Tunneling of ultracold atoms in time-independent potentials

We present theoretical as well as experimental results on resonantly enhanced quantum tunneling of Bose-Einstein condensates in optical lattices both in the linear case of single particle dynamics and in the presence of atom-atom interactions. Our results demonstrate the usefulness of condensates in optical lattices for the dynamical control of tunneling and for simulating Hamiltonians originally used for describing solid state phenomena.Comment: slightly amended version published as ch. 11 of a book edited by S. Keshavamurthy and P. Schlagheck with the title "Dynamical Tunneling: Theory and Experiment

Correlation functions for a Bose-Einstein condensate in the Bogoliubov approximation

In this article we introduce a differential equation for the first order correlation function $G^{(1)}$ of a Bose-Einstein condensate at T=0. The Bogoliubov approximation is used. Our approach points out directly the dependence on the physical parameters. Furthermore it suggests a numerical method to calculate $G^{(1)}$ without solving an eigenvector problem. The $G^{(1)}$ equation is generalized to the case of non zero temperature.Comment: 9 pages, ps format. This article was published in EPJD vol. 14(1) (2001), pp.105-11

Bose-Einstein condensates in 1D optical lattices: nonlinearity and Wannier-Stark spectra

We present our experimental investigations on the subject of nonlinearity-modified Bloch-oscillations and of nonlinear Landau-Zener tunneling between two energy bands in a rubidium Bose Einstein condensate in an accelerated periodic potential. Nonlinearity introduces an asymmetry in Landau-Zener tunneling. We also present measurements of resonantly enhanced tunneling between the Wannier-Stark energy levels for Bose-Einstein condensates loaded into an optical lattice.Comment: Chapter of "Nonlinearities of Periodic Structures and Metamaterials" (edited by C. Denz, S. Flach, and Yu. Kivshar) to be published by Springe

Multi-orbital bosons in bipartite optical lattices

We study interacting bosons in a two dimensional bipartite optical lattice. By focusing on the regime where the first three excited bands are nearly degenerate we derive a three orbital tight-binding model which captures the most relevant features of the bandstructure. In addition, we also derive a corresponding generalized Bose-Hubbard model and solve it numerically under different situations, both with and without a confining trap. It is especially found that the hybridization between sublattices can strongly influence the phase diagrams and in a trap enable even appearances of condensed phases intersecting the same Mott insulating plateaus.Comment: Minor change

Two-photon and EIT-assisted Doppler cooling in a three-level cascade system

Laser cooling is theoretically investigated in a cascade three-level scheme, where the excited state of a laser-driven transition is coupled by a second laser to a top, more stable level, as for alkali-earth atoms. The second laser action modifies the atomic scattering cross section and produces temperatures lower than those reached by Doppler cooling on the lower transition. When multiphoton processes due to the second laser are relevant, an electromagnetic induced transparency modifies the absorption of the first laser, and the final temperature is controlled by the second laser parameters. When the intermediate state is only virtually excited, the dynamics is dominated by the two-photon process and the final temperature is determined by the spontaneous decay rate of the top state.Comment: 5 pages, 3 figures. Revised version, accepted for publication in Phys. Rev A (Rapid Comm.

Four-level N-scheme crossover resonances in Rb saturation spectroscopy in magnetic fields

We perform saturated absorption spectroscopy on the D$\_2$ line for room temperature rubidium atoms immersed in magnetic fields within the 0.05-0.13 T range. At those medium-high field values the hyperfine structure in the excited state is broken by the Zeeman effect, while in the ground state hyperfine structure and Zeeman shifts are comparable. The observed spectra are composed by a large number of absorption lines. We identify them as saturated absorptions on two-level systems, on three-level systems in a V configuration and on four-level systems in a N or double-N configuration where two optical transitions not sharing a common level are coupled by spontaneous emission decays. We analyze the intensity of all those transitions within a unified simple theoretical model. We concentrate our attention on the double-N crossovers signals whose intensity is very large because of the symmetry in the branching ratios of the four levels. We point out that these structures, present in all alkali atoms at medium-high magnetic fields, have interesting properties for electromagnetically induced transparency and slow light applications.Comment: Submitted to Physical Review

Gain without inversion in quantum systems with broken parities

For a quantum system with broken parity symmetry, selection rules can not hold and cyclic transition structures are generated. With these loop-transitions we discuss how to achieve inversionless gain of the probe field by properly setting the control and auxiliary fields. Possible implementations of our generic proposal with specific physical objects with broken parities, e.g., superconducting circuits and chiral molecules, are also discussed.Comment: 12 pages, 4 figure