We examine interactions between atoms continuously and coherently driven between the ground state and a Rydberg state, producing ``Rydberg-dressed atoms.'' Because of the large dipolar coupling between two Rydberg atoms, a small admixture of Rydberg character into a ground state can produce an atom with a dipole moment of a few debye, the appropriate size to observe interesting dipolar physics effects in cold atom systems. We have calculated the interaction energies for atoms that interact via the dipole-dipole interaction and find that because of blockade effects, the
R dependent two-atom interaction terms are limited in size and can be
R independent up until the dipolar energy is equal to the detuning. This produces
R dependent interactions different from the expected
1/R3 dipolar form that have no direct analogy in condensed-matter physics and could lead to interesting quantum phases in trapped Rydberg systems.
Hysteresis can be found in driven many-body systems such as magnets and superfluids. Rate-dependent hysteresis arises when a system is driven periodically while relaxing towards equilibrium. A two-state paramagnet driven by an oscillating magnetic field in the relaxation approximation clearly demonstrates rate-dependent hysteresis. A noninteracting atomic Fermi gas in an optical ring potential, when driven by a periodic artificial gauge field and subjected to dissipation, is shown to exhibit hysteresis loops of atomic current due to a competition of the driving time and the relaxation time. This is in contrast to electronic systems exhibiting equilibrium persistent current driven by magnetic flux due to rapid relaxation. Universal behavior of the dissipated energy in one hysteresis loop is observed in both magnetic and atomic systems, showing linear and inverse-linear dependence on the relaxation time in the strong and weak dissipation regimes. While interactions in general invalidate the framework for rate-dependent hysteresis, an atomic Fermi gas with artificial spin-orbit coupling can exhibit hysteresis loops of atomic currents. Cold atoms in ring-shape potentials are thus promising for demonstrating rate-dependent hysteresis and its associated phenomena.
We study a two-leg fermionic Hubbard ladder model with a state-dependent hopping. We find that, contrary to the case without a state-dependent hopping, for which the system has a superfluid nature regardless of the sign of the interaction at incommensurate filling, in the presence of such a hopping a spin-triplet superfluid, spin-density wave, and charge-density wave phases emerge. We examine our results in the light of recent experiments on periodically driven optical lattices in cold atoms. We give protocols allowing us to realize the spin-triplet superfluid elusive in the cold atoms.