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

Superadiabatic generation of cat states in bosonic Josephson junctions under particle losses