Abstract
Absolute temperature, the fundamental temperature scale in thermodynamics, is
usually bound to be positive. Under special conditions, however, negative
temperatures - where high-energy states are more occupied than low-energy
states - are also possible. So far, such states have been demonstrated in
localized systems with finite, discrete spectra. Here, we were able to prepare
a negative temperature state for motional degrees of freedom. By tailoring the
Bose-Hubbard Hamiltonian we created an attractively interacting ensemble of
ultracold bosons at negative temperature that is stable against collapse for
arbitrary atom numbers. The quasi-momentum distribution develops sharp peaks at
the upper band edge, revealing thermal equilibrium and bosonic coherence over
several lattice sites. Negative temperatures imply negative pressures and open
up new parameter regimes for cold atoms, enabling fundamentally new many-body
states and counterintuitive effects such as Carnot engines above unity
efficiency.
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