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I'm not sure about negative mass, but negative energy density can be achieved with the Casimir effect.

https://en.wikipedia.org/wiki/Casimir_effect

My understanding is that this is not really negative energy, rather only energy lower than the quantum background. There is still an absolute zero energy as a hard floor, akin to how negative temperatures just mean lower than an agreed norm and one cannot have true negative temperature.

There are actual negative temperatures (Kelvin scale!). One example are lasers in which a population inversion facilitates lasing.

https://en.wikipedia.org/wiki/Laser

https://en.wikipedia.org/wiki/Population_inversion

https://en.wikipedia.org/wiki/Negative_temperature#Lasers

(Negative thermodynamic temperature has very unintuitive effects in general, so maybe read all of the last article to get an idea)

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