We investigate the probe field induced shift for atomic lattice-based and ion-trap clocks, which can be considered as a near resonant ac-Stark shift, connected to the Zeeman structure of atomic levels and their splitting in a dc magnetic field. This shift arises from possible residual ellipticity in the polarization of the probe field and uncertainty in the magnetic field orientation. Such a shift can have an arbitrary sign and, for some experimental conditions, can reach the fractional value of the order of 10$^{-18}$-10$^{-19}$, i.e., it is not negligible. Thus, it should be taken into account in the uncertainty budgets for the modern ultra-precise atomic clocks. In addition, it is shown that when using hyper-Ramsey spectroscopy, this shift can be reduced to a level much lower than $10^{-19}$.
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…
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.
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 …
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 …
A precise, accurate, and relatively straightforward in-situ method to measure and control the ellipticity of light resonantly interacting with an atomic vapor is described. The technique can be used to minimize vector light shifts. The method involves measurement of ellipticity-induced resonances in the magnetic-field dependence of nonlinear magneto-optical rotation of frequency-modulated light. The light propagation direction is orthogonal to the applied magnetic field $\textbf{B}$ and the major axis of the light polarization ellipse is along $\textbf{B}$. When the light modulation frequency …
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 $1\times 10^{-18}$.
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 investigate the strong-field ionization of atomic hydrogen in a few-cycle elliptically polarized infrared pulse by solving the time-dependent Schrödinger equation. The dependence of the photoelectron momentum distribution on the pulse intensity, ellipticity, length, envelope, and carrier envelope phase is analyzed. In particular, we explain the variation of the electron offset angle with asymptotic electron energy through the combined action of the field and the Coulomb potential, and demonstrate that low-ellipticity pulses make it possible to access the electron release time.
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 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.
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…
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…
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 …
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.
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…
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…
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.
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 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…
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.
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 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…
A Wannier-Stark optical lattice clock has demonstrated unprecedented measurement precision for optical atomic clocks. We present a systematic evaluation of the lattice light shift, a necessary next step for establishing this system as an accurate atomic clock. With precise control of the atomic motional states in the lattice, we report accurate measurements of the multipolar and the hyperpolar contributions and the operational lattice light shift with a fractional frequency uncertainty of 3.5$\times$10${}^{-19}$.
