Universal methods for suppressing the light shift in atomic clocks using power modulation
V. I. Yudin, M. Yu. Basalaev, A. V. Taichenachev, J. W. Pollock, Z. L. Newman, M. Shuker, A. Hansen, M. T. Hummon, R. Boudot, E. A. Donley, J. Kitching
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 high-precision scientific instruments and for a wide range of commercial clocks, including chip-scale atomic clocks.
With the uncertainty of the optical clocks improving to the order of 10-18, the probe light used to detect the clock transition has demonstrated nonnegligible Stark shift, provoking to precisely evaluate this shift. Here, we demonstrate a frequency modulation technique to realize a large measurement lever arm of the probe Stark shift with no cost of the measurement accuracy of the interleaved stabilization method. This frequency-modulated spectrum is theoretical described and experimental verified. The probe Stark shift coefficient of the 87Sr optical lattice clock is experimentally determined…
We demonstrate precision measurement and control of inhomogeneous broadening in a multi-ion clock consisting of three $^{176}$Lu$^+$ ions. Microwave spectroscopy between hyperfine states in the $^3D_1$ level is used to characterise differential systematic shifts between ions, most notably those associated with the electric quadrupole moment. By appropriate alignment of the magnetic field, we demonstrate suppression of these effects to the $\sim 10^{-17}$ level relative to the $^1S_0\leftrightarrow{}^3D_1$ optical transition frequency. Correlation spectroscopy on the optical transition demonstr…
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.
The coherent population trapping (CPT) atomic clock is very promising for use in next-generation spaceborne applications owing to its compactness and high performance. In this paper, we propose and implement a CPT atomic clock based on the direct modulation of a large-modulation-bandwidth and narrow-linewidth distributed Bragg reflector laser, which replaces the usually used external bulk modulator in the high-performance CPT clock. Our method retains the high performance while significantly reducing the size. Using this highly compact bichromatic light source and simplest CPT configuration, i…
We demonstrate a vapor cell atomic clock prototype based on continuous-wave (CW) interrogation and double-modulation coherent population trapping (DM-CPT) technique. The DM-CPT technique uses a synchronous modulation of polarization and relative phase of a bi-chromatic laser beam in order to increase the number of atoms trapped in a dark state, i.e. a non-absorbing state. The narrow resonance, observed in transmission of a Cs vapor cell, is used as a narrow frequency discriminator in an atomic clock. A detailed characterization of the CPT resonance versus numerous parameters is reported. A sho…
Current attempts to test local position invariance (LPI) compare different clock transition rates with classically exchanged signals. We propose an experimental scheme for the quantum test of LPI: an internal atomic clock interferometer comprising two interfering clocks within one atom. We prepare the atom in a superposition of two clock states and one ground state, which evolves coherently along two quantum clock oscillations into stable internal Ramsey interference patterns. The interference pattern with the shared ground state shows a visibility modulation, which can be interpreted as the b…
When performing precision measurements, the quantity being measured is often perturbed by the measurement process itself. This includes precision frequency measurements for atomic clock applications carried out with Ramsey spectroscopy. With the aim of eliminating probe-induced perturbations, a method of generalized auto-balanced Ramsey spectroscopy (GABRS) is presented and rigorously substantiated. Here, the usual local oscillator frequency control loop is augmented with a second control loop derived from secondary Ramsey sequences interspersed with the primary sequences and with a different …
Raman interactions in alkali vapours are used in applications such as atomic clocks, optical signal processing, generation of squeezed light and Raman quantum memories for temporal multiplexing. To achieve a strong interaction the alkali ensemble needs both a large optical depth and a high level of spin-polarisation. We implement a technique known as quenching using a molecular buffer gas which allows near-perfect spin-polarisation of over $99.5\%$ in caesium vapour at high optical depths of up to $\sim 2 \times 10^5$; a factor of 4 higher than can be achieved without quenching. We use this sy…
Questioning the presumably most basic assumptions about the structure of space and time has revolutionized our understanding of Nature. State-of-the-art atomic clocks make it possible to precisely test fundamental symmetry properties of spacetime, and search for physics beyond the standard model at low energy scales of just a few electron volts. Here, we experimentally demonstrate for the first time agreement of two single-ion clocks at the $10^{-18}$ level and directly confirm the validity of their uncertainty budgets over a half-year long comparison period. The two clock ions are confined in…
We report on the performance of the first table-top prototype atomic clock based on coherent population trapping (CPT) resonances with parallel linearly polarized optical fields (lin||lin configuration). Our apparatus uses a vertical cavity surface emitting laser (VCSEL) tuned to the D1 line of 87Rb with current modulation at the 87Rb hyperfine frequency. We demonstrate cancellation of the first-order light shift by proper choice of rf modulation power, and further improve our prototype clock stability by optimizing the parameters of the microwave lock loop. Operating in these optimal conditio…
We propose a new scheme for interrogating a warm rubidium vapor using two different clock lasers. Performance-wise, this approach is distinctly different from the recently proposed two-color two-photon rubidium clocks as our scheme does not trade off the AC Stark suppression against an increased sensitivity to the cell-temperature/pressure. Instead, our approach compensates all, the AC-Stark shift and the temperature & pressure-induced frequency shifts. The proposed scheme also makes use of the modulation transfer technique, which enables a two-orders of magnitude increase in the signal-to-noi…
Coherent population trapping (CPT) is extensively studied for future vapor cell clocks of high frequency stability. In the constructive polarization modulation CPT scheme, a bichromatic laser field with polarization and phase synchronously modulated is applied on an atomic medium. A high contrast CPT signal is observed in this so-called double-modulation configuration, due to the fact that the atomic population does not leak to the extreme Zeeman states, and that the two CPT dark states, which are produced successively by the alternate polarizations, add constructively. Here we experimentally …
A method of dynamic continuous-wave spectroscopy of coherent population trapping (CPT) resonances using phase modulation of the jump type is developed. The time evolution of the spectroscopic signal is investigated. A method for the formation of an error signal for frequency stabilization is proposed. We show that our approach has a reduced sensitivity to the lineshape asymmetry of the CPT resonance. The experimental results are in good qualitative agreement with theoretical predictions based on a mathematical model of a three-level $Λ$ system in a bichromatic field. This method can be used in…
We consider optimization of a rubidium atom clock that uses magnetically trapped Bose condensed atoms in a highly elongated trap, and determine the optimal conditions for minimum Allan variance of the clock using microwave Ramsey fringe spectroscopy. Elimination of magnetic field shifts and collisional shifts are considered. The effects of spin-dipolar relaxation are addressed in the optimization of the clock. We find that for the interstate interaction strength equal to or larger than the intrastate interaction strengths, a modulational instability results in phase separation and symmetry bre…
We search for ultralight scalar dark matter candidates that induce oscillations of the fine structure constant, the electron and quark masses, and the quantum chromodynamics energy scale with frequency comparison data between an $^{171}$Yb optical lattice clock and a $^{133}$Cs fountain microwave clock that span 298 days with an uptime of 15.4 $\%$. New limits on the couplings of the scalar dark matter to electrons and gluons in the mass range from $10^{-22}$ eV/$c^{2}$ to $10^{-20}$ eV/$c^{2}$ are set, assuming that each of these couplings is the dominant source of the modulation in the frequ…
Experiments involving optical traps often require careful control of the ac Stark shifts induced by strong confining light fields. By carefully balancing light shifts between two atomic states of interest, optical traps at the magic wavelength have been especially effective at suppressing deleterious effects stemming from such shifts. Highlighting the power of this technique, optical clocks today exploit Lamb-Dicke confinement in magic-wavelength optical traps, in some cases realizing shift cancellation at the ten parts per billion level. Theory and empirical measurements can be used at varyin…
We have developed a universal method to form the reference signal for the stabilization of arbitrary atomic clocks based on Ramsey spectroscopy. Our approach uses an interrogation scheme of the atomic system with two different Ramsey periods and a specially constructed combined error signal (CES) computed by subtracting two error signals with the appropriate calibration factor. CES spectroscopy allows for perfect elimination of probe-induced light shifts and does not suffer from the effects of relaxation, time-dependent pulse fluctuations and phase-jump modulation errors and other imperfection…
The short-term stability of passive atomic frequency standards, especially in pulsed operation, is often limited by local oscillator noise via intermodulation effects. We present an experimental demonstration of the intermodulation effect on the frequency stability of a continuous atomic fountain clock where, under normal operating conditions, it is usually too small to observe. To achieve this, we deliberately degrade the phase stability of the microwave field interrogating the clock transition. We measure the frequency stability of the locked, commercial-grade local oscillator, for two modul…
We demonstrate a means of detecting weak optical transitions in cold atoms that undergo cyclic routines with high sensitivity. The gain in sensitivity is made by probing atoms on alternate cycles leading to a regular modulation of the ground state atom population when at the resonance frequency. The atomic transition is identified by conducting a fast Fourier transform via algorithm or instrument. We find an enhancement of detection sensitivity compared to more conventional scanning methods of $\sim 20$ for the same sampling time, and can detect clock lines with fewer than $10^3$ atoms in a ma…
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…
Optical clock interrogation protocols, based on laser-pulse spectroscopy, are suffering from probe-induced frequency shifts and their variations induced by laser power. Original Hyper-Ramsey probing scheme, which was proposed to alleviate those issues, does not fully eliminate the shift, especially when decoherence and relaxation by spontaneous emission or collisions are present. We propose to solve the fundamental problem of frequency shifts induced by laser probe by deriving the exact canonical form of a multi-pulse generalized Hyper-Ramsey (GHR) resonance, including decoherence and relaxati…
We have found that the error-signal frequency corresponding to the coherent population trapping resonance can be displaced from that of "$0-0$" transition unperturbed by the optical field, although the frequency is not sensitive to changes in its intensity. We consider the double $Λ$-system of levels interacting with the asymmetric polychromatic optical field to demonstrate that this effect arises due to intensity nonlinearity of the error-signal frequency shift. The experiment with $^{87}$Rb atoms in Ar-N$_2$ buffer gas atomic cell shows how the displacement value depends on different paramet…
Tsinghua University（清华大学）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences（中国科学院上海光学精密机械研究所）；University of Chinese Academy of Sciences（中国科学院大学）
