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Abstract Triple-photon generation (TPG) is based on a third-order nonlinear optical interaction, which is the most direct way to produce pure quantum three-photon states. These states can exhibit three-body quantum correlations, and their statistics cannot be reproduced by any Gaussian statistics of coherent sources or optical parametric twin-photon generator, making them potentially useful for quantum information processing tasks such as quantum state distillation, quantum error-correction and universal quantum computing. Furthermore, the generation of entangled photon pairs heralded by the detection of a third photon can be used in advanced quantum communication protocols. We made the first experimental demonstration of TPG in 2004 using a bi-stimulation scheme in a bulk KTP crystal, followed by the quantum theory. The new challenges are now to achieve a spontaneous TPG and the corresponding quantum experiments and protocols using oriented ridge KTP waveguides, which ensures both birefringence phase-matching and light confinement. The waveguides are cut by a precision dicing saw. We recently performed their characterization using third-harmonic generation measurements, which showed their good quality. A rate of about 5 triplets per second is expected when pumping a 5-cm-long waveguide with a 5-W 532 nm beam in the CW regime. Such a spontaneous TPG exhibits low rate of triple photons, which makes the certification of quantum features hard. In this article, we review our theoretical and experimental work on TPG and the associated quantum modeling. We also develop theoretical tools for the certification of quantum features of spontaneous triple-photon states. Graphic abstract

The expanding and highly greedy Algerian transport sector is totally depending on petro-products, due to the rising numbers of automobile fleets and the excessive dependence on road transportation. Irrecoverable Greenhouse gases GHGs emitted by this sector are constantly increasing. As a result, consumption of diesel and gasoline reached record levels. Consequently, there is a strong need of cleaner, eco-friendly and economically viable alternative fuels. Biofuels, electric, compressed natural gas CNG, liquefied petroleum gas LGP vehicles, are expected to play a crucial role in meeting energy and environmental policies targets. In this paper, the Algerian transport sector perspectives and Greenhouse gases mitigations, in different shaped scenarios based on semi-empirical models, are analyzed and discussed. For adequate policy shaped in a scenario, in 2050, annual Algerian consumption could decrease up to 35%, 43% of CO2 emissions and 73% of NOx emissions could be mitigated compared to no-intervention scenario. These promising findings indicate the huge potential of resource diversification on the transportation sector. Therefore, implementing such policies is fundamental for a durable Algerian’s transportation sector transition policy.

Photon-pair sources based on thin film lithium niobate on insulator technology have a great potential for integrated optical quantum information processing. We report on such a source of correlated twin-photon pairs generated by spontaneous parametric down conversion in a silicon nitride (SiN) rib loaded thin film periodically poled lithium niobate (LN) waveguide. The generated correlated photon pairs have a wavelength centred at 1560 nm compatible with present telecom infrastructure, a large bandwidth (21 THz) and a brightness of ∼2.5 × 105 pairs/s/mW/GHz. Using the Hanbury Brown and Twiss effect, we have also shown heralded single photon emission, achieving an autocorrelation g H ( 2 ) ( 0 ) ≃ 0.04 .

In this paper, the system dealt with consisting of an ultra-cold neutral spin-polarized Fermi gas undergoing rotation (or in the so-called synthetic magnetic field) trapped by an anisotropic harmonic potential in a two and three-dimensional space at zero temperature. Using the so-called Bloch propagator as a tool, we derive exact closed-form expressions for particle density in Fourier space which are valid for an arbitrary particle number confined by a two and three-dimensional rotating anisotropic harmonic trap. Numerical illustrations and discussions are presented. The results can be easily generalized at finite temperatures. The crossover from two-dimensional to the one-dimensional regime is shown to be reflected in the shape of the density distribution in Fourier space at very fast rotating velocity (or at strong synthetic magnetic field). In addition, an exact analytical expression of the elastic scattering factor is found, a quantity of interest used to probe the spatial distribution of the quantum gases.

We demonstrate supermode-based second harmonic generation in an integrated nonlinear interferometer made of linear and nonlinear directional couplers. We use a fully-fibered pump shaper to demonstrate second harmonic generation pumped by the symmetric or anti-symmetric fundamental spatial modes. The selection of the pumping mode and thus of a specific SHG spectral profile is achieved through the selection of the fundamental wavelength and via a robust phase setting scheme. We use two methods: either post-selecting or actively setting the pumping mode. Such a modal phase matching paves the way for classical and quantum applications of coupled nonlinear photonic circuits, where multimode excitation, encoding and detection are a route for multiplexing and scaling up light-processing., 14 pages, 7 figures

Reaching a regime of strong coupling between light and atoms is a long-sought goal in quantum optics, as it will enable non-linear optics at the photon level. Interfacing atoms with guided light in nanophotonic waveguides is a promising route to achieve such regimes. Experimental platforms include nanofibers [1] and photonic crystal waveguides (PCWs), owing to the large transverse confinement of their guided modes. With PCWs, tuning the dispersion relation gives rise to the additional benefit of a very low group velocity of the guided light [2] , allowing for strong coupling even in single pass. Moreover these systems can help explore waveguide-QED and probe exciting novel bandgap physics [3] . While encouraging values of couplings have been observed with first corrugated devices [4] , a photonic platform with trapped atoms via guided modes in the vicinity of a waveguide and lying deep in the strong coupling regime has yet to be demonstrated.

Continuous-variable encoding of quantum information in the optical domain has recently yielded large temporal and spectral entangled states instrumental for quantum computing and quantum communication. We introduce a protocol for the generation of spatial multipartite entanglement based on phase-matching of a propagation eigenmode in a monolithic photonic device: the array of quadratic nonlinear waveguides. We theoretically demonstrate in the spontaneous parametric downconversion regime the generation of large multipartite entangled states useful for multimode quantum networks. Our protocol is remarkably simple and robust as it does not rely on specific values of coupling, nonlinearity or length of the sample., 8 pages, 5 figures, title modified and new results added. Accepted for publication in Physical Review Research

The entanglement produced by a bilinear Hamiltonian in continuous variables has been thoroughly studied and widely used. In contrast, the physics of entanglement resulting from nonlinear interaction described by partially degenerate high-order Hamiltonians remains unclear. Here, we derive a hierarchy of sufficient and necessary conditions for the positive-partial-transposition separability of bipartite nonlinear quantum states. The proposed criteria detect the nonpositive-partial-transposition inseparability of higher-order moments of states, which provides a systematic framework for the characterization of this kind of entanglement. Through numerical simulation of cubic and quartic Hamiltonians, we demonstrate the existence and competition of a hierarchy of entanglement witnesses, revealing the mechanism underlying such entanglement. Our results may provide a new direction in continuous variable quantum information processing., Comment: 6 pages, 2 figures

We present a proposal for trapping Rubidium cold atoms near a novel design of a GaInP photonic crystal waveguide with characteristics optimized through systematic and inverse design. Purcell factors higher than unity are predicted.

Producción Científica, For a harmonically trapped system consisting of two bosons in one spatial dimension with infinite contact repulsion (hard core bosons), we derive an expression for the onebody density matrix ρB in terms of center of mass and relative coordinates of the particles. The deviation from ρF, the density matrix for the two fermions case, can be clearly identified. Moreover, the obtained ρB allows us to derive a closed form expression of the corresponding momentum distribution nB(p). We show how the result deviates from the noninteracting fermionic case, the deviation being associated with the short-range character of the interaction. Mathematically, our analytical momentum distribution is expressed in terms of one and two variables confluent hypergeometric functions. Our formula satisfies the correct normalization and possesses the expected behavior at zero momentum. It also exhibits the high momentum 1/p4 tail with the appropriate Tan’s coefficient. Numerical results support our findings., Junta de Castilla y León y FEDER (proyecto BU229P18)

Multimode entanglement is an essential resource for quantum information in continuous-variable systems. Light-based quantum technologies will arguably not be built upon table-top bulk setups, but will presumably rather resort to integrated optics. Sequential bulk optics-like proposals based on cascaded integrated interferometers are not scalable with the current state-of-the-art low-loss materials used for continuous variables. We analyze the multimode continuous-variable entanglement capabilities of a compact currently-available integrated device without bulk-optics analog: the array of nonlinear waveguides. We theoretically demonstrate that this simple and compact structure, together with a reconfigurable input pump distribution and multimode coherent detection of the output modes, is a versatile entanglement synthesizer in the spatial domain. We exhibit this versatility through analytical and numerically optimized multimode squeezing, entanglement, and cluster state generation in different encodings. Our results re-establish spatial encoding as a contender in the game of continuous-variable quantum information processing., Comment: 17 pages, 5 figures, v4 closer to the published version

In the current quest for efficient and experimentally feasible platforms for implementation of multimode squeezing and entanglement in the continuous variable regime, we underpin and complement our results on the generation of versatile multimode entanglement and cluster states in nonlinear waveguide arrays presented by Barral et al., Phys. Rev. Appl. $\bf{14}$, 044025 (2020). We present detailed derivations of the equations that describe the propagation of light through this system, and then we focus on parameter regimes where these equations can be solved analytically. These analytical solutions build an intuition for the wide landscape of quantum states that are accessible through the activation of pumping, coupling and measurement schemes. Furthermore, we showcase the acquired insights by using one of the identified analytical solutions to exhibit the generation, optimization and scalability of spatial linear cluster states., 20 pages, 9 figures, v2 closer to the published version. arXiv admin note: substantial text overlap with arXiv:1912.11154

How to prepare deterministically non-Gaussian entangled states is a fundamental question for continuous-variable quantum information technology. Here, we theoretically demonstrate through numerical methods that the triple-photon state generated by three-photon spontaneous parametric down-conversion is a pure super-Gaussian resource of non-Gaussian entanglement. Interestingly, the degree of entanglement between the modes of the triple-photon state is stronger than that corresponding to the two-mode squeezed vacuum state produced by a quadratic Hamiltonian with the same parameters. Furthermore, we propose a model to prepare two-mode non-Gaussian entangled states with tunable non-Gaussianity based on quadrature projection measurements., 5 pages, 4 figures

Coupling quantum emitters and nanostructures, in particular cold atoms and waveguides, has recently raised a large interest due to unprecedented possibilities of engineering light-matter interactions. However, the implementation of these promising concepts has been hampered by various theoretical and experimental issues. In this work, we propose a new type of periodic dielectric waveguide that provides strong interactions between atoms and guided photons with an unusual dispersion. We design an asymmetric comb waveguide that supports a slow mode with a quartic (instead of quadratic) dispersion and an electric field that extends far into the air cladding for an optimal interaction with atoms. We compute the optical trapping potential formed with two guided modes at frequencies detuned from the atomic transition. We show that cold Rubidium atoms can be trapped as close as 100 nm from the structure in a 1.3-mK-deep potential well. For atoms trapped at this position, the emission into guided photons is largely favored, with a beta factor as high as 0.88 and a radiative decay rate into the slow mode 10 times larger than the free-space decay rate.

International audience; Triple photon generation (TPG)is based on a third-order nonlinear optical interaction, which is the most direct way to produce pure quantum three-photon states. These states can exhibit three-body quantum entanglement and their statistics go beyond the usual Gaussian statistics of coherent sources and optical parametric twin-photon generators, offering new tools for quantum mechanics(Fig. 1 –left).Furthermore, from the application point of view, the generation of entangled photon pairs heralded by the detection of a third photon can be used in advanced quantum communication protocols.We made the first experimental demonstration of TPG in 2004 using a bi-stimulation schemein a bulk KTiOPO4(KTP)crystal[1], followed by the quantum theory [2,3].

We study time evolution of Wigner function of an initially interacting one-dimensional quantum gas following the switch-off of the interactions. For the scenario where at t=0the interactions are suddenly suppressed, we derive a relationship between the dynamical Wigner function and its initial value. A two-particle system initially interacting through two different interactions of Dirac delta type is examined. For a system of particles that is suddenly let to move ballistically (without interactions) in a harmonic trap in d dimensions, and using time evolution of one-body density matrix, we derive a relationship between the time dependent Wigner function and its initial value. Using the inverse Wigner transform we obtain, for an initially harmonically trapped noninteracting particles in ddimensions, the scaling law satisfied by the density matrix at time tafter a sudden change of the trapping frequency. Finally, the effects of interactions are analyzed in the dynamical Wigner function., Ministerio de Economía, Industria y Competitividad (grant MTM2014-57129-C2-1-P), Junta de Castilla y León (grants BU229P18, VA057U16, and VA137G18)

Wave-vector quasi-phase-matching was devised in the 1960s as a way to boost nonlinear interactions with efficient quantum noise squeezing as one outstanding outcome. In the era of quantum technologies, we propose a coupling quasi-phase-matching for efficient generation of multimode down-converted quantum light in nonlinear waveguide arrays. We highlight this technique achieving multimode quantum entanglement and Einstein-Podolsky-Rosen steering buildup. We discuss the feasibility of this method with current technology and demonstrate its competitiveness as a resource for continuous variables quantum information.

We report on the design and the fabrication of 1D photonic crystal (PhC) nanobeam cavities with optical resonances around 800 nm, compatible with Rubidium, Cesium or Argon atomic transitions. The cavities are made of Indium Gallium Phosphide (InGaP) material, a III-V semi-conductor compound which has a large index of refraction ($n \simeq 3.3$) favoring strong optical confinement and small mode volumes. Nanobeam cavities with inline and side coupling have been designed and fabricated, and quality factors up to $2\times 10^4$ have been measured.

In general, the ubiquitous χ^{(2)} nonlinear directional coupler, where nonlinearity and evanescent coupling are intertwined, is nonintegrable. We rigorously demonstrate that matching excitation to the even or odd fundamental supermodes yields dynamical analytical solutions for any phase matching in a symmetric coupler. We analyze second harmonic generation and optical parametric amplification regimes and study the influence of fundamental field parity and power on the operation of the device. These fundamental solutions are useful to develop applications in classical and quantum fields such as all-optical modulation of light and quantum-states engineering.

In general, the ubiquitous χ^{(2)} nonlinear directional coupler, where nonlinearity and evanescent coupling are intertwined, is nonintegrable. We rigorously demonstrate that matching excitation to the even or odd fundamental supermodes yields dynamical analytical solutions for any phase matching in a symmetric coupler. We analyze second harmonic generation and optical parametric amplification regimes and study the influence of fundamental field parity and power on the operation of the device. These fundamental solutions are useful to develop applications in classical and quantum fields such as all-optical modulation of light and quantum-states engineering.

Atabani, Abdulaziz/0000-0001-6793-5589 WOS: 000484794800030 Application of biodiesel synthesized from waste-based raw materials with numerous solvents (higher chain alcohols) in diesel engines is a topic of great interest. This article examines the effect of biodiesel-diesel-propanol ternary blends. Physio-chemical properties, fatty acids composition (FAC), FT-IR, TGA, DSC, NMR along with some selected engine and emissions performance parameters were examined. Biodiesel was produced from waste cooking oil and exhibits excellent FAC that yields kinematic viscosity, cetane number, oxidation stability, higher heating value and iodine value of 3.93mm(2)/s, 58.88, 7.43 h, 39.45 MJ/kg and 64.92 g/100 g. Propanol blended biodiesel depicted an affirmative improvement in cold flow properties and decremented density. FT-IR and NMR results confirms the existence of biodiesel-diesel-propanol and prove their qualities as reliable methods. DSC and TGA results confirm that propanol reduces the onset and crystallization temperatures of the blends. Engine and emissions performance revealed that propanol addition further increased brake specific energy consumption (BSEC) and brake specific fuel consumption (BSFC) and reduced carbon monoxide (CO), exhaust gas temperature (EGT), nitrogen oxides (NOx) and smoke. This study proves the feasibility of the ternary blends with rewarding benefits in cold flow properties and densities besides acceptable engine and emissions performance results.

In a recent paper [Phys. Rev. A {\bf 96}, 053822 (2017)], we proposed a strategy to generate bipartite and quadripartite continuous-variable entanglement of bright quantum states based on degenerate down-conversion in a pair of evanescently coupled nonlinear $\chi^{(2)}$ waveguides. Here, we show that the resources needed for obtaining these features can be optimized by exploiting the regime of second harmonic generation: the combination of depletion and coupling among pump beams indeed supplies all necessary wavelengths and appropriate phase mismatch along propagation. Our device thus entangles the two fundamental classical input fields without the participation of any harmonic ancilla. Depending on the propagation distance, the generated harmonics are entangled in bright or vacuum modes. We also evidence two-color bipartite and quadripartite entanglement over the interacting modes. The proposed device represents a boost in continuous-variable integrated quantum optics since it enables a broad range of quantum effects in a very simple scheme, which optimizes the resources and can be easily realized with current technology., Comment: 8 pages, 8 figures

International audience; High-quality factor whispering gallery mode microcavities doped with rare earth materials are used i) to study the dynamical and noise properties of micro-lasers and ii) to demonstrate slow-light effects in miniaturized devices.

Several third-harmonic generation processes were performed in a single step-index germanium-doped silica optical fiber under intermodal phase-matching conditions. The nanosecond fundamental beam range between 1400 and 1600 nm. The transverse distributions of the energy were successfully modeled in the form of Ince-Gauss modes, pointing out some ellipticity of fiber core. From these experiments and theoretical calculations, we discuss the implementation of frequency degenerated triple photon generation that shares the same phase-matching condition as third-harmonic generation, which is its reverse process.

We study continuous-variable entanglement of bright quantum states in a pair of evanescently coupled nonlinear $\chi^{(2)}$ waveguides operating in the regime of degenerate down-conversion. We consider the case where only the energy of the nonlinearly generated fields is exchanged between the waveguides while the pump fields stay independently guided in each original waveguide. We show that this device, when operated in the depletion regime, entangles the two non-interacting bright pump modes due to a nonlinear cascade effect. It is also shown that two-colour quadripartite entanglement can be produced when certain system parameters are appropriately set. This device works in the traveling-wave configuration, such that the generated quantum light shows a broad spectrum. The proposed device can be easily realized with current technology and therefore stands as a good candidate for a source of bipartite or multipartite entangled states for the emerging field of optical continuous-variable quantum information processing., Comment: 10 pages, 12 figures

We investigate the quantum entanglement of the three modes associated with the three-photon states obtained by triple-photon generation in a phase-matched third-order nonlinear optical interaction. Although the second order processes have been extensively dealt with, there is no direct analogy between the second and third-order mechanisms. We show for example the absence of quantum entanglement between the quadratures of the three modes in the case of spontaneous parametric triple-photon generation. However, we show that genuine triple-photon entanglement is obtained in the fully seeded case, and its efficiency increases with the seeding level.

Optical microcavities with high quality factors Q are of great interest in integrated micro- and nanophotonics. Their narrow resonance and long photon lifetime (τ cav ) can be used in fundamental physics, sensing applications, microwave signal optical processing or for optical delay line and memory miniaturization [1]. Considering a Lorentzian resonance profile, the quality factor and the photon lifetime of a microcavity with a resonant angular frequency ωο = 2·πe/λ 0 reads: Q = ω 0 τ cab = n G (ω 0 )LF/λ 0 , (1) where n g is the group index of the material constituting the microcavity, F is the finesse and L is the cavity round-trip length. The usual method to obtain ultra-high quality factors consists in optimizing the manufacturing process to reach high finesse values. Following this approach record quality factors up to 1011 have been measured in millimetric CaF2 whispering gallery mode (WGM) resonators [2]. Otherwise, Eq. (1) shows that for a given finesse, the use of resonators made with slow-light materials displaying high group indices can also increase the quality factor. This method has already been successfully implemented in bulky resonators including a highly dispersive slow-light medium [3]. We have recently demonstrated that this approach can be applied to solid-state optical micro-resonators [4]. The slow-light effect was introduced thanks to population oscillations in an Er3+ doped WGM fluoride glass microsphere (diameter 100 μm). Since the lifetime of the 4I 13/2 level is very long (T ≈ 10 ms) strong group index up to 106 can be obtained. Using a cavity-ring-down method (see Fig. 1) in a pump probe configuration, we have measured a photon lifetime of 2.5 ms at 1530 nm corresponding to a quality factor of 3 × 1012 [4].

The semiclassical $\hbar$-expansion of the one-particle density matrix for a two-dimensional Fermi gas is calculated within the Wigner transform method of Grammaticos and Voros, originally developed in the context of nuclear physics. The method of Grammaticos and Voros has the virture of preserving both the Hermiticity and idempotency of the density matrix to all orders in the $\hbar$-expansion. As a topical application, we use our semiclassical expansion to go beyond the local-density approximation for the construction of the total dipole-dipole interaction energy functional of a two-dimensional, spin-polarized dipolar Fermi gas. We find a {\em finite}, second-order gradient correction to the Hartree-Fock energy, which takes the form $\varepsilon (\nabla \rho)^2/\sqrt{\rho}$, with $\varepsilon$ being small ($|\varepsilon| \ll1$) and negative. We test the quality of the corrected energy by comparing it with the exact results available for harmonic confinement. Even for small particle numbers, the gradient correction to the dipole-dipole energy provides a significant improvement over the local-density approximation., Comment: 1 figure

International audience; Optical microcavities with ultralong photon storage times are of central importance for integrated nanophotonics. To date, record quality (Q) factors up to 10^11 have been measured in millimetric-size single-crystal whispering-gallery-mode (WGM) resonators, and 10^10 in silica or glass microresonators. We show that, by introducing slow-light effects in an active WGM microresonator, it is possible to enhance the photon lifetime by several orders of magnitude, thus circumventing both fabrication imperfections and residual absorption. The slow-light effect is obtained from coherent population oscillations in an erbium-doped fluoride glass microsphere, producing strong dispersion of the WGM (group index ng∼106). As a result, a photon lifetime up to 2.5 ms at room temperature has been measured, corresponding to a Q factor of 3×10^12 at 1530 nm. This system could yield a new type of optical memory microarray with ultralong storage times.

In this article we report on ultraslow or fast light propagation, exciting behavior that become achievable thanks to the Coherent Population Oscillations effect (CPO). We show that the group velocity, the speed at which light propagates, can be drastically modified and engineered using the CPO effect in a crystal doped with triply ionized erbium ions, namely: Er3+:Y2SiO5. The steep dispersion of the index of refraction caused by the CPO effect is at the origin of group velocities as low as v g = 3 m / s . By inverting the slope of the index dispersion, we can make, in the same crystal, light go faster than if it was propagating in vacuum. This particular regime is characterized by larger than c or negative group velocities. In the 3-mm-long Er3+:Y2SiO5 crystal, we have achieved a delay of − 0.2 ms corresponding to a group velocity of v g = − 15 m / s . To cite this article: E. Baldit et al., C. R. Physique 10 (2009).

Closed-form analytical expressions and asymptotic results are obtained for the density distribution in Fourier space of harmonically trapped fermion gases at zero and nonzero temperatures in d dimensions. The result is applied to weakly interacting Fermi gases and to the elastic scattering from atomic nuclei. The Fourier transform of the momentum density for a d-dimensional harmonic confinement is also found.

National audience; Le facteur de qualité ou les propriétés dispersives de micro-résonateurs à modes de galerie en verre ZBLALiP dopé Erbium peut être contrôlé de deux façons différentes : i) soit en compensant les pertes de propagation par du gain optique ii) soit en augmentant artificiellement l'indice de groupe par des effets de ralentissement de la lumière

We performed an intermodal third-harmonic generation around 516 nm in a germanium-doped silica optical fiber. The analysis of the complex polarization behavior that was observed allowed us to determine the orientation symmetry group of the fiber and the relative values of the independent coefficients of the third-order electric susceptibility tensor.

International audience

Le ralentissement de la lumiere est le resultat d'une forte dispersion de l'indice de refraction. Nous observons un tel effet obtenu par oscillation coherente de population dans un cristal dope aux ions d'Erbium triplement ionises. La lumiere s'y propage avec une vitesse de groupe de 2.7 m/s. La largeur inhomogene de la transition est exploitee comme un parametre additionnel pour controler a la fois cette vitesse de groupe et la transmission.

Using the Wigner transform, we present an alternative derivation of the partial differential equation satisfied by the Slater sum, which is the diagonal element of the canonical Bloch density matrix. This is done in one dimension for the case of a general confining potential and also for the case of N independent fermions harmonically confined in d dimensions. We also present a simple proof of the so-called differential virial theorem for each of these cases.

We present a generalization of the Extended Thomas Fermi (ETF) theory to fermionic systems at finite temperature and finite angular momentum. In fact the present approach is more general in the sense that it is able to treat an excited system of fermions subject to an external vector field which in the case of nuclear rotations, developed more extensively here, is simply [Formula: see text].

The point canonical transformations map the Schrodinger equation with constant mass to a wave equation with a position-dependent effective mass. Using such a technique we derive, for a one-dimensional inhomogeneous system of noninteracting fermions with density ρ(x) and spatially dependent effective mass distribution m(x), the semiclassical kinetic energy density functional τ(ρ) in the so-called extended Thomas–Fermi model up to order 2. For a given position-dependent mass, we compare numerically the total semiclassical kinetic energy with its exact quantum mechanical counterpart. The qualitative agreement is excellent.

Starting from the spin-current-density-functional theory for electronic systems, we extend the formulation to include spin–orbit coupling. Particular attention is devoted to the symmetry of the problem. Here we show that the exchange-correlation energy functional is invariant by the U(1)em × SU(2)spin gauge transformations. We give the transformation laws of the paramagnetic current and also the paramagnetic spin current density by the U(1)em × SU(2)spin gauge transformations. For the case where the spin–orbit coupling is taken into account, we generalize the equations of continuity satisfied by the current density and the spin current density, derived by Vignale and Rasolt.

Semiclassical expansions derived in the framework of the Extended Thomas-Fermi approach for the kinetic energy density τ( r) and the spin-orbit density J( r) as functions of the local density ρ( r) are used to determine the central nuclear potentials V n( r) and V p( r) of the neutron and proton distribution for effective interactions of the Skyrme type. We demonstrate that the convergence of the resulting semiclassical expansions for these potentials is fast and that they reproduce quite accurately the corresponding Hartree-Fock average fields.

We performed intermodal third harmonic generation around 515 nm in a germanium-doped silica optical fiber. The complex polarization behavior that was observed is well-described by uniaxial symmetry of the third order electric susceptibility.

We study the equilibrium current density profiles of harmonically trapped ultra-cold Fermi gases in quantum Hall-like states that appear when the quasi-two-dimensional trap is set in fast rotation. The density profile of the gas (in the rotating reference frame) consists of incompressible strips of constant quantized density separated by compressible regions in which the density varies. Remarkably, we find that the atomic currents flow in opposite directions in the compressible and incompressible regions -- a prediction that should be amenable to experimental verification., Comment: 5 pages, 2 figures

We study a new quantum cryptography protocol with continuous variables for the construction of secret quantum keys. The protocol is based on pairs of Einstein-Podolsky-Rosen entangled quadratures o...

Electron paramagnetic resonance spectroscopy of rare earth ions in crystals is an interesting tool to analyze the hyperfine structure of the rare earth ground state. This can be useful for coherent spectroscopy and quantum information applications where the hyperfine structure of the electronic levels is used. In this work, we give a detailed analysis of the hyperfine structure of the ground state ( I 4 15 / 2 ( 0 ) ) of Er3+ ions in Y2SiO5.