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.

We study the Feshbach resonance assisted stimulated adiabatic passage of an effective coupling field for creating stable molecules from atomic Bose condensate. By exploring the properties of the coherent population trapping state, we show that, contrary to the previous belief, mean-field shifts need not to limit the conversion efficiency as long as one chooses an adiabatic passage route that compensates the collision mean-field phase shifts and avoids the dynamical unstable regime.PACS numbers: 03.75. Mn, 05.30.Jp, 32.80.Qk Molecules offer a whole new dimension in the study of ultracold atomic physics. In particular, resonant photo-or magneto-association (Feshbach resonance [1]) of cold atoms to molecules represents a matter-wave analog of second harmonic generation and has become a new paradigm of coupled macroscopic quantum systems. Due to energy conservation, such processes generally produce molecules in a vibrationally and/or electronically excited quasibound level and hence are not energetically stable. This does not seem to be a serious problem in the case of fermionic atoms due to the suppression of molecular decay by Pauli blocking. In fact, several groups have now successfully Bose condensed so-formed molecules [2]. In contrast, although evidence of macroscopic coherence has been observed in several experiments, excited molecules formed by a pair of bosonic atoms have very short lifetime ( a few ms) and the atom-molecule conversion efficiency is limited to 10% [3,4]. Hence it is very important to be able to create deeply-bound ground state molecules from atomic Bose condensates with high efficiency, which is the focus of the current work.First proposed for photoassociating nondegenerate atoms into stable molecules [7], stimulated Raman adiabatic passage (STIRAP) aided by Feshbach resonance is considered a more efficient way of converting atomic condensates into molecular ones [5,6] than the bare STI-RAP implementation of photoassociation [7,8]. In this scheme, the free atomic, the quasibound and the ground molecular states form the three-level Λ-system to which STIRAP can apply [10]. The success of STIRAP relies on the existence of the coherent population trapping (CPT) state [9]. In a linear Λ-system, the CPT state exists when the two-photon resonance condition is satisfied, hence STIRAP can be straightforwardly implemented by appropriately choosing the laser frequencies. In the case of condensate, collisions between particles give rise to nonlinear mean-field shifts which dynamically changes when population is transferred from atomic state to molecular state. This poses a serious problem for STIRAP as collisions shift the system out of the two-photon resonance. For typical experimental parameters, a conversion efficiency of only ∼ 20% is predicted with a somewhat complicated laser sequence containing seven Raman pulses [5]. A possible remedy is to use a low-density atomic condensate where the effect of collisions can be minimized [11]. This, however, creates new problems as stronger coupling fields...

The full set of stationary states of the mean field of a Bose-Einstein condensate in the presence of a potential step or point-like impurity are presented in closed analytic form. The nonlinear Schrödinger equation in one dimension is taken as a model. The nonlinear analogs of the continuum of stationary scattering states, as well as evanescent waves, are discussed. The solutions include asymmetric soliton trains and other wavefunctions of novel form, such as a pair of dark solitons bound by an impurity.

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Bose gases in rotating optical lattices combine two important topics in quantum physics: superfluid rotation and strong correlations. In this paper, we examine square two-dimensional systems at zero temperature comprised of strongly repulsive bosons with filling factors of up to one atom per lattice site. The entry of vortices into the system is characterized by jumps of 2 in the phase winding of the condensate wave function. A lattice of size L ϫ L can have at most L − 1 quantized vortices in the lowest Bloch band. In contrast to homogeneous systems, angular momentum is not a good quantum number since the continuous rotational symmetry is broken by the lattice. Instead, a quasiangular momentum captures the discrete rotational symmetry of the system. Energy level crossings indicative of quantum phase transitions are observed when the quasiangular momentum of the ground state changes.

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The band structure of a Bose-Einstein condensate is studied for lattice traps of sinusoidal, Jacobi elliptic, and Kronig-Penney form, all in the context of the nonlinear Schrödinger equation. It is demonstrated that the physical properties of the system are independent of the type of lattice. The Kronig-Penney potential, which admits a full exact solution in closed analytical form, is then used to understand the swallowtails, or loops, that form in the band structure. The appearance of swallowtails is explained by adiabatically tuning a second lattice with half the period. Such a two-color lattice, which can be easily realized in experiments, has intriguing physical properties. For instance, swallowtails appear even for weak nonlinearity, which is the experimental regime. We determine the stability properties of this system and relate them to current experiments.

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