Synergy between the negative absolute temperature and the external trap for a Bose-Einstein condensate under optical lattices

Abstract

We provide a generic but exact analytical model for realizing negative absolute temperature in ultracold atoms under a quasi-periodic optical lattice (bi-chromatic) and an expulsive trap. We keep freedom for maximum tunability for both kinds of trap profile, where bi-chromatic lattice is quasi-periodic except two tunable limits, from a pure optical lattice to another doubly periodic optical lattice. The expulsive trap can be tuned from zero to a stronger one. All the required conditions for achieving negative temperature domain have been explored by identifying appropriate trap parameters. Condensate density in each lattice site is controlled and Anderson-like localization is emphasized. A thorough study of a quantitative estimate of the temperature is performed in the negative domain by controlling the trap, where the roles of all the trap parameters are precisely identified. A numerical stability analysis by Fourier split-step method makes the study more useful and the proposed family of solution are found quite stable. This is also connected to the merit of negative temperature through mean deviation data with varied trap parameters.