Entanglement-enhanced test proposal for local Lorentz-symmetry violation via spinor atoms

Quantum 6, 859 (2022).

https://doi.org/10.22331/q-2022-11-14-859

Invariance under Lorentz transformations is fundamental to both the standard model and general relativity. Testing Lorentz-symmetry violation (LSV) via atomic systems attracts extensive interests in both theory and experiment. In several test proposals, the LSV violation effects are described as a local interaction and the corresponding test precision can asymptotically reach the Heisenberg limit via increasing quantum Fisher information (QFI), but the limited resolution of collective observables prevents the detection of large QFI. Here, we propose a multimode many-body quantum interferometry for testing the LSV parameter $kappa$ via an ensemble of spinor atoms. By employing an $N$-atom multimode GHZ state, the test precision can attain the Heisenberg limit $Delta kappa propto 1/(F^2N)$ with the spin length $F$ and the atom number $N$. We find a realistic observable (i.e. practical measurement process) to achieve the ultimate precision and analyze the LSV test via an experimentally accessible three-mode interferometry with Bose condensed spin-$1$ atoms for example. By selecting suitable input states and unitary recombination operation, the LSV parameter $kappa$ can be extracted via realizable population measurement. Especially, the measurement precision of the LSV parameter $kappa$ can beat the standard quantum limit and even approach the Heisenberg limit via spin mixing dynamics or driving through quantum phase transitions. Moreover, the scheme is robust against nonadiabatic effect and detection noise. Our test scheme may open up a feasible way for a drastic improvement of the LSV tests with atomic systems and provide an alternative application of multi-particle entangled states.