How does an interacting many-body system tunnel through a potential barrier to open space?

The tunneling process in a many-body system is a phenomenon which lies at the very heart of quantum mechanics. It appears in nature in the form of alpha-decay, fusion and fission in nuclear physics, photoassociation and photodissociation in biology and chemistry. A detailed theoretical description of the decay process in these systems is a very cumbersome problem, either because of very complicated or even unknown interparticle interactions or due to a large number of constitutent particles. In this work, we theoretically study the phenomenon of quantum many-body tunneling in a more transparent and controllable physical system, in an ultracold atomic gas. We analyze a full, numerically exact many-body solution of the Schr\"odinger equation of a one-dimensional system with repulsive interactions tunneling to open space. We show how the emitted particles dissociate or fragment from the trapped and coherent source of bosons: the overall many-particle decay process is a quantum interference of single-particle tunneling processes emerging from sources with different particle numbers taking place simultaneously. The close relation to atom lasers and ionization processes allows us to unveil the great relevance of many-body correlations between the emitted and trapped fractions of the wavefunction in the respective processes.Comment: 18 pages, 4 figures (7 pages, 2 figures supplementary information

Absence of Fragmentation in Two-Dimensional Bose-Einstein Condensation

We investigate the possibility that the BEC-like phenomena recently detected on two-dimensional finite trapped systems consist of fragmented condensates. We derive and diagonalize the one-body density matrix of a two-dimensional isotropically trapped Bose gas at finite temperature. For the ideal gas, the procedure reproduces the exact harmonic-oscillator eigenfunctions and the Bose distribution. We use a new collocation-minimization method to study the interacting gas in the Hartree-Fock approximation and obtain a ground-state wavefunction and condensate fraction consistent with those obtained by other methods. The populations of the next few eigenstates increase at the expense of the ground state but continue to be negligible; this supports the conclusion that two-dimensional BEC is into a single state.Comment: 6 pages, 1 figur

Anisotropic Spin Diffusion in Trapped Boltzmann Gases

Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows diffusion anisotropy. Moreover, the lack of spin isotropy in the interactions leads to the non-conservation of transverse spin, which in turn has novel effects on the hydrodynamic modes.Comment: 10 pages, 4 figures; submitted to PR

Maximal length of trapped one-dimensional Bose-Einstein condensates

I discuss a Bogoliubov inequality for obtaining a rigorous bound on the maximal axial extension of inhomogeneous one-dimensional Bose-Einstein condensates. An explicit upper limit for the aspect ratio of a strongly elongated, harmonically trapped Thomas-Fermi condensate is derived.Comment: 6 pages; contributed paper for Quantum Fluids and Solids, Trento 2004, to appear in JLT

Superfluid to Mott insulator transition in one, two, and three dimensions

We have created one-, two-, and three-dimensional quantum gases and study the superfluid to Mott insulator transition. Measurements of the transition using Bragg spectroscopy show that the excitation spectra of the low-dimensional superfluids differ significantly from the three-dimensional case

Possibilities for francium spectroscopy in a light trap

An experimental program is under way to capture neutral francium atoms in a magneto-optic trap. Production and transport of the radioactive Fr atoms near to the trapping region have been tested, with a steady state of 107 atoms. If one hundred atoms are captured from the Maxwell-Boltzmann distribution into a magneto-optic trap, this will be a sufficient number for spectroscopy of the unknown excited states. These measurements would then open the path to investigations of parity-violating transitions in francium. Introduction Alkali atoms have provided a wealth of information about the electronic as well as the nuclear structure of atoms. The single electron in the outer shell is a superb probe for subtle effects and is a very good handle for quantitative comparisons with theory. The energy levels of the alkalis are well known except for the heaviest of them, francium, with atomic number 87, because it has an unstable nucleus. Its required production in accelerators or as a daughter of radioactive processes has limited the study of its spectroscopy. A series of experiments during the last fifteen years [1,2] located the wavelength of the D1 and D2 lines of francium, as well as the hyperfine splitting of some of the different isotopes. Up until now, there are no experimental measurements of the position of the 8S energy level, although some calculations exist New and important studies of the spectrum of francium are now becoming feasible with the aid of novel techniques. The determination of the 8S energy level would be the first measurement to do in a light trap and would provide a good test of state-of-the-art calculations. It would also initiate the way towards the future detection of parity-non-conserving transitions. Our efforts at Stony Brook during the last year have brought together two pieces of technology that can facilitate the search for the 8S energy level. We have developed a francium production apparatus consisting of a target, an ion transport system and a neutralizer. This apparatus provides up to 2 x 105 francium atoms per second at thermal energies. The production of francium atoms is optimized for the isotopes 209, 210, and 211, whose lifetimes exceed 30 seconds. Parallel to the © J.C. Baltzer AG, Science Publisher