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The development of scalable sources of non-classical light is fundamental to unlock the technological potential of quantum photonics\cite{Kimble:Nat2008}. Among the systems under investigation, semiconductor quantum dots are currently emerging as near-optimal sources of indistinguishable single photons. However, their performances as sources of entangled-photon pairs are in comparison still modest. Experiments on conventional Stranski-Krastanow InGaAs quantum dots have reported non-optimal levels of entanglement and indistinguishability of the emitted photons. For applications such as entanglement teleportation and quantum repeaters, both criteria have to be met simultaneously. In this work, we show that this is possible focusing on a system that has received limited attention so far: GaAs quantum dots grown via droplet etching. Using a two-photon resonant excitation scheme, we demonstrate that these quantum dots can emit triggered polarization-entangled photons with high purity (g^(2)(0)=0.002 +/-0.002), high indistinguishability (0.93 +/-0.07) and high entanglement fidelity (0.94 +/-0.01). Such unprecedented degree of entanglement, which in contrast to InGaAs can theoretically reach near-unity values, allows Bell's inequality (2.64 +/-0.01) to be violated without the aid of temporal or spectral filtering. Our results show that if quantum-dot entanglement resources are to be used for future quantum technologies, GaAs might be the system of choice., Comment: 10 pages, 3 figures

Inelastic tunneling of electrons can generate the emission of photons with energies intuitively limited by the applied bias voltage. However, experiments indicate that more complex processes involving the interaction of electrons with plasmon polaritons lead to photon emission with overbias energies. We recently proposed a model of this observation in Phys. Rev. Lett. \textbf{113}, 066801 (2014), in analogy to the dynamical Coulomb blockade, originally developed for treating the electromagnetic environment in mesoscopic circuits. This model describes the correlated tunneling of two electrons interacting with a local plasmon-polariton mode, represented by a resonant circuit, and shows that the overbias emission is due to the non-Gaussian fluctuations. Here we extend our model to study the overbias emission at finite temperature. We find that the thermal smearing strongly masks the overbias emission. Hence, the detection of the correlated tunneling processes requires temperatures $k_BT$ much lower than the bias energy $eV$ and the plasmon energy $\hbar\omega_0$, a condition which is fortunately realized experimentally., Comment: 11 pages, 11 figures

It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of motion quadratic in the momenta. The procedure of quantization here considered, transforms the Hamiltonian into the Laplace-Beltrami operator plus a scalar potential. In order to transform the constants of motion into symmetry operators of the quantum Hamiltonian, additional scalar potentials, known as quantum corrections, must be introduced, depending on the Riemannian structure of the manifold. We give here a complete geometric characterization of the quantum corrections necessary for the case considered. St\"ackel systems are studied in particular details. Examples in conformally and non-conformally flat manifolds are given., Comment: 18 pages

We revisit the calculation of holographic correlation functions in IIB supergravity on $AdS_5\times S^5$. Results for four-point functions simplify drastically when expressed in Mellin space. We conjecture a compact formula for the four-point functions of one-half BPS single-trace operators of arbitrary weight. Our methods rely on general consistency conditions and eschew detailed knowledge of the supergravity effective action., Comment: 5 pages; v2: improved discussion, minor changes

We review the calculation and properties of the supersymmetric index for four dimensional N=1 theories, illustrating its physical significance in several examples., Comment: This is a contribution to the review volume `Localization techniques in quantum field theories' (eds. V. Pestun and M. Zabzine) which contains 17 Chapters. The complete volume is summarized in arXiv:1608.02952 and it can be downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pdf

This is the foreword to the special volume on localization techniques in quantum field theory. We summarize the individual chapters and their relation., Comment: The complete volume can be downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pdf

Hole spins have gained considerable interest in the past few years due to their potential for fast electrically controlled qubits. Here, we study holes confined in Ge hut wires, a so far unexplored type of nanostructure. Low temperature magnetotransport measurements reveal a large anisotropy between the in-plane and out-of-plane g-factors of up to 18. Numerical simulations verify that this large anisotropy originates from a confined wave function which is of heavy hole character. A light hole admixture of less than 1% is estimated for the states of lowest energy, leading to a surprisingly large reduction of the out-of-plane g-factors. However, this tiny light hole contribution does not influence the spin lifetimes, which are expected to be very long, even in non isotopically purified samples.

In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior samples for the latent allocation variables can be effectively obtained in a wide range of clustering models, including finite mixtures, infinite mixtures, hidden Markov models and block models for networks. However, due to the categorical nature of the clustering variables and the lack of scalable algorithms, summary tools that can interpret such samples are not available. We adopt a Bayesian decision theoretic approach to define an optimality criterion for clusterings, and propose a fast and context-independent greedy algorithm to find the best allocations. One important facet of our approach is that the optimal number of groups is automatically selected, thereby solving the clustering and the model-choice problems at the same time. We consider several loss functions to compare partitions, and show that our approach can accommodate a wide range of cases. Finally, we illustrate our approach on a variety of real-data applications for three different clustering models: Gaussian finite mixtures, stochastic block models and latent block models for networks., Comment: 26 pages, 6 figures

We apply the Born-Jordan and Weyl quantization formulas for polynomials in canonical coordinates to the constants of motion of some examples of the superintegrable 2D anisotropic harmonic oscillator. Our aim is to study the behaviour of the algebra of the constants of motion after the different quantization procedures. In the examples considered, we have that the Weyl formula always preserves the original superintegrable structure of the system, while the Born-Jordan formula, when producing different operators than the Weyl's one, does not.

We demonstrate the first wavelength-tunable electrically-pumped source of non-classical light that can emit photons with wavelength in resonance with the D2 transitions of 87Rb atoms. The device is fabricated by integrating a novel GaAs single-quantum-dot light-emitting-diode (LED) onto a piezoelectric actuator. By feeding the emitted photons into a 75-mm-long cell containing warm 87Rb atom vapor, we observe slow-light with a temporal delay of up to 3.4 ns. In view of the possibility of using 87Rb atomic vapors as quantum memories, this work makes an important step towards the realization of hybrid-quantum systems for future quantum networks.

We study a quantum harmonic oscillator linearly coupled through the position operator $\hat{q}$ to a first bath and through the momentum operator $\hat{p}$ to a second bath yielding an Ohmic-Drude dissipation. We analyse the oscillator's fluctuations as a function of the ratio between the strength of the two couplings, focusing in particular on the situation in which the two dissipative interactions are comparable. Analytic formulas are derived in the relevant regimes corresponding to the low temperature limit and when the Drude high frequency cutoff is much larger than all other frequencies. At low temperature, each bath operates to suppress the oscillator's ground state quantum fluctuations ${\langle \Delta \hat{q}^2 \rangle}_0$ or ${\langle \Delta \hat{p}^2 \rangle}_0$ appearing in the corresponding interaction. When one of the two dissipative interactions dominates over the other, the fluctuations for the coupling operator are squeezed. When the two interactions are comparable, the two baths enter in competition as the two conjugate operators do not commute yielding quantum frustration. In this regime, remarkably, the fluctuations of both two quadratures can be enhanced by increasing the dissipative coupling., Comment: 12 pages, 2 figures

We investigate the structure of certain protected operator algebras that arise in three-dimensional N=4 superconformal field theories. We find that these algebras can be understood as a quantization of (either of) the half-BPS chiral ring(s). An important feature of this quantization is that it has a preferred basis in which the structure constants of the quantum algebra are equal to the OPE coefficients of the underlying superconformal theory. We identify several nontrivial conditions that the quantum algebra must satisfy in this basis. We consider examples of theories for which the moduli space of vacua is either the minimal nilpotent orbit of a simple Lie algebra or a Kleinian singularity. For minimal nilpotent orbits, the quantum algebras (and their preferred bases) can be uniquely determined. These algebras are related to higher spin algebras. For Kleinian singularities the algebras can be characterized abstractly - they are spherical subalgebras of symplectic reflection algebras - but the preferred basis is not easily determined. We find evidence in these examples that for a given choice of quantum algebra (defined up to a certain gauge equivalence), there is at most one choice of canonical basis. We conjecture that this is the case for general N=4 SCFTs., Comment: 37 + 8 pages (plus references). v2: references added, typos corrected, additional equations added and error corrected in section 5.1

Strain engineering allows the physical properties of materials and devices to be widely tailored, as paradigmatically demonstrated by strained transistors and semiconductor lasers employed in consumer electronics. For this reason, its potential impact on our society has been compared to that of chemical alloying. Although significant progress has been made in the last years on strained nanomaterials, strain fields (which are of tensorial nature, with six independent components) are still mostly used in a "scalar" and/or static fashion. Here we present a new class of strain actuators which allow the three components of the in-plane stress tensor in a nanomembrane to be independently and reversibly controlled. The actuators are based on monolithic piezoelectric substrates, which are micro-machined via femtosecond-laser processing. Their functionality is demonstrated by "programming" arbitrary stress states in a semiconductor layer, whose light emission is used as a local and sensitive strain gauge. The results shown in this work open a new route to investigate and make use of strain effects in materials and devices., Comment: 16 pages, 4 figures

We study the ground-state cooling of a mechanical oscillator linearly coupled to the charge of a quantum dot inserted between a normal metal and a superconducting contact. Such a system can be realized, e.g., by a suspended carbon nanotube quantum dot with a capacitive coupling to a gate contact. Focusing on the subgap transport regime, we analyze the inelastic Andreev reflections which drive the resonator to a nonequilibrium state. For small coupling, we obtain that vibration-assisted reflections can occur through two distinct interference paths. The interference determines the ratio between the rates of absorption and emission of vibrational energy quanta. We show that ground-state cooling of the mechanical oscillator can be achieved for many of the oscillator's modes simultaneously or for single modes selectively, depending on the experimentally tunable coupling to the superconductor.

The coupling-constant metamorphosis is applied to modified extended Hamiltonians and sufficient conditions are found in order that the transformed high-degree first integral of the transformed Hamiltonian is determined by the same algorithm which computes the corresponding first integral of the original extended Hamiltonian. As examples, we consider the Post-Winternitz system and the 2D caged anisotropic oscillator.

We report results important for the creation of a best-of-both-worlds quantum hybrid system consisting of a solid-state source of single photons and an atomic ensemble as quantum memory. We generate single photons from a GaAs quantum dot (QD) frequency-matched to the Rb D2-transitions and then use the Rb transitions to analyze spectrally the quantum dot photons. We demonstrate lifetime-limited QD linewidths (1.48 GHz) with both resonant and non-resonant excitation. The QD resonance fluorescence in the low power regime is dominated by Rayleigh scattering, a route to match quantum dot and Rb atom linewidths and to shape the temporal wave packet of the QD photons. Noise in the solid-state environment is relatively benign: there is a blinking of the resonance fluorescence at MHz rates but negligible upper state dephasing of the QD transition. We therefore establish a close-to-ideal solid-state source of single photons at a key wavelength for quantum technologies.

The prospect of using the quantum nature of light for secure communication keeps spurring the search and investigation of suitable sources of entangled-photons. Semiconductor quantum dots are arguably the most attractive. They can generate indistinguishable entangled-photons deterministically, and are compatible with current photonic-integration technologies, a set of properties not shared by any other entanglement resource. However, as no two quantum dots are identical, they emit entangled-photons with random energies. This hinders their exploitation in communication protocols requiring entangled-states with well-defined energies. Here, we introduce scalable quantum-dot-based sources of polarization-entangled-photons whose energy can be controlled via dynamic strain-engineering without degrading the degree of entanglement of the source. As a test-bench, we interface quantum dots with clouds of atomic vapours, and we demonstrate slow-entangled-photons from a single quantum emitter. These results pave the way towards the implementation of hybrid quantum networks where entanglement is distributed among distant parties using scalable optoelectronic devices.

We develop the conformal bootstrap program for six-dimensional conformal field theories with $(2,0)$ supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on OPE coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the lightcone expansion of the crossing equation. Our principal result is strong evidence that the $A_1$ theory realizes the minimal allowed central charge $(c=25)$ for any interacting $(2,0)$ theory. This implies that the full stress tensor four-point function of the $A_1$ theory is the unique unitary solution to the crossing symmetry equation at $c=25$. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting $(2,0)$ theory of central charge $c$. For large $c$, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity., Comment: 58 pages (41 plus three appendices), 15 figures

We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree correlations. We introduce the Gaussian Latent Position Model, and derive analytic expressions and asymptotic approximations for its network properties. We pay particular attention to one special case, the Gaussian Latent Position Models with Random Effects, and show that it can represent the heavy-tailed degree distributions, positive asymptotic clustering coefficients and small-world behaviours that are often observed in social networks. Several real and simulated examples illustrate the ability of the models to capture important features of observed networks.

We demonstrate a compact, spectrally-selective, and tunable delay line for single photons emitted by quantum dots. This is achieved by fine-tuning the wavelength of the optical transitions of such "artificial atoms" into a spectral window in which a cloud of natural atoms behaves as slow-light medium. By employing the ground-state fine-structure-split exciton confined in an InGaAs/GaAs quantum dot as a source of single photons at different frequencies and the hyperfine-structure-split $D_1$ transition of Cs-vapors as a tunable delay-medium, we achieve a differential delay of up 2.4 ns on a 7.5 cm long path for photons that are only 60 \mu eV (14.5 GHz) apart. To quantitatively explain the experimental data we develop a theoretical model that accounts for both the inhomogeneously broadening of the quantum-dot emission lines and the Doppler-broadening of the atomic lines. The concept we proposed here may be used to implement time-reordering operations aimed at erasing the "which-path" information that deteriorates entangled-photon emission from excitons with finite fine-structure-splitting., Comment: 29 pages, 5 figures

Triggered sources of entangled photons play crucial roles in almost any existing protocol of quantum information science. The possibility to generate these non-classical states of light with high speed and using electrical pulses could revolutionize the field. Entangled-light-emitting-diodes (ELEDs) based on semiconductor quantum dots (QDs) are at present the only devices that can address this task 5. However, ELEDs are plagued by a source of randomness that hampers their practical exploitation in the foreseen applications: the very low probability (~10-2) of finding QDs with sufficiently small fine-structure-splitting for entangled-photon-generation. Here, we overcome this hurdle by introducing the first strain-tunable ELEDs (S-ELEDs) that exploit piezoelectric-induced strains to tune QDs for entangled-photon-generation. We demonstrate that up to 30% of the QDs in S-ELEDs emit polarization-entangled photon pairs with entanglement-fidelities as high as f+ = 0.83(5). Driven at the highest operation speed of 400 MHz ever reported so far, S-ELEDs emerge as unique devices for high-data rate entangled-photon applications., Comment: 28 pages in total, including supplementary information. 5 figures

We find the admittance of a topological Josephson junction $Y(\omega,\varphi_0, T)$ as a function of frequency $\omega$, the static phase bias $\varphi_0$ applied to the superconducting leads, and temperature $T$. The dissipative part of $Y$ allows for spectroscopy of the sub-gap states in the junction. The resonant frequencies $\omega_{\mathcal{M}, n} (\varphi_0)$ for transitions involving the Majorana ($\mathcal{M}$) doublet exhibit characteristic kinks in the $\varphi_0$-dependence at $\varphi_0=\pi$. The kinks -- associated with decoupled Majorana states -- remain sharp and the corresponding spectroscopic lines are bright at any temperature, as long as the leads are superconducting. The developed theory may help extracting quantitative information about Majorana states from microwave spectroscopy., Comment: 5+16 pages, 2 figures

The possibility to generate and manipulate non-classical light using the tools of mature semiconductor technology carries great promise for the implementation of quantum communication science. This is indeed one of the main driving forces behind ongoing research on the study of semiconductor quantum dots. Often referred to as artificial atoms, quantum dots can generate single and entangled photons on demand and, unlike their natural counterpart, can be easily integrated into well-established optoelectronic devices. However, the inherent random nature of the quantum dot growth processes results in a lack of control of their emission properties. This represents a major roadblock towards the exploitation of these quantum emitters in the foreseen applications. This chapter describes a novel class of quantum dot devices that uses the combined action of strain and electric fields to reshape the emission properties of single quantum dots. The resulting electro-elastic fields allow for control of emission and binding energies, charge states, and energy level splittings and are suitable to correct for the quantum dot structural asymmetries that usually prevent these semiconductor nanostructures from emitting polarization-entangled photons. Key experiments in this field are presented and future directions are discussed., Comment: to appear as a book chapter in a compilation "Engineering the Atom-Photon Interaction" published by Springer in 2015, edited by A. Predojevic and M. W. Mitchell

We consider the dynamics of a quantum phase-slip junction (QPSJ) -- a dual Josephson junction -- connected to a microwave source with frequency $\omega_\textrm{mw}$. With respect to an ordinary Josephson junction, a QPSJ can sustain dual Shapiro steps, consisting of well-defined current plateaus at multiple integers of $ e \omega_\textrm{mw} / \pi$ in the current-voltage (I-V) characteristic. The experimental observation of these plateaus has been elusive up to now. We argue that thermal as well as quantum fluctuations can smear the I-V characteristic considerably. In order to understand these effects, we study a current-biased QPSJ under microwave irradiation and connected to an inductive and resistive environment. We find that the effect of these fluctuations are governed by the resistance of the environment and by the ratio of the phase-slip energy and the inductive energy. Our results are of interest for experiments aimed at the observation of dual Shapiro steps in QPSJ devices for the definition of a new quantum current standard., Comment: 12 pages, 9 figures, comments and suggestions would be greatly appreciated