Negative absolute temperatures for mobile particles

Absolute temperature, that is the fundamental temperature scale in thermodynamics, is usually bound to be positive. Under special con- ditions, however, negative temperatures - where high-energy states are more occupied than low-energy states - are also possible. In this talk, I will present a negative temperature state for motional degrees of freedom: By tailoring the Bose-Hubbard Hamiltonian we exper- imentally created an attractively interacting ensemble of ultracold bosons, which is stable against collapse for arbitrary atom numbers. In this negative temperature state, the quasi-momentum distribu- tion develops sharp peaks at the upper band edge, revealing thermal equilibrium and bosonic coherence over several lattice sites. Nega- tive temperatures imply negative pressures and open up new param- eter regimes for cold atoms, enabling fundamentally new many-body states and counterintuitive effects such as Carnot engines above unity efficiency. In addition, this system enabled us to study the dynam- ics of the phase transition from Mott insulator to superfluid and to experimentally investigate how fast phase coherence can spread.