We investigate the band structure of a Bose-Einstein condensate in a one-dimensional periodic potential by calculating stationary solutions of the Gross-Pitaevskii equation which have the form of Bloch waves. We demonstrate that loops ("swallow tails") in the band structure occur both at the Brillouin zone boundary and at the center of the zone, and they are therefore a generic feature. A physical interpretation of the swallow tails in terms of periodic solitons is given. The linear stability of the solutions is investigated as a function of the strength of the mean-field interaction, the magnitude of the periodic potential, and the wave vector of the condensate. The regions of energetic and dynamical stability are identified by considering the behavior of the Gross-Pitaevskii energy functional for small deviations of the condensate wave function from a stationary state. It is also shown how for long-wavelength disturbances the stability criteria may be obtained within a hydrodynamic approach. * machholm@nordita.dk;

We consider impulsive excitation of a linear polar molecule by a plane polarized electromagnetic "half-cycle" pulse in the terahertz range. A rotational wave packet is created with angular momentum states of different parity. The time evolution of the wave packet corresponds to alternating molecular orientations with respect to the polarization axis of the field. This field-free time-dependent orientation of the molecule is computationally demonstrated, also at finite temperatures, with LiH and NaI as examples.

We demonstrate that there exist stationary states of Bose-Einstein condensates in an optical lattice that do not satisfy the usual Bloch periodicity condition. Using the discrete model appropriate to the tight-binding limit we determine energy bands for period-doubled states in a one-dimensional lattice. In a complementary approach we calculate the band structure from the Gross-Pitaevskii equation, considering both states of the usual Bloch form and states which have the Bloch form for a period equal to twice that of the optical lattice. We show that the onset of dynamical instability of states of the usual Bloch form coincides with the occurrence of period-doubled states with the same energy. The period-doubled states are shown to be related to periodic trains of solitons.

We calculate the light-induced collisional loss of laser-cooled and trapped magnesium atoms for detunings up to 50 atomic linewidths to the red of the 1 S0-1 P1 cooling transition. We evaluate loss rate coefficients due to both radiative and nonradiative state-changing mechanisms for temperatures at and below the Doppler cooling temperature. We solve the Schrödinger equation with a complex potential to represent spontaneous decay, but also give analytic models for various limits. Vibrational structure due to molecular photoassociation is present in the trap loss spectrum. Relatively broad structure due to absorption to the Mg2 1 Σu state occurs for detunings larger than about 10 atomic linewidths. Much sharper structure, especially evident at low temperature, occurs even at smaller detunings due to of Mg2 1 Πg absorption, which is weakly allowed due to relativistic retardation corrections to the forbidden dipole transition strength. We also perform model studies for the other alkaline earth species Ca, Sr, and Ba and for Yb, and find similar qualitative behavior as for Mg.34.50. Rk, 34.10.+x, 32.80.Pj

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Using two identical 110 femtosecond (fs) optical pulses separated by 310 fs, we launch two dissociative wave packets in I2. We measure the square of the wave function as a function of both the internuclear separation, /Psi(R)/(2), and of the internuclear velocity, /Psi(v(R))/(2), by ionizing the dissociating molecule with an intense 20 fs probe pulse. Strong interference is observed in both /Psi(R)/(2) and in /Psi(v(R))/(2). The interference, and therefore the shape of the wave function, is controlled through the phase difference between the two dissociation pulses in good agreement with calculations.

Classical/quantal method for multistate dynamics: A computational studyFragmentation dynamics of the molecular ion Na 2 ϩ irradiated by an intense femtosecond pulse laser is studied using quantum wave packet propagations. It is demonstrated that the pulse duration ͑20-250 fs͒ can be used as a control parameter for both the total dissociation probability and the branching ratio between different dissociation channels. This pulse length effect is important when the duration of the pulse is shorter than the vibrational period of the molecular ion in the ground state. The effects of laser intensity ͑10 11 -3ϫ10 12 W/cm 2 ͒, wavelength ͑680-780 nm͒ and initial vibrational level on the dissociation dynamics are also studied.

Alignment of molecules under field free conditions with negligible vibrational or electronic excitation is created by a short off-resonant low frequency laser pulse. Typically the global maximum in postpulse alignment occurs at a rotational wave packet revival close to half a rotational period after the short pulse. The alignment effect is robust to thermal averaging at the revivals, but averaging cancels the alignment in between. The permanent dipole–field interaction can be efficient for alignment with off-resonant frequencies between the rotational and the vibrational frequencies of the molecule.