There exists nothing as negative temperature (in Kelvin scale), at least not in ‘normal’ systems; this is something we learn in physics. This is a scale devised by Lord Kelvin (and hence the name of the unit) and according to this scale, there can be no negative value of temperature. Temperature was thought to be the measure of the energy of the particles in a system. While this isn’t untrue, the modern definition of temperature is broader.
For a system with energy levels, temperature is a measure of the probability of the occupation of an energy level with respect to energy. As we access more and more energetic states, the probability of occupation generally decreases and this leads to a positive temperature state. Now, imagine a system having the reverse configuration, like the higher energy states being more populated than the lower energy states. This kind of system will then have a negative temperature.
Try and note that negative temperature states are extremely rare and do not occur in our day-to-day lives. Particles will always like to occupy the lower energy states first and then go for the higher energy ones. In a room of air, you’ll always find more molecules with very low energies than molecules with very high energies. This is because the energy has a lower limit, viz E=0. The lowest energy possible is if the molecule were completely static. However, there is no upper limit.
But if you did have an upper limit, things would be interesting! Say there is an upper limit of the energy spectrum, meaning that no particle can have any energy beyond this limit (just like no particle could go below the lower limit). Now, under certain conditions, the system would occupy the upper energy levels more than the lower ones! This causes an inversion of the sign of temperature, according to the modern definition. Thus, we have negative temperature!
So what’s the big deal, you ask? Negative temperatures have been known for magnetic systems (which have an upper and a lower limit), but we haven’t known of any system with motional degrees of freedom (like an atom free to move in 3 dimensions) to have such an energy spectrum.
Ulrich Schneider, a physicist at the Ludwig Maximilian University in Munich, Germany and his team created an ultra-cold quantum gas made up of potassium atoms and they confined these atoms to a lattice (i.e. a crystal like arrangement). At positive temperatures, the atoms repelled each other, but the team was able to flip the magnetic field fast enough for the atoms to start attracting each other. This also flips the sign of the temperature. Explains Prof. Schneider:
This suddenly shifts the atoms from their most stable, lowest-energy state to the highest possible energy state, before they can react. It’s like walking through a valley, then instantly finding yourself on the mountain peak.
The temperature measured was a billionths of a degree below absolute zero! Wolfgang Ketterle, Nobel Laureate, called this an ‘experimental Tour de Force’. It truly is!
Link to paper in Nature: doi:10.1038/nature.2013.12146