Sebastian Kling

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.

Klein tunneling of a quasirelativistic Bose-Einstein condensate in an optical lattice.

A proof-of-principle experiment simulating effects predicted by relativistic wave equations with ultracold atoms in a bichromatic optical lattice that allows for a tailoring of the dispersion relation is reported. We observe the analog of Klein tunneling, the penetration of relativistic particles through a potential barrier without the exponential damping that is characteristic for nonrelativistic quantum tunneling. Both linear (relativistic) and quadratic (nonrelativistic) dispersion relations are investigated, and significant barrier transmission is observed only for the relativistic case.

Thermodynamical properties of a rotating ideal Bose gas

In a recent experiment, a Bose-Einstein condensate was trapped in an anharmonic potential that is well approximated by a harmonic and a quartic part. The condensate was set into such a fast rotation that the centrifugal force in the corotating frame overcompensates the harmonic part in the plane perpendicular to the rotation axis. Thus, the resulting trap potential becomes sombrero shaped. We present an analysis for an ideal Bose gas that is confined in such an anharmonic rotating trap within a semiclassical approximation, where we calculate the critical temperature, the condensate fraction, and the heat capacity. In particular, we examine in detail how these thermodynamical quantities depend on the rotation frequency.

Effective Dirac dynamics of ultracold atoms in bichromatic optical lattices

We study the dynamics of ultracold atoms in tailored bichromatic optical lattices. By tuning the lattice parameters, one can readily engineer the band structure and realize a Dirac point, i.e., a true crossing of two Bloch bands. The dynamics in the vicinity of such a crossing is described by the one-dimensional Dirac equation, which is rigorously shown beyond the tight-binding approximation. Within this framework we analyze the effects of an external potential and demonstrate numerically that it is possible to demonstrate Klein tunneling with current experimental setups.

Dynamical properties of a rotating Bose-Einstein condensate

Within a variational approach to solving the Gross-Pitaevskii equation we investigate dynamical properties of a rotating Bose-Einstein condensate confined in an anharmonic trap. In particular, we calculate the eigenfrequencies of low-energy excitations out of the equilibrium state and the aspect ratio of the condensate widths during the free expansion.

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

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].

Directed transport of ultracold atoms in a Hamiltonian quantum ratchet

We report on the successful experimental realization of a quantum ratchet for ultracold atoms in a driven spatially asymmetric optical lattice. Ratchets are usually considered as a tool, which rectify an otherwise undirected, for instance oscillating or fluctuating, motion of particles or objects. In order to observe a directed transport of atoms one has to break the space-time symmetry of the system [1–3]. Here, we report on the realization of a quantum ratchet in the absence of dissipative processes (Hamiltonian regime) within the interaction time.

Phase-dependent Landau-Zener effect in asymmetric optical lattices

We report experimental results on transport properties of Bose-Einstein condensates in periodic optical potentials of variable asymmetry. By studying the Landau-Zener effect and Bloch oscillations, we have explored the band structure of both ratchet-type asymmetric and symmetric optical potentials.