into an area of 3 $\mu$m$^2$. Photon correlation measurements show that careful tuning of the coupled system allows for a modest photon blockade effect as evidenced by a reduction of simultaneous two-polariton generation probability by 5 %. Concurrently, our experiments provide an unequivocal measurement of the polariton interaction strength, thereby resolving the controversy stemming from recent experimental reports. Our findings constitute a first essential step towards the realization of strongly interacting photonic systems.

We show that optically active coupled quantum dots embedded in a superconducting microwave cavity can be used to realize a fast quantum interface between photonic and transmon qubits. Single photon absorption by a coupled quantum dot results in generation of a large electric dipole, which in turn ensures efficient coupling to the microwave cavity. Using cavity parameters achieved in prior experiments, we estimate that bi-directional microwave-optics conversion in nanosecond timescales with efficiencies approaching unity is experimentally feasible with current technology. We also outline a protocol for in-principle deterministic quantum state transfer from a time-bin photonic qubit to a transmon qubit. Recent advances in quantum dot based quantum photonics technologies indicate that the scheme we propose could play a central role in connecting quantum nodes incorporating cavity-coupled superconducting qubits.

Photonic losses pose a major limitation for implementation of quantum state transfer between nodes of a quantum network. A measurement that heralds successful transfer without revealing any information about the qubit may alleviate this limitation. Here, we demonstrate heralded absorption of a single photonic qubit generated by a single neutral quantum dot, by a single-electron charged quantum dot that is located 5 meters away. The transfer of quantum information to the spin degree of freedom takes place upon emission of a photon: for a properly chosen or prepared quantum dot, detection of this photon yields no information about the qubit. We show that this process can be combined with local operations optically performed on the destination node, by measuring classical correlations between the absorbed photon color and the final state of the electron spin. Our work suggests alternative avenues for realization of quantum information protocols based on cascaded quantum systems.

Ramsey interferometry provides a natural way to determine the coherence time of most qubit systems. Recent experiments on quantum dots however, demonstrated that dynamical nuclear spin polarization can strongly influence the measurement process, making it difficult to extract the $T_2^*$ coherence time using optical Ramsey pulses. Here, we demonstrate an alternative method for spin coherence measurement that is based on first-order coherence of photons generated in spin-flip Raman scattering. We show that if a quantum emitter is driven by a weak monochromatic laser, Raman coherence is determined exclusively by spin coherence, allowing for a direct determination of spin $T_2^*$ time. When combined with coherence measurements on Rayleigh scattered photons, our technique enables us to identify coherent and incoherent contributions to resonance fluorescence, and to minimize the latter. We verify the validity of our technique by comparing our results to those determined from Ramsey interferometry for electron and heavy-hole spins., Comment: 8 pages, 6 figures

Quantum entanglement emerges naturally in interacting quantum systems and plays a central role in quantum information processing. Remarkably, it is possible to generate entanglement even in the absence of direct interactions: provided that which path information is erased, weak spin-state dependent light scattering can be used to project two distant spins onto a maximally entangled state upon detection of a single photon. Even though this approach is necessarily probabilistic, successful generation of entanglement is heralded by the photon detection event. Here, we demonstrate heralded quantum entanglement of two quantum dot heavy-hole spins separated by 5 meters using single-photon interference. Thanks to the long coherence time of hole spins and the efficient spin-photon interface provided by self-assembled quantum dots embedded in leaky microcavity structures, we generate 2300 entangled spin pairs per second, which represents an improvement approaching three orders of magnitude as compared to prior experiments. Delayed two-photon interference scheme we developed allows for efficient verification of quantum correlations. Our results lay the groundwork for the realization of quantum networks in semiconductor nanostructures. Combined with schemes for transferring quantum information to a long-lived memory qubit, fast entanglement generation we demonstrate could also impact quantum repeater architectures., Comment: 12 pages, 3 figures

Single-shot read-out of individual qubits is typically the slowest process among the elementary single- and two-qubit operations required for quantum information processing. Here, we use resonance fluorescence from a single-electron charged quantum dot to read-out the spin-qubit state in 800 nanoseconds with a fidelity exceeding 80%. Observation of the spin evolution on longer timescales reveals quantum jumps of the spin state: we use the experimentally determined waiting-time distribution to characterize the quantum jumps. Embedding a quantum dot in a photonic nanostructure could be used to enhance the collection efficiency by a factor of 10, enabling single-shot read-out with a fidelity exceeding 97%., Comment: 5 pages, 3 figures

The optical response of a heavily doped quantum well, with two occupied subbands, has been investigated as a function of the electronic density. It is shown that the two optically active transitions are mutually coupled by dipole-dipole Coulomb interaction, which strongly renormalizes their absorption amplitude. In order to demonstrate this effect, we have measured a set of optical spectra on a device in which the electronic density can be tuned by the application of a gate voltage. Our results show that the absorption spectra can be correctly described only by taking into account the Coulomb coupling between the two transitions. As a consequence, the optical dipoles originating from intersubband transitions are not independent, but rather coupled oscillators with an adjustable strength.

We report on an extensive experimental study of intersubband excitations in the THz range arising from the coupling between a quantum well and a zero-dimensional metal-metal microcavities. Because of the conceptual simplicity of the resonators we obtain an extremely predictable and controllable system to investigate light-matter interaction. The experimental data is modelled by combining a quantum mechanical approach with an effective medium electromagnetic simulation that allows us to take into account the losses of the system. By comparing our modelling with the data we are able to retrieve microscopic information, such as the electronic populations on different subbands as a function of the temperature. Our modelling approach sets the base of a designer tool for intersubband light-matter coupled systems.

We have investigated the transition from strong to ultra-strong coupling regime between a mid-infrared intersubband excitation and the fundamental mode of a metal-dielectric-metal microcavity. The ultra-strong coupling regime is demonstrated up to room temperature for a wavelength of $11.7 \mu$m by using 260 nm thick cavities, which impose an extreme sub-wavelength confinement. By varying the doping of our structures we show that the experimental signature of the transition to the ultra-strong coupling regime is the opening of a photonic gap in the polariton dispersion. The width of this gap depends quadratically on the ratio between the Rabi and intersubband transition energies.

In this work we investigate a low dimensional semiconductor system, in which the light-matter interaction is enhanced by the cooperative behavior of a large number of dipolar oscillators, at different frequencies, mutually phase locked by Coulomb interaction. We experimentally and theoretically demonstrate that, owing to this phenomenon, the optical response of a semiconductor quantum well with several occupied subbands is a single sharp resonance, associated to the excitation of a bright multisubband plasmon. This effect illustrates how the whole oscillator strength of a two-dimensional system can be concentrated into a single resonance independently from the shape of the confining potential. When this cooperative excitation is tuned in resonance with a cavity mode, their coupling strength can be increased monotonically with the electronic density, allowing the achievement of the ultra-strong coupling regime up to room temperature.