Carsten Geckeler

Directed Transport of Atoms in a Hamiltonian Quantum Ratchet

Moving Cold Atoms with Quantum Ratchets The nanoscale dimensions of biological motors make them susceptible to thermal noise, but such motors can produce force in one direction by alternating application of an asymmetric potential, or ratchet, with periods of thermal drift in the motion. The quantum version of such motors can operate without dissipation, as long as there is some means to break time-reversal symmetry in the system. Salger et al. (p. 1241) report on a coherent quantum ratchet device consisting of Bose-Einstein condensate cold atoms placed into an asymmetric sawtooth-potential created by optical lattices. Symmetry breaking was accomplished by phase shifts in the driving potentials. As expected for such a quantum ratchet, the current depended on the initial phase of the driving potential. A quantum ratchet, which operates without dissipation, is created with a Bose-Einstein condensate and optical potentials. Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential.

Atomic Landau-Zener Tunneling in Fourier-Synthesized Optical Lattices

We report on an experimental study of quantum transport of atoms in variable periodic optical potentials. The band structure of both ratchet-type asymmetric and symmetric lattice potentials is explored. The variable atom potential is realized by superimposing a conventional standing wave potential of lambda/2 spatial periodicity with a fourth-order multiphoton potential of lambda/4 periodicity. We find that the Landau-Zener tunneling rate between the first and the second excited Bloch band depends critically on the relative phase between the two spatial lattice harmonics.

Fourier synthesis of optical potentials for atomic quantum gases

We demonstrate a scheme for the Fourier synthesis of periodic optical potentials with asymmetric unit cells for atoms. In a proof of principle experiment, an atomic Bose-Einstein condensate is exposed to either symmetric or sawtooth-like asymmetric potentials by superimposing a conventional standing wave potential of {lambda}/2 spatial periodicity with a fourth-order lattice potential of {lambda}/4 periodicity. The high periodicity lattice is realized using dispersive properties of multiphoton Raman transitions. Future applications of the demonstrated scheme could range from the search for novel quantum phases in unconventionally shaped lattice potentials up to dissipationless atomic quantum ratchets.

Bose–Einstein condensation in a CO2-laser optical dipole trap

We report the achievement of Bose–Einstein condensation of a dilute atomic gas based on trapping atoms in tightly confining CO2-laser dipole potentials. Quantum degeneracy of rubidium atoms is reached by direct evaporative cooling in both crossed- and single-beam trapping geometries. At the heart of these all-optical condensation experiments is the ability to obtain high initial atomic densities in quasi-static dipole traps by laser-cooling techniques. Finally, we demonstrate the formation of a condensate in a field-insensitive mF=0 spin projection only, which suppresses fluctuations of the chemical potential from stray magnetic fields.

Bose-Einstein Condensation in a CO_2-laser Optical Dipole Trap

We report the achievement of Bose–Einstein condensation of a dilute atomic gas based on trapping atoms in tightly confining CO2-laser dipole potentials. Quantum degeneracy of rubidium atoms is reached by direct evaporative cooling in both crossed- and single-beam trapping geometries. At the heart of these all-optical condensation experiments is the ability to obtain high initial atomic densities in quasi-static dipole traps by laser-cooling techniques. Finally, we demonstrate the formation of a condensate in a field-insensitive mF=0 spin projection only, which suppresses fluctuations of the chemical potential from stray magnetic fields.

Interference of a variable number of coherent atomic sources

We have studied the interference of a variable number of independently created m{sub F}=0 microcondensates in a CO{sub 2}-laser optical lattice. The observed average interference contrast decreases with condensate number N. Our experimental results agree well with the predictions of a random walk model. While the exact result can be given in terms of Kluyvers formula, for a large number of sources a 1/{radical}(N) scaling of the average fringe contrast is obtained. This scaling law is found to be of more general applicability when quantifying the decay of coherence of an ensemble with N independently phased sources.

Interference of an array of atom lasers

We report on the observation of interference of a series of atom lasers. A comblike array of atomic beams is generated by outcoupling atoms from distinct Bose-Einstein condensates confined in the different sites of a mesoscopic optical lattice. The observed interference signal arises from the spatial beating of the overlapped atom laser beams, which is monitored over a range corresponding to

Atomic Bose-Einstein Condensates in Optical Lattices with Variable Spatial Symmetry

2\phantom{\rule{0.3em}{0ex}}\mathrm{ms}

Phase-dependent Landau-Zener effect in asymmetric optical lattices

of freefall time. The relative de Broglie frequencies and phases of the atom lasers were measured.

All-optical realization of an atom laser

Optical lattices for atomic Bose-Einstein condensates raised enormous interest, as they mirror features known from solid state physics to the field of atom optics. In perfect solid state crystals atoms are arranged in a regular array creating a periodic potential for the electrons inside. Felix Bloch was one of the first who investigated in his dissertation (1928) the quantum mechanics of individual electrons in such crystalline solids. In the independent electron approximation interatomic and interelectronic interactions are neglected. Each electron obeys the one electron Schrodinger equation with a periodic potential V (x + a) = V(x) with period a. According to Bloch’s theorem the stationary eigenstates ψ n,q (r) are plane waves modulated by a periodic function revealing the periodicity of the atom lattice [1]. With proper periodicity and boundary conditions the eigenstates are quantized, characterized by the band index n = 0, 1,…. The plane waves propagate in the direction of the wave vector q with the associated quasimomentum ħq, which it is sometimes referred to as the crystal or lattice momentum. The energy levels E n (q) are periodic continuous functions of the wave vector q forming the energy bands. Pictures of the energy bands showing the bandstructure are conventionally restricted the first Brillouin-zone of the reciprocal lattice −ħk ≤ q ≤ ħk. One milestone of Bloch theory and the band structure of particles is the finding of a natural physical explanation of the some 20 orders of magnitude difference in electrical conductivity between an insulator and a good conductor [2].