  We investigate a superadiabatic scheme to produce a cat state in a bosonic
Josephson junction in absence and presence of particle losses. The generation
scheme is based on shortcuts to adiabaticity and strongly relies on the parity
conservation. The parity conservation also ensures that the produced state is a
superposition of cat states with various sizes, i.e., a "cats state". Parity is
also the quantity to be measured in order to utilize the produced state in
interferometry. The generation scheme still works even if a number of particle
losses during generation are substantial.
