Orbital physics of polar Fermi molecules

We study a system of polar dipolar fermions in a two-dimensional optical lattice and show that multi-band Fermi-Hubbard model is necessary to discuss such system. By taking into account both on-site, and long-range interactions between different bands, as well as occupation-dependent inter- and intra-band tunneling, we predict appearance of novel phases in the strongly-interacting limit

Many body population trapping in ultracold dipolar gases

A system of interacting dipoles is of paramount importance for understanding of many-body physics. The interaction between dipoles is {\it anisotropic} and {\it long-range}. While the former allows to observe rich effects due to different geometries of the system, long-range ($1/r^3$) interactions lead to strong correlations between dipoles and frustration. In effect, interacting dipoles in a lattice form a paradigmatic system with strong correlations and exotic properties with possible applications in quantum information technologies, and as quantum simulators of condensed matter physics, material science, etc. Notably, such a system is extremely difficult to model due to a proliferation of interaction induced multi-band excitations for sufficiently strong dipole-dipole interactions. In this article we develop a consistent theoretical model of interacting polar molecules in a lattice by applying the concepts and ideas of ionization theory which allows us to include highly excited Bloch bands. Additionally, by involving concepts from quantum optics (population trapping), we show that one can induce frustration and engineer exotic states, such as Majumdar-Ghosh state, or vector-chiral states in such a system.Comment: many interesting page

Coupling nanomechanical cantilevers to dipolar molecules

We investigate the coupling of a nanomechanical oscillator in the quantum regime with molecular (electric) dipoles. We find theoretically that the cantilever can produce single-mode squeezing of the center-of-mass motion of an isolated trapped molecule and two-mode squeezing of the phonons of an array of molecules. This work opens up the possibility of manipulating dipolar crystals, which have been recently proposed as quantum memory, and more generally, is indicative of the promise of nanoscale cantilevers for the quantum detection and control of atomic and molecular systems.Comment: 3 figures, 4page

EQUILIBRIUM AGENDA FORMATION

We develop a definition of equilibrium for agenda formation in general voting settings. The definition is independent of any protocol. We show that the set of equilibrium outcomes for any Pareto efficient voting rule is uniquely determined. We also show that for such voting rules, if preferences are strict then the set of equilibrium outcomes coincides with that of the outcomes generated by considering all full agendas for voting by successive elimination and show that the set of equilibrium outcomes corresponds with the Banks set. We also examine the implications in several other settings.Agenda ; Equilibrium ; Voting

Equilibrium Agenda Formation

We develop a definition of equilibrium for agenda formation in general voting settings. The definition is independent of any protocol. We show that the set of equilibrium outcomes for any Pareto efficient voting rule is uniquely determined, and in fact coincides with that of the outcomes generated by considering all full agendas. Under voting by successive elimination (or amendment), the set of equilibrium outcomes corresponds with the Banks set. We also examine the implications in several specific settings and show that studying equilibrium agendas can lead to sharp predictions, in contrast with well-known ``chaos'' theorems.agenda, equilibrium, voting, agenda formation