Temperature is casually associated with hot and cold. How can something be “colder” than absolute zero? The answer lies in a more precise notion of temperature. Temperature is a single-parameter curve fit to a probability distribution. Given a large number of particles, we can say each of them has a probability to have some energy, P(E). Most will be in low-energy states and a few in higher-energy states. This probability distribution can be fit very well with an exponential falling away to zero. Of course, the actual distribution may be very noisy, but an exponential fit is still a good approximation (see the figure, panel A). Negative temperature means most particles are in a high-energy state, with a few in a low-energy state, so that the exponential rises instead of falls (see the figure, panel E).

To create negative temperature, Braun et al. had to produce an upper bound in energy, so particles could pile up in high-energy rather than low-energy states. In their experiment, there are three important kinds of energy: kinetic energy, or the energy of motion in the optical lattice; potential energy, due to magnetic fields trapping the gas; and interaction energy, due to interactions between the atoms in their gas. The lattice naturally gives an upper bound to kinetic energy via the formation of a band gap, a sort of energetic barrier to higher-energy states. The potential energy was made negative by the clever use of an anti-trap on top of the lattice, taking the shape of an upside-down parabola. Finally, the interactions were tuned to be attractive (negative). Thus, all three energies had an upper bound and, in principle, the atoms could pile up in high-energy states.

It's not a very important question that if we should stop calling absolute zero by it's current name. It's just a name, and misleading though it may be for works such as those mentioned, it is the general case.

More info:

http://www.sciencemag.org/content/339/6115/42.full

http://www.sciencemag.org/content/339/6115/52

Temperature is casually associated with hot and cold. How can something be “colder” than absolute zero? The answer lies in a more precise notion of temperature. Temperature is a single-parameter curve fit to a probability distribution. Given a large number of particles, we can say each of them has a probability to have some energy, P(E). Most will be in low-energy states and a few in higher-energy states. This probability distribution can be fit very well with an exponential falling away to zero. Of course, the actual distribution may be very noisy, but an exponential fit is still a good approximation (see the figure, panel A). Negative temperature means most particles are in a high-energy state, with a few in a low-energy state, so that the exponential rises instead of falls (see the figure, panel E).

To create negative temperature, Braun et al. had to produce an upper bound in energy, so particles could pile up in high-energy rather than low-energy states. In their experiment, there are three important kinds of energy: kinetic energy, or the energy of motion in the optical lattice; potential energy, due to magnetic fields trapping the gas; and interaction energy, due to interactions between the atoms in their gas. The lattice naturally gives an upper bound to kinetic energy via the formation of a band gap, a sort of energetic barrier to higher-energy states. The potential energy was made negative by the clever use of an anti-trap on top of the lattice, taking the shape of an upside-down parabola. Finally, the interactions were tuned to be attractive (negative). Thus, all three energies had an upper bound and, in principle, the atoms could pile up in high-energy states.

It's not a very important question that if we should stop calling absolute zero by it's current name. It's just a name, and misleading though it may be for works such as those mentioned, it is the general case. Quite like most engineering books which contain circuit diagrams with positive charges moving! That is quite obscene, but it's what they call convention.

More info:

http://www.sciencemag.org/content/339/6115/42.full

http://www.sciencemag.org/content/339/6115/52