Entanglement between a muon spin and $I>\frac{1}{2}$ nuclear spins

Abstract

We report on the first example of quantum coherence between the spins of muons and quadrupolar nuclei. We observe this effect in vanadium intermetallic compounds which adopt the A15 crystal structure, and whose members include all technologically dominant superconductors. The entangled states are extremely sensitive to the local structural and electronic environments through the electric field gradient at the quadrupolar nuclei. This case-study demonstrates that positive muons can be used as a quantum sensing tool to probe also structural and charge related phenomena in materials, even in the absence of magnetic order.

Radio-frequency manipulation of state populations in an entangled fluorine-muon-fluorine system

“…where r ij = r i − r j are the position vectors connecting moments i and j, µ 0 is the vacuum permeability, γ i are the gyromagnetic ratios [12], Ĵi = ( Ĵi,x , Ĵi,y , Ĵi,z ) are the angular momentum vector operators, n ij = r ij /|r ij |, and the prefactor (1/2) avoids double counting. Quadrupolar coupling to nuclear spins with I ≥ 1 from finite electric field gradients has recently been discussed in detail [20,21], however, these interactions have been neglected in our model since they are relatively weak for 7 Li (I = 3/2) so will only affect the µ + polarization at longer times [6,7].…”