I've often seen the Casimir effect cited as a source of negative energy/exotic matter with regards to ideas like the Alcubierre drive. The articles then go on to note that the energy required by the ...
The total energy of a mode in a quantum mechanical resonator is given by $E_n ~=~ (n+ 1/2)hf$ where $n$ is the number of modes. So when there are no modes or vibrations, i.e. $n=0$, the energy is ...