Narrow Results

Review of recent works devoted to the variation of the fine structure constant α, strong interaction and fundamental masses (Higgs vacuum) is presented. The results from Big Bang nucleosynthesis, quasar absorption spectra, and Oklo natural nuclear reactor data give us the space-time variation on the Universe lifetime scale. Comparison of different atomic clocks gives us the present time variation. Assuming linear variation with time we can compare different results. The best limit on the variation of the electron-to-proton mass ratio μ = m_e/M_p and X_e = m_e/Λ_QCD follows from the quasar absorption spectra:¹. A combination of this result and the atomic clock results^2,3 gives the best limt on variation of . The Oklo natural reactor gives the best limit on the variation of X_s = m_s/Λ_QCD where m_s is the strange quark mass:^4,5. Note that the Oklo data can not give us any limit on the variation of α since the effect of α there is much smaller than the effect of X_s and should be neglected.

Huge enhancement of the relative variation effects happens in transitions between close atomic, molecular and nuclear energy levels. We suggest several new cases where the levels are very narrow. Large enhancement of the variation effects is also possible in cold atomic and molecular collisions near Feshbach resonance.

How changing physical constants and violation of local position invariance may occur? Light scalar fields very naturally appear in modern cosmological models, affecting parameters of the Standard Model (e.g. α). Cosmological variations of these scalar fields should occur because of drastic changes of matter composition in Universe: the latest such event is rather recent (about 5 billion years ago), from matter to dark energy domination. Massive bodies (stars or galaxies) can also affect physical constants. They have large scalar charge S proportional to number of particles which produces a Coulomb-like scalar field U = S/r. This leads to a variation of the fundamental constants proportional to the gravitational potential, e.g. δα/α = k_αδ(GM/rc²). We compare different manifestations of this effect. The strongest limits⁶k_α + 0.17k_e = (-3.5 ±6) × 10^-7 and k_α + 0.13k_q = (-1 ± 17) × 10^-7 are obtained from the measurements of dependence of atomic frequencies on the distance from Sun^2,7 (the distance varies due to the ellipticity of the Earth's orbit).

We present a review of our clock science conducted under the NASA Microgravity Fundamental Physics program. Our work has led to the development of rubidium atomic clocks, designs for ground- and space-based clocks that juggle atoms to achieve ultrahigh stability and accuracy, improved microwave cavities for atomic clocks, and elucidation of new systematic errors such as the atomic recoil from microwave photons. High stability clocks can be used for precise tests of fundamental physics and accurate deep-space navigation.

One of the classical tests of general relativity is the precision measurements by Pound and Rebka of red-shift/blue-shift of photons in a gravitational field. In this essay, we lay out a temporal version of the Pound–Rebka experiment. The emission and absorption of photons occurs at different times, rather than at different spatial locations as in the original Pound–Rebka experiment. This temporal Pound–Rebka experiment is equivalent to a gravitational Aharonov–Bohm Effect and is testable via current or near future satellite experiments.

Atomic clocks are the core of a navigation system. Since an error in time results in an error in the user localization, it is fundamental that the stability is very high and constant with time. In this paper we discuss the dynamic Allan variance, or DAVAR, a representation of the time-varying stability of an atomic clock. We show by simulation its effectiveness in tracking common nonstationary behaviors of a clock.

Review of recent works devoted to the variation of the fine structure constant α, strong interaction and fundamental masses (Higgs vacuum) is presented. The results from Big Bang nucleosynthesis, quasar absorption spectra, and Oklo natural nuclear reactor data give us the space-time variation on the Universe lifetime scale. Comparison of different atomic clocks gives us the present time variation. Assuming linear variation with time we can compare different results. The best limit on the variation of the electron-to-proton mass ratio μ = m_e/M_p and X_e = m_e/Λ_QCD follows from the quasar absorption spectra:¹. A combination of this result and the atomic clock results^2,3 gives the best limt on variation of . The Oklo natural reactor gives the best limit on the variation of X_s = m_s/Λ_QCD where m_s is the strange quark mass:^4,5. Note that the Oklo data can not give us any limit on the variation of a since the effect of α there is much smaller than the effect of X_s and should be neglected.

Huge enhancement of the relative variation effects happens in transitions between close atomic, molecular and nuclear energy levels. We suggest several new cases where the levels are very narrow. Large enhancement of the variation effects is also possible in cold atomic and molecular collisions near Feshbach resonance.

How changing physical constants and violation of local position invariance may occur? Light scalar fields very naturally appear in modern cosmological models, affecting parameters of the Standard Model (e.g. α). Cosmological variations of these scalar fields should occur because of drastic changes of matter composition in Universe: the latest such event is rather recent (about 5 billion years ago), from matter to dark energy domination. Massive bodies (stars or galaxies) can also affect physical constants. They have large scalar charge S proportional to number of particles which produces a Coulomb-like scalar field U = S/r. This leads to a variation of the fundamental constants proportional to the gravitational potential, e.g. δα/α = k_αδ(GM/rc²). We compare different manifestations of this effect. The strongest limits⁶k_α + 0.17k_e = (-3.5 ± 6) × 10^-7 and k_α + 0.13k_q = (-1 ± 17) × 10^-7 are obtained from the measurements of dependence of atomic frequencies on the distance from Sun^2,7 (the distance varies due to the ellipticity of the Earth's orbit).

This article describes recent frequency measurements performed with the LNE-SYRTE atomic clock ensemble. First, we report a new determination of the rubidium 87 hyperfine frequency, performed using Rb and Cs atomic fountains. The measurement has a statistical uncertainty below 10^-16 and an overall uncertainty of 1.1 parts in 10¹⁵. Second, we report the first laser spectroscopy of the ¹S₀-³P₀ optical clock transition at 265.6 nm in laser-cooled fermionic isotopes of neutral mercury. The absolute frequency is measured with a fractional uncertainty of ~ 5 parts in 10¹² which improves upon previous indirect determinations by more than 4 orders of magnitude, an important step toward the realization of an optical lattice clock.

We discuss prospects for the most stable space-qualified atomic clocks to test general relativity in potential future satellite missions in Earth orbit. By comparing the tick rate of a clock on a satellite to ground clocks, the redshift is obtained. Choosing a highly eccentric orbit will boost relativistic effects at pericenter due to low altitude and high velocity. We find that with a clock having a fractional timing instability of 10⁻¹⁵ to 10⁻¹⁶ on such an orbit, one can measure a host of relativistic effects. These include frame-dragging and the Shapiro delay of the signal light pulses. In optimistic scenarios, higher order (spin-squared) effects are measurable. Additionally, this kind of mission tests alternative theories of gravity in the neighborhood of the Earth. We find that the PPN parameters γ and β can be constrained to the 10⁻⁶ level. Current constraints are at the 10⁻⁵ level coming from radio signals of the Cassini mission traveling through the Sun’s gravitational field and planetary ephemerides. It is important to probe gravitation around different central objects since some alternative theories predict different behavior around e.g. the Earth and the Sun due to screening mechanisms.

We present a review of our clock science conducted under the NASA Microgravity Fundamental Physics program. Our work has led to the development of rubidium atomic clocks, designs for ground- and space-based clocks that juggle atoms to achieve ultrahigh stability and accuracy, improved microwave cavities for atomic clocks, and elucidation of new systematic errors such as the atomic recoil from microwave photons. High stability clocks can be used for precise tests of fundamental physics and accurate deep-space navigation.

Frequency standards (atomic clocks) based on narrow optical transitions in ²⁷Al⁺ and ¹⁹⁹Hg⁺ have been developed over the past several years at NIST. Both types of standards are based on single ions confined in Paul traps, but differ in the methods used to prepare and detect the internal atomic states. Al⁺ lacks a strong, laser-accessible transition for laser-cooling and for state preparation and detection. Coupling with a Be⁺ ion, trapped simultaneously with the Al⁺ ion, enables state manipulation, detection, and cooling of the Al⁺ ion. Both standards have achieved absolute reproducibilities of a few parts in 10¹⁷. Development of femtosecond laser frequency combs makes it possible to directly compare optical frequencies. The present determination of f_Al/f_Hg is 1.052 871 833 148 990 438 (55), where the uncertainty is expressed in units of the least significant digit. Measurements of f_Al/f_Hg made over about one year show a drift rate consistent with zero. This result can be used to place limits on time variations of fundamental constants such as the fine structure constant α.