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We study rainbow (fold) and cusp catastrophes that form in Fock space following a quench in a Bose Josephson junction. In the Gross-Pitaevskii mean-field theory, the rainbows are singular caustics, but in the second-quantized theory a Poisson resummation of the wave function shows that they are described by well-behaved Airy functions. The structural stability of these Fock space caustics against variations in the initial conditions and Hamiltonian evolution is guaranteed by catastrophe theory. We also show that the long-time dynamics are ergodic. Our results are relevant to the question posed by Berry [M. V. Berry, Nonlinearity 21, T19 (2008)]: Are there circumstances when it is necessary to second quantize wave theory in order to avoid singularities? [ABSTRACT FROM AUTHOR]

A gaseous Bose-Einstein condensate irradiated by a far off-resonance laser has long-range interatomic correlations caused by laser-induced dipole-dipole interactions. These correlations, which are tunable via the laser intensity and frequency, can produce a "roton" minimum in the excitation spectrum--behavior reminiscent of the strongly correlated superfluid liquid He II.