Fermionic coherent states and homodyne detection - Tomas Tyc

Coherent states of light have many useful physical and mathematical properties, e.g. they are transformed in a very simple way on a beam splitter and they factorize the correlation functions of the field to all orders. It would be desirable to have states with similar properties for fermionic fields. It is indeed possible to define fermionic coherent states but only at the expense of going outside the Hilbert space of physical states. One can also define \"coherent states\" within the Hilbert space but their properties are by far not as useful as those of their boson counterparts. In particular, the factorization of the correlation functions turns out to be impossible. In my talk I will present the results of our recent research on this subject and will also mention the generalization of homodyne detection to fermionic fields.