Mass-independent scheme for enhancing spatial quantum superpositions

Abstract

Placing a large mass in a large spatial superposition, such as a Schrödinger cat state, is a significant and important challenge. In particular, the large spatial superposition [O(10-100) µm] of mesoscopic masses [m ∼ O(10 −14 -10 −15 ) kg] makes it possible to test the quantum nature of gravity via entanglement in the laboratory. To date, the proposed methods of achieving this spatial delocalization are to use wave-packet expansions or quantum ancilla-(for example, spin-) dependent forces, all of whose efficacy reduces with mass. Thus increasing the spatial splitting independently of the mass is an important open challenge. In this paper we present a method of achieving a mass-independent enhancement of superposition via diamagnetic repulsion from current-carrying wires. We analyze an example system which uses the Stern-Gerlach effect to creating a small initial splitting and then apply our diamagnetic repulsion method to enhance the superposition size O(400-600) µm from an initial modest split of the wave function. We provide an analytical and numerical analysis of our scheme.

Gravito-diamagnetic forces for mass independent large spatial superpositions

“…The physical picture presented here differs from the configuration described in our earlier work [52]. That previous paper aspired to create a superposition where the Earths gravitational potential is zero, a situation that could potentially arise if the superposition is created in a diamagnetic trap [60].…”

“…If this minimum distance is considered (as an upper limit) to be the maximum radius of the wire, then the current density is ∼1.9 A/μm 2 for the splitting wire, and ∼1.8 A/μm 2 for the left (right) wire, which is currently achievable in a laboratory with carbon nanotubes and graphene [61][62][63]. The current density through the wire, ρ current , the incident velocity of the wave packets, v in , and the impact parameter, b, satisfy the relation [52]…”

“…We now consider the process of a wave packet incident at a velocity v in , and then scattered by the magnetic field generated by the current-carrying wire. This scattering process can be solved analytically, see [52]. The scattering angle of the wave packet scattered by the central magnetic field is given by [52]:…”

“…This scattering process can be solved analytically, see [52]. The scattering angle of the wave packet scattered by the central magnetic field is given by [52]:…”

“…Addressing this challenge, recent work has introduced a mass-independent scheme leveraging diamagnetic repulsion to enhance spatial superposition from an initial size of 1 μm [52]. Nevertheless, two key challenges impede the realization of this mass-independent approach.…”