Ground Band and a Generalized GP-equation for Spinor Bose-Einstein Condensates

For the spinor Bose-Einstein condensates both the total spin $S$ and its Z-component $S_{Z}$ should be conserved. However, in existing theories, only the conservation of $S_{z}$ has been taken into account. To remedy, this paper is the first attempt to take the conservation of both $$ and $S_{Z}$ into account. For this purpose, a total spin-state with the good quantum numbers $S$ and $S_{Z}$ is introduced in the trial wave function, thereby a generalized Gross-Pitaevskii equation has been derived. With this new equation, the ground bands of the $^{23}$Na and $$Rb condensates have been studied, where the levels distinct in $S$ split. It was found that the level density is extremely dense in the bottom of the ground band of $^{23}$Na, i.e., in the vicinity of the ground state. On the contrary, for $^{87}$Rb, the levels are extremely dense in the top of the ground band,Comment: 7 page, 5 figure

Two-body scattering in a trap and a special periodic phenomenon sensitive to the interaction

Two-body scattering of neutral particles in a trap is studied theoretically. The control of the initial state is realized by using optical traps. The collisions inside the trap occur repeatedly; thereby the effect of interaction can be accumulated. Two periodic phenomena with a shorter and a much longer period, respectively, are found. The latter is sensitive to the interaction. Instead of measuring the differential cross section as usually does, the measurement of the longer period and the details of the periodic behavior might be a valid source of information on weak interactions among neutral particles.Comment: 5 pages, 5 figure

Repeating head-on collisions in an optical trap and the evaluation of spin-dependent interactions among neutral particles

A dynamic process of repeating collisions of a pair of trapped neutral particles with weak spin-dependent interaction is designed and studied. Related theoretical derivation and numerical calculation have been performed to study the inherent coordinate-spin and momentum-spin correlation. Due to the repeating collisions the effect of the weak interaction can be accumulated and enlarged, and therefore can be eventually detected. Numerical results suggest that the Cr-Cr interaction, which has not yet been completely clear, could be thereby determined. The design can be in general used to determine various interactions among neutral atoms and molecules, in particular for the determination of very weak forces.Comment: 15 pages, 7 figure

Superconductivity mediated by the antiferromagnetic spin-wave in chalcogenide iron-base superconductors

The ground state of K$_{0.8+x}$Fe$_{1.6+y}$Se$_2$ and other iron-based selenide superconductors are doped antiferromagnetic semiconductors. There are well defined iron local moments whose energies are separated from those of conduction electrons by a large band gap in these materials. We propose that the low energy physics of this system is governed by a model Hamiltonian of interacting electrons with on-site ferromagnetic exchange interactions and inter-site superexchange interactions. We have derived the effective pairing potential of electrons under the linear spin-wave approximation and shown that the superconductivity can be driven by mediating coherent spin wave excitations in these materials. Our work provides a natural account for the coexistence of superconducting and antiferromagnetic long range orders observed by neutron scattering and other experiments.Comment: 4 pages, 3 figure

First excited band of a spinor Bose-Einstein condensate

The analytical expression of the fractional parentage coefficients for the total spin-states of a spinor N-boson system has been derived. Thereby an S-conserved theory for the spinor Bose-Einstein condensation has been proposed. A set of equations has been established to describe the first excited band of the condensates. Numerical solution for $^{23}$Na has been given as an example.Comment: 6 pages, 3 figure