Indication of a cosmological variation of the proton-electron mass ratio based on laboratory measurement and reanalysis of H2 spectra

Electrostatic Trapping of N_{2} Molecules in High Rydberg States

N_{2} molecules traveling in pulsed supersonic beams have been excited from their X ^{1}Σ_{g}^{+} ground electronic state to long-lived Rydberg states with principal quantum numbers between 39 and 48 using a resonance-enhanced two-color three-photon excitation scheme. The Rydberg states populated had static electric dipole moments exceeding 5000 D which allowed deceleration of the molecules to rest in the laboratory-fixed frame of reference and three-dimensional trapping using inhomogeneous electric fields. The trapped molecules were confined for up to 10 ms, with effective trap decay time constants increasing with principal quantum number, and ranging from 450 to 700  μs. These observations, and comparison with the results of similar measurements with He atoms, indicate that the decay dynamics of the trapped Rydberg N_{2} molecules are dominated by spontaneous emission and do not exhibit significant contributions from effects of intramolecular interactions that lead to non-radiative decay.

Viscosity and diffusion in life processes and tuning of fundamental constants

Viewed as one of the grandest questions in modern science, understanding fundamental physical constants has been discussed in high-energy particle physics, astronomy and cosmology. Here, I review how condensed matter and liquid physics gives new insights into fundamental constants and their tuning. This is based on two observations: first, cellular life and the existence of observers depend on viscosity and diffusion. Second, the lower bound on viscosity and upper bound on diffusion are set by fundamental constants, and I briefly review this result and related recent developments in liquid physics. I will subsequently show that bounds on viscosity, diffusion and the newly introduced fundamental velocity gradient in a biochemical machine can all be varied while keeping the fine-structure constant and the proton-to-electron mass ratio intact. This implies that it is possible to produce heavy elements in stars but have a viscous planet where all liquids have very high viscosity (for example that of tar or higher) and where life may not exist. Knowing the range of bio-friendly viscosity and diffusion, we will be able to calculate the range of fundamental constants which favour cellular life and observers and compare this tuning with that discussed in high-energy physics previously. This invites an inter-disciplinary research between condensed matter physics and life sciences, and I formulate several questions that life science can address. I finish with a conjecture of multiple tuning and an evolutionary mechanism.

Erbium-doped-fiber-based broad visible range frequency comb with a 30 GHz mode spacing for astronomical applications

We have realized a comb system with a 30 GHz mode spacing, 62 % available wavelength coverage in the visible region, and nearly 40 dB spectral contrast by combining a robust erbium-doped-fiber-based femtosecond laser, mode filtering with newly designed optical cavities, and broadband-visible-range comb generation using a chirped periodically-poled LiNbO₃ ridge waveguide. Furthermore, it is suggested that this system produces a spectrum with little change over 29 months. These features of our comb will contribute to fields requiring broad-mode-spacing combs, including astronomical observations, such as exoplanet exploration and the verification of the cosmic accelerating expansion.

Is the θ[over ¯] Parameter of QCD Constant?

Testing the cosmological variation of fundamental constants of nature can provide valuable insights into new physics scenarios. While many such constraints have been derived for standard model coupling constants and masses, the θ[over ¯] parameter of QCD has not been as extensively examined. In this Letter, we discuss potentially promising paths to investigate the time dependence of the θ[over ¯] parameter. While laboratory searches for CP-violating signals of θ[over ¯] yield the most robust bounds on today's value of θ[over ¯], we show that CP-conserving effects provide constraints on the variation of θ[over ¯] over cosmological timescales. We find no evidence for a variation of θ[over ¯] that could have implied an "iron-deficient" Universe at higher redshifts. By converting recent atomic clock constraints on a variation of constants, we infer d(θ[over ¯]^{2})/dt≤6×10^{-15}  yr^{-1}, at 1σ. Finally, we also sketch an axion model that results in a varying θ[over ¯] and could lead to excess diffuse gamma ray background, from decays of axions produced in high redshift supernova explosions.

New Limit on Space-Time Variations in the Proton-to-Electron Mass Ratio from Analysis of Quasar J110325-264515 Spectra

Astrophysical tests of current values for dimensionless constants known on Earth, such as the fine-structure constant, α , and proton-to-electron mass ratio, μ = m p / m e , are communicated using data from high-resolution quasar spectra in different regions or epochs of the universe. The symmetry wavelengths of [Fe II] lines from redshifted quasar spectra of J110325-264515 and their corresponding values in the laboratory were combined to find a new limit on space-time variations in the proton-to-electron mass ratio, ∆ μ / μ = ( 0.096 ± 0.182 ) × 10 − 7 . The results show how the indicated astrophysical observations can further improve the accuracy and space-time variations of physics constants.

Saturation cavity ring-down spectrometry using a dynamical relaxation model

We propose a new simple approximate solution to the two-state rate equation model for analyzing decay signals of saturation cavity ring-down spectrometry in the adiabatic and low-saturation regime. It helps obtain baseline-immune Doppler-free spectra for hyperfine transitions and linear absorption coefficients of a gas in the saturation regime. To demonstrate it, a baseline-immune Lamb dip spectrum of the R1A2 transitions in the 2v₂ + v₃ band of methane was recorded. The line position was determined to be 6 076.108 457 7(11) cm^-1, the relative uncertainty being 1.8 × 10^-10.

Stringent Constraints on Fundamental Constant Evolution Using Conjugate 18 cm Satellite OH Lines

We have used the Arecibo Telescope to carry out one of the deepest-ever integrations in radio astronomy, targeting the redshifted conjugate satellite OH 18 cm lines at z≈0.247 towards PKS 1413+135. The satellite OH 1720 and 1612 MHz lines are, respectively, in emission and absorption, with exactly the same line shapes due to population inversion in the OH ground state levels. Since the 1720 and 1612 MHz line rest frequencies have different dependences on the fine structure constant α and the proton-electron mass ratio μ, a comparison between their measured redshifts allows one to probe changes in α and μ with cosmological time. In the case of conjugate satellite OH 18 cm lines, the predicted perfect cancellation of the sum of the line optical depths provides a strong test for the presence of systematic effects that might limit their use in probing fundamental constant evolution. A nonparametric analysis of our new Arecibo data yields [ΔX/X]=(+0.97±1.52)×10^{-6}, where X≡μα^{2}. Combining this with our earlier results from the Arecibo Telescope and the Westerbork Synthesis Radio Telescope, we obtain [ΔX/X]=(-1.0±1.3)×10^{-6}, consistent with no changes in the quantity μα^{2} over the last 2.9 Gyr. This is the most stringent present constraint on fractional changes in μα^{2} from astronomical spectroscopy, and with no evidence for systematic effects.

Astronomical time-of-flight photon speedometer

A dual-band, fiber-optic, photon time-of-flight instrument was developed. Its design was optimized for measuring the velocity of visible photons emanating from relatively dim astronomical sources (apparent magnitude m>12), such as distant galaxies and quasars. We report the first direct photon group velocity measurements for extragalactic objects. The photon group velocity is found to be 3.00±0.03×10⁸ ms^-1 and is invariant, within experimental error, over the range of redshifts measured (0≤z≤1.33). This measurement provides additional validation of general relativity and is consistent with the Friedmann-Lemaître-Robertson-Walker and hyperbolic anti-de Sitter metrics but not with the elliptical de Sitter metric.

Hunting for dark matter with ultra-stable fibre as frequency delay system

Many cosmological observations point towards the existence of dark-matter(DM) particles and consider them as the main component of the matter content of the universe. The goal of revealing the nature of dark-matter has triggered the development of new, extremely sensitive detectors. It has been demonstrated that the frequencies and phases of optical clock have a transient shift during the DMs’ arrival due to the DM-SM(Standard Model) coupling. A simple, reliable and feasible experimental scheme is firstly proposed in this paper, based on “frequency-delay system” to search dark-matter by “self-frequency comparison” of an optical clock. During the arrival of a dark-matter, frequency discrepancy is expected between two signals with a short time difference(~ms) of the same optical clock to exhibit the interaction between atoms and dark-matter. Furthermore, this process can determine the exact position of dark-matter when it is crossing the optical clocks, therefore a network of detecting stations located in different places is recommended to reduce the misjudgment risk to an acceptable level.

Searching for dark matter and variation of fundamental constants with laser and maser interferometry

Any slight variations in the fundamental constants of nature, which may be induced by dark matter or some yet-to-be-discovered cosmic field, would characteristically alter the phase of a light beam inside an interferometer, which can be measured extremely precisely. Laser and maser interferometry may be applied to searches for the linear-in-time drift of the fundamental constants, detection of topological defect dark matter through transient-in-time effects, and for a relic, coherently oscillating condensate, which consists of scalar dark matter fields, through oscillating effects. Our proposed experiments require either minor or no modifications of existing apparatus, and offer extensive reach into important and unconstrained spaces of physical parameters.

Improved limit on a temporal variation of mp/me from comparisons of Yb+ and Cs atomic clocks

Accurate measurements of different transition frequencies between atomic levels of the electronic and hyperfine structure over time are used to investigate temporal variations of the fine structure constant α and the proton-to-electron mass ratio μ. We measure the frequency of the (2)S1/2→(2)F7/2 electric octupole (E3) transition in (171)Yb(+) against two caesium fountain clocks as f(E3)=642,121,496,772,645.36  Hz with an improved fractional uncertainty of 3.9×10(-16). This transition frequency shows a strong sensitivity to changes of α. Together with a number of previous and recent measurements of the (2)S1/2→(2)D3/2 electric quadrupole transition in (171)Yb(+) and with data from other elements, a least-squares analysis yields (1/α)(dα/dt)=-0.20(20)×10(-16)/yr and (1/μ)(dμ/dt)=-0.5(1.6)×10(-16)/yr, confirming a previous limit on dα/dt and providing the most stringent limit on dμ/dt from laboratory experiments.

Limits on a gravitational field dependence of the proton-electron mass ratio from H2 in white dwarf stars

Spectra of molecular hydrogen (H2) are employed to search for a possible proton-to-electron mass ratio (μ) dependence on gravity. The Lyman transitions of H2, observed with the Hubble Space Telescope towards white dwarf stars that underwent a gravitational collapse, are compared to accurate laboratory spectra taking into account the high temperature conditions (T∼13 000  K) of their photospheres. We derive sensitivity coefficients Ki which define how the individual H2 transitions shift due to μ dependence. The spectrum of white dwarf star GD133 yields a Δμ/μ constraint of (-2.7±4.7stat±0.2syst)×10(-5) for a local environment of a gravitational potential ϕ∼10(4) ϕEarth, while that of G29-38 yields Δμ/μ=(-5.8±3.8stat±0.3syst)×10(-5) for a potential of 2×10(4) ϕEarth.

Highly Sensitive Ammonia Probes of a Variable Proton-to-Electron Mass Ratio

The mass sensitivity of the vibration-rotation-inversion energy levels of ammonia is probed using the nonrigid inverter theory. It is shown that the sensitivity exhibits non-negligible centrifugal distortion dependence, which is currently disregarded. The centrifugal distortion effects are especially important in the case of the Δk = ±3 "forbidden" transitions involving accidentally coinciding ro-inversional states |a,J,K = 3⟩ and |s,J,K = 0⟩ of the ν2 vibrational state of (14)NH3. The energy differences of these states exhibit very anomalous mass sensitivities (see Jansen etal. J. Chem. Phys. 2014 , 140 , 010901 ), thus appearing as new highly sensitive probes of the cosmological variability of the proton-to-electron mass ratio.

A stringent limit on a drifting proton-to-electron mass ratio from alcohol in the early universe

The standard model of physics is built on the fundamental constants of nature, but it does not provide an explanation for their values, nor require their constancy over space and time. Here we set a limit on a possible cosmological variation of the proton-to-electron mass ratio μ by comparing transitions in methanol observed in the early universe with those measured in the laboratory. From radio-astronomical observations of PKS1830-211, we deduced a constraint of Δμ/μ = (0.0 ± 1.0) × 10(-7) at redshift z = 0.89, corresponding to a look-back time of 7 billion years. This is consistent with a null result.

First constraint on cosmological variation of the proton-to-electron mass ratio from two independent telescopes

A high signal-to-noise spectrum covering the largest number of hydrogen lines (90 H(2) lines and 6 HD lines) in a high-redshift object was analyzed from an observation along the sight line to the bright quasar source J2123-005 with the Ultraviolet and Visual Echelle Spectrograph on the European Southern Observatory Very Large Telescope (Paranal, Chile). This delivers a constraint on a possible variation of the proton-to-electron mass ratio of Δμ/μ=(8.5 ± 3.6(stat) ± 2.2(syst))×10(-6) at redshift z(abs) = 2.059, which agrees well with a recently published result on the same system observed at the Keck telescope yielding Δμ/μ=(5.6 ± 5.5(stat) ± 2.9(syst))×10(-6). Both analyses used the same robust absorption line fitting procedures with detailed consideration of systematic errors.

Varying Constants, Gravitation and Cosmology

Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. Thus, it is of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We detail the relations between the constants, the tests of the local position invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, solar system observations, meteorite dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of different constants. To finish, we discuss the more speculative possibility of understanding their numerical values and the apparent fine-tuning that they confront us with.

Methanol as a sensitive probe for spatial and temporal variations of the proton-to-electron mass ratio

The 6.7 and 12.2 GHz masers, corresponding to the 5(1) → 6(0)A+ and 2(0) → 3(-1)E transitions in methanol (CH3OH), respectively, are among the brightest radio objects in the sky. We present calculations for the sensitivity of these and other transitions in the ground state of methanol to a variation of the proton-to-electron mass ratio. We show that the sensitivity is greatly enhanced due to a cancellation of energies associated with the hindered internal rotation and the overall rotation of the molecule. We find sensitivities of K(μ) = -42 and K(μ) = -33, for the 5(1) → 6(0)A+ and 2(0) → 3(-1)E transitions, respectively. The sensitivities of other transitions in the different isotopologues of methanol range from -88 to 330. This makes methanol a sensitive probe for spatial and temporal variations of the proton-to-electron mass ratio.

Spectral identification of diffuse resonances in H2 above the n = 2 dissociation limit

The resonance structure in molecular hydrogen above the n = 2 dissociation limit is experimentally investigated in a 1 XUV + 1 VIS coherent two-step laser excitation process, with subsequent ionization of H(n = 2) products. Diffuse spectral features exhibiting widths of several cm(-1) in the excitation range of 118,500-120,500 cm(-1) are probed. Information on angular momentum selection rules for parallel and crossed polarizations, combination differences, the para-ortho distinction, extrapolation from rovibrational structure in the bound region below the n = 2 threshold, and mass-selective detection of H(2)(+) parent and H(+) daughter fragments is used as input. This allows for an assignment of the diffuse resonances observed in terms of (1)Σ(g)(+), (1)Π(g), and (1)Δ(g) states, specified with vibrational and rotational quantum numbers.

Saturated-absorption cavity ring-down spectroscopy

We report on a novel approach to cavity ring-down spectroscopy with the sample gas in saturated-absorption regime. This technique allows us to decouple and simultaneously retrieve the empty-cavity background and absorption signal, by means of a theoretical model that we developed and tested. The high sensitivity and frequency precision for spectroscopic applications are exploited to measure, for the first time, the hyperfine structure of an excited vibrational state of 17O12C16O in natural abundance with an accuracy of a few parts in 10{-11}.

Ultra-stable, widely tunable and absolutely linked mid-IR coherent source

We report on a new coherent source that, using a phase-lock scheme to an optical frequency-comb synthesizer, achieves a 10-Hz intrinsic linewidth, is tunable from 4 to 4.5 microm with a presettable absolute frequency and, when coupled to a high-finesse cavity, can provide a short-term absorption sensitivity of 1.3 x 10(-11) cm(-1)Hz,(-1/2). These unique spectral features make this source a precise tool for molecular physics.

Stringent null constraint on cosmological evolution of the proton-to-electron mass ratio

We present a strong constraint on variation of the proton-to-electron mass ratio mu over cosmological time scales using molecular hydrogen transitions in optical quasar spectra. Using high quality spectra of quasars Q0405-443, Q0347-383, and Q0528-250, variation in micro relative to the present day value is limited to Deltamicro/micro=(2.6+/-3.0)x10;{-6}. We reduce systematic errors compared to previous works by substantially improving the spectral wavelength calibration method and by fitting absorption profiles to the forest of hydrogen Lyman alpha transitions surrounding each H2 transition. Our results are consistent with no variation, and inconsistent with a previous approximately 4sigma detection of mu variation involving Q0405-443 and Q0347-383. If the results of this work and those suggesting that alpha may be varying are both correct, then this would tend to disfavor certain grand unification models.

Improved laboratory values of the H2 Lyman and Werner lines for constraining time variation of the proton-to-electron mass ratio

Two distinct high-accuracy laboratory spectroscopic investigations of the H2 molecule are reported. Anchor lines in the EF1Sigmag+-X1Sigmag+ system are calibrated by two-photon deep-UV Doppler-free spectroscopy, while independent Fourier-transform spectroscopic measurements are performed that yield accurate spacings in the B1Sigmau+-EF1Sigmag+ and I1Pig-C1Piu systems. From combination differences accurate transition wavelengths for the B-X Lyman and the C-X Werner lines can be determined with accuracies better than approximately 5 x 10(-9), representing a major improvement over existing values. This metrology provides a practically exact database to extract a possible variation of the proton-to-electron mass ratio based on H2 lines in high-redshift objects. Moreover, it forms a rationale for equipping a future class of telescopes, carrying 30-40 m dishes, with novel spectrometers of higher resolving powers.

Eötvös bounds on couplings of fundamental parameters to gravity

The possible dependence of fundamental couplings and mass ratios on the gravitational potential has been bounded by comparing atomic clock frequencies over Earth's elliptical orbit. Here we evaluate bounds on such a dependence from Eötvös-type experiments that test the weak equivalence principle, including previously neglected contributions from nuclear binding energy. We find that variations of fundamental parameters correlated with the gravitational potential are limited at 10(-8)-10(-9), an improvement of 2-3 orders of magnitude over atomic clock bounds.

Stability of the proton-to-electron mass ratio

We report a limit on the fractional temporal variation of the proton-to-electron mass ratio as 1/(m(P)/m(e)) partial differential/partial differential(t)(m(P)/m(e))=(-3.8+/-5.6) x 10(-14) yr(-1), obtained by comparing the frequency of a rovibrational transition in SF6 with the fundamental hyperfine transition in Cs. The SF6 transition was accessed using a CO2 laser to interrogate spatial 2-photon Ramsey fringes. The atomic transition was accessed using a primary standard controlled with a Cs fountain. This result is direct and model-free.

HD as a probe for detecting mass variation on a cosmological time scale

The strong electronic absorption systems of the B1 Sigma u+-X1 Sigma g+ Lyman and the C1Pi u-X1 Sigma g+ Werner bands can be used to probe possible mass-variation effects on a cosmological time scale from spectra observed at high redshift, not only in H2 but also in the second most abundant hydrogen isotopomer HD. High resolution laboratory determination of the most prominent HD lines at extreme ultraviolet wavelengths is performed at an accuracy of delta lambda/lambda approximately 5 x 10(-8), forming a database for comparison with astrophysical data. Sensitivity coefficients Ki = d ln lambda i/d ln mu are determined for HD from quantum ab initio calculations as a function of the proton-electron mass ratio mu. Strategies to deduce possible effects beyond first-order baryon/lepton mass ratio deviations are discussed.

Highly coherent spectroscopy of ultracold atoms and molecules in optical lattices

Cooling and trapping of neutral atoms using laser techniques has enabled extensive progress in precise, coherent spectroscopy. In particular, trapping ultracold atoms in optical lattices in a tight confinement regime allows us to perform high-resolution spectroscopy unaffected by atomic motion. We report on the recent developments of optical lattice atomic clocks that have led to optical spectroscopy coherent at the one second timescale. The lattice clock techniques also open a promising pathway toward trapped ultracold molecules and the possible precision measurement opportunities such molecules offer.

Precision test of mass-ratio variations with lattice-confined ultracold molecules

We propose a precision measurement of time variations of the proton-electron mass ratio using ultracold molecules in an optical lattice. Vibrational energy intervals are sensitive to changes of the mass ratio. In contrast to measurements that use hyperfine-interval-based atomic clocks, the scheme discussed here is model independent and does not require separation of time variations of different physical constants. The possibility of applying the zero-differential-Stark-shift optical lattice technique is explored to measure vibrational transitions at high accuracy.

Enhanced Sensitivity to Variation of m(e)/m(p) in molecular spectra

We propose new experiments with high sensitivity to a possible variation of the electron-to-proton mass ratio mu identical with m(e)/m(p). We consider a nearly degenerate pair of molecular vibrational levels, each associated with a different electronic potential. With respect to a change in mu, the change in the splitting between such levels can be large both on an absolute scale and relative to the splitting. We demonstrate the existence of such pairs of states in Cs2, where the narrow spectral lines achievable with ultracold molecules make the system promising for future searches for small variations in mu.

Frequency comb Vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra

A femtosecond frequency comb provides a vast number of equidistantly spaced narrow band laser modes that can be simultaneously tuned and frequency calibrated with 15 digit accuracy. Our Vernier spectrometer utilizes all of theses modes in a massively parallel manner to rapidly record both absorption and dispersion spectra with a sensitivity that is provided by a high finesse broadband optical resonator and a resolution that is only limited by the frequency comb line width while keeping the required setup simple.

Enhanced sensitivity to the time variation of the fine-structure constant and m{p}/m{e} in diatomic molecules

Sensitivity to temporal variation of the fundamental constants may be strongly enhanced in transitions between narrow close levels of different nature. This enhancement may be realized in a large number of molecules due to cancellation between the ground state fine-structure omega{f} and vibrational interval omega{v} [omega=omega{f}-nomega{v} approximately 0, delta omega/omega=K(2delta alpha/alpha+0.5 delta mu/mu), K>>1, mu=m{p}/m{e}]. The intervals between the levels are conveniently located in microwave frequency range and the level widths are very small. Required accuracy of the shift measurements is about 0.01-1 Hz. As examples, we consider molecules Cl(+)(2), CuS, IrC, SiBr, and HfF(+).

Limit on the cosmological variation of mp/me from the inversion spectrum of ammonia

We obtain the limit on the space-time variation of the ratio of the proton mass to the electron mass, mu=m(p)/m(e), based on comparison of quasar absorption spectra of NH3 with CO, HCO+ and HCN rotational spectra. For the inversion transition in NH3 (lambda approximately 1.25 cm(-1)) the relative frequency shift is significantly enhanced: deltaomega/omega=-4.46deltamu/mu. This enhancement allows one to increase sensitivity to the variation of mu using NH3 spectra for high redshift objects. We use published data on microwave spectra of the object B0218+357 to place the limit deltamu/mu=(0.6+/-1.9) x 10(-6) at redshift z=0.6847; this limit is several times better than the limits obtained by different methods and may be significantly improved. Assuming linear time dependence we obtain mu/mu=(-1+/-3) x 10(-16) yr(-1).

Hydrogenlike highly charged ions for tests of the time independence of fundamental constants

Hyperfine transitions in the electronic ground state of cold, trapped hydrogenlike highly charged ions have attractive features for use as frequency standards because the majority of systematic frequency shifts are smaller by orders of magnitude compared to many microwave and optical frequency standards. Frequency measurements of these transitions hold promise for significantly improved laboratory tests of local position invariance of the electron and quark masses.

Limit on the temporal variation of the fine-structure constant using atomic dysprosium

Over 8 months, we monitored transition frequencies between nearly degenerate, opposite-parity levels in two isotopes of atomic dysprosium (Dy). These frequencies are sensitive to variation of the fine-structure constant (alpha) due to relativistic corrections of opposite sign for the opposite-parity levels. In this unique system, in contrast to atomic-clock comparisons, the difference of the electronic energies of the opposite-parity levels can be monitored directly utilizing a rf electric-dipole transition between them. Our measurements show that the frequency variation of the 3.1-MHz transition in (163)Dy and the 235-MHz transition in (162)Dy are 9.0+/-6.7 Hz/yr and -0.6+/-6.5 Hz/yr, respectively. These results provide a rate of fractional variation of alpha of (-2.7+/-2.6) x 10(-15) yr(-1) (1 sigma) without assumptions on constancy of other fundamental constants, indicating absence of significant variation at the present level of sensitivity.