Time-reversal interferometry using Schrödinger-cat states with scalable entangling resources

We propose a method for generating Schrödinger-cat states—defined as equal superpositions of arbitrary coherent spin states—using a concise sequence of rapid, alternating one-axis twisting and rotation pulses. We demonstrate that the required shearing strength for the protocol, which scales linearly with time, decreases with increasing number of atoms ( N ) in proportion to 1 / N . The resulting states achieve optimal quantum Fisher information among superpositions of two coherent spin states with a specified angular separation. This makes them well suited to exceed the classical phase sensitivity limit in quantum metrology applications. Notably, our protocol is compatible with a time-reversal strategy for quantum metrology, ensuring its practical viability. We also demonstrate that the Heisenberg-limit scaling remains intact when reducing the twisting alongside the number of atoms, mitigating losses from photon scattering. Although the states are then prepared only approximately, they retain enough catlike structure to sustain this scaling.