Collisional Shift Research Articles

Clock with 8×10^{-19} Systematic Uncertainty.

We report an optical lattice clock with a total systematic uncertainty of 8.1×10^{-19} in fractional frequency units, representing the lowest uncertainty of any clock to date. The clock relies on interrogating the ultranarrow ^{1}S_{0}→^{3}P_{0} transition in a dilute ensemble of fermionic strontium atoms trapped in a vertically-oriented, shallow, one-dimensional optical lattice. Using imaging spectroscopy, we previously demonstrated record high atomic coherence time and measurement precision enabled by precise control of collisional shifts and the lattice light shift. In this work, we revise the black body radiation shift correction by evaluating the 5s4d ^{3}D_{1} lifetime, necessitating precise characterization and control of many body effects in the 5s4d ^{3}D_{1} decay. Last, we measure the second order Zeeman coefficient on the least magnetically sensitive clock transition. All other systematic effects have uncertainties below 1×10^{-19}.

Collisional shifts of hyperfine resonances of ground-state atoms calculated with modified pseudopotential and orthogonalization

Collisional shifts of hyperfine resonances of ground-state atoms calculated with modified pseudopotential and orthogonalization

Collisional shift and broadening of Rydberg states in nitric oxide at room temperature

Collisional shift and broadening of Rydberg states in nitric oxide at room temperature

Collisional broadening and shift of the hyperfine lines for complex atomic systems in atmosphere of the buffer inert gases

An effective approach to determination of the collisional hyperfine lines shift and broadening in a buffer gas medium is presented and based on the generalized kinetic theory of spectral lines, the exchange perturbation theory and relativistic gauge-invariant perturbation theory with the optimized model potential approximation for computing the optimized basises of the relativistic wave functions.The results of calculating the shift and broadening of the hyperfine structure spectral lines due to collisions for complex atoms (here thallium is considered) in an atmosphere of inert gases (Kr, Xe) are presented and compared with other available alternative theoretical and experimental data. It is shown that the ratio of an adiabaticbroadening to a collisional shift for the pair of Tl–Kr (Га/р)/ fр is ~1/75 and for the pair of Tl- Xe(Га/р)/fр ~1/60.These estimates testify to a violation of well-known Foley relationship, which is, as a rule, inviolable in the standard atomic spectroscopy.

Estimation of Collisional Broadening and Shift for Argon Lines at 811.5 nm and 912.3 nm in Pure Gas and Ar–Ne Mixture

Estimation of Collisional Broadening and Shift for Argon Lines at 811.5 nm and 912.3 nm in Pure Gas and Ar–Ne Mixture

Characterization of the collisional frequency shift in an atomic fountain clock using absorption imaging

The collisional frequency shift is a dominant contribution to the uncertainty of many caesium fountain clocks. Minimizing the effect can be difficult, as lowering the atomic density comes at the cost of a reduced signal-to-noise ratio. Also, it is typically not atomic density, but total atom number that is measured in the experiment, which can lead to a potential measurement bias. In this paper, we describe a direct measurement of the atomic density using absorption imaging of the atomic cloud. For the caesium fountain clock, NRC-FCs2, at the National Research Council Canada, these measurements have led to a reduction in the uncertainty due to the collisional shift by a factor of 10.

High-precision cavity-enhanced spectroscopy for studying the H2-Ar collisions and interactions.

Information about molecular collisions is encoded in the shapes of collision-perturbed molecular resonances. This connection between molecular interactions and line shapes is most clearly seen in simple systems, such as the molecular hydrogen perturbed by a noble gas atom. We study the H2-Ar system by means of highly accurate absorption spectroscopy and ab initio calculations. On the one hand, we use the cavity-ring-down-spectroscopy technique to record the shapes of the S(1) 3-0 line of molecular hydrogen perturbed by argon. On the other hand, we simulate the shapes of this line using ab initio quantum-scattering calculations performed on our accurate H2-Ar potential energy surface (PES). In order to validate the PES and the methodology of quantum-scattering calculations separately from the model of velocity-changing collisions, we measured the spectra in experimental conditions in which the influence of the latter is relatively minor. In these conditions, our theoretical collision-perturbed line shapes reproduce the raw experimental spectra at the percent level. However, the collisional shift, δ0, differs from the experimental value by 20%. Compared to other line-shape parameters, collisional shift displays much higher sensitivity to various technical aspects of the computational methodology. We identify the contributors to this large error and find the inaccuracies of the PES to be the dominant factor. With regard to the quantum scattering methodology, we demonstrate that treating the centrifugal distortion in a simple, approximate manner is sufficient to obtain the percent-level accuracy of collisional spectra.

Ab initio quantum scattering calculations for the CO-O2 system and a new CO-O2 potential energy surface: O2 and air broadening of the R(0) line in CO.

We present ab initio calculations of the collisional broadening of the R(0) pure rotational line in CO (at 115GHz) perturbed by O2. Our calculations are done in a fully quantum way by solving close-coupling quantum-scattering equations without any approximations. We also report a new, highly accurate CO-O2 potential energy surface on which we did the quantum-scattering calculations. The calculated collisional broadening agrees with the available experimental data in a wide temperature range. The calculated collisional shift is negligible compared to the broadening, which is also consistent with the experimental data. We combine this result with our previous calculations for the same line in CO perturbed by N2 [Jóźwiak et al., J. Chem. Phys. 154, 054314 (2021)]; the obtained air-perturbed broadening of the R(0) pure rotational line in CO and its temperature dependence perfectly agree with the HITRAN database. This result constitutes an important step toward developing a methodology for providing accurate ab initio reference data on spectroscopic collisional line-shape parameters for molecular systems relevant to the Earth's atmosphere and for populating spectroscopic line-by-line databases.

High-precision measurement of the hyperfine splitting and ac Stark shift of the 7d D3/22 state in atomic cesium

We report the measurement of hyperfine splitting in the $7d$ $^{2}D_{3/2}$ state of $^{133}\mathrm{Cs}$ using high-resolution Doppler-free two-photon spectroscopy in a Cs vapor cell. We determine the hyperfine coupling constants $A=7.3509(9)$ MHz and $B=\ensuremath{-}0.041(8)$ MHz, which represent an order of magnitude improvement in the precision. We also obtain bounds on the magnitude of the nuclear magnetic octupole coupling constant $C$. Additionally, we measure the ac Stark shift of the $6s\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{S}_{1/2}\ensuremath{\rightarrow}7d$ $^{2}D_{3/2}$ transition at 767.8 nm to be $\ensuremath{-}49\ifmmode\pm\else\textpm\fi{}5\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}/(\mathrm{W}/\mathrm{c}{\mathrm{m}}^{2})$, in agreement with theoretical calculations. We further report the measurement of collisional shift (\ensuremath{-}32.6 \ifmmode\pm\else\textpm\fi{} 2.0 kHz/mTorr) and pressure broadening for the individual hyperfine levels of the $6s\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{S}_{1/2}\ensuremath{\rightarrow}7d$ $^{2}D_{3/2}$ transition. These measurements provide valuable inputs for analysis of systematic effects in optical frequency standards based on the cesium $6s\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{S}_{1/2}\ensuremath{\rightarrow}7d$ $^{2}D_{3/2}$ two-photon transition.

Hyperfine coupling constants of the cesium 7D5/2 state measured up to the octupole term.

We report the measurement of hyperfine splitting (HFS) in the 7D5/2 state of 133Cs using high-resolution Doppler-free two-photon spectroscopy enabled by precise frequency scans using an acousto-optic modulator (AOM). All six hyperfine levels are resolved in our spectra. We determine the hyperfine coupling constants A = -1.70867(62) MHz and B = 0.050(14) MHz which represent an over 20-times improvement in the precision of both A and B. Moreover, our measurement is sufficiently precise to put bounds on the value of the magnetic octupole coupling constant C = 0.4(1.4) kHz for the 7D5/2 state. We additionally report the measurement of the ac Stark shift [-46 ± 4 Hz/(W/cm2)], collisional shift, and pressure broadening which are important for optical frequency standards based on the 6S1/2 → 7D5/2 two-photon transition.

Improved Evaluation of BBR and Collisional Frequency Shifts of NIM-Sr2 with 7.2 × 10−18 Total Uncertainty

NIM-Sr2 optical lattice clock has been developed on the Changping campus of National Institute of Metrology (NIM). Considering the limitations in NIM-Sr1, several improved parts have been designed including a differential pumping stage in the vacuum system, a permanent magnet Zeeman slower, water-cooled anti-Helmholtz coils, an extended viewport for Zeeman slower, etc. A clock laser with a short-time stability better than 3 × 10−16 is realized based on a self-designed 30-cm-long ultra-low expansion cavity. The systematic frequency shift has been evaluated to an uncertainty of 7.2 × 10−18, with the uncertainty of BBR shift and the collisional frequency shift being an order of magnitude lower than the last evaluation of NIM-Sr1.

Inhomogeneous broadening, narrowing and shift of molecular lines under frequent velocity-changing collisions

We demonstrate that speed-dependent hard-collision profiles collapse into a simple Lorentz profile in the regime dominated by the velocity-changing collisions. We present simple analytical formulas for the effective width and shift of the Lorentzian, derived from the speed-dependent collisional broadening and shift. While the effective width increases with speed dependence of collisional shift, it is reduced by speed dependence of collisional width. On the other hand, the effective shift is modified by thermal average of speed dependence of the product of collisional width and shift. We validate these formula numerically applying the quadratic speed dependence of the collisional width and shift.

First uncertainty evaluation of the cesium fountain primary frequency standard NMIJ-F2

We report the first uncertainty evaluation of NMIJ-F2, the second atomic fountain primary frequency standard at the National Metrology Institute of Japan. To improve the frequency stability, we increase the number of detected atoms to 9 × 105 using high-power cooling laser beams for vapor-loaded optical molasses and optical pumping into the Zeeman sublevel m F = 0. We also employ an ultra-stable cryogenic sapphire oscillator as a local oscillator to prevent the degradation of frequency stability due to the Dick effect. After correcting the collisional frequency shift by alternating atom densities, the frequency stability typically reaches 2.5 × 10−13(τ/s)−1/2. Its value is 1.9 × 10−16 after 20 days of measurement. Type B uncertainty is typically evaluated at 4.7 × 10−16; the largest contribution is from a distributed cavity phase shift, followed by a microwave leakage shift. In long-term comparison, the frequency of NMIJ-F2 is found to be consistent with that of the other primary and secondary frequency standards within the uncertainty.

Rubidium excited state line shapes from [formula omitted] to [formula omitted] and [formula omitted] broadened by helium

Pump modulated laser absorption spectroscopy was used to measure five excited state line shapes for electric dipole allowed transitions beginning in the Rb 5P manifold. Helium was used as the collisional buffer gas, with pressures from 0 to 250 Torr. Center frequency, FWHM, and asymmetry parameters were extracted from the fits and plotted versus pressure to determine rates. Lines terminating in the 5D manifold had collisional broadening rates, γ, of 49.5–54.6 MHz/Torr, collisional shift rates, δ of less than ±1.3 MHz/Torr, and asymmetry rates, β0, of less than ±0.08 mrad/Torr. Lines terminating in the 72S1/2 state showed significantly higher rates, with broadening rates of 109.1–111.0 MHz/Torr, shift rates of 11.5–13.3 MHz/Torr, and asymmetry rates of 0.28–0.47 mrad/Torr. These trends qualitatively match numerically computed difference potentials, which also predict large rates for the 7S lines and smaller rates for the 5D lines.

Demonstration of the Systematic Evaluation of an Optical Lattice Clock Using the Drift-Insensitive Self-Comparison Method

The self-comparison method is a powerful tool in the uncertainty evaluation of optical lattice clocks, but any drifts will cause a frequency offset between the two compared clock loops and thus lead to incorrect measurement result. We propose a drift-insensitive self-comparison method to remove this frequency offset by adjusting the clock detection sequence. We also experimentally demonstrate the validity of this method in a one-dimensional 87Sr optical lattice clock. As the clock laser frequency drift exists, the measured frequency difference between two identical clock loops is (240 ± 34) mHz using the traditional self-comparison method, while it is (−15 ± 16) mHz using the drift-insensitive self-comparison method, indicating that this frequency offset is cancelled within current measurement precision. We further use the drift-insensitive self-comparison technique to measure the collisional shift and the second-order Zeeman shift of our clock and the results show that the fractional collisional shift and the second-order Zeeman shift are 4.54(28) × 10−16 and 5.06(3) × 10−17, respectively.

Fundamental Limit of Phase Coherence in Two-Component Bose-Einstein Condensates.

We experimentally and theoretically study phase coherence in two-component Bose-Einstein condensates of ^{87}Rb atoms on an atom chip. Using Ramsey interferometry we determine the temporal decay of coherence between the |F=1,m_{F}=-1⟩ and |F=2,m_{F}=+1⟩ hyperfine ground states. We observe that the coherence is limited by random collisional phase shifts due to the stochastic nature of atom loss. The mechanism is confirmed quantitatively by a quantum trajectory method based on a master equation which takes into account collisional interactions, atom number fluctuations, and losses in the system. This decoherence process can be slowed down by reducing the density of the condensate. Our findings are relevant for experiments on quantum metrology and many-particle entanglement with Bose-Einstein condensates and the development of chip-based atomic clocks.

Rabi spectroscopy of three-dimensional optical lattice clocks

Recent realisation of three-dimensional optical lattice clocks circumvents short range collisional clock shifts which have been the bottle neck towards higher precision; the long range electronic dipole-dipole interaction between the atoms becomes the primary source of clock shift due to interatomic interactions. We study the Rabi spectroscopy of three-dimensional optical lattice clocks with unity filling. From the Lindblad equation governing the time evolution of the density matrix of the atoms, we derive the Bloch equations in the presence of the external Rabi driving laser field, and solve the equations approximately to the first order of the coupling strength of the dipole-dipole interaction between the atoms. We find that the clock shift equals to the product of the coupling strength, a factor determined by the parameters of the Rabi pulse, and another factor depending on the configuration of the three-dimensional optical lattice. Our result on the clock shift within the Rabi spectroscopy can be checked by measurement in future experiment.

Improved estimate of the collisional frequency shift in Al+ optical clocks

Collisions between background gas particles and the trapped ion in an atomic clock can subtly shift the frequency of the clock transition. The uncertainty in the correction for this effect makes a significant contribution to the total systematic uncertainty budget of trapped-ion clocks. Using a non-perturbative analytic framework that was developed for this problem, we estimate the frequency shift in Al$^+$ ion clocks due to collisions with helium and hydrogen. Our calculations significantly improve the uncertainties in the collisional shift coefficients, and show that the collisional frequency shifts for Al$^+$ are zero to within uncertainty.

Systematic uncertainty due to background-gas collisions in trapped-ion optical clocks

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an 27Al+ clock to enable a total fractional systematic uncertainty below 10-18. For this clock, with 38(19) nPa of room-temperature H2 background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order 10-16 at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be -0.6(2.4) × 10-19, where the shift is due to collisional heating time dilation and the uncertainty is dominated by the worst case ±π/2 bound used for collisional phase shift of the 27Al+ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.

Evaluation of different parameterizations of temperature dependences of the line-shape parameters based on ab initio calculations: Case study for the HITRAN database

Temperature dependences of molecular line-shape parameters are important for the spectroscopic studies of the atmospheres of the Earth and other planets. A number of analytical functions have been proposed as candidates that may approximate the actual temperature dependences of the line-shape parameters. In this article, we use our ab initio collisional line-shape calculations for several molecular systems to compare the four temperature ranges (4TR) representation, adopted in the HITRAN database [J. Quant. Spectrosc. Radiat. Transfer 2017;203:3] in 2016, with the double-power-law (DPL) representation. Besides the collisional broadening and shift parameters, we consider also the most important line-shape parameters beyond Voigt, i.e., the speed dependence of broadening and shift parameters, and real and imaginary parts of the complex Dicke parameter. We demonstrate that DPL gives better overall approximation of the temperature dependencies than 4TR. It should be emphasized that DPL requires fewer parameters and its structure is much simpler and more self-consistent than the structure of 4TR. We recommend the usage of DPL representation in HITRAN, and present DPL parametrization for Voigt and beyond-Voigt line profiles that will be adopted in the HITRAN database. We also discuss the problem of the Hartmann-Tran profile parametrization in which the correlation parameter, η, and frequency of the velocity-changing collisions parameter, νvc, diverges to infinity when collisional shift crosses zero; we recommend a simple solution for this problem.