So you thought absolute zero was absolute zero, huh?

No. Entropy is S = log of the number of microstates. Temperature is 1/T = dS/dE. We are used to living in an open system, where only absolute zero has a single microstate. In a closed system at the maximum amount of energy, there is also only one microstate, so it entropy and temperature is zero. Drop the energy slightly, more microstates are available, and dS/dE is negative, leading to a negative temperature.

Bear in mind, it's been a long time since undergraduate level statistical mechanics. I may have the details wrong. But this title sounds like needlessly taunting. The actual title is simply "A temperature below absolute zero".

What's new about this work is "We have thus created the first negative absolute temperature state for moving particles". Previous negative temperatures were seen in things like spin-systems.

I would suggest the title "Moving particles with negative temperature".