Negative Absolute Temperature for Motional Degrees of Freedom
Negative Is Hotter A common-sense perception of temperature tells us that the lower the temperature, the colder it is. However, below absolute zero, there is a netherworld of negative temperatures, which are, counterintuitively, hotter than positive temperatures. Usually, such states are achieved in the laboratory and are characterized by a higher occupation of high-energy versus low-energy states. This is most easily done for systems that have a finite spectrum of energy states, bounded from above and below. Braun et al. (p. 52; see the Perspective by Carr) achieved negative temperature for a system in which its spectrum was only bounded on one side. Starting with a gas of 39K bosonic atoms with repulsive interactions in a dipole trap and an optical lattice, a final state with negative temperature was reached where the atoms attract each other. A gas of potassium atoms in an optical lattice displays an inverted population of energy levels. Absolute temperature is usually bound to be positive. Under special conditions, however, negative temperatures—in which high-energy states are more occupied than low-energy states—are also possible. Such states have been demonstrated in localized systems with finite, discrete spectra. Here, we prepared 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 quasimomentum 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.