  Particle-wave duality has allowed physicists to establish atomic
interferometers as celebrated complements to their optical counterparts in a
broad range of quantum devices. However, interactions naturally lead to
decoherence and have been considered as a longstanding obstacle in implementing
atomic interferometers in precision measurements. Here, we show that
interactions lead to dynamical quantum phase transitions between
Schr\"{o}dinger's cats in an atomic interferometer. These transition points
result from zeros of Loschmidt echo, which approach the real axis of the
complex time plane in the large particle number limit, and signify pair
condensates, another type of exotic quantum states featured with prevailing
two-body correlations. Our work suggests interacting atomic interferometers as
a new tool for exploring dynamical quantum phase transitions and creating
highly entangled states to beat the standard quantum limit.
