  Cat states, which were initially proposed to manifest macroscopic
superpositions, play an outstanding role in fundamental aspects of quantum
dynamics. In addition, they have potential applications in quantum computation
and quantum sensing. However, cat states are vulnerable to dissipation, which
puts the focus of cat-state generation on higher speed and increased
robustness. Dissipative cat-state generation is a common approach based on the
nonlinear coupling between a lossy pump field and a half-frequency signal
field. In such an approach, the pump field is usually kept in equilibrium,
which limits the cat-state generation. We show that the equilibrium requirement
can be removed by leveraging a synchronous pump method. In this nonequilibrium
regime, the speed of the cat-state generation can be increased by one order of
magnitude, and the robustness to single-photon loss can be enhanced. The
realization of synchronous pumps is discussed for both time-multiplexed systems
and standing modes.
