Spin-Dependent Force and Inverted Harmonic Potential for Rapid Creation of Macroscopic Quantum Superpositions

Creating macroscopic spatial superposition states is crucial for investigating matter-wave interferometry and advancing quantum sensor technology. Currently, two potential methods exist to achieve this objective. The first involves using inverted harmonic potential (IHP) to spatially delocalize quantum states through coherent inflation [1]. The second method employs a spin-dependent force to separate two massive wave packets spatially [2]. The disadvantage of the former method is the slow initial coherent inflation, while the latter is hindered by the diamagnetism of spin-embedded nanocrystals, which suppresses spatial separation. In this study, we integrate two methods: first, we use the spin-dependent force to generate initial spatial separation, and second, we use IHP to achieve coherent inflating trajectories of the wavepackets. This approach enables the attainment of massive large spatial superposition in minimal time. For instance, a spatial superposition with a mass of $10^{-15}$ kg and a size of 50 $\mu$m is realized in $0.1$ seconds. We also calculate the evolution of wave packets in both harmonic potential (HP) and IHP using path integral approach.