Angular displacement estimation of Heisenberg scaling: Tunable squeezed Bell state via the enhancement of spin and orbital angular momenta

Abstract

We demonstrate an angular momentum-enhanced protocol that permits an angular displacement estimation by using tunable squeezed Bell state and parity detection. We consider the resolution and the sensitivity, super-resolution is presented along with Heisenberg scaling sensitivity for arbitrary tunable factor, the tunable factor which can optimize the sensitivity is also discussed. Additionally, we analyze the advantages of using angular momentum via considering and comparing simulation results. Under the situation of the optimal tunable factor, the Heisenberg-limited sensitivity and $2\left(\ell+1\right)$-fold super-resolution peak with quantum number $\ell$ are achieved.