Images of a Bose-Einstein condensate in position and momentum space

In the Bogoliubov theory a condensate initially prepared in its ground state described by stationary Bogoliubov vacuum and later perturbed by a time-dependent potential or interaction strength evolves into a time-dependent excited state which is dynamical Bogoliubov vacuum. The dynamical vacuum has a simple diagonal form in a time-dependent orthonormal basis of single particle modes. This diagonal representation leads to a gaussian probability distribution for possible outcomes of density measurements in position and momentum space. In these notes we also discuss relations with the U(1) symmetry breaking version of the Bogoliubov theory and give two equivalent gaussian integral representations of the dynamical vacuum state.Comment: 4 pages; Talk given at the Laser Physics Workshop, July 2005, Kyoto, Japa

Einstein-Infeld-Hoffman method and soliton dynamics in a parity noninvariant system

We consider slow motion of a pointlike topological defect (vortex) in the nonlinear Schrodinger equation minimally coupled to Chern-Simons gauge field and subject to external uniform magnetic field. It turns out that a formal expansion of fields in powers of defect velocity yields only the trivial static solution. To obtain a nontrivial solution one has to treat velocities and accelerations as being of the same order. We assume that acceleration is a linear form of velocity. The field equations linearized in velocity uniquely determine the linear relation. It turns out that the only nontrivial solution is the cyclotron motion of the vortex together with the whole condensate. This solution is a perturbative approximation to the center of mass motion known from the theory of magnetic translations.Comment: 6 pages in Latex; shortened version to appear in Phys.Rev.

Interference of Fock states in a single measurement

We study analytically the structure of an arbitrary order correlation function for a pair of Fock states and prove without any approximations that in a single measurement of particle positions interference effects must occur as experimentally observed with Bose-Einstein condensates. We also show that the noise level present in the statistics is slightly lower than for a respective measurement of phase states.Comment: 4 page

Laser cooling all the way down to molecular condensate

Numerical simulations show that laser cooling of fermions on the repulsive side of the Feshbach resonance can sympathetically cool molecules well below their condensation temperature.Comment: 7 pages, 2 .eps figure

More on scattering of Chern-Simons vortices

I derive a general formalism for finding kinetic terms of the effective Lagrangian for slowly moving Chern-Simons vortices. Deformations of fields linear in velocities are taken into account. From the equations they must satisfy I extract the kinetic term in the limit of coincident vortices. For vortices passing one over the other there is locally the right-angle scattering. The method is based on analysis of field equations instead of action functional so it may be useful also for nonvariational equations in nonrelativistic models of Condensed Matter Physics.Comment: discussion around Eq.(45) is generalised, one more condition for the local right-angle scattering is adde

Optimal cooling strategies for magnetically trapped atomic Fermi-Bose mixtures

We discuss cooling efficiency for different-species Fermi-Bose mixtures in magnetic traps. A better heat capacity matching between the two atomic species is achieved by a proper choice of the Bose cooler and the magnetically trappable hyperfine states of the mixture. When a partial spatial overlap between the two species is also taken into account, the deepest Fermi degeneracy is obtained for an optimal value of the trapping frequency ratio. This can be achieved by assisting the magnetic trap with a deconfining light beam, as shown in the case of fermionic 6Li mixed with 23Na, 87Rb, and 133Cs, with optimal conditions found for the not yet explored 6Li-87Rb mixture.Comment: 5 pages, 3 figures, to appear in Physical Review