Paper detail

What does it mean for half of an empty cavity to be full?

It is well known that the vacuum state of a quantum field is spatially entangled. This is true both in free and confined spaces, for example in an optical cavity. The obvious consequence of this, however, is surprising and intuitively challenging; namely, that in a mathematical sense half of an empty cavity is not empty. Formally this is clear, but what does this physically mean in terms of, say, measurements that can actually be made? In this paper we utilize the tools of Gaussian quantum mechanics to easily characterize the reduced state of a subregion in a cavity and expose the spatial profile of its entanglement with the opposite region. We then go on to discuss a thought experiment in which a mirror is introduced between the regions. In so doing we expose a simple and physically concrete answer to the above question: the vacuum excitations resulting from entanglement are mathematically equivalent to the real excitations generated by suddenly introducing a mirror. Performing such an experiment in the laboratory may be an excellent method of verifying vacuum entanglement, and we conclude by discussing different possibilities of achieving this aim.