Magnetic levitation and spatial superposition of a nanodiamond with a current-carrying chip

We propose a current-carrying-chip scheme for generating spatial quantum superpositions using a levitating nanodiamond with a built-in nitrogen-vacancy (NV) centre defect. Our setup is quite versatile and we aim to create the superposition for a mass range of 10⁻¹⁹~ kg< m< 10⁻¹⁵~ kg and a superposition size O(10) μm < Δx < O(1) nm, respectively, in t≤ 0.1s, depending on the position we launch from the center of the diamagnetic trap. We provide an in-depth analysis of two parallel chips that can create levitation and spatial superposition along the x-axis, while producing a very tight trap in the y direction, and the direction of gravity, i.e., the z direction. Numerical simulations demonstrate that our setup can create a one-dimensional spatial superposition state along the x-axis. Throughout this process, the particle is stably levitated in the z-direction, and its motion is effectively confined in the y-direction for a Gaussian initial condition. This setup presents a viable platform for a diamagnetically levitated nanoparticle for a table-top experiment exploring the possibility of creating a macroscopic Schrödinger Cat state to test the quantum gravity induced entanglement of masses (QGEM) protocol.