Macro–Macro Schrödinger Cat States in a Levitated Ferromagnetic Needle for Heisenberg-Limited Magnetometry

Macroscopic quantum superpositions, epitomized by Schrödinger's cat when entangling a microscopic degree of freedom with a macroscopic one, remain central to understanding quantum–classical transition and realizing quantum-enhanced sensing. In this talk, we present the generation of macro–macro entanglement between billions of spins and a levitated needle as a rotor [1]. The spin-rotor entanglement arises from strong spin–lattice coupling in ferromagnets, enabling fast angular momentum exchange between the two macroscopic subsystems [2-3]. By applying an angular double-well potential to the rotor, we can use the mechanical degree of freedom to split the collective spin into two coherent branches, forming macro-macro entanglement.  Switching off the angular potential allows a natural recombination of the gigantic superposition state, producing interference that witnesses coherence. We also quantify the metrological advantages of such macro-macro entanglement, via the quantum Fisher information and its Heisenberg scaling with the spin number and the evolution time. We have also analyzed key decoherence channels, particularly gas collisions in high vacuum, and specified feasible experimental conditions for possible experimental observation. Our results show that a levitated ferromagnet can generate macro–macro entanglement on logarithmic timescales, enabling Heisenberg-limited magnetometry with the spin and sensitive force detection with the mechanical degree of freedom.