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

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 col-lective observables prevents the detection of large QFI. Here, we propose a multi -mode many-body quantum interferometry for testing the LSV parameter i via an ensemble of spinor atoms. By employing an N-atom multimode GHZ state, the test precision can attain the Heisenberg limit delta K proportional to 1/((FN)-N-2) 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 ex-tracted via realizable population measurement. Especially, the measurement pre-cision of the LSV parameter kappa can beat the standard quantum limit and even approach the Heisenberg limit via spin mix- ing dynamics or driving through quantum phase transitions. Moreover,the scheme is robust against nonadiabatic effect and de-tection noise. Our test scheme may open up a feasible way for a drastic improve-ment of the LSV tests with atomic systems and provide an alternative application of multi-particle entangled states.

Automated summary

By employing a multi-mode many-body quantum interferometry, we can test the LSV parameter with ultimate precision and potentially surpass the standard quantum limit. This approach opens up a feasible way for significant improvement in LSV tests with atomic systems and highlights the potential of multi-particle entangled states in quantum measurements.