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Physical Review A

Testing Lorentz invariance with atomic-beam interferometry

Jürgen Audretsch, Ulrich Bleyer, Cláus Lämmerzahl

Published Jun 1, 1993• 28 citations
Publisher

Abstract

Atomic- and neutron-beam interferometry offer a sensible technique for tests of the space-time structure. One important ingredient of the space-time structure is given by the null cones, which are related to local Lorentz invariance. A possible deviation from this structure described as splitting of the null cones gives rise to non-Lorentz invariance effects. It is shown that in the nonrelativistic limit this typically amounts to a new type of spin-momentum coupling. Starting from a generalization of the Dirac equation, based on fundamental principles, reasons are given for this special kind of coupling. The outcome of this model theory is taken to propose experiments which use atomic-beam interferometry and give improved upper limits on possible non-Lorentz invariance parameters.

DOI
10.1103/physreva.47.4632

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Atomic- and neutron-beam interferometry offer a sensible technique for tests of the space-time structure. One important ingredient of the space-time structure is given by the null cones, which are related to local Lorentz invariance. A possible deviation from this structure described as splitting of the null cones gives rise to non-Lorentz invariance effects. It is shown that in the nonrelativistic limit this typically amounts to a new type of spin-momentum coupling. Starting from a generalization of the Dirac equation, based on fundamental principles, reasons are given for this special kind of coupling. The outcome of this model theory is taken to propose experiments which use atomic-beam interferometry and give improved upper limits on possible non-Lorentz invariance parameters.
A new test theory for describing tests of fundamental principles of special and general relativity is presented. Using a generalized Pauli equation which may be based on a generalized Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes-Drever-type experiments or by atom interferometry. It is proposed that an atom interferometric test of local position invariance will give a three orders of magnitude improvement over existing estimates.
A new test theory for describing tests of fundamental principles of special and general relativity is presented. Using a generalized Pauli equation which may be based on a generalized Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes-Drever-type experiments or by atom interferometry. It is proposed that an atom interferometric test of local position invariance will give a three orders of magnitude improvement over existing estimates. PACS numbers: 0480C, 0375D, 0365
A new test theory for describing tests of fundamental principles of Special and General Relativity is presented. Using a generalised Pauli equation which may be based on a generalised Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes–Drever type experiments or by atom interferometry. It is proposed that an atom interferometric test of Local Position Invariance will give a three order improvement of existing estimates. 1
If the structure of spacetime is discrete, then Lorentz symmetry should only be an approximation, valid at long length scales. At finite lattice spacings there will be small corrections to the Dirac evolution. In particular, the lattice structure will be reflected in a modification of the free-particle dispersion relation. We show that these can produce a surprisingly large phase shift between the two arms of a nonparallel interferometer. This method could be employed to test any model that predicts a direction-dependent dispersion relation. Here, we calculate the size of this phase shift for a particular model, the three-dimensional quantum walk on the body-centered cubic lattice, which has been shown to give rise to the Dirac equation in the continuum limit. Though the details of this model will affect the size of the shift, its magnitude is set largely by dimensional analysis, so there is reason to believe that other models would yield similar results. We find that, with current technology, a modest-sized neutron interferometer could detect lattice spacings as small as ${10}^{\ensuremath{-}31}\text{ }\text{ }\mathrm{m}$, 13 orders of magnitude smaller than the scale probed by the LHC. A suitably scaled-up experiment could possibly detect lattice spacings even at the Planck scale.
Non-local forces exist in nature for two reasons. First that the recent experiments on locality are supposed to be accurate enough. Second that there is no local theory that can reproduce all the predictions of orthodox quantum theory which, almost for about a century, have been proved to be correct experimentally again and again. This thesis concerns both of these. A brief discussion of the measurement in quantum theory is followed by two comments which show that the quantum description is frame dependent and that the collapse of the wave-function of a system may occur without the relevant measurement being performed. After this the Bohm model and a modified version of the Bohm model are described. Next we introduce a new method for obtaining the Bell-type inequalities which can be used for testing locality. We derive more inequalities by this method than obtained by other existing procedures. Using Projection Valued(PV) and Positive Operator Valued Measures(POVM) measurements we have designed experiments which violates one of the Bell inequalities by a larger factor than existing violations which in turn could increase the accuracy of experiments to test for non-locality. This is our first result. After discussing the non-locality and non-Lorentz invariant features of the Bohm model, its retarded version, namely Squires' model - which is local and Lorentz invariant - is introduced. A problem with this model, that is the ambiguity in the cases where the wave-function depends on time, is removed by using the multiple-time wave-function. Finally, we apply the model to one of the experiments of locality and prove that it is in good agreement with the orthodox quantum theory.
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 κ via an ensemble of spinor atoms. By employing an N -atom multimode GHZ state, the test precision can attain the Heisenberg limit Δκ∝1/(F2N) 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 κ can be extracted via realizable population measurement. Especially, the measurement precision of the LSV parameter κ 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.