Introduction Presented here is a study of the revival of a rotational wavepacket in deuterium observed in a pump-probe experiment, which demonstrates impulsive alignment of the molecule to the laser field polarization direction. The polarization angle of the ultrafast pump pulse was rotated, causing impulsive alignment of the molecule to this axis. While cooling translational degrees of freedom in atoms has been demonstrated (from magneto-optic traps to Bose-Einstein Condensates), and optical lattices can be generated to introduce regular crystal-like structure into a large number of atoms, such manipulation is rather more difficult with molecules. The complex level structure reflects extensive nuclear and electronic degrees of freedom. However, following original suggestions of Friedrich and Herschbach, and Seideman two methods have been demonstrated to spatially align an ensemble of molecules using linearly polarized laser fields.

Phonons in expanding Bose-Einstein condensates with wavelengths much larger than the healing length behave in the same way as quantum fields within a universe undergoing an accelerated expansion. This analogy facilitates the application of many tools and concepts known from general relativity (such as horizons) and the prediction of the corresponding effects such as the freezing of modes after horizon crossing and the associated amplification of quantum fluctuations. Basically the same amplification mechanism is (according to our standard model of cosmology) supposed to be responsible for the generation of the initial inhomogeneities - and hence the seeds for the formation of structures such as our galaxy - during cosmic inflation (i.e., a very early epoch in the evolution of our universe). After a general discussion of the analogy (analogue cosmology), we calculate the frozen and amplified density-density fluctuations for quasi-two dimensional (Q2D) and three dimensional (3D) condensates which undergo a free expansion after switching off the (longitudinal) trap.

The population dynamics of a trapped Bose-Einstein condensate, subject to the action of an external field, is studied. This field produces a spatio-temporal modulation of the trapping potential with the frequency close to the transition frequency between the ground state and a higher energy level. For the evolution equations of fractional populations, a critical line is found. It is demonstrated that there exists a direct analogy between dynamical instability at this line and critical phenomena at a critical line of an averaged system. The related critical indices are calculated. The spatio-temporal evolution of atomic density is analyzed.

us with the opportunity to address the specific issue of the role of intervalence band coherences. Figure 2 shows the observed coherently coupled lh-exciton Stark shift together with the conventional hh-exciton Stark shift measured with 0’ and d probe pulses, respectively. Our theoretical analysis is based on a thirdorder expansion of the dynamics-controlled truncation formalism.1° Other than the restriction to 1s-excitons, no further approximations are made.” In Figure 3 we show results with and without intervalence band coherences. In the limit of large detunings, the semiconductor response approaches that of a three-level system, in which case the coherently-coupled lh-exciton Stark shift vanishes in the absence of the Raman coherence. Clearly, the experimental observations can only be understood in the presence of the Raman coherence. The fact that the observed hhlh shift ratio increases at small detunings can be attributed to and simulated with the assumption of an optically induced decay of the Raman coherence, which is likely to be most effective at smaller than at large detunings. We acknowledge support by NSF, JSOP and COEDIP.

A mixture of the multicomponent Bose-Einstein condensate is considered, where each component moves with its own velocity. As a result of the relative motion, the mixture stratifies when the relative velocity reaches a critical value. Stability conditions for a binary moving mixture are derived and the critical velocity is found.

A generalized-Laguerre-Hermite pseudospectral method is proposed for com- puting symmetric and central vortex states in Bose-Einstein condensates (BECs) in three dimensions with cylindrical symmetry. The new method is based on the properly scaled generalized-Laguerre & Hermite functions and a normalized gradient ∞ow. It enjoys three important advantages: (i) it reduces a three dimensional (3D) problem with cylindrical sym- metry into an efiective two-dimensional (2D) problem; (ii) it solves the problem in the whole space instead of in a truncated artiflcial computational domain; and (iii) it is spectrally ac- curate. Extensive numerical results for computing symmetric and central vortex states in BECs are presented for one-dimensional (1D) BEC, 2D BEC with radial symmetry and 3D BEC with cylindrical symmetry. ¢ + W t(z) with r = p x2 + y2, !r and !z the trap frequencies in radial and axial direction, respectively, mb the mass of BEC atoms, and Wt(z) is a real-valued bounded function of z. We assume that the

A rotating bosonic many-body system in a harmonic trap is studied with the 3D-Cranked Hartree-Fock-Bogoliubov method at zero temperature, which has been applied to nuclear many- body systems at high spin. This method is a variational method extended from the Hartree-Fock theory, which can treat the pairing correlations in a self-consistent manner. An advantage of this method is that a finite-range interaction between constituent particles can be used in the calcula- tion, unlike the original Gross-Pitaevskii approach. To demonstrate the validity of our method, we present a calculation for a toy model, that is, a rotating system of ten bosonic particles interacting through the repulsive quadrupole-quadrupole interaction in a harmonic trap. It is found that the yrast states, the lowest-energy states for the given total angular momentum, does not correspond to the Bose-Einstein condensate, except a few special cases. One of such cases is a vortex state, which appears when the total angular momentum L is twice the particle number N (i.e., L = 2N).

The development of high sensitivity and high accuracy atom interferometers requires new theoretical tools for their modelization: in this article we emphasize specifically a generalized Fresnel-Kirchhoff formula for atom optics in the form of ABCD matrices and covariant wave equations in the form of a Dirac equation for atom optics in the presence of gravito-inertial fields. As examples, we derive the phase shift for the atom gravimeter and the output of an atom laser. Some of the physics of the beam splitters is described. We present a second-quantized field theory of massive spin one-half particles or antiparticles in the presence of a weak gravitational field treated as a spin two external field in a flat Minkowski background. This theory is used to calculate and discuss relativistic phase shifts in the context of matter-wave interferometry (especially atom or antiatom interferometry). In this way, many effects are introduced in a unified relativistic framework, including spin- gravitation terms: gravitational red shift, Thomas precession, Sagnac effect, spin-rotation effect, orbital and spin Lense-Thirring effects, de Sitter geodetic precession and finally the effect of gravitational waves.  2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS

Experimental and numerical studies of the velocity field of dark solitons in Bose-Einstein condensates are presented. The formation process after phase imprinting as well as the propagation of the emerging soliton are investigated using spatially resolved Bragg-spectroscopy of soliton states in Bose-Einstein condensates of 87 Rubidium. A comparison of experimental data to results from numerical simulations of the Gross-Pitaevskii equation clearly identifies the flux underlying a dark soliton propagating in a Bose-Einstein condensate. The results allow further optimization of the phase imprinting method for creating collective exitations of Bose-Einstein condensates.

The coherent and collective nature of a Bose-Einstein condensate can enhance or suppress physical processes. Bosonic stimulation enhances scattering in already occupied states which leads to matter wave amplification, and the suppression of dissipation leads to superfluidity. In this article we present several experiments where enhancement and suppression have been observed and discuss the common roots of and differences between these phenomena.  2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Bose-Einstein condensation / superfluidity / structure factor / superradiance / amplification of light / matter wave amplification

We consider a spinor Bose-Einstein condensate in its polar ground state. We analyze magnetization waves of a finite amplitude and show that their nonlinear cou- pling to the density waves change the dependence of the frequency on the wavenum- ber dramatically. In contrary, the density wave propagation is much less modified by the nonlinearity effects. A similar phenomenon in a miscible two-component condensate is studied, too.

We investigate dynamical properties of bright solitons with a finite background in the F = 1 spinor Bose-Einstein condensate (BEC), based on an integrable spinor model which is equivalent to the matrix nonlinear Schrodinger equation with a self-focusing nonlineality. We apply the inverse scattering method formulated for nonvanishing boundary conditions. The resulting soliton solutions can be regarded as a generalization of those under vanishing boundary conditions. One-soliton solutions are derived in an explicit manner. According to the behaviors at the infinity, they are classified into two kinds, domain-wall (DW) type and phase-shift (PS) type. The DW-type implies the ferromagnetic state with nonzero total spin and the PS-type implies the polar state, where the total spin amounts to zero. We also discuss two-soliton collisions. In particular, the spin-mixing phenomenon is confirmed in a collision involving the DW-type. The results are consistent with those of the previous studies for bright solitons under vanishing boundary conditions and dark solitons. As a result, we establish the robustness and the usefulness of the multiple matter-wave solitons in the spinor BECs.