Study On Using Methods Of Precision Measurement To Test Lorentz Symmetry Violation

Lorentz invariance was one of the most important discoveries in the history of physics.At the small scale,it has been verified by more and more accurate experiments.But at the large scale,many observations suggest that something unusual(dark energy,for example)does break the Lorentz symmetry.With the development of science and technology,the precision measurement such as using the atomic interferometer can achieve so high accuracy that the effects of Lorentz symmetry violation can be tested in these precision experiments.In this thesis,we first review the basic knowledge of precise measurement,including phase estimation,quantum interferometer and entanglement theory,and introduce the criteria for determining useful entangled states related to experiments.Then the SU(2)interferometer and common interferometer operation are introduced.In particular,we study the spin squeezing that can improve the sensitivity of phase estimation,and give the entanglement criterion,which is one of the important criteria for the sensitivity of precise measurement.Based on the introduction about Lorentz symmetry and its possible violation,we mainly analyze the violation effect described in the frame of Standard Model Extension(SME)and investigate the recent measurements of precision experiment using atoms or ions.We find that in nearly all these experiments,either the measurement can be improved using the quantum entangled systems but the number of the particle is too small,or the measurement can using the particles of large number but these particles is hard to be prepared in the entangled state,so it is not easy to much improve sensitivity of precision measurement.In this thesis,we study a model using the Hamiltonian consisting of such term proportional to the square of z-component of angular momentum to describe the Lorentz symmetry violation and the corresponding experiment measurement.We find that using the balanced spin-1 Dicke state that is entangled among atoms of large number and using a proper measurement method,ones can realize the measurement beyond standard quantum limit for the above violation.We also investigate the Lorentz violation effect in the frame of SME and that in the frame of recent quantum formulation of equivalence principle,and find that the violation effect measured by quantum precision experiments is in essence classical.Lorentz symmetry is significant and important for the modern physics,so studying its possible violation through theoretical and experimental ways is also significant for the future physical development.