A compact dual atom interferometer gyroscope based on laser-cooled rubidium

We present a compact and transportable inertial sensor for precision sensing of rotations and accelerations. The sensor consists of a dual atom interferometer operated with laser-cooled ⁸⁷Rb. Raman processes are employed to coherently manipulate the matter waves. We describe and characterize the experimental apparatus. A method for passing from a compact geometry to an extended interferometer with three independent atom-light interaction zones is proposed and investigated. The extended geometry will enhance the sensitivity by more than two orders of magnitude which is necessary to achieve sensitivities better than 10^-8rad/s/.     

Towards a monolithic optical cavity for atom detection and manipulation

We study a Fabry-Perot cavity formed from a ridge waveguide on a AlGaAs substrate. We experimentally determined the propagation losses in the waveguide at 780 nm, the wavelength of Rb atoms. We have also made a numerical and analytical estimate of the losses induced by the presence of the gap which would allow the interaction of cold atoms with the cavity field. We found that the intrinsic finesse of the gapped cavity can be on the order of F∼30, which, when one takes into account the losses due to mirror transmission, corresponds to a cooperativity parameter for our system C∼1.     

Atom interferometers manipulated through the toroidal trap realized by the interference patterns of Laguerre-Gaussian beams

In this paper, we proposed new constructions of atom interferometers manipulated through the toroidal trap formed by the interference patterns of two co-propagation Laguerre-Gaussian (LG) beams. The coherent splitting and merging of the atomic ensemble, which is essential for the atom interferometer, is realized by the interference pattern of two LG beams. Along the beam propagation direction, a single-well trap is evolved into a double-well trap and then recombined back into a single-well trap, which can be used to form an atom interferometer.     

On the interaction of a beam of polar molecules with a static and a resonant RF field as a source of molecular interferences

A molecular beam interference model is presented based on a two-state interaction between a polar molecule and a resonant RF field as it occurs in the so-called C-field of a typical molecular beam electric resonant spectrometer. The treatment shows the onset of interferences in the beam transmission spectra as well as in its transverse profile. It is demonstrated how the molecular interferences are originated by the wavefunction phase shift introduced by the resonant RF field. Furthermore it is shown that for a given beam velocity and oscillating field frequency the fringes’ visibility depends on the strength of the RF field, i.e. the Rabi frequency, in the transmission spectra. Likewise the presence of a RF field gradient in the perpendicular beam direction gives rise to a peak structure in the transverse beam profile. The theoretical model was applied to simulate a variety of beam transmission spectra under resonant conditions as well as some experimental data already published by our group showing a satisfactory agreement between experimental and simulated data. Finally, the potentiality of this internal state molecular interferometer to carry out studies in matter-wave interferometry is remarked.     

Schlieren imaging of nano-scale atom-surface inelastic transition using a Fresnel biprism atom interferometer

Surface-induced exo-energetic inelastic transitions among atomic Zeeman states in a magnetic field (“van der Waals – Zeeman” transitions) are useable as tuneable beam splitters. A transversally coherent atom beam impinging a pair of opposite surfaces (e.g. 2 edges of a slit or of an ensemble of periodic slits) gives rise to two coherently diffracted wave packets. Within the wave packet overlap, non-localised interference fringes of the Young-slit type are predicted. From the diffraction pattern observed in the Fraunhofer regime (Schlieren image), detailed information about the transition amplitude on a scale of a few nanometers should be derived.     

Nonclassical correlations from dissociation-time entanglement

We discuss a strongly entangled two-particle state of motion that emerges naturally from the double-pulse dissociation of a diatomic molecule. This state, which may be called dissociation-time entangled, permits the unambiguous demonstration of nonclassical correlations by violating a Bell inequality based on switched single-particle interferometry and only position measurements. We apply time-dependent scattering theory to determine the detrimental effect of dispersion. The proposed setup brings into reach the possibility of establishing nonclassical correlations with respect to system properties that are truly macroscopically distinct.     

Faddeev–Jackiw canonical path integral quantization for a general scenario,its proper vertices and generating functionals

We generalize the Faddeev–Jackiw canonical path integral quantization for the scenario of a Jacobian with J=1 to that for the general scenario of non-unit Jacobian, give the representation of the quantum transition amplitude with symplectic variables and obtain the generating functionals of the Green function and connected Green function. We deduce the unified expression of the symplectic field variable functions in terms of the Green function or the connected Green function with external sources. Furthermore, we generally get generating functionals of the general proper vertices of any n-points cases under the conditions of considering and not considering Grassmann variables, respectively; they are regular and are the simplest forms relative to the usual field theory.     

Interference-induced enhancement of intensity and energy of a quantum optical field by a subwavelength array of coherent light sources

Recently, we have shown a mechanism that could provide great resonant and nonresonant transmission enhancements of the classical (nonquantum) light waves passed through subwavelength aperture arrays in thin metal films not by the plasmon–polariton waves, but by the constructive interference of diffracted waves (beams generated by the apertures) at the detector placed in the far-field zone. We now present a quantum reformulation of the model. The Hamiltonian describing the phenomenon of interference-induced enhancement and suppression of both the intensity and energy of a quantum optical field is derived. The basic properties of the field energy determining by the Hamiltonian are analyzed. Normally, the interference (addition) of two or more waves causes enhancement or suppression of the light intensity, but not the light energy. The model shows that the phenomenon could be observed experimentally, for instance, by using a subwavelength array of the coherent quantum light-sources (one- and two-dimensional subwavelength apertures, fibers, dipoles, and atoms).     

Pion-source geometry deduced from soft-pion interferometry in heavy-ion collisions at 650 A MeV

We report transverse,R _T , and longitudinal,R _L , source sizes extracted from two-pion interferometry analysis in the Au+Au and Nb + Nb interactions at 650 A MeV. For the Nb+Nb interactions, both,R _T andR _L , do not exceed the niobium nucleus radius. In the case of Au+Au collisions, the transverse size is larger than the longitudinal one being about 12 fm for the selection ofP ⁺ < 120=" mev/c.=" we=" also=" corroborate=" the=" existence=" of=" the=" previously=" reported=" specific=" three-pion=">One of us (T.S.) wishes to thank Professor M.I. Podgoretsky and Professor R.M. Weiner for interesting discussions and comments. We also wish to acknowledge remarks of Dr. B. Lörstad.     

Atom interferometry measurement of the electric polarizability of lithium

Using an atom interferometer, we have measured the static electric polarizability of ⁷Li α=(24.33 ±0.16)×10^-30 m³ = 164.2±1.1 atomic units with a 0.66% uncertainty. Our experiment, which is similar to an experiment done on sodium in 1995 by Pritchard and co-workers, consists in applying an electric field on one of the two interfering beams and measuring the resulting phase-shift. With respect to Pritchard's experiment, we have made several improvements which are described in detail in this paper: the capacitor design is such that the electric field can be calculated analytically; the phase sensitivity of our interferometer is substantially better, near 16 mrad/ ; finally our interferometer is species selective so that impurities present in our atomic beam (other alkali atoms or lithium dimers) do not perturb our measurement. The extreme sensitivity of atom interferometry is well illustrated by our experiment: our measurement amounts to measuring a slight increase Δv of the atom velocity v when it enters the electric field region and our present sensitivity is sufficient to detect a variation Δv/v ≈6 ×10^-13.     

Potential scattering in Dirac field theory

We develop the potential scattering of a spinor within the context of perturbation field theory. As an application, we reproduce, up to second order in the potential, the diffusion results for a potential barrier of quantum mechanics. An immediate consequence is a simple generalization to arbitrary potential forms, a feature not possible in quantum mechanics.     

A field-theoretic model for Hodge theory

We demonstrate that the four-dimensional (4D) ((3+1)-dimensional) free Abelian 2-form gauge theory presents a tractable field-theoretical model for the Hodge theory where the well-defined symmetry transformations correspond to the de Rham cohomological operators of differential geometry. The conserved charges, corresponding to the above continuous symmetry transformations, obey an algebra that is reminiscent of the algebra obeyed by the cohomological operators. The discrete symmetry transformation of the theory represents the realization of the Hodge duality operation that exists in the relationship between the exterior and co-exterior derivatives of differential geometry. Thus, we provide the realizations of all the mathematical quantities, associated with the de Rham cohomological operators, in the language of the symmetries of the present 4D free Abelian 2-form gauge theory.     

Nonlinear interferometry and phase measurements for surface second-harmonic generation in a dispersive geometry

Direct measurement of the phase of the surface nonlinear susceptibility is based on the interference of nonlinear optical signals. Up to now, this has not been possible for Second-Harmonic Generation (SHG) in geometries such as Total Internal Reflection (TIR) due to the refractive dispersion of harmonic and fundamental light created in TIR. We demonstrate two schemes which enable us to overcome this dispersion, leading to interference between two second-harmonic signals generated consecutively by the same laser. The advantages and limitations of the two approaches are discussed. We use this technique to check the theoretical predictions for the nonlinear Fresnel factors for SHG in the TIR geometry.Paper presented at the 129th HE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

Abelian 2-form gauge theory: superfield formalism

We derive the off-shell nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a free Abelian 2-form gauge theory by exploiting the geometrical superfield approach to the BRST formalism. The above four (3+1)-dimensional (4D) theory is considered on a (4, 2)-dimensional supermanifold parameterized by the four even spacetime variables x ^μ (with μ=0,1,2,3) and a pair of odd Grassmannian variables θ and (with ). One of the salient features of our present investigation is that the above nilpotent (anti-) BRST symmetry transformations turn out to be absolutely anticommuting due to the presence of a Curci–Ferrari (CF) type of restriction. The latter condition emerges due to the application of our present superfield formalism. The actual CF condition, as is well known, is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that our present 4D Abelian 2-form gauge theory imbibes some of the key signatures of the 4D non-Abelian 1-form gauge theory. We briefly comment on the generalization of our superfield approach to the case of Abelian 3-form gauge theory in four, (3+1), dimensions of spacetime.     

Stern Gerlach interferometry with metastable argon atoms: an immaterial mask modulating the profile of a supersonic beam

A new Stern Gerlach interferometer operating with a nozzle beam of metastable argon atoms Ar^* (3p⁵ 4s, ³ P ₂) is described. The selection of incoming (polarisation) and outgoing (analysis) Zeeman sublevels is achieved by use of laser induced transitions at two wavelengths, 811.5 nm (closed J = 2 → J = 3 transition) and 801.5 nm (open J = 2 → J = 2 transition). Linear superpositions of Zeeman sublevels, just beyond the polariser and just before the analyser, are prepared by means of two zones where Majorana transitions take place. In between, a controlled magnetic field configuration (the phase object) is produced within a triple μ-metal shielding. Standard interference patterns are obtained by scanning the field and detecting the atoms by secondary electron emission from a Faraday cup. When a static radial magnetic gradient is used, the beam profile is modulated by interference. The transverse pattern, which can be translated at will by adding a homogeneous field, is observed for the first time using a multi-channel electron multiplier followed by a phosphor screen and a CCD camera. The results satisfactorily agree with all theoretical predictions. Received 27 June 2002 / Received in final form 20 September 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: perales@lpl.univ-paris13.fr RID="b" ID="b"UMR 7538 du CNRS     

Multi-color XUV interferometry using high-order harmonics

We present a novel interferometric setup operating in the XUV spectral range. The interferometer consists of a combination of a double pinhole (similar to Young’s double slit) and a transmission grating. In the case of a light source consisting of discrete spectral lines, it allows recording interferograms for multi-colors simultaneously. We present two experiments in which high-order harmonics generated by a titanium sapphire laser were used as the light source for the interferometer. First, the temporal coherence lengths of the single harmonics were determined, and second, the index of refraction and the absorption of a thin beryllium foil were measured simultaneously in the range of 17–25 nm.     

Transverse energy dependence of neutron squeeze-out in relativistic heavy ion collisions

We present a microscopic calculation of neutronsqueeze-out in relativistic heavy ion collisions at beam energies betweeen 400 and 1000 MeV/nucleon. After demonstrating the importance of the correct isospin treatment for the neutron to proton ratio, our main emphasis is put on the investigation of the properties of neutronsqueeze-out. Thesqueeze-out ratio increases monotonously with the transverse momentum of the neutrons. This ratio is independent of the incident beam energy if plotted versusp _t /p _proj . Most importantly, we observe a strong dependence on the nuclear equation of state and momentum dependent interaction.Supported by GSI, BMFT and DFG     

The neutron/proton ratio of fast nucleon emission in antiproton annihilation on nuclei

The measurement of fast protons and neutrons emitted after antiproton annihilation at rest on²³⁸U and⁶³Cu reveals a large neutron/proton ratioR. Its value for⁶³Cu is larger than expected from the conventional model of intranuclear pion rescattering. A value ofR essentially constant over the whole range of mass number, from¹²C up to²³⁸U, is also announced by the experimentalists. It is shown that, on the contrary, the conventional scheme predicts a regular increase ofR with mass number. Alternative explanations of the effect are looked for. Within the usual scheme, an excess of negative pions, leading to more emitted neutrons, is not compatible with final pion multiplicities. The influence of meson resonances on the neutron/proton ratio is considered, as well as the possible occurrence of annihilations on two nucleons. They cannot warrant an increase ofR at low mass targets sufficient to explain a constant value over the whole range of target masses.     

Spinor molecule in atomic Bose–Einstein condensate

We have performed two-photon photoassociation experiments in atomic Bose–Einstein condensate (BEC) of ⁸⁷Rb with spin degree of freedom which is created by all-optical method with CO₂ lasers. The spinor character of the molecules has been revealed by the photoassociation spectrum with a new structure. The hyperfine structure of the molecules near the dissociation limit is identified by observations of the Zeeman and AC-Stark effects of the molecules. The molecules have been spin-selectively probed by the use of the light shift. This result would open the new possibility of research on novel spinor molecular BEC.     

Relativistic mean-field parametrization of effective interaction in nuclear matter

The results of the modern relativistic Dirac-Brueckner calculations of nuclear matter are parametrized in terms of the relativistic- mean-field theory with scalar and vector nonlinear selfinteractions. It is shown that the inclusion of the isoscalar vector-meson quartic selfinteraction is essential for obtaining a proper density dependence of the vector potential in the mean-field model. The obtained mean-field parameters represent a simple parametrization of effective interaction in nuclear matter. This interaction may be used in the mean-field studies of the structure of finite nuclei without the introduction of additional free parameters.This work was supported in part by the Grant Agency of the Slovak Academy of Sciences under Grant No. GA SAV-517/1991.