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ABSTRACT: A new, non adiabatic, description of the H2
+ molecular ion and its isotopomers is proposed: the molecular system is treated as a three body Coulomb system, in the framework
of non relativistic quantum mechanics. The method takes advantage of the dynamical symmetries of the system. It relies on
the choice of the perimetric coordinates to describe the system, and of a generalized Hylleraas basis, in which the Hamiltonian
exhibits strong coupling rules. The method is described in detail both for S and P states (i.e., states of total angular momentum J = 0 or 1). We calculate the energies of all J = 0 or 1 vibrational levels of the H2
+ and D2
+ molecular ions with a very high accuracy (typically 10−14 atomic unit). This a considerable improvement over previous calculations. The dependence of these results on the proton to
electron mass ratio is also discussed.
The European Physical Journal D 04/2012; 12(3):449-466. · 1.48 Impact Factor
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ABSTRACT: Using Fourier transform on a time series generated by unitary evolution, we
extract many-body eigenstates of the Bose-Hubbard model corresponding to low
energy excitations, which are generated when the insulator-superfluid phase
transition is realized in a typical experiment. The analysis is conducted in a
symmetric external potential both without and with and disorder. A simple
classification of excitations in the absence disorder is provided. The
evolution is performed assuming the presence of the parity symmetry in the
system rendering many-body quantum states either symmetric or antisymmetric.
Using symmetry-breaking technique, those states are decomposed into elementary
one-particle processes.
07/2011;
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Physical Review A 01/2011; 84:023402. · 2.88 Impact Factor
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ABSTRACT: At very low temperature, a quasi-one-dimensional ensemble of atoms with attractive interactions tend to form a bright soliton. When exposed to a sufficiently weak external potential, the shape of the soliton is not modified, but its external motion is affected. We develop in detail the Bogoliubov approach for the problem, treating, in a non-perturbative way, the motion of the center of mass of the soliton. Quantization of this motion allows us to discuss its long time properties. In particular, in the presence of a disordered potential, the quantum motion of the center of mass of a bright soliton may exhibit Anderson localization, on a localization length which may be much larger than the soliton size and could be observed experimentally. Comment: complementary material to arXiv:0907.0338; accepted for publication in Acta Physica Polonica A
11/2009;
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ABSTRACT: We report a numerical analysis of the Anderson transition in a
quantum-chaotic system, the quasiperiodic kicked rotor with three
incommensurate frequencies. It is shown that this dynamical system exhibits the
same critical phenomena as the truly random 3D-Anderson model. By taking proper
account of systematic corrections to one-parameter scaling, the universality of
the critical exponent is demonstrated. Our result $\nu = 1.59 \pm 0.01$ is in
perfect agreement with the value found for the Anderson model.
04/2009;
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ABSTRACT: We study Anderson localization of ultracold atoms in weak one-dimensional speckle potentials using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between energy regions where localization lengths differ by orders of magnitude. We also point out that the correction to the Born term explicitly depends on the sign of the potential. Our results are in agreement with numerical calculations in a regime relevant for experiments. Finally, we analyze our findings in the light of a diagrammatic approach.
Phys. Rev. A. 01/2009; 80.
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ABSTRACT: This paper investigates quantum diffusion of matter waves in two-dimensional random potentials, focussing on expanding Bose-Einstein condensates in spatially correlated optical speckle potentials. Special care is taken to describe the effect of dephasing, finite system size, and an initial momentum distribution. We derive general expressions for the interference-renormalized diffusion constant, the disorder-averaged probability density distribution, the variance of the expanding atomic cloud, and the localized fraction of atoms. These quantities are studied in detail for the special case of an inverted-parabola momentum distribution as obtained from an expanding condensate in the Thomas-Fermi regime. Lastly, we derive quantitative criteria for the unambiguous observation of localization effects in a possible 2D experiment. Comment: some structural changes and corrected fig. 2, final version
07/2008;
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ABSTRACT: Statistical properties of resonances of the hydrogen atom in a static, experimentally available magnetic field are studied. We show that the relevant parameter is the number of open channels. A rough agreement with a random matrix model is observed, but significant deviations due to the long-range Coulomb potential are reported and explained.
EPL (Europhysics Letters) 07/2007; 31(5-6):251. · 2.17 Impact Factor
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ABSTRACT: We establish the existence of strongly localized wave packets tracing without dispersion the classical dynamics of a Rydberg electron in a circularly polarized microwave field over up to 106 periods of the driving field, which at the same time are single eigenstates of the atom dressed by the microwave field. These "single-state wave packets" are shown to be robust towards small changes of the external field and can be prepared experimentally.
EPL (Europhysics Letters) 07/2007; 32(2):107. · 2.17 Impact Factor
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ABSTRACT: In a recent Letter (Phys. Rev. Lett. \textbf{98}, 083601 (2007), arXiv:cond-mat/0610804), O. Assaf and E. Akkermans claim that the angular correlations of the light intensity scattered by a cloud of cold atoms with internal degeneracy (Zeeman sublevels) of the ground state overcome the usual Rayleigh law. More precisely, they found that they become exponentially large with the size of the sample. In what follows, we will explain why their results are wrong and, in contrary, why the internal degeneracy leads to lower intensity correlations. Comment: 1 page. Comment submitted to PRL
05/2007;
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ABSTRACT: This article studies multiple scattering of matter waves by a disordered
optical potential in two and in three dimensions. We calculate fundamental
transport quantities such as the scattering mean free path $\ell_s$, the
Boltzmann transport mean free path $\elltrb$, and the Boltzmann diffusion
constant $D_B$, using a diagrammatic Green functions approach. Coherent
multiple scattering induces interference corrections known as weak localization
which entail a reduced diffusion constant. We derive the corresponding
expressions for matter wave transport in an correlated speckle potential and
provide the relevant parameter values for a possible experimental study of this
coherent transport regime, including the critical crossover to the regime of
strong or Anderson localization.
02/2007;
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ABSTRACT: We calculate the photo-ionization cross-section from the ground state of the helium atom, using the complex rotation method and diagonalization of sparse matrices. This produces directly the positions and widths of the doubly excited 1Po resonances together with the photo-ionization cross-section. Our calculations up to the N = 9 threshold are in perfect agreement with recent experimental data and show the transition from a regular structure at low energy to a chaotic one at high energy, where various resonances strongly overlap.
EPL (Europhysics Letters) 01/2007; 40(4):363. · 2.17 Impact Factor
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ABSTRACT: We study the mechanisms responsible for quantum diffusion in the quasiperiodic kicked rotor. We report experimental measurements of the diffusion constant on the atomic version of the system and develop a theoretical approach (based on the Floquet theorem) explaining the observations, especially the "sub-Fourier" character of the resonances observed in the vicinity of exact periodicity, i.e. the ability of the system to distinguish two neighboring driving frequencies in a time shorter than the inverse of the difference of the two frequencies.
EPL (Europhysics Letters) 01/2007; 69(3):327. · 2.17 Impact Factor
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ABSTRACT: A new vibrational level of the H2+ molecular ion with binding energy of 1.09 × 10−9 a.u. ≈ 30 neV below the first dissociation limit is predicted, using highly accurate numerical non-relativistic quantum calculations, which go beyond the Born-Oppenheimer approximation. It is the first-excited vibrational level v = 1 of the 2pσu electronic state, antisymmetric with respect to the exchange of the two protons, with orbital angular momentum L = 0. It manifests itself as a huge p-H scattering length of a = 750 ± 5 Bohr radii.
EPL (Europhysics Letters) 01/2007; 64(3):316. · 2.17 Impact Factor
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ABSTRACT: Coherent backscattering (CBS) of quasi-resonant light by cold atoms presents some specific features due to the internal structure of the atomic scatterers. We present the first quantitative comparison between the experimentally observed CBS cones and Monte Carlo calculations which take into account the shape of the atomic cloud as well as the internal atomic structure.
EPL (Europhysics Letters) 01/2007; 61(3):327. · 2.17 Impact Factor
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ABSTRACT: We use the coherent backscattering interference effect to investigate experimentally and theoretically how coherent transport of light inside a cold atomic vapor is affected by the residual motion of atomic scatterers. As the temperature of the atomic cloud increases, the interference contrast decreases dramatically. This emphasizes the role of motion-induced decoherence for resonant scatterers even in the sub-Doppler regime of temperature. We derive analytical expressions for the corresponding coherence time.
Physical Review Letters 08/2006; 97(1):013004. · 7.37 Impact Factor
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ABSTRACT: We consider ultracold atoms in 2D disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport in the noninteracting regime. We derive the diffusion constant as a function of all relevant microscopic parameters and show that coherent multiple scattering induces significant weak localization effects. In particular, we find that even the strong localization regime is accessible with current experimental techniques and calculate the corresponding localization length.
Physical Review Letters 01/2006; 95(25):250403. · 7.37 Impact Factor
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ABSTRACT: We experimentally study radiation trapping of near-resonant light in a cloud of laser-cooled rubidium atoms. Unlike in most
previous studies, dealing with hot vapors, collisional broadening is here negligible and Doppler broadening due to the residual
atomic velocity is narrower than the homogeneous broadening. This is an interesting new regime, at the boundary between coherent
and incoherent radiation transport. We analyze in detail our low-temperature data (quasi-elastic regime) and then provide
some experimental evidence for Doppler-based frequency redistribution. The data are compared with an analytical model valid
for coherent transport and a Monte Carlo simulation including the Doppler effect.
Applied Physics B 10/2005; 81(7):1001-1008. · 2.19 Impact Factor
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ABSTRACT: We consider ultracold atoms in 2D-disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport in the non-interacting regime. We derive the diffusion constant as function of all relevant microscopic parameters and show that coherent multiple scattering induces significant weak localization effects. In particular, we find that even the strong localization regime is accessible with current experimental techniques and calculate the corresponding localization length.
07/2005;
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ABSTRACT: We theoretically study the propagation of light in a disordered medium with nonlinear scatterers. We especially focus on interference effects between reversed multiple scattering paths, which lead to weak localization and coherent backscattering. We show that, in the presence of weakly nonlinear scattering, constructive interferences exist in general between three different scattering amplitudes. This effect influences the nonlinear backscattering enhancement factor, which may thus exceed the linear barrier two.
Physical Review E 06/2005; 71(5 Pt 2):055603. · 2.26 Impact Factor
