Negative absolute temperature?

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System at negative absolute temperature
If more particles are at the upper level than at the lower one, absolute temperature of a system is negative

As soon as the high energy level is populated more that the low energy one, we have negative absolute temperature. Can such a state be realised?

Yes, it can, but not by cooling. The formula, as well as the picture, show that a state of matter to which negative absolute temperature can be attributed has more energy than the states at usual temperatures, because more particles are at high energy level than at low energy level. Thus one has to add energy to get negative absolute temperature. It has been emphasized that such states cannot be reached by adding heat to a body.