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.
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.
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 use the technique of coherent population trapping (CPT) to access the ground hyperfine interval (clock transition) in $^{133}$Cs. The probe and control beams required for CPT are obtained from a single compact diode laser system. The phase coherence between the beams, whose frequency difference is the clock frequency, is obtained by frequency modulating the laser with an electro-optic modulator (EOM). The EOM is fiber coupled and hence does not require alignment, and the atoms are contained in a vapor cell. Both of these should prove advantageous for potential use as atomic clocks in satell…
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.
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…
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）
We demonstrate a high-performance coherent-population-trapping (CPT) Cs vapor cell atomic clock using the push-pull optical pumping technique (PPOP) in the pulsed regime, allowing the detection of high-contrast and narrow Ramsey-CPT fringes. The impact of several experimental parameters onto the clock resonance and short-term fractional frequency stability, including the laser power, the cell temperature and the Ramsey sequence parameters, has been investigated. We observe and explain the existence of a slight dependence on laser power of the central Ramsey-CPT fringe line-width in the pulsed …
Clock-comparison experiments are among the sharpest existing tests of Lorentz symmetry in matter. We characterize signals in these experiments arising from modifications to electron or nucleon propagators and involving Lorentz- and CPT-violating operators of arbitrary mass dimension. The spectral frequencies of the atoms or ions used as clocks exhibit perturbative shifts that can depend on the constituent-particle properties and can display sidereal and annual variations in time. Adopting an independent-particle model for the electronic structure and the Schmidt model for the nucleus, we deter…
We present two new measurements constraining Lorentz and CPT violation using the Xe-129 / He-3 Zeeman maser and atomic hydrogen masers. Experimental investigations of Lorentz and CPT symmetry provide important tests of the framework of the standard model of particle physics and theories of gravity. The two-species Xe-129 / He-3 Zeeman maser bounds violations of CPT and Lorentz symmetry of the neutron at the 10^-31 GeV level. Measurements with atomic hydrogen masers provide a clean limit of CPT and Lorentz symmetry violation of the proton at the 10^-27 GeV level.
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 …
We propose a two-step pulse observation method to enhance frequency stability for coherent population trapping (CPT) atomic clocks. The proposed method is a Raman-Ramsey scheme with low light intensity at resonance observation, and provides a Ramsey-CPT resonance with both reduced frequency sensitivity to the light intensity and a high signal-to-noise ratio by reducing the repumping into a steady dark state. The resonance characteristics were calculated based on density matrix analysis of a $Λ$-type three level system that was modeled on the $^{133}$Cs-D$_1$ line, and the characteristics were …
Vapor cell atomic clocks exhibit reduced frequency stability for averaging time between about one hundred and a few thousand seconds. Here we report a study on the impact of the main parameters on the mid-to-long term instability of a buffer-gas vapor cell Cs clock, based on coherent population trapping (CPT). The CPT signal is observed on the Cs D1 line transmission, using a double $Λ$ scheme and a Ramsey interrogation technique. The effects on the clock frequency of the magnetic field, the cell temperature, and the laser intensities are reported. We show in particular that the laser intensit…
We experimentally investigated the characteristics of two-photon transmission resonances in Rb vapor cells with different amount of buffer gas under the conditions of steady-state coherent population trapping (CPT) and pulsed Raman-Ramsey (RR-) CPT interrogation scheme. We particularly focused on the influence of the Rb atoms diffusing in and out of the laser beam. We showed that this effect modifies the shape of both CPT and Raman-Ramsey resonances, as well as their projected performance for CPT clock applications. In particular we found that at moderate buffer gas pressures RR-CPT did not im…
Light-induced frequency shifts can be a key limiting contribution to the mid and long-term frequency instability in atomic clocks. In this letter, we demonstrate the experimental implementation of the combined error signal interrogation protocol to a cold-atom clock based on coherent population trapping (CPT) and Ramsey spectroscopy. The method uses a single error signal that results from the normalized combination of two error signals extracted from two Ramsey sequences of different dark periods. The single combined error signal is used to stabilize the atomic clock frequency. Compared to the…
We present two new measurements constraining Lorentz and CPT violation using the Xe-129 / He-3 Zeeman maser and atomic hydrogen masers. Experimental investigations of Lorentz and CPT symmetry provide important tests of the framework of the standard model of particle physics and theories of gravity. The two-species Xe-129 / He-3 Zeeman maser bounds violations of CPT and Lorentz symmetry of the neutron at the 10^-31 GeV level. Measurements with atomic hydrogen masers provide a clean limit of CPT and Lorentz symmetry violation of the proton at the 10^-27 GeV level.
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…
We demonstrate how to construct and operate a simple and affordable experimental apparatus, appropriate for an undergraduate setting, in order to produce and study coherent effects in atomic vapor and to investigate their applications for metrology. The apparatus consists of a vertical cavity surface emitting diode laser (VCSEL) directly current-modulated using a tunable microwave oscillator to produce multiple optical fields needed for the observation of the coherent population trapping (CPT). This effect allows very accurate measurement of the transition frequency between two ground state hy…
The Dick effect can be a limitation of the achievable frequency stability of a passive atomic frequency standard when the ancillary frequency source is only periodically sampled. Here we analyze the Dick effect for a pulsed vapor cell clock using coherent population trapping (CPT). Due to its specific interrogation process without atomic preparation nor detection outside of the Ramsey pulses, it exhibits an original shape of the sensitivity function to phase noise of the oscillator. Numerical calculations using a three-level atom model are successfully compared with measurements; an approximat…
Sophisticated Ramsey-based interrogation protocols using composite laser pulse sequences have been recently proposed to provide next-generation high-precision atomic clocks with a near perfect elimination of frequency shifts induced during the atom-probing field interaction. We propose here a simple alternative approach to the auto-balanced Ramsey (ABR) interrogation protocol and demonstrate its application to a cold-atom microwave clock based on coherent population trapping. The main originality of the method, based on two consecutive Ramsey sequences with different dark periods, is to sample…
We report the detection of high-contrast and narrow Coherent Population Trapping (CPT) Ramsey fringes in a Cs vapor cell using a simple-architecture laser system. The latter allows the combination of push-pull optical pumping (PPOP) and a temporal Ramsey-like pulsed interrogation. An originality of the optics package is the use of a single Mach-Zehnder electro-optic modulator (MZ EOM) both for optical sidebands generation and light switch for pulsed interaction. Typical Ramsey fringes with a linewidth of 166 Hz and a contrast of 33 % are detected in a cm-scale buffer-gas filled Cs vapor cell. …
We report on a theoretical study and experimental characterization of coherent population trapping (CPT) resonances in buffer gas-filled vapor cells with push-pull optical pumping (PPOP) on Cs D1 line. We point out that the push-pull interaction scheme is identical to the so-called lin per lin polarization scheme. Expressions of the relevant dark states, as well as of absorption, are reported. The experimental setup is based on the combination of a distributed feedback (DFB) diode laser, a pigtailed intensity Mach-Zehnder electro-optic modulator (MZ EOM) for optical sidebands generation and a …
We have experimentally demonstrated that magnetic-field-insensitive coherent-population-trapping (CPT) resonances are generated between the ground hyperfine levels on the $D_1$ line of $^{133}$Cs using a two-photon $Λ$ scheme excited by lin || lin polarizations. The frequency shift of the CPT resonance is 0.04 Hz for the deviation of 1 $μ$T at a "magic" magnetic field of 139 $μ$T and is 50 times smaller than that of the conventional clock transition at a typical bias magnetic field for the clock operation. The amplitude of the CPT spectrum excited by lin || lin polarizations is enhanced as the…
The temperature dependence of the Cs clock transition frequency in a vapor cell filled with Ne buffer gas has been measured. The experimental setup is based on the coherent population trapping (CPT) technique and a temporal Ramsey interrogation allowing a high resolution. A quadratic dependence of the frequency shift is shown. The temperature of the shift cancellation is evaluated. The actual Ne pressure in the cell is determined from the frequency shift of the 895nm optical transition. We can then determine the Cs-Ne collisional temperature coefficients of the clock frequency. These results c…
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…
We study resonance contrast by a two-step pulse observation method to enhance the frequency stability of coherent population trapping (CPT) atomic clocks. The proposed method is a two-step Raman--Ramsey scheme with low intensity during resonance observation and high intensity after the observation. This method reduces the frequency variation in the light intensity and maintains a high signal-to-noise ratio. The resonance characteristics were calculated by density matrix analysis of a $Λ$-type three-level system that was modeled on the $^{133}$Cs D1 line, and the characteristics were also measu…
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…
The AC Stark shift induced by blackbody radiation is a major source of systematic uncertainty in present-day cesium microwave frequency standards. The shift is parametrized in terms of a third-order electric polarizability $α_0^{(3)}$ that can be inferred from the static electric field displacement of the clock transition resonance. In this paper, we report on an all-optical CPT pump-probe experiment measuring the differential polarizability $Δα_0^{(3)} = α_0^{(3)}(F{=}4) - α_0^{(3)}(F{=}3)$ on a thermal Cs atomic beam, from which we infer $ α_0^{(3)}(F{=}4) = 2.023(6)_{stat}(9)_{syst}~Hz/(kV/…
We report the realization and characterization using coherent population trapping (CPT) spectroscopy of an octadecyltrichlorosilane (OTS)-coated centimeter-scale Cs vapor cell. The dual-structure of the resonance lineshape, with presence of a narrow structure line at the top of a Doppler-broadened structure, is clearly observed. The linewidth of the narrow resonance is compared to the linewidth of an evacuated Cs cell and of a buffer gas Cs cell of similar size. The Cs-OTS adsorption energy is measured to be (0.42 $\pm$ 0.03) eV, leading to a clock frequency shift rate of $2.7\times10^{-9}/$K …
We show that a characteristic two photon lineshape asymmetry arises in coherent population trapping (CPT) and three photon (N) resonances because both resonances are simultaneously induced by modulation sidebands in the interrogating laser light. The N resonance is a three-photon resonance in which a two-photon Raman excitation is combined with a resonant optical pumping field. This joint CPT and N resonance can be the dominant source of lineshape distortion, with direct relevance for the operation of miniaturized atomic frequency standards. We present the results of both an experimental study…
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 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.
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…
Atomic magnetometers have very high absolute precision and sensitivity to magnetic fields but suffer from a fundamental problem: the vectorial or tensorial interaction of light with atoms leads to "dead zones", certain orientations of magnetic field where the magnetometer loses its sensitivity. We demonstrate a simple polarization modulation scheme that simultaneously creates coherent population trapping (CPT) in orientation and alignment, thereby eliminating dead zones. Using $^{87}$Rb in a 10 Torr buffer gas cell we measure narrow, high-contrast CPT transparency peaks in all orientations and…
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 present a joint theoretical and experimental characterization of the coherent population trapping (CPT) resonance excited on the D1 line of 87Rb atoms by bichromatic linearly polarized laser light. We observe high-contrast transmission resonances (up to 25%), which makes this excitation scheme promising for miniature all-optical atomic clock applications. We also demonstrate cancellation of the first-order light shift by proper choice of the frequencies and relative intensities of the two laser field components. Our theoretical predictions are in good agreement with the experimental results…
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…
We observe bimodal fluorescence patterns from atoms in a fast atomic beam when the laser excitation occurs in the presence of a magnetic field and the atoms sample only a portion of the laser profile. The behavior is well explained by competition between the local intensity of the laser, which tends to generate a coherent-population-trapping (CPT) dark state in the $J=1$ to $J'=0$ system, and the strength of an applied magnetic field that can frustrate the CPT process. This work is relevant for understanding and optimizing the detection process for clocks or other coherent systems utilizing th…
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…
We developed a method based on crossed polarizers to observe high-contrast coherent population trapping (CPT) resonance. Since crossed polarizers have a simple optical system, our method is suitable for chip-scale atomic clocks (CSACs). We calculated the Faraday rotation in CPT in a linearly polarized light field (lin || lin) using two pairs of lambda system models based on the density matrix and estimated the spectrum of the Faraday rotation. After that, we measured the contrast and linewidth with the crossed polarizers method. A comparison of the theoretical model and experiment data showed …
The Anti-Matter Factory at CERN is gearing up, commissioning of the Extra Low ENergy Antiprotons (ELENA) ring is ongoing and the first anti-protons are foreseen to circulate in the decelerator very soon. The unprecedented flux of low energy antiprotons delivered by ELENA will open a new era for precision tests with antimatter including laser and microwave spectroscopy and tests of its gravitational behaviour. Here we propose a scheme to load the ultra cold anti-hydrogen atoms that will be produced by the GBAR experiment in an optical lattice tuned at the magic wavelength of the 1S-2S transitio…
A search for an annual variation of a daily sidereal modulation of the frequency difference between co-located ${}^{129}$Xe and ${}^{3}$He Zeeman masers sets a stringent limit on boost-dependent Lorentz and CPT violation involving the neutron, consistent with no effect at the level of 150 nHz. In the framework of the general Standard-Model Extension, the present result provides the first clean test for the fermion sector of the symmetry of spacetime under boost transformations at a level of $10^{-27}$ GeV.
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…
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…
An automated magnetometer suitable for long lasting measurement under stable and controllable experimental conditions has been implemented. The device is based on Coherent Population Trapping (CPT) produced by a multi-frequency excitation. CPT resonance is observed when a frequency comb, generated by diode laser current modulation, excites Cs atoms confined in a $π/4\times(2.5)^2\times1 \textrm{cm}^3$, 2 Torr $N_2$ buffered cell. A fully optical sensor is connected through an optical fiber to the laser head allowing for truly remote sensing and minimization of the field perturbation. A detaile…
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 …
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…
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…
An effective model for describing coherent population trapping resonances, which correctly takes into account the off-resonant frequency components in periodically modulated laser field
