Analysis of atomic-clock data to constrain variations of fundamental constants
Nathaniel Sherrill, Adam O. Parsons, Charles F. A. Baynham, William Bowden, E. Anne Curtis, Richard Hendricks, Ian R. Hill, Richard Hobson, Helen S. Margolis, B… 展开作者
Nathaniel Sherrill, Adam O. Parsons, Charles F. A. Baynham, William Bowden, E. Anne Curtis, Richard Hendricks, Ian R. Hill, Richard Hobson, Helen S. Margolis, Billy I. Robertson, Marco Schioppo, Krzysztof Szymaniec, Alexandra Tofful, Jacob Tunesi, Rachel M. Godun, Xavier Calmet
We present a new framework to study the time variation of fundamental constants in a model-independent way. Model independence implies more free parameters than assumed in previous studies. Using data from atomic clocks based on $^{87}$Sr, $^{171}$Yb$^+$ and $^{133}$Cs, we set bounds on parameters controlling the variation of the fine-structure constant, $α$, and the electron-to-proton mass ratio, $μ$. We consider variations on timescales ranging from a minute to almost a day. In addition, we use our results to derive some of the tightest limits to date on the parameter space of models of ultralight dark matter and axion-like particles.
We perform calculations of the dependence of nuclear magnetic moments on quark masses and obtain limits on the variation of m_q/Lambda_{QCD} from recent atomic clock experiments with hyperfine transitions in H, Rb, Cs, Hg+ and optical transtion in Hg+.
Optical atomic clocks represent the state-of-the-art in the frontier of modern measurement science. In this article we provide a detailed review on the development of optical atomic clocks that are based on trapped single ions and many neutral atoms. We discuss important technical ingredients for optical clocks, and we present measurement precision and systematic uncertainty associated with some of the best clocks to date. We conclude with an outlook on the exciting prospect for clock applications.
We study a wide range of neutral atoms and ions suitable for ultra-precise atomic optical clocks with naturally suppressed black body radiation shift of clock transition frequency. Calculations show that scalar polarizabilities of clock states cancel each other for at least one order of magnitude for considered systems. Results for calculations of frequencies, quadrupole moments of the states, clock transition amplitudes and natural widths of upper clock states are presented.
We perform calculations of the dependence of nuclear magnetic moments on quark masses and obtain limits on the variation of the ratio of quark mass and strong interaction scale (m_q/Lambda_{QCD}) from recent atomic clock experiments with hyperfine transitions in H, Rb, Cs, Yb+, Hg+ and optical transition in Hg+. Experiments with Cd+, deuterium/hydrogen, molecule SF_6, Zeeman transitions in He_3/Xe are also discussed.
A microwave atomic clock scheme based on Rb and Cs atoms trapped in optical lattice with magic wavelength for clock transition is proposed. The ac Stark shift of clock transition due to trapping laser can be canceled at some specific laser wavelengths. Comparing with in fountain clock, the cavity related shifts, the collision shift, and the Doppler effect are eliminated or suppressed dramatically in atomic clock when the magic optical lattice is exploited. By carefully analyzing various sources of clock uncertainty, we conclude that a microwave atomic clock with an accuracy of better than $2\t…
Light-shifts are known to be an important limitation to the mid- and long-term fractional frequency stability of different types of atomic clocks. In this article, we demonstrate the experimental implementation of an advanced anti-light shift interrogation protocol onto a continuous-wave (CW) microcell atomic clock based on coherent population trapping (CPT). The method, inspired by the Auto-Balanced Ramsey (ABR) spectroscopy technique demonstrated in pulsed atomic clocks, consists in the extraction of atomic-based information from two successive light-shifted clock frequencies obtained at two…
The environmental perturbation on atoms is the key factor restricting the performance of atomic frequency standards, especially in long term scale. In this letter, we demonstrate a real-time noise distinguish operation of atomic clocks. The operation improves the statistical uncertainty by about an order of magnitude of our fountain clock which is deteriorated previously by extra noises. The frequency offset bring by the extra noise is also corrected. The experiment proves the real-time noise distinguish operation can reduce the contribution of ambient noises and improve the uncertainty limit …
We analyze the AC Stark shift of the Cs microwave atomic clock transition theoretically and experimentally. Theoretical and experimental data are in a good agreement with each other. Results indicate the absence of a magic wavelength at which there would be no differential shift of the clock states having zero projections of the total angular momentum.
The mid-term fractional frequency stability of miniaturized atomic clocks can be limited by light-shift effects. In this Letter, we demonstrate the implementation of a symmetric Auto-Balanced Ramsey (SABR) interrogation sequence in a microcell-based atomic clock based on coherent population trapping (CPT). Using this advanced protocol, the sensitivity of the clock frequency to laser power, microwave power and laser frequency variations is reduced, at least by one order of magnitude, in comparison with continuous-wave (CW) or Ramsey interrogation schemes. Light-shift mitigation obtained with th…
The rapid increase in accuracy and stability of optical atomic clocks compared to the caesium atomic clock as primary standard of time and frequency asks for a future re-definition of the second in the International System of Units (SI). The status of the optical clocks based on either single ions in radio-frequency traps or on neutral atoms stored in an optical lattice is described with special emphasis of the current work at the Physikalisch-Technische Bundesanstalt (PTB). Besides the development and operation of different optical clocks with estimated fractional uncertainties in the 10^-18 …
Theories unifying gravity and other interactions suggest the possibility of spatial and temporal variation of physical ``constants''. Accuracy achieved for the atomic optical frequency standards (optical clocks) approaches the level when possible time evolution of the fine structure constant $α$ can be studied by comparisons of rates between clocks based on different atomic transitions in different atoms. The sensitivity to variation of $α$ is due to relativistic corrections which are different in different atoms ($\sim Z^2α^2$). We have calculated the values of the relativistic energy shifts …
Recent progress in optical lattice clocks requires unprecedented precision in controlling systematic uncertainties at $10^{-18}$ level. Tuning of nonlinear light shifts is shown to reduce lattice-induced clock shift for wide range of lattice intensity. Based on theoretical multipolar, nonlinear, anharmonic and higher-order light shifts, we numerically demonstrate possible strategies for Sr, Yb, and Hg clocks to achieve lattice-induced systematic uncertainty below $1\times 10^{-18}$.
We consider an application of precision frequency measurements to searches for possible time variations of the fundamental physical constants. Current laboratory constraints on variations of the fine structure constant alpha and other fundamental constants are presented.
The possibility of using neutral and double ionized erbium for atomic clocks of high precision is investigated. In both cases the narrow electric quadrupole clock transition between the ground and first exited state of the same configuration lies in optical region. The estimated ratio of decay width to transition energy is less then 10 20. We demonstrate that this transitions are not sensitive to black body radiation and if other perturbations are also considered the relative accuracy of the clocks can probably reach the level of 10 (pow minus 18) or better.
Spherically-symmetric ground states of alkali-metal atoms do not posses electric quadrupole moments. However, the hyperfine interaction between nuclear moments and atomic electrons distorts the spherical symmetry of electronic clouds and leads to non-vanishing atomic quadrupole moments. We evaluate these hyperfine-induced quadrupole moments using techniques of relativistic many-body theory and compile results for Li, Na, K, Rb, and Cs atoms. For heavy atoms we find that the hyperfine-induced quadrupole moments are strongly (two orders of magnitude) enhanced by correlation effects. We further a…
We perform calculations of the dependence of nuclear magnetic moments on quark masses and obtain limits on the variation of $(m_q/Λ_{QCD})$ from recent measurements of hydrogen hyperfine (21 cm) and molecular rotational transitions in quasar absorption systems, atomic clock experiments with hyperfine transitions in H, Rb, Cs, Yb$^+$, Hg$^+$ and optical transition in Hg$^+$. Experiments with Cd$^+$, deuterium/hydrogen, molecular SF$_6$ and Zeeman transitions in $^3$He/Xe are also discussed.
The cosmological applications of atomic clocks so far have been limited to searches of the uniform-in-time drift of fundamental constants. In this paper, we point out that a transient in time change of fundamental constants can be induced by dark matter objects that have large spatial extent, and are built from light non-Standard Model fields. The stability of this type of dark matter can be dictated by the topological reasons. We point out that correlated networks of atomic clocks, some of them already in existence, can be used as a powerful tool to search for the topological defect dark matt…
We report on design and construction of a Zeeman slower for strontium atoms which will be used in an optical atomic clock experiment. The paper describes briefly required specifications of the device, possible solutions, and concentrates on the chosen design. The magnetic field produced by the built Zeeman slower has been measured and compared with the simulations. The system consisting of an oven and Zeeman slower are designed to produce an atomic beam of 10-12 s-1 flux and final velocity of ~30 m/s.
We calculate the dependence of the nuclear magnetic moments on the quark masses including the spin-spin interaction effects and obtain limits on the variation of the fine structure constant $α$ and $(m_q/Λ_{QCD})$ using recent atomic clock experiments examining hyperfine transitions in H, Rb, Cs, Yb$^+$ and Hg$^+$ and the optical transition in H, Hg$^+$ and Yb$^+$ .
We propose and demonstrate a novel detection scheme of clock signals and obtain an ultra-high resonance contrast above 90%. The precision of the signal's detection and the signal-to-noise ratio (SNR) of atomic clock signal is improved remarkably. The frequency stability in terms of Allan deviation has been improved by an order for the new detection under the equivalent conditions. We also investigate density effect which produces the splitting of the transmission peak and consequently a narrower linewidth of Ramsey fringes.
Controlling light shifts in chip-scale atomic beam clocks
National Institute of Standards and Technology（美国国家标准与技术研究院）；University of Colorado Boulder（科罗拉多大学博尔德分校）；Infleqtion（英飞格蒂昂）；HRL Laboratories（HRL实验室）；DARPA（美国国防部高级研究计划局）
With the development of microwave atomic clocks, the Zeeman shifts for the spectral lines of black-body radiation need to be investigated carefully. In this Letter, the frequency shifts of hyperfine splittings of atomic ground states due to the magnetic field of black-body radiation are reported. The relative frequency shifts of different alkali atoms and alkali-like ions, which could be candidates of microwave atomic clocks, were calculated. The results vary from $-0.977\times10^{-17}[T(K)/300]^{2}$ to $-1.947\times10^{-17}[T(K)/300]^{2}$ for different atoms considered. These results are cons…
We explore a feasibility of measuring atom-wall interaction using atomic clocks based on atoms trapped in engineered optical lattices. Optical lattice is normal to the wall. By monitoring the wall-induced clock shift at individual wells of the lattice, one would measure a dependence of the atom-wall interaction on the atom-wall separation. We rigorously evaluate the relevant clock shifts and show that the proposed scheme may uniquely probe the long-range atom-wall interaction in all three qualitatively-distinct regimes of the interaction: van der Waals (image-charge interaction), Casimir-Polde…
We report the evaluation of the second order Zeeman shift in the continuous atomic fountain clock FoCS-2. Because of the continuous operation and of its geometrical constraints, the methods used in pulsed fountains are not applicable. We use here time-resolved Zeeman spectroscopy to probe the magnetic field profile in the clock. The pulses of ac magnetic excitation allow us to spatially resolve the Zeeman frequency and to evaluate the Zeeman shift with a relative uncertainty smaller than 10E-16.
We evaluate the use of Coherent Population Trapping (CPT) excited with parallely polarized laser fields in vapour cell atomic clocks. We study the resonance shape, the discriminator slope and signal-to-noise ratio as a function of relevant parameters such as the laser frequency detuning and the applied magnetic field. We show that a stability of $6 \cdot 10^{-12}$ $τ^{-1/2}$ may be reached in a compact system using a modulated VCSEL.
A black-body radiation (BBR) shifts of (nsnp ^3P_0) - (ns^2 ^1S_0) clock transition in divalent atoms Mg, Ca, Sr, and Yb are evaluated. A theory of multipolar BBR shifts is developed and its implications are discussed. At room temperatures, the resulting uncertainties in the BBR shifts are relatively large and substantially affect the projected 10^{-18} fractional accuracy of the optical-lattice-based clocks.
A method for highly accurate calculations of atomic electric quadrupole moments (EQM) is presented, using relativistic general-excitation-rank configuration interaction wavefunctions based on Dirac spinors. Application to the clock transition states of the thulium atom employing up to full Quadruple excitations for the atomic wavefunction yields a final value of $Q_{zz}({^2F}_{7/2}) = 0.07 \pm 0.07$ a.u., establishing that the thulium electronic ground state has an exceptionally small EQM. A detailed analysis of this result is presented which has implications for EQMs of other atoms with unpai…
We show that the light shift in atomic clocks can be suppressed using time variation of the interrogation field intensity. By measuring the clock output at two intensity levels, error signals can be generated that simultaneously stabilize a local oscillator to an atomic transition and correct for the shift of this transition caused by the interrogating optical field. These methods are suitable for optical clocks using one- and two-photon transitions, as well as for microwave clocks based on coherent population trapping or direct interrogation. The proposed methods can be widely used both for h…
We propose a novel class of atomic clocks based on highly charged ions. We consider highly-forbidden laser-accessible transitions within the $4f^{12}$ ground-state configurations of highly charged ions. Our evaluation of systematic effects demonstrates that these transitions may be used for building exceptionally accurate atomic clocks which may compete in accuracy with recently proposed nuclear clock.
The frequency stability achieved by an optical atomic clock ultimately depends on the coherence of its local oscillator. Even the best ultrastable lasers only allow interrogation times of a few seconds, at present. Here we present a universal measurement protocol that overcomes this limitation. Engineered dynamic decoupling of laser phase noise allows any optical atomic clock with high signal-to-noise ratio in a single interrogation to reconstruct the laser's phase well beyond its coherence limit. A compound clock is then formed in combination with another optical clock of any type, allowing t…
We consider possible extensions to quantum mechanics proposed by Steven Weinberg, and re-analyze his prediction of a new test based upon three atomic clocks in the same atom. We propose realistic experimental systems where this hypothesis can be tested. Two systems already set limits on deviations from quantum mechanics, while with another system, one would be able to search for new physics at the limit of sensitivity of the best atomic clocks.
We develop a method of spectroscopy that uses a weak static magnetic field to enable direct optical excitation of forbidden electric-dipole transitions that are otherwise prohibitively weak. The power of this scheme is demonstrated using the important application of optical atomic clocks based on neutral atoms confined to an optical lattice. The simple experimental implementation of this method -- a single clock laser combined with a DC magnetic field-- relaxes stringent requirements in current lattice-based clocks (e.g., magnetic field shielding and light polarization), and could therefore ex…
We investigate systematic errors associated with a common modulation technique used for phase sensitive detection of a coherent population trapping (CPT) resonance. In particular, we show that modification of the CPT resonance lineshape due to the presence of off-resonant fields leads to frequency shifts which may limit the stability of CPT-based atomic clocks. We also demonstrate that an alternative demodulation technique greatly reduces these effects.
A review is given of the implications of the absence of an intrinsic notion of instantaneous 3-space, so that a clock synchronization convention has to be introduced, for relativistic theories.
We consider the general class of theories in which there is a new ultralight scalar field that mediates an equivalence principle violating, long-range force. In such a framework, the sun and the earth act as sources of the scalar field, leading to potentially observable location dependent effects on atomic and nuclear spectra. We determine the sensitivity of current and next-generation atomic and nuclear clocks to these effects and compare the results against the existing laboratory and astrophysical constraints on equivalence principle violating fifth forces. We show that in the future, the a…
The total mass density of the Universe appears to be dominated by dark matter. However, beyond its gravitational interactions at the galactic scale, little is known about its nature. Extensions of the quantum electrodynamics Lagrangian with dark-matter coupling terms may result in changes to Standard Model parameters. Recently, it was proposed that a network of atomic clocks could be used to search for transient signals of a hypothetical dark matter in the form of stable topological defects. The clocks become desynchronized when a dark-matter object sweeps through the network. This pioneering …
Atomic clocks use atomic transitions as frequency references. The susceptibility of the atomic transition to external fields limits clock stability and introduces systematic frequency shifts. Here, we propose to realize an atomic clock that utilizes an entangled superposition of states of multiple atomic species, where the reference frequency is a sum of the individual transition frequencies. The superposition is selected such that the susceptibilities of the respective transitions, in individual species, destructively interfere leading to improved stability and reduced systematic shifts. We p…
The pursuit of better atomic clocks has advanced many research areas, providing better quantum state control, new insights in quantum science, tighter limits on fundamental constant variation, and improved tests of relativity. The record for the best stability and accuracy is currently held by optical lattice clocks. This work takes an important step towards realizing the full potential of a many-particle clock with a state-of-the-art stable laser. Our 87Sr optical lattice clock now achieves fractional stability of 2.2e-16 at 1 s. With this improved stability, we perform a new accuracy evaluat…
In this article, we report on the work done with the LNE-SYRTE atomic clock ensemble during the last 10 years. We cover progress made in atomic fountains and in their application to timekeeping. We also cover the development of optical lattice clocks based on strontium and on mercury. We report on tests of fundamental physical laws made with these highly accurate atomic clocks. We also report on work relevant to a future possible redefinition of the SI second.
The superb precision of an atomic clock is derived from its stability. Atomic clocks based on optical (rather than microwave) frequencies are attractive because of their potential for high stability, which scales with operational frequency. Nevertheless, optical clocks have not yet realized this vast potential, due in large part to limitations of the laser used to excite the atomic resonance. To address this problem, we demonstrate a cavity-stabilized laser system with a reduced thermal noise floor, exhibiting a fractional frequency instability of $2 \times 10^{-16}$. We use this laser as a st…
We demonstrate subpicosecond-time-scale population transfer between the pair of hyperfine ground states of atomic rubidium using a single laser-pulse. Our scheme utilizes the geometric and dynamic phases induced during Rabi oscillation through the fine-structure excited state in order to construct an $X$ rotation gate for the hyperfine-state qubit system. Experiment performed with a femtosecond laser and cold rubidium atoms, in a magneto-optical trap, shows over 98\% maximal population transfer between the clock states.
We derive an expression for the magnetic blackbody shift of hyperfine transitions such as the cesium primary reference transition which defines the second. The shift is found to be a complicated function of temperature, and has a T^2 dependence only in the high-temperature limit. We also calculate the shift of ground-state p_1/2 hyperfine transitions which have been proposed as new atomic clock transitions. In this case interaction with the p_3/2 fine-structure multiplet may be the dominant effect.
The sensitivity of an atomic interferometer increases when the phase evolution of its quantum superposition state is measured over a longer interrogation interval. In practice, a limit is set by the measurement process, which returns not the phase, but its projection in terms of population difference on two energetic levels. The phase interval over which the relation can be inverted is thus limited to the interval $[-π/2,π/2]$; going beyond it introduces an ambiguity in the read out, hence a sensitivity loss. Here, we extend the unambiguous interval to probe the phase evolution of an atomic en…
Hyperfine-induced electric dipole contributions may significantly increase probabilities of otherwise very weak electric octupole and magnetic quadrupole atomic clock transitions (e.g. transitions between $s$ and $f$ electron orbitals). These transitions can be used for exceptionally accurate atomic clocks, quantum information processing and search for dark matter. They are very sensitive to new physics beyond the Standard Model, such as temporal variation of the fine structure constant, the Lorentz invariance and Einstein equivalence principle violation. We formulate conditions under which th…
We analyze possible effects of the dark matter environment on the atomic clock stability measurements. The dark matter is assumed to exist in a form of waves of ultralight scalar fields or in a form of topological defects (monopoles and strings). We identify dark matter signal signatures in clock Allan deviation plots that can be used to constrain the dark matter coupling to the Standard Model fields. The existing data on the Al+/Hg+ clock comparison are used to put new limits on the dilaton dark matter in the region of masses m > 10^{-15} eV. We also estimate the sensitivities of future atomi…
We present the latest developments in the field of atomic clocks and their applications in metrology and fundamental physics. In the light of recent advents in the accuracy of optical clocks, we present an introduction to the relativistic modelization of frequency transfer and a detailed review of chronometric geodesy.
For most passive atomic clocks, the Dick effect is one of the main limits to reach its frequency stability limitation due to quantum projection noise. In this paper, we demonstrate that the minimization of the Dick effect for the Ramsey-CPT atomic clock can be accomplished by interleaving lock. By optimizing the duty circle of laser pulses, averaging time during detection and optical intensity of laser beam, the Dick effect induced Allan deviation can be reduced to the level of 10^-14.
In the last ten years extraordinary results in time and frequency metrology have been demonstrated. Frequency-stabilization techniques for continuous-wave lasers and femto-second optical frequency combs have enabled a rapid development of frequency standards based on optical transitions in ultra-cold neutral atoms and trapped ions. As a result, today's best performing atomic clocks tick at an optical rate and allow scientists to perform high-resolution measurements with a precision approaching a few parts in $10^{18}$. This paper reviews the history and the state of the art in optical-clock re…
We consider a free massive particle inside a box which is dragged by Rindler observers. Admitting that the particle obeys the Klein-Gordon equation, we find the frequencies of the stationary states of this system. Transitions between the stationary states are employed to set a standard frequency for a toy atomic clock. Comparing the energy spectrum of the accelerated system with the energy spectrum of an identical system in an inertial frame, we determine the influence of the instantaneous acceleration on the rate of atomic clocks. We argue that our result does not violate the clock hypothesis…
Tests of local position invariance (LPI) made by comparing the relative redshift of atomic clocks based on different atoms have been carried out for a variety of pairs of atomic species. In most cases, several absolute frequency measurements per year are used to look for an annual signal, resulting in tests that can span on order of a decade. By using the output of continuously running clocks, we carry out LPI tests with comparable or higher precision after less than 1.5 years. These include new measurements of the difference in redshift anomalies β for hyperfine transitions in Rb87 and Cs133 …
We report an experimental study of an all-optical three-photon-absorption resonance (known as a "N-resonance") and discuss its potential application as an alternative to atomic clocks based on coherent population trapping (CPT). We present measurements of the N-resonance contrast, width and light-shift for the D1 line of 87Rb with varying buffer gases, and find good agreement with an analytical model of this novel resonance. The results suggest that N-resonances are promising for atomic clock applications.
For the past 15 years, tremendous progress within the fields of laser stabilization, optical frequency combs and atom cooling and trapping have allowed the realization of optical atomic clocks with unrivaled performances. These instruments can perform frequency comparisons with fractional uncertainties well below $10^{-17}$, finding applications in fundamental physics tests, relativistic geodesy, and time and frequency metrology. Even though most optical clocks are currently laboratory setups, several proposals for using these clocks for field measurements or within an optical clock network ha…
We report on the first earth-scale quantum sensor network based on optical atomic clocks aimed at dark matter (DM) detection. Exploiting differences in the susceptibilities to the fine-structure constant of essential parts of an optical atomic clock, i.e. the cold atoms and the optical reference cavity, we can perform sensitive searches for dark matter signatures without the need of real-time comparisons of the clocks. We report a two orders of magnitude improvement in constraints on transient variations of the fine-structure constant, which considerably improves the detection limit for the st…
