### Description

Negative absolute temperature entails a situation where the entropy of a system reduces as the internal energy increases. As the idea was put forward by N. Ramsey in the 1950s [1], the concept of negative absolute temperature has been actively discussed, and has led to the eventual observation with cold atoms in a square lattice [2]. In this poster, we describe our experiment with K(39) atoms on the observation of negative absolute temperature in a triangular optical lattice — a non-bipartite lattice containing geometric frustration. Due to its non-bipartite nature, the lowest energy band of a triangular lattice hosts two non-equivalent highest-energy points ($K$ and $K'$ points in Fig. 1(a)) that are not connected via a reciprocal lattice vector. We study the influence of these non-equivalent points by comparing positive and negative temperature states in this lattice. In Fig. 1(b), atoms in negative absolute temperature state are shown in the superfluid state where the atoms occupy the two highest energy points equally.

**Figure 1**: (a) The band structure of the first band for a triangular optical lattice. The inequivalent energy maxima are located at the $K$ and $K'$ points while the minimum of the energy is at the $\Gamma$ point. (b) The measured optical density after an 11 ms time-of-flight, of a negative temperature gas. The region enclosed by the black thin lines represents the first Brillouin zone.

Moreover, we have created a phase-stabilized optical Kagome lattice by superimposing a 532-nm triangular lattice and a 1064-nm honeycomb lattice. We have also observed the superfluid to Mott insulator transition in the Kagome lattice.

**References**:

[1] N.F. Ramsey “Thermodynamics and statistical mechanics at negative absolute Temperatures” Phys. Rev. **103**, 20 (1956).

[2] S. Braun, J.P. Ronzheimer, M. Schreiber, S.S. Hodgman, T. Rom, I. Bloch, and U. Schneider “Negative absolute temperature for motional degrees of freedom” Science **339**, 53 (2013).

Presenter name | Mehedi Hasan |
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