Measuring the temporal coherence of an atom laser beam

We report on the measurement of the temporal coherence of an atom laser beam extracted from a $^{87}$Rb Bose-Einstein condensate. Reflecting the beam from a potential barrier creates a standing matter wave structure. From the contrast of this interference pattern, observed by magnetic resonance imaging, we have deduced an energy width of the atom laser beam which is Fourier limited by the duration of output coupling. This gives an upper limit for temporal phase fluctuations in the Bose-Einstein condensate.Comment: 4 pages, 3 figure

Optics with an Atom Laser Beam

We report on the atom optical manipulation of an atom laser beam. Reflection, focusing and its storage in a resonator are demonstrated. Precise and versatile mechanical control over an atom laser beam propagating in an inhomogeneous magnetic field is achieved by optically inducing spin-flips between atomic ground states with different magnetic moment. The magnetic force acting on the atoms can thereby be effectively switched on and off. The surface of the atom optical element is determined by the resonance condition for the spin-flip in the inhomogeneous magnetic field. A mirror reflectivity of more than 98% is measured

Quantitative Determination of Temperature in the Approach to Magnetic Order of Ultracold Fermions in an Optical Lattice

We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as 0.77k(B) which is about twice as large as the entropy at the Neel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy

Hydrodynamic flow of expanding Bose-Einstein condensates

We study expansion of quasi-one-dimensional Bose-Einstein condensate (BEC) after switching off the confining harmonic potential. Exact solution of dynamical equations is obtained in framework of the hydrodynamic approximation and it is compared with the direct numerical simulation of the full problem showing excellent agreement at realistic values of physical parameters. We analyze the maximum of the current density and estimate the velocity of expansion. The results of the 1D analysis provides also qualitative understanding of some properties of BEC expansion observed in experiments.Comment: 5 pages, 3 figures, RevTeX4. To appear in Physical Review

Giant Oscillations of Acoustoelectric Current in a Quantum Channel

A theory of d.c. electric current induced in a quantum channel by a propagating surface acoustic wave (acoustoelectric current) is worked out. The first observation of the acoustoelectric current in such a situation was reported by J. M. Shilton et al., Journ. Phys. C (to be published). The authors observed a very specific behavior of the acoustoelectric current in a quasi-one-dimensional channel defined in a GaAs-AlGaAs heterostructure by a split-gate depletion -- giant oscillations as a function of the gate voltage. Such a behavior was qualitatively explained by an interplay between the energy-momentum conservation law for the electrons in the upper transverse mode with a finite temperature splitting of the Fermi level. In the present paper, a more detailed theory is developed, and important limiting cases are considered.Comment: 7 pages, 2 Postscript figures, RevTeX 3.

Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms

We investigate the dynamics of neutral atoms in a 2D optical lattice which traps two distinct internal states of the atoms in different columns. Two Raman lasers are used to coherently transfer atoms from one internal state to the other, thereby causing hopping between the different columns. By adjusting the laser parameters appropriately we can induce a non vanishing phase of particles moving along a closed path on the lattice. This phase is proportional to the enclosed area and we thus simulate a magnetic flux through the lattice. This setup is described by a Hamiltonian identical to the one for electrons on a lattice subject to a magnetic field and thus allows us to study this equivalent situation under very well defined controllable conditions. We consider the limiting case of huge magnetic fields -- which is not experimentally accessible for electrons in metals -- where a fractal band structure, the Hofstadter butterfly, characterizes the system.Comment: 6 pages, RevTe

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

Quantum statistics of atoms in microstructures

This paper proposes groove-like potential structures for the observation of quantum information processing by trapped particles. As an illustration the effect of quantum statistics at a 50-50 beam splitter is investigated. For non-interacting particles we regain the results known from photon experiments, but we have found that particle interactions destroy the perfect bosonic correlations. Fermions avoid each other due to the exclusion principle and hence they are far less sensitive to particle interactions. For bosons, the behavior can be explained with simple analytic considerations which predict a certain amount of universality. This is verified by detailed numerical calculations.Comment: 18 pages incl. 13 figure

Sound and Heat Absorption by a 2D Electron Gas in an Odd-Integer Quantized-Hall Regime

The absorption of bulk acoustic phonons in a two-dimensional (2D) GaAs/AlGaAs heterostructure is studied (in the clean limit) where the 2D electron-gas (2DEG), being in an odd-integer quantum-Hall state, is in fact a spin dielectric. Of the two channels of phonon absorption associated with excitation of spin waves, one, which is due to the spin-orbit (SO) coupling of electrons, involves a change of the spin state of the system and the other does not. We show that the phonon-absorption rate corresponding to the former channel (in the paper designated as the second absorption channel) is finite at zero temperature ($T$), whereas that corresponding to the latter (designated as the first channel) vanishes for $T\to 0$. The long-wavelength limit, being the special case of the first absorption channel, corresponds to sound (bulk and surface) attenuation by the 2DEG. At the same time, the ballistic phonon propagation and heat absorption are determined by both channels. The 2DEG overheat and the attendant spin-state change are found under the conditions of permanent nonequilibrium phonon pumping.Comment: 26 pages, 2 figure

Acoustoelectric effects in quantum constrictions

A dc current induced in a quantum constriction by a traveling acoustic wave (or by non-equilibrium ballistic phonons) is considered. We show that in many important situations the effect is originated from acoustically-induced scattering between the propagating and reflecting states in the constriction. Two particular regimes corresponding to relatively high and low acoustic frequencies are discussed. In the first regime, the acoustoelectric effect in a smooth constriction can be understood by semi-classical considerations based on local conservation laws. For the low frequency regime, we show that the acousto-conductance is closely related to the zero field conductance. The qualitative considerations are confirmed by numerical calculations both for smooth and abrupt channels.Comment: 10 pages, RevTeX, 9 postscript figures, submitted to Phys. Rev.