Limits on gravitational Einstein equivalence principle violation from monitoring atomic clock frequencies during a year

Abstract

Sun's gravitation potential at earth varies during a year due to varying Earth-Sun distance.Comparing the results of very accurate measurements of atomic clock transitions performed at different time in the year allows us to study the dependence of the atomic frequencies on the gravitational potential. We examine the measurement data for the ratio of the frequencies in Hg + and Al + clock transitions and absolute frequency measurements (with respect to caesium frequency standard) for Dy, Sr, H, hyperfine transitions in Rb and H, and obtain significantly improved limits on the values of the gravity related parameter of the Einstein Equivalence Principle violating term in the Standard Model Extension Hamiltonian c00 = (3.0 ± 5.7) × 10 −7 and the parameter for the gravity-related variation of the fine structure constant κα = (−5.3 ± 10) × 10 −8 . where c 00 is the parameter characterising the magnitude of EEP violation, U is the gravitation potential, c is the speed of light, p is the operator of the electron momentum (p = −ih∇). The change of the frequency of atomic transition between states a and b between two dates in the year isTo avoid any confusion with the sign let us assume that state a is always above state b on the energy scale so that hω ab = E a −E b > 0. ∆U in (2) is the change of the Sun's gravitation potential due to changing of the Earth-Sun distance,2m a is the expectation value of the kinetic energy of electrons in state a, and δK ab is the difference between the kinetic energies of the states a and b. The maximal change of the gravitation potential is between January and July, ∆U/c 2 ≈ 3.3 × 10 −10 [5, 6]. Therefore, comparing accurate frequency measurements performed in January and July, or fitting several measurements with a cosine function with the zero phase in the beginning of January and with period of one year, one can put constrains on the parameter c 00 ,Measuring atomic frequency means comparing it to some reference frequency, e.g. caesium primary frequency standard or another microwave or optical reference frequency. Therefore, we need to consider a ratio of two frequencies. In the non-relativistic limit one can use the Virial theorem ( p 2 /2m = −E total ) and obtain from Eq. (2)i.e. ∆ω/ω is the same for all electron transitions (except for the hyperfine transitions where the splitting is due to the "relativistic" magnetic interaction). This means that in the non-relativistic limit the effect in the ratio of optical frequencies is unobservable. Therefore, we should perform relativistic calculations. It is convenient to introduce relativistic factors R which describe deviation of the expectation value of the kinetic energy from the value, given by the Virial theorem,Here ∆E a is the energy shift of the state a due to the kinetic energy operator. In the non-relativistic limit R = 1. In the relativistic case R can be larger or smaller than one and can even be negative. For the relative change of two frequencies we now haveIt is clear from (6) that for higher sensitivity one should compar...

Constraints on Space-Time-Matter Theory in the Framework of the Standard-Model Extension

“…Experimental limits on (c rod ) TT are summarized in the SME Data Tables [61]. For electrons, they come from synchroton energy losses in accelerators [62], atomic interferometry [63], spectroscopy [64], nuclear binding energy [65], observations of the Crab Nebula flare [66], and clock frequencies [67], implying that (c e ) TT −5 × 10 −21 and |(c e ) TT | < 4 × 10 −15 . For protons and neutrons, they come from atom interferometry [63], nuclear binding energy [65], and atomic fountain clocks [68].…”

Long term measurement of the $^{87}$Sr clock frequency at the limit of primary Cs clocks

“…Typically, a potential violation of the Einstein equivalence principle (EEP) is investigated that would manifest itself as drift or modulation of the measured frequency ratio. A violation may be caused by temporal variations of fundamental constants or their coupling to a gravitational potential [9,[11][12][13][14][15][16][17]52]. We first investigate the data in Tab.…”

Non-Minimal Lorentz Violation in Macroscopic Matter

“…To date, constraints on minimal c w (4) eff coefficients have been placed in studies involving astrophysics [15,[34][35][36][37][38][39][40][41], tests of the equivalence principle [34,42,43], gravimeters [44], accelerators [45][46][47], electromagnetic cavities [48][49][50], atomic systems [51][52][53][54][55][56][57][58][59][60][61][62], and acoustic resonators [63]. The sensitivities in electrons have reached levels of parts in 10 20 in experiments involving atomic clocks [58] and trapped ions [59,60].…”