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.
Temperature depends on the energy landscape (Image: Ludwig Maximilian University of Munich)
According to temperature's entropic definition, the highest positive temperature possible corresponds to the most disordered state of the system. This would be an equal number of particles at every point on the landscape. Increase the energy any further and you'd start to lower the entropy again, because the particles wouldn't be evenly spread. As a result, this point represents the end of the positive temperature scale.
In principle, though, it should be possible to keep heating the particles up, while driving their entropy down. Because this breaks the energy-entropy correlation, it marks the start of the negative temperature scale, where the distribution of energies is reversed – instead of most particles having a low energy and a few having a high, most have a high energy and just a few have a low energy. The end of this negative scale is reached when all particles are at the top of the energy hill.
To enter the negative realm, Schneider and his colleagues began by cooling atoms to a fraction above absolute zero and placing them in a vacuum. They then used lasers to place the atoms along the curve of an energy valley with the majority of the atoms in lower energy states. The atoms were also made to repel each other to ensure they remained fixed in place.
Schneider's team then turned this positive temperature system negative by doing two things. They made the atoms attract and adjusted the lasers to change the atoms' energy levels, making the majority of them high-energy, and so flipping the valley into an energy hill. The result was an inverse energy distribution, which is characteristic of negative temperatures.
The atoms can't lose energy and "roll down" this hill because doing so would require them to increase their kinetic energy and this is not possible because the system is in a vacuum and there is no outside energy source. "We create a system with a lot of energy, but the particles cannot redistribute their energy so they have to stay on top of the hill," says Schneider.
The new negative temperature set-up could be used to create simulated interactions that are not possible with positive temperatures. "They are a new technical tool in the business of quantum simulations," says Schneider.
Negative temperature may also have implications for cosmology. Dark energy, thought to explain the accelerating expansion of the universe, exerts negative pressure, which suggests it might have negative temperature – Schneider is currently discussing the idea with cosmologists.
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