  We consider ultracold quantum gases of scalar bosons, residing in a coupling
strength--density regime in which they constitute a twofold fragmented
condensate trapped in a single well. It is shown that the corresponding quantum
states are, in the appropriate Fock space basis, identical to the photon cat
states familiar in quantum optics, which correspond to superpositions of
coherent states of the light field with a phase difference of $\pi$. In marked
distinction to photon cat states, the very existence of matter wave cat states
however crucially depends on the many-body correlations of the constituent
particles. We consequently establish that the quadratures of the effective
"photons," expressing the highly nonclassical nature of the macroscopic matter
wave superposition state, can be experimentally accessed by measuring the
density-density correlations of the interacting quantum gas.
