Atomtronics focuses on atom analogs of electronic materials, devices and circuits. A strongly interacting ultracold Bose gas in a lattice potential is analogous to electrons in solid-state crystalline media. As a consequence of the band structure, cold atoms in a lattice can exhibit insulator or conductor properties. P-type and N-type material analogs can be created by introducing impurity sites into the lattice. Current through an atomtronic wire is generated by connecting the wire to an atomtronic battery which maintains the two contacts at different chemical potentials. The design of an atomtronic diode with a strongly asymmetric current-voltage curve exploits the existence of superfluid and insulating regimes in the phase diagram. The atomtronic analog of a bipolar junction transistor exhibits large negative gain. Our results provide the building blocks for more advanced atomtronic devices and circuits such as amplifiers, oscillators and fundamental logic gates.

The hydrodynamic equations of superfluids for a weakly interacting Bose gas are generalized to include the effects of periodic optical potentials produced by stationary laser beams. The new equations are characterized by a renormalized interaction coupling constant and by an effective mass accounting for the inertia of the system along the laser direction. For large laser intensities the effective mass is directly related to the tunneling rate between two consecutive wells. The predictions for the frequencies of the collective modes of a condensate confined by a magnetic harmonic trap are discussed for both 1D and 2D optical lattices and compared with recent experimental data.The experimental realization of optical lattices [1-6] is stimulating new perpectives in the study of coherence phenomena in trapped Bose-Einstein condensates. A first direct measurement of the critical Josephson current has been recently obtained in [3] by studying the center of mass motion of a magnetically trapped gas in the presence of a 1D periodic optical potential. Under these conditions the propagation of collective modes is a genuine quantum effect produced by the tunneling through the barriers and by the superfluid behaviour associated with the coherence of the order parameter between different wells. The effect of the optical potential is to increase the inertia of the gas along the direction of the laser giving rise to a reduction of the frequency of the oscillation.The purpose of the present work is to investigate the collective oscillations of a magnetically trapped gas in the presence of 1D and 2D optical lattices taking into account the effect of tunneling, the role of the mean field interaction and the 3D nature of the sample. Under suitable conditions these effects can be described by properly generalizing the hydrodynamic equations of superfluids [7].Let us assume that the gas, at T = 0, be trapped by an external potential given by the sum of a harmonic trap of magnetic origin V ho and of a stationary optical potential V opt modulated along the z-axis. The resulting potential is given bywhere ω x , ω y , ω z are the frequencies of the harmonic trap, q = 2π/λ is fixed by the wavelength of the laser light creating the stationary 1D lattice wave, E R =h 2 q 2 /2m is the so called recoil energy and s is a dimensionless parameter providing the intensity of the laser beam. The optical potential has periodicity d = π/q = λ/2 along the z-axis. The case of a 2D lattice will be discussed later. In the following we will assume that the laser intensity be large enough to create many separated wells giving rise to an array of several condensates. Still, due to quantum tunneling, the overlap between the wave functions of two consecutive wells can be sufficient to ensure full coherence. In this case one is allowed to use the GrossPitaevskii (GP) theory for the order parameter to study both the equilibrium and the dynamic behaviour of the system at zero temperature [8]. Eventually, if the tunnelling becomes too small, the fluctuations of...

We study the response of a Bose-Einstein condensate to a periodic modulation of the depth of an optical lattice. Using Gross-Pitaevskii theory, we show that a modulation at frequency Ω drives the parametric excitation of Bogoliubov modes with frequency Ω/2. The ensuing nonlinear dynamics leads to a rapid broadening of the momentum distribution and a consequent large increase of the condensate size after free expansion. We show that this process does not require the presence of a large condensate depletion. Our results reproduce the main features of the spectrum measured in the superfluid phase by Stöferle et al., Phys. Rev. Lett. 92, 130403 (2004).

Using the Kubo formalism, we demonstrate fractional quantum Hall features in a rotating Bose-Einstein condensate in a co-rotating two-dimensional optical lattice. The co-rotating lattice and trap potential allow for an effective magnetic field and compensation of the centrifugal potential. Fractional quantum Hall features are seen for the single-particle system and for few strongly interacting many-particle systems.Comment: 11 pages, 13 figure