Tobias Salger

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.

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.

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.

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.