In another question someone mentioned that it couldn't happen. Why not?
For example I asked about the speed an object would have to move at sea level to create a vacuum behind it; in the comments someone asked what I meant by vacuum because there couldn't be a perfect vacuum.
What you're describing is theoretically possible, or at least there is no contradiction inherent in its conception any more than any other "pure" quantum state is: you simply need to prepare the pure quantum state which is the zero particle number observable eigenstate for all the quantum fields (electron, photon, ...). This of course corresponds to all the quantum fields' being in their ground energy eigenstate.
Now, how to prepare this state in practice is another matter. There are both practical and theoretical difficulties. First the question of matter quantum fields. The key idea here is that regions of space only evacuate through diffusion: we don't have any magic means of calling up all the particles in a region and saying "hey guys, could you all please shift to one side of this chamber now?" You simply place the region of space you want to evacuate in contact with another region of space with a lower particle density and let particles freely diffuse back and forth between the two. We can prepare low particle densities through piston apparatus and the like, and one could imagine in theory using pistons with non return valves over many cycles to achieve a high probability of no matter particles in a region (somewhat like the old joke about homeopathic procedures diluting medicine to below single molecule in the bottle concentrations), but in practice this procedure is hard to make perfect. Some of the practical difficulties (outgassing and so forth) are talked about in the Wikipedia article "Ultra-high Vacuum". Moreover, even if you did get rid of all matter particles, then your chamber walls are at nonzero thermodynamic temperature, so now the inside of the chamber contains blackbody radiation. This you cannot get rid of unless the chamber walls are at truly absolute zero thermodynamic temperature.
A perfect vacuum is defined as a state with no matter particles, and also no photons. This state is impossible to achieve experimentally because it is nearly impossible to remove the matter, and is impossible to eliminate all the photons. Since there is also some energy available, virtual particles can hop into and out of existence.
A perfect vacuum would be empty space with no atoms or any particles in it. But there is no such thing because virtual particles are always popping in and out of existence. Even "empty space" is seething with virtual particles.
