We have fabricated and measured superconducting single-electron transistors with Al leads and Nb islands. At bias voltages below the gap of Nb we observe clear signatures of resonant tunneling of Cooper pairs, and of Coulomb blockade of the subgap currents due to linewidth broadening of the energy levels in the superconducting density of states of Nb. The experimental results are in good agreement with numerical simulations.The single-electron transistor 1 (SET) and its superconducting version is one of the most versatile tools in mesoscopic physics. It has been used for extremely sensitive charge measurements, 2 for the construction of Cooper pair pumps and other adiabatic devices with applications in metrology, 3 and more recently for building up superconducting quantum bits. 4 The IV characteristics of superconducting SETs present the usual features of quasiparticle tunneling (at voltages above 2∆ Nb + 2∆ Al ), Josephson-quasiparticle tunneling (at half of these values), and Josephson effect (around zero bias). These features have been thoroughly investigated by now by many groups and the physics of a charge transport at these bias voltages is well understood. However, at low bias voltages also other transport processes could become important and can alter the performance of Josephson-based devices. In this paper, we study two such processes appearing in our Nb-based SET: Resonant tunneling of Cooper pairs, and transport through states inside the gap of Nb (subgap currents).We have fabricated Al/AlO x /Nb/AlO x /Al single electron transistors using a lithographic technique described elsewhere. 5 Measurements were done using a small dilution refrigerator equipped with well-thermalized and electrically filtered measuring lines. The superconducting gaps obtained for Nb and Al (∆ Nb = 1.4 mV, ∆ Al = 0.2 meV), and also the measured critical temperatures for Nb (T C,Nb ≈ 8.0 − 8.5 K), show that the films are indeed of good quality.At voltages below the gap of Nb, a series of gatedependent resonance peaks appears in the IV characteristics of the SET (Fig. 1). We interpret this as resonant tunneling of Cooper pairs, a transport phenomenon first predicted theoretically and later observed in Al symmetrically-biased superconducting SETs. 6 Below we describe the same process for our Nb-island SETs under the asymmetric bias shown in Fig. 1. We consider a generic process in which a charge δq 1 tunnels through the left junction and a charge δq 2 tunnels through the second junction, both into the island. During the process, a charge δq = δq 1 + δq 2 is transferred into the island and a charge δQ = δq 1 − δq 2 is transferred through the external circuit in the forward direction. The change in the electrostatic free energy (including work done by the sources) associated with this process iswhere q 0 is the initial charge of the island, C 1 and C 2 are the capacitances of the left and right junctions, C g is the gate capacitance, and C Σ = C 1 + C 2 + C g . Resonant Cooper pair tunneling in superconducting SETs occurs when no en...

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We investigate magnetic properties of Mott-insulating phases of ultracold Bose and Fermi spinor gases in optical lattices. We consider in particular the F = 2 Bose gas, and the F = 3/2 and F = 5/2 Fermi gases. We derive effective spin Hamiltonians for one and two atoms per site and discuss the possibilities of manipulating the magnetic properties of the system using optical Feshbach resonances. We discuss low temperature quantum phases of a 87 Rb gas in the F = 2 hyperfine state, as well as possible realizations of high spin Fermi gases with either 6 Li or 132 Cs atoms in the F = 3/2 state, and with 173 Yb atoms in the F = 5/2 state.

We consider a strongly repulsive two-component Fermi gas in a one-dimensional optical lattice described in terms of a Hubbard Hamiltonian. We analyze the response of the system to a periodic modulation of the hopping amplitude in the presence of a large two-body interaction. By (essentially) the exact simulations of the time evolution, we find a nontrivial double occupancy frequency dependence. We show how the dependence relates to the spectral features of the system given by the Bethe ansatz. The discrete nature of the spectrum is clearly reflected in the double occupancy after a long enough modulation time. We also discuss the implications of the 1D results to experiments in higher dimensional systems.

We propose that with ultracold Fermi gases one can realize a spin-asymmetric Josephson effect in which the two spin components of a Cooper pair are driven asymmetrically--corresponding to driving a Josephson junction of two superconductors with different voltages V(↑) and V(↓) for spin up and down electrons, respectively. We predict that the spin up and down components oscillate at the same frequency but with different amplitudes. Furthermore our results reveal that the standard interpretation of the Josephson supercurrent in terms of coherent bosonic pair tunneling is insufficient. We provide an intuitive interpretation of the Josephson supercurrent as interference in Rabi oscillations of pairs and single particles, the latter causing the asymmetry.