The controlled generation of complex entangled states plays a central
role in the context of quantum simulation and quantum computation. At
the single-mode level, protocols based on photonic Schrödinger cat
states hold strong promise as they present unprecedentedly long-lived
coherence and may be combined with powerful error correction schemes.
However, little is known about the preparation of large ensembles of cat
states in coupled multi-mode devices. In this work, we demonstrate that
robust arrays of "many-body Schrödinger cat states" can be generated
via a spontaneous symmetry breaking mechanism associated with a pairing
effect. The emergence of many-body cat states occurs for arbitrary
system size and geometry, and can be observed either at equilibrium or
under driven-dissipative conditions. In the thermodynamic limit, the
discussed phenomenology is connected to a Mott insulator to
pair-superfluid phase transition. Our proposal is of potential relevance
for the development of large-scale quantum memories.