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Center for Nonlinear Studies |
We investigate a quasi-2D BEC of polar molecules in an external field by explicitly incorpo- rating the internal states of the molecules. Within a two-state approximation, we develop a set of two coupled non-linear Schr¨ odinger equations and find the quasi-particle dispersion relations using the Bogoliubov-de Gennes approximation. Using this theory, we can interpo-late between the high-field limit of a fully-polarized gas and the zero-field limit of a perfectly screened, dipolar BEC. In the high-field regime, we reproduce the known results of a roton instability at large enough densities or interaction strengths. This instability is suppressed by dielectric effects for smaller applied fields, but there is a further instability that we interpret as a dielectric instability, where the dipoles want to orient themselves anti-parallel to the applied field. To further understand this behavior, we calculate density-density correlation functions via Bogoliubov theory, tracing along the instability threshold. In the fully polarized limit, we reproduce the precursors to crystalline order previously predicted. At zero-field, despite perfect screening, an instability still appears, the nature of which is unclear. Between these limits, we observe in the density-density correlations an up-down separation which possibly indicates spin-waves in the ground state.
Host: Christopher Ticknor