Exact Eigenstates and Magnetic Response of Spin-1 and Spin-2 Vectorial Bose-Einstein Condensates

The exact eigenspectra and eigenstates of spin-1 and spin-2 vectorial Bose-Einstein condensates (BECs) are found, and their response to a weak magnetic field is studied and compared with their mean-field counterparts. Whereas mean-field theory predicts the vanishing population of the zero magnetic-quantum-number component of a spin-1 antiferromagnetic BEC, the component is found to become populated as the magnetic field decreases. The spin-2 BEC exhibits an even richer magnetic response due to quantum correlation between 3 bosons.Comment: 5 pages, no figures. LaTeX20

Некоторые результаты применения метода геометрического анализа дизъюнктов для поисков смещенного крыла пласта в Прокопьевском районе Кузбасса

In this paper we present the development of a compact, thermo-optically stable and vibration and mechanical shock resistant mounting technique by soldering of optical components. Based on this technique, new generations of laser pump sources for aerospace applications are designed. In these laser systems the used soldering technique replaces the glued connection between the optical component and its join partner. The main challenges are the alignment accuracy in the arc second range and the realization of the long term stability of every single part in the laser system (e.g. resonator mirrors)

О необходимости прослеживания Балейско-Дарасунского разлома в пределах Борщевочного кряжа

In this paper we present the development of a compact, thermo-optically stable and vibration and mechanical shock resistant mounting technique by soldering of optical components. Based on this technique a new generation of laser sources for aerospace applications is designed. In these laser systems solder technique replaces the glued and bolted connections between optical component, mount and base plate. Alignment precision in the arc second range and realization of long term stability of every single part in the laser system is the main challenge. At the Fraunhofer Institute for Laser Technology ILT a soldering and mounting technique has been developed for high precision packaging. The specified environmental boundary conditions (e.g. a temperature range of -40 °C to +50 °C) and the required degrees of freedom for the alignment of the components have been taken into account for this technique. In general the advantage of soldering compared to gluing is that there is no outgassing. In addition no flux is needed in our special process. The joining process allows multiple alignments by remelting the solder. The alignment is done in the liquid phase of the solder by a 6 axis manipulator with a step width in the nm range and a tilt in the arc second range. In a next step the optical components have to pass the environmental tests. The total misalignment of the component to its adapter after the thermal cycle tests is less than 10 arc seconds. The mechanical stability tests regarding shear, vibration and shock behavior are well within the requirements

Quantum tunneling across spin domains in a Bose-Einstein condensate

Quantum tunneling was observed in the decay of metastable spin domains in gaseous Bose-Einstein condensates. A mean-field description of the tunneling was developed and compared with measurement. The tunneling rates are a sensitive probe of the boundary between spin domains, and indicate a spin structure in the boundary between spin domains which is prohibited in the bulk fluid. These experiments were performed with optically trapped F=1 spinor Bose-Einstein condensates of sodium.Comment: 5 pages, 4 figure

Bose-Einstein condensation in shallow traps

In this paper we study the properties of Bose-Einstein condensates in shallow traps. We discuss the case of a Gaussian potential, but many of our results apply also to the traps having a small quadratic anharmonicity. We show the errors introduced when a Gaussian potential is approximated with a parabolic potential, these errors can be quite large for realistic optical trap parameter values. We study the behavior of the condensate fraction as a function of trap depth and temperature and calculate the chemical potential of the condensate in a Gaussian trap. Finally we calculate the frequencies of the collective excitations in shallow spherically symmetric and 1D traps.Comment: 6 pages, 4 figure

Theory of spin-2 Bose-Einstein condensates: spin-correlations, magnetic response, and excitation spectra

The ground states of Bose-Einstein condensates of spin-2 bosons are classified into three distinct (ferromagnetic, ^^ ^^ antiferromagnetic", and cyclic) phases depending on the s-wave scattering lengths of binary collisions for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic response of the condensate in each of these phases are studied in a mesoscopic regime, while low-lying excitation spectra are investigated in the hermodynamic regime. In the mesoscopic regime, where the system is so tightly confined that the spatial degrees of freedom are frozen, the exact, many-body ground state for each phase is found to be expressed in terms of the creation operators of pair or trio bosons having spin correlations. These pairwise and trio-wise units are shown to bring about some unique features of spin-2 BECs such as a huge jump in magnetization from minimum to maximum possible values and the robustness of the minimum-magnetization state against an applied agnetic field. In the thermodynamic regime, where the system is spatially uniform, low-lying excitation spectra in the presence of magnetic field are obtained analytically using the Bogoliubov approximation. In the ferromagnetic phase, the excitation spectrum consists of one Goldstone mode and four single-particle modes. In the antiferromagnetic phase, where spin-singlet ^^ ^^ pairs" undergo Bose-Einstein condensation, the spectrum consists of two Goldstone modes and three massive ones, all of which become massless when magnetic field vanishes. In the cyclic phase, where boson ^^ ^^ trios" condense into a spin-singlet state, the spectrum is characterized by two Goldstone modes, one single-particle mode having a magnetic-field-independent energy gap, and a gapless single-particle mode that becomes massless in the absence of magnetic field.Comment: 28 pages, 4 figure

Two-component Bose-Einstein Condensates with Large Number of Vortices

We consider the condensate wavefunction of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine states of $^{87}$Rb or $^{23}$Na) we find that the two components contain identical rectangular vortex lattices, where the unit cell has an aspect ratio of $\sqrt{3}$, and one lattice is displaced to the center of the unit cell of the other. Our results are based on an exact evaluation of the vortex lattice energy in the large angular momentum (or quantum Hall) regime.Comment: 4 pages, 2 figures, RevTe