Laboratory Limits for Temporal Variations of Fundamental Constants: An Update

Abstract

Precision comparisons of different atomic frequency standards over a period of a few years can be used for a sensitive search for temporal variations of fundamental constants. We present recent frequency measurements of the 688 THz transition in the 171 Yb + ion. For this transition frequency a record over six years is now available, showing that a possible frequency drift relative to a cesium clock can be constrained to (−0.54 ± 0.97) Hz/yr, i.e. at the level of 2 · 10 −15 per year. Combined with precision frequency measurements of an optical frequency in 199 Hg + and of the hyperfine ground state splitting in 87 Rb a stringent limit on temporal variations of the fine structure constant α: d ln α/dt = (−0.26 ± 0.39) · 10 −15 yr −1 and a model-dependent limit for variations of the proton-to-electron mass ratio µ in the present epoch can be derived:−15 yr −1 . We discuss these results in the context of astrophysical observations that apparently indicate changes in both of these constants over the last 5-10 billion years. Search for variations of constants in astrophysics and with atomic clocksOver the past few years there has been great interest in the possibility that the fundamental constants of nature might show temporal variations over cosmological time scales [1,2,3,4,5]. Such an effect -as incompatible as it seems with the present foundations of physics -appears quite naturally in the attempt to find a unified theory of the fundamental interactions. An active search for an indication of variable constants is pursued mainly in two areas: observational astrophysics and laboratory experiments with atomic frequency standards. The two most important quantities under test are Sommerfeld's fine structure constant α = e 2 /(4πǫ 0h c) and the proton-to-electron mass ratio µ = m p /m e . While α is the coupling constant of the electromagnetic interaction, µ also depends on the strength of the strong force and on the quark masses via the proton mass. It is important that these quantities are dimensionless numbers so that results can be interpreted independently from the conventions of a specific system of units. Quite conveniently, both constants appear prominently in atomic and molecular transition energies: α in atomic fine structure splittings and other relativistic contributions, and µ in molecular vibration and rotation frequencies as well as in hyperfine structure.A multitude of data on variations of α and µ has been obtained from astrophysical observations but the present picture that is obtained is not completely consistent: Evidence for a variation of α has been derived from a shift of wavelengths of metal ion absorption lines produced by interstellar clouds in the light from distant quasars [6]. These observations suggest that about 10 billion years ago (redshift range 0.5 < z < 3.5), the value of α was 1

Optical Clocks Based on Single Ions and Neutral Atoms

“…These data have been used to tackle the question of the constancy of fundamental constants. Combined with precision frequency measurements of an optical frequency in 199 Hg + and of the hyperfine ground state splitting in 87 Rb a stringent limit on temporal variations of the fine structure constant α: d ln α /dt = ( 0.26 ± 0.39) · 10 15 yr 1 and a model-dependent limit for variations of the proton-to-electron mass ratio in the present epoch can be derived: d ln /dt = ( 1.2 ± 2.2) · 10 15 yr 1 [3].…”

About some possible empirical evidences in favor of a cosmological time variation of the speed of light

“…However, introducing a time dependent vacuum permitivity (Sumner 1994) should not prove enough, since there is another combination of physical constants nowadays known to be not time-dependent, namely, Ry, the Rydberg constant (Peik et al 2006):…”

Assessing the time constancy of the proton-to-electron mass ratio by precision ro-vibrational spectroscopy of a cold molecular beam

“…The prime target is the fine structure constant, α = e 2 /(4πε 0 c), which defines the scale of quantum electrodynamics; the second prominent quantity is the proton-to-electron mass ratio, β = m p /m e , which characterizes the strength of strong interaction in terms of the electro-weak one. While in the former case the temporal stability is conveniently probed through atomic transitions [6], the β ratio is more accurately addressed with molecular systems where resorting to the inaccurate nuclear Schmidt model is bypassed [7,8]. One approach is to compare the wavelengths of molecular lines measured in the present epoch on Earth with the corresponding ones from astronomical objects at high redshifts [9,10,11].…”