We analyze the interference pattern produced by ultracold atoms released from an optical lattice. Such interference patterns are commonly interpreted as the momentum distributions of the trapped quantum gas. We show that for finite time-of-flights th
e resulting density distribution can, however, be significantly altered, similar to a near-field diffraction regime in optics. We illustrate our findings with a simple model and realistic quantum Monte Carlo simulations for bosonic atoms, and compare the latter to experiments.
We propose a controlled method to create and detect d-wave superfluidity with ultracold fermionic atoms loaded in two-dimensional optical superlattices. Our scheme consists in preparing an array of nearest-neighbor coupled square plaquettes or ``supe
rplaquettes and using them as building blocks to construct a d-wave superfluid state. We describe how to use the coherent dynamical evolution in such a system to experimentally probe the pairing mechanism. We also derive the zero temperature phase diagram of the fermions in a checkerboard lattice (many weakly coupled plaquettes) and show that by tuning the inter-plaquette tunneling spin-dependently or varying the filling factor one can drive the system into a d-wave superfluid phase or a Cooper pair density wave phase. We discuss the use of noise correlation measurements to experimentally probe these phases.
Tunnelling of material particles through a classically impenetrable barrier constitutes one of the hallmark effects of quantum physics. When interactions between the particles compete with their mobility through a tunnel junction, intriguing novel dy
namical behaviour can arise where particles do not tunnel independently. In single-electron or Bloch transistors, for example, the tunnelling of an electron or Cooper pair can be enabled or suppressed by the presence of a second charge carrier due to Coulomb blockade. Here we report on the first direct and time-resolved observation of correlated tunnelling of two interacting atoms through a barrier in a double well potential. We show that for weak interactions between the atoms and dominating tunnel coupling, individual atoms can tunnel independently, similar to the case in a normal Josephson junction. With strong repulsive interactions present, two atoms located on one side of the barrier cannot separate, but are observed to tunnel together as a pair in a second order co-tunnelling process. By recording both the atom position and phase coherence over time, we fully characterize the tunnelling process for a single atom as well as the correlated dynamics of a pair of atoms for weak and strong interactions. In addition, we identify a conditional tunnelling regime, where a single atom can only tunnel in the presence of a second particle, acting as a single atom switch. Our work constitutes the first direct observation of second order tunnelling events with ultracold atoms, which are the dominating dynamical effect in the strongly interacting regime. Similar second-order processes form the basis of superexchange interactions between atoms on neighbouring lattice sites of a periodic potential, a central component of quantum magnetism.
