Measurement and cancellation of the cold collision frequency shift in an 87Rb fountain clock

Development of a space cold atom clock

Atomic clocks with cold atoms play important roles in the field of fundamental physics as well as primary frequency standards. Operating such cold atom clocks in space paves the way for further exploration in fundamental physics, for example dark matter and general relativity. We developed a space cold atom clock (SCAC), which was launched into orbit with the Space Lab TG-2 in 2016. Before it deorbited with TG-2 in 2019, the SCAC had been working continuously for almost 3 years. During the period in orbit, many scientific experiments and engineering tests were performed. In this article, we summarize the principle, development and in-orbit results. These works provide the basis for construction of a space-borne time-frequency system in deep space.

Observation of Spin-Spin Fermion-Mediated Interactions between Ultracold Bosons

Interactions in an ultracold boson-fermion mixture are often manifested by elastic collisions. In a mixture of a condensed Bose gas (BEC) and spin polarized degenerate Fermi gas (DFG), fermions can mediate spin-spin interactions between bosons, leading to an effective long-range magnetic interaction analogous to Ruderman-Kittel-Kasuya-Yosida [Phys. Rev. 96, 99 (1954); Prog. Theor. Phys. 16, 45 (1956); Phys. Rev. 106, 893 (1957)] interaction in solids. We used Ramsey spectroscopy of the hyperfine clock transition in a ^{87}Rb BEC to measure the interaction mediated by a ^{40}K DFG. By controlling the boson density we isolated the effect of mediated interactions from mean-field frequency shifts due to direct collision with fermions. We measured an increase of boson spin-spin interaction by a factor of η=1.45±0.05^{stat}±0.13^{syst} in the presence of the DFG, providing clear evidence of spin-spin fermion mediated interaction. Decoherence in our system was dominated by inhomogeneous boson density shift, which increased significantly in the presence of the DFG, again indicating mediated interactions. We also measured a frequency shift due to boson-fermion interactions in accordance with a scattering length difference of a_{bf_{2}}-a_{bf_{1}}=-5.36±0.44^{stat}±1.43^{syst}a_{0} between the clock-transition states, a first measurement beyond the low-energy elastic approximation [R. Côté, A. Dalgarno, H. Wang, and W. C. Stwalley, Phys. Rev. A 57, R4118 (1998); A. Dalgarno and M. Rudge, Proc. R. Soc. A 286, 519 (1965)] in this mixture. This interaction can be tuned with a future use of a boson-fermion Feshbach resonance. Fermion-mediated interactions can potentially give rise to interesting new magnetic phases and extend the Bose-Hubbard model when the atoms are placed in an optical lattice.

In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms

Atomic clocks based on laser-cooled atoms are widely used as primary frequency standards. Deploying such cold atom clocks (CACs) in space is foreseen to have many applications. Here we present tests of a CAC operating in space. In orbital microgravity, the atoms are cooled, trapped, launched, and finally detected after being interrogated by a microwave field using the Ramsey method. Perturbing influences from the orbital environment on the atoms such as varying magnetic fields and the passage of the spacecraft through Earth’s radiation belt are also controlled and mitigated. With appropriate parameters settings, closed-loop locking of the CAC is realized in orbit and an estimated short-term frequency stability close to 3.0 × 10⁻¹³τ^−1/2 has been attained. The demonstration of the long-term operation of cold atom clock in orbit opens possibility on the applications of space-based cold atom sensors.

Cold atom clocks are among the most precise measuring devices and play key roles in everyday life and scientific explorations. Here the authors demonstrate the first in-orbit atomic clock using cold Rb atoms operating in microgravity and opening possibilities of space surveys and tests of fundamental physics.

Compact Rb optical frequency standard with 10-15 stability

We achieved a low-cost and small-sized Rb optical frequency standard based on ⁸⁵Rb 5S_1/2 → 6P_3/2 transition with 10^-15 stability, which is comparable with that of the best 532 nm I₂ optical frequency standards. In this system, we directly lock the 420 nm diode laser on the 5S_1/2 F = 3 → 6P_3/2 F^' = 4 hyperfine transition line without an additional Pound-Drever-Hall pre-locking system. The signal-to-noise-ratio reaches as high as 350 000 when the averaging time is at 1 s. Eventually by the fluctuation of the residual error signal after locking, the preliminary stability of the optical frequency standard reaches 1.2×10^-14/τ, decreasing to 2.1 × 10^-15 at 80 s. It shows potential in stability performance, experimental cost, and system volume compared with the 532 nm I₂ optical frequency standard as a wavelength standard. It also opens a door for the achievement of wavelength standards by using higher excited states of alkalies.

Atomic Clock Measurements of Quantum Scattering Phase Shifts Spanning Feshbach Resonances at Ultralow Fields

We use an atomic fountain clock to measure quantum scattering phase shifts precisely through a series of narrow, low-field Feshbach resonances at average collision energies below 1  μK. Our low spread in collision energy yields phase variations of order ±π/2 for target atoms in several F, m_{F} states. We compare them to a theoretical model and establish the accuracy of the measurements and the theoretical uncertainties from the fitted potential. We find overall excellent agreement, with small statistically significant differences that remain unexplained.

Measurement of the Spin-Dipolar Part of the Tensor Polarizability of ^{87}Rb

We report on the measurement of the contribution of the magnetic-dipole hyperfine interaction to the tensor polarizaility of the electronic ground state in ^{87}Rb. This contribution was isolated by measuring the differential shift of the clock transition frequency in ^{87}Rb atoms that were optically trapped in the focus of an intense CO_{2} laser beam. By comparing to previous tensor polarizability measurements in ^{87}Rb, the contribution of the interaction with the nuclear electric-quadrupole moment was isolated as well. Our measurement will enable better estimation of blackbody shifts in Rb atomic clocks. The methods reported here are applicable for future spectroscopic studies of atoms and molecules under strong quasistatic fields.

Progress in atomic fountains at LNE-SYRTE

We give an overview of the work done with the Laboratoire National de Métrologie et d'Essais-Systèmes de Référence Temps-Espace (LNE-SYRTE) fountain ensemble during the last five years. After a description of the clock ensemble, comprising three fountains, FO1, FO2, and FOM, and the newest developments, we review recent studies of several systematic frequency shifts. This includes the distributed cavity phase shift, which we evaluate for the FO1 and FOM fountains, applying the techniques of our recent work on FO2. We also report calculations of the microwave lensing frequency shift for the three fountains, review the status of the blackbody radiation shift, and summarize recent experimental work to control microwave leakage and spurious phase perturbations. We give current accuracy budgets. We also describe several applications in time and frequency metrology: fountain comparisons, calibrations of the international atomic time, secondary representation of the SI second based on the (87)Rb hyperfine frequency, absolute measurements of optical frequencies, tests of the T2L2 satellite laser link, and review fundamental physics applications of the LNE-SYRTE fountain ensemble. Finally, we give a summary of the tests of the PHARAO cold atom space clock performed using the FOM transportable fountain.

Demonstration of a dual alkali Rb/Cs fountain clock

We report the operation of a dual Rb/Cs atomic fountain clock. (133)Cs and (87)Rb atoms are cooled, launched, and detected simultaneously in LNE-SYRTE's FO2 double fountain. The dual clock operation occurs with no degradation of either the stability or the accuracy. We describe the key features for achieving such a simultaneous operation. We also report on the results of the first Rb/Cs frequency measurement campaign performed with FO2 in this dual atom clock configuration, including a new determination of the absolute (87)Rb hyperfine frequency.

Accuracy evaluation of an optical lattice clock with bosonic atoms

We report what we believe to be the first accuracy evaluation of an optical lattice clock based on the S01-->P03 transition of an alkaline earth boson, namely, Sr88 atoms. This transition has been enabled by using a static coupling magnetic field. The clock frequency is determined to be 429228066418009(32)Hz. The isotopic shift between Sr87 and Sr88 is 62188135Hz with fractional uncertainty 5x10(-7). We discuss the necessary conditions to reach a clock accuracy of 10(-17) or less by using this scheme.

A quantum scattering interferometer

The collision of two ultracold atoms results in a quantum mechanical superposition of the two possible outcomes: each atom continues without scattering, and each atom scatters as an outgoing spherical wave with an s-wave phase shift. The magnitude of the s-wave phase shift depends very sensitively on the interaction between the atoms. Quantum scattering and the underlying phase shifts are vitally important in many areas of contemporary atomic physics, including Bose-Einstein condensates, degenerate Fermi gases, frequency shifts in atomic clocks and magnetically tuned Feshbach resonances. Precise experimental measurements of quantum scattering phase shifts have not been possible because the number of scattered atoms depends on the s-wave phase shifts as well as the atomic density, which cannot be measured precisely. Here we demonstrate a scattering experiment in which the quantum scattering phase shifts of individual atoms are detected using a novel atom interferometer. By performing an atomic clock measurement using only the scattered part of each atom's wavefunction, we precisely measure the difference of the s-wave phase shifts for the two clock states in a density-independent manner. Our method will enable direct and precise measurements of ultracold atom-atom interactions, and may be used to place stringent limits on the time variations of fundamental constants.

Imaging the Mott Insulator Shells by Using Atomic Clock Shifts

Microwave spectroscopy was used to probe the superfluid-Mott insulator transition of a Bose-Einstein condensate in a three-dimensional optical lattice. By using density-dependent transition frequency shifts, we were able to spectroscopically distinguish sites with different occupation numbers and to directly image sites with occupation numbers from one to five, revealing the shell structure of the Mott insulator phase. We used this spectroscopy to determine the onsite interaction and lifetime for individual shells.

Precision spectroscopy and density-dependent frequency shifts in ultracold Sr

By varying the density of an ultracold 88Sr sample from 10(9) to>10(12) cm(-3), we make the first definitive measurement of the density-related frequency shift and linewidth broadening of the 1S0-3P1 optical clock transition in an alkaline earth system. In addition, we report the most accurate measurement to date of the 88Sr 1S0-3P1 optical clock transition frequency. Including a detailed analysis of systematic errors, the frequency is [434 829 121 312 334+/-20(stat)+/-33(syst)] Hz.

Intense, narrow atomic-clock resonances

We present experimental and theoretical results showing that magnetic resonance transitions from the "end" sublevels of maximum or minimum spin in alkali-metal vapors are a promising alternative to the conventional 0-0 transition for small-size gas-cell atomic clocks. For these "end resonances," collisional spin-exchange broadening, which often dominates the linewidth of the 0-0 resonance, decreases with increasing spin polarization and vanishes for 100% polarization. The end resonances also have much stronger signals than the 0-0 resonance, and are readily detectable in cells with high buffer-gas pressure.

Forbidden transitions in a magneto-optical trap

We report the first observation of a nondipole transition in an ultracold atomic vapor. We excite the 3P-4P electric quadrupole (E2) transition in 23Na confined in a magneto-optical trap, and we demonstrate its application to high-resolution spectroscopy by making the first measurement of the hyperfine structure of the 4P(1/2) level and extracting the magnetic dipole constant A=30.6+/-0.1 MHz. We use cw optical-optical double resonance accompanied by photoionization to probe the transition.

Radio-frequency spectroscopy of ultracold fermions

Radio-frequency techniques were used to study ultracold fermions. We observed the absence of mean-field "clock" shifts, the dominant source of systematic error in current atomic clocks based on bosonic atoms. This absence is a direct consequence of fermionic antisymmetry. Resonance shifts proportional to interaction strengths were observed in a three-level system. However, in the strongly interacting regime, these shifts became very small, reflecting the quantum unitarity limit and many-body effects. This insight into an interacting Fermi gas is relevant for the quest to observe superfluidity in this system.

Controlling the cold collision shift in high precision atomic interferometry

We present a new method based on a transfer of population by adiabatic passage that allows one to prepare cold atomic samples with a well-defined ratio of atomic density and atom number. This method is used to perform a measurement of the cold collision frequency shift in a laser cooled cesium clock at the percent level, which makes the evaluation of the cesium fountain accuracy at the 10(-16) level realistic. With improvements, the adiabatic passage would allow measurements of density-dependent phase shifts at the 10(-3) level in high precision experiments.

Interferometer-type structures for guided atoms

We experimentally demonstrate interferometer-type guiding structures for neutral atoms based on dipole potentials created by microfabricated optical systems. As a central element we use an array of atom waveguides being formed by focusing a red-detuned laser beam with an array of cylindrical microlenses. Combining two of these arrays, we realize X-shaped beam splitters and more complex systems like the geometries for Mach-Zehnder and Michelson-type interferometers for atoms.

Interisotope determination of ultracold rubidium interactions from three high-precision experiments

Combining the measured binding energies of four of the most weakly bound rovibrational levels of the 87Rb2 molecule with results of two other recent high-precision experiments, we obtain exceptionally strong constraints on the atomic interaction parameters in a highly model independent analysis. The comparison of (85)Rb and (87)Rb data, where the two isotopes are related by a mass scaling procedure, plays a crucial role. We predict scattering lengths, clock shifts, and Feshbach resonances with an unprecedented level of accuracy. Two of the Feshbach resonances occur at easily accessible magnetic fields in mixed-spin channels. One is related to a d-wave shape resonance.

Reduction of the cold collisions frequency shift in a multiple velocity fountain: a new proposal

In this paper, we propose a new scheme for operating an atomic fountain frequency standard. A sequence of time-spaced balls of atoms, launched over non-overlapping trajectories, makes possible a reduction of the atomic density and consequently the cold collision frequency shift by one order of magnitude without significant reduction of the useful signal and of the overall stability of the clock. The ultimate accuracy of a Cs fountain could be improved below the 10(-15) level currently achieved in operating clocks.

Manipulation of cold atomic collisions by cavity QED effects

We show how the dynamics of collisions between cold atoms can be manipulated by a modification of spontaneous emission times. This is achieved by placing the atomic sample in a resonant optical cavity. Spontaneous emission is enhanced by a combination of multiparticle entanglement together with a higher density of modes of the modified vacuum field, in a situation akin to superradiance. A specific situation is considered and we show that this effect can be experimentally observed as a large suppression in trap-loss rates.

Cold collision frequency shifts in a 87Rb atomic fountain

We present measurements of cavity frequency pulling and collisional frequency shifts in a 87Rb fountain with a frequency resolution of 3x10(-16). Agreement with theory is found for the cavity pulling and the measured collisional shifts. The clock shift is found at least 50 times smaller than in 133Cs.