Spin Waves realizing the classical analog of a quantum state superposition for computation and sensing

Spin Waves are the coherent oscillations of the magnetic moments of a medium, their propagation does not involve energy dissipation by Joule effect, and in periodic systems their wave function profile can be nonuniform and crucially dependent on the (tunable) symmetry of the underlying magnetization[1]. Their intrinsic wave nature, together with the quantization of their energy, suggests to use them to implement an entangled state superposition, which can collapse due to any symmetry breaking in the underlying magnetization texture[2,3]. The symmetry breaking can result from the measurement of any external quantity in sensing applications (e.g., a tiny external field or induced anisotropy) or from an intentional operation in computing applications[4]. With the help of micromagnetic simulations, we present an overview of two different situations: spin waves in a vortex magnetization state (Fig. 1 shows an illustration of a possible state superposition, exploiting the properties of spin waves in vortex magnetized rings[5]), and spin waves occurring as hybrids in a lattice of macrospins (elongated elements). In both cases, we suggest how to address the Bloch sphere through the complex amplitude of the spin-wave profiles, how to implement a gate operation which preserves the entanglement, and how to break the symmetry (i.e., the measurement) and force the system to collapse in one of the originally irreducible states, producing a result detectable, in principle, by any space-resolved spectroscopy (e.g., micro-focused Brillouin light scattering or X-ray microscopy[6,7]). [1] R. Negrello, F. Montoncello, M.T. Kaffash et al., APL Mater. 10, 091115 (2022). [2] Dany Lachance-Quirion et al., Appl. Phys. Express 12, 070101 (2019). [3] M. Mohseni, V.I. Vasyuchka, V.S. L’vov, A.A. Serga and B. Hillebrands, Communications Physics 5, 196 (2022). [4] C. L. Degen, F. Reinhard, and P. Cappellaro Rev. Mod. Phys. 89, 035002 (2017). [5] G. Gubbiotti, M. Madami, S. Tacchi, et al., Phys. Rev. Lett. 97, 247203 (2006). [6] T. Sebastian, K. Schultheiss, B. Obry, B. Hillebrands and H. Schultheiss, Front. Phys. 3, 35 (2015). [7] Nick Träger, Felix Groß, Johannes Förster et al., Scientific Reports 10, 18146 (2020).