We measured the absolute frequency of the $^1S_0$ - $^3P_0$ transition of $^{171}$Yb atoms confined in a one-dimensional optical lattice relative to the SI second. The determined frequency was 518 295 836 590 863.38(57) Hz. The uncertainty was reduced by a factor of 14 compared with our previously reported value in 2013 due to the significant improvements in decreasing the systematic uncertainties. This result is expected to contribute to the determination of a new recommended value for the secondary representations of the second.
As optical clocks are improved to reach the frequency uncertainty below the 10$^{-17}$ level, the frequency shift due to the blackbody radiation (BBR) has been one of the major systematic effects hindering further improvement. To evaluate the BBR shift of an Yb optical lattice clock at KRISS, we installed an in-vacuum BBR shield and made radiation thermometry using a black-coated-sphere thermal probe. After we quantitatively measured the conduction loss of the thermal probe and the effects of all the external radiation sources, we determined the temperature at the atom trap site with an uncert…
We measured the absolute frequency of the optical clock transition 1S0 (F = 1/2) - 3P0 (F = 1/2) of 171Yb atoms confined in a one-dimensional optical lattice and it was determined to be 518 295 836 590 863.5(8.1) Hz. The frequency was measured against Terrestrial Time (TT; the SI second on the geoid) by using an optical frequency comb of which the frequency was phase-locked to an H-maser as a flywheel oscillator traceable to TT. The magic wavelength was also measured as 394 798.48(79) GHz. The results are in good agreement with two previous measurements of other institutes within the specified…
The absolute frequency of the 1S0-3P0 clock transition of 87Sr has been measured to be 429 228 004 229 873.65 (37) Hz using lattice-confined atoms, where the fractional uncertainty of 8.6x10-16 represents one of the most accurate measurements of an atomic transition frequency to date. After a detailed study of systematic effects, which reduced the total systematic uncertainty of the Sr lattice clock to 1.5x10-16, the clock frequency is measured against a hydrogen maser which is simultaneously calibrated to the US primary frequency standard, the NIST Cs fountain clock, NIST-F1. The comparison i…
We report a stability below $7\times 10{}^{-17}$ of two independent optical lattice clocks operating with bosonic ${}^{88}$Sr isotope. The value (429228066418008.3(1.9)${}_{syst}$(0.9)${}_{stat}$~Hz) of the absolute frequency of the ${}^{1}S_{0}$ - ${}^{3}P_{0}$ transition was measured with an optical frequency comb referenced to the local representation of the UTC by the 330 km-long stabilized fibre optical link. The result was verified by series of measurements on two independent optical lattice clocks and agrees with recommendation of Bureau International des Poids et Mesures.
We report on the first absolute transition frequency measurement at the 10^{-15} level with a single, laser-cooled 40Ca+ ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the S1/2-D5/2 electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency f_Ca+ = 411 042 129 776 393.2 (1.0) Hz is obtained, which corresponds to a fractional uncertainty within a factor of three of the Cs standard. Future improvements are expected to lead to …
Advanced satellite-based frequency transfers by TWCP and IPPP have been performed between NICT and KRISS. We confirm that the disagreement between them is less than 1x10^{-16} at an averaging time of several days. Additionally, an intercontinental frequency ratio measurement of Sr and Yb optical lattice clocks was directly performed by TWCP. We achieved an uncertainty at the mid-10^{-16} level after a total measurement time of 12 hours. The frequency ratio was consistent with the recently reported values within the uncertainty.
We present a measurement of the absolute frequency of the 5s$^2$ $^1$S$_0$ to 5s5p $^3$P$_0$ transition in $^{87}$Sr, which is a secondary representation of the SI second. We describe the optical lattice clock apparatus used for the measurement, and we focus in detail on how its systematic frequency shifts are evaluated with a total fractional uncertainty of $1 \times 10^{-17}$. Traceability to the International System of Units is provided via comparison to International Atomic Time (TAI). Gathering data over 5- and 15-day periods, with the lattice clock operating on average 74$\%$ of the time…
We report the direct excitation of the highly forbidden (6s^2) 1S0 - (6s6p) 3P0 optical transition in two odd isotopes of ytterbium. As the excitation laser frequency is scanned, absorption is detected by monitoring the depletion from an atomic cloud at ~70 uK in a magneto-optical trap. The measured frequency in 171Yb (F=1/2) is 518,295,836,593.2 +/- 4.4 kHz. The measured frequency in 173Yb (F=5/2) is 518,294,576,850.0 +/- 4.4 kHz. Measurements are made with a femtosecond-laser frequency comb calibrated by the NIST cesium fountain clock and represent nearly a million-fold reduction in uncertai…
We performed an absolute frequency measurement of the $^1S_{0}$-$^3P_{0}$ transition in $^{87}$Sr with a fractional uncertainty of $1.2 \times 10^{-15}$, which is less than one third that of our previous measurement. A caesium fountain atomic clock was used as a transfer oscillator to reduce the uncertainty of the link between a strontium optical lattice clock and the SI second. The absolute value of the transition frequency is 429 228 004 229 873.56(49) Hz.
The highly forbidden $^2$S$_{1/2} \rightarrow ^2$F$_{7/2}$ electric octupole transition in $^{171}$Yb$^+$ is a potential candidate for a redefinition of the SI second. We present a measurement of the absolute frequency of this optical transition, performed using a frequency link to International Atomic Time to provide traceability to the SI second. The $^{171}$Yb$^+$ optical frequency standard was operated for 76% of a 25-day period, with the absolute frequency measured to be 642 121 496 772 645.14(26) Hz. The fractional uncertainty of $4.0 \times 10 ^{-16}$ is comparable to that of the best p…
$^{88}$Sr$^{+}$ optical clock with $7.9\times 10^{-19}$ systematic uncertainty and measurement of its absolute frequency with $9.8\times 10^{-17}$ uncertainty
We demonstrated transferring the stability of one highly stable clock laser operating at 729 nm to another less stable laser operating at 698 nm. The two different wavelengths were bridged using an optical frequency comb. The improved stability of the clock laser at 698 nm enabled us to evaluate the systematic frequency shifts of the Sr optical lattice clock with shorter averaging time. We determined the absolute frequency of the clock transition 1S0 - 3P0 in 87Sr to be 429 228 004 229 873.9 (1.4) Hz referenced to the SI second on the geoid via International Atomic Time (TAI).
We have measured the absolute frequency of the optical lattice clock based on $^{87}$Sr at PTB with an uncertainty of $3.9\times 10^{-16}$ using two caesium fountain clocks. This is close to the accuracy of today's best realizations of the SI second. The absolute frequency of the 5s$^2$ $^1$S$_0$-5s5p $^3$P$_0$ transition in $^{87}$Sr is 429,228,004,229,873.13(17) Hz. Our result is in excellent agreement with recent measurements performed in different laboratories worldwide. We improved the total systematic uncertainty of our Sr frequency standard by a factor of five and reach $3\times 10^{-17…
The frequency ratio of the 1S0(F=1/2)-3P0(F=1/2) clock transition in 171Yb and the 1S0(F=9/2)-3P0(F=9/2) clock transition in 87Sr is measured by an optical-optical direct frequency link between two optical lattice clocks. We determined the ratio (ν_{Yb}/ν_{Sr}) to be 1.207 507 039 343 340 4(18) with a fractional uncertainty of 1.5x10^{-15}. The measurement uncertainty of the frequency ratio is smaller than that obtained from absolute frequency measurements using the International Atomic Time (TAI) link. The measured ratio agrees well with that derived from the absolute frequency measurement re…
The optical lattice clock NICT-Sr1 regularly reports calibration measurements of the international timescale TAI. By comparing measurement results to the reports of eight Primary Frequency Standards, we find the absolute frequency of the $^{87}\mathrm{Sr}$ clock transition to be f(Sr)=$429\,228\,004\,229\,873.082(76)$, with a fractional uncertainty of less than 1.8x10$^{-16}$ approaching the systematic limits of the best realization of SI second. Our result is consistent with other recent measurements and further supported by the loop closure over the absolute frequencies of $^{87}\mathrm{Sr}$…
We report the absolute frequency measurement of the 5s2 1S0-5s5p 3P0 transition in 87Sr optical lattice clock (Sr1) at National Time Service Center (NTSC). Its systematic frequency shifts are evaluated carefully with a total relative uncertainty of 5.1E10-17. The measured absolute frequency is 429 228 004 229 872.91(18) Hz with a relative uncertainty of 4.13E10-16, with reference to the ensemble of primary and secondary frequency standards published in the Circular T bulletin by BIPM through a global navigation satellite system (GNSS) link.
We experimentally investigate an optical clock based on $^{171}$Yb ($I=1/2$) atoms confined in an optical lattice. We have evaluated all known frequency shifts to the clock transition, including a density-dependent collision shift, with a fractional uncertainty of $3.4 \times 10^{-16}$, limited principally by uncertainty in the blackbody radiation Stark shift. We measured the absolute clock transition frequency relative to the NIST-F1 Cs fountain clock and find the frequency to be 518 295 836 590 865.2(0.7) Hz.
We report on the development and phase noise performance of a 9.1926 GHz microwave frequency synthesizer to be used as the local oscillator for a Cs fountain clock. It is based on frequency multiplication and synthesis from an ultralow phase noise 5 MHz Oven Controlled Crystal Oscillator (OCXO) and 100 MHz Voltage Controlled Crystal Oscillator (VCXO).The key component of the frequency multiplication is a non-linear transmission-line (NLTL) used as a frequency comb generator. The phase noise of the synthesizer is improved by carefully optimizing the input power, the input and output impedances …
An Al$^+$ clock with $1.6\times10^{-18}$ systematic uncertainty and its frequency ratios
Physikalisch-Technische Bundesanstalt（德国联邦物理技术研究院）；Institut für Quantenoptik, Leibniz Universität Hannover（汉诺威莱布尼茨大学量子光学研究所）；Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France（索邦大学、法国国家科学研究中心、巴黎文理研究大学、法兰西公学院卡斯特尔-布罗塞尔实验室）
We demonstrate a one-dimensional optical lattice clock with a spin-polarized fermionic isotope designed to realize a collision-shift-free atomic clock with neutral atom ensembles. To reduce systematic uncertainties, we developed both Zeeman shift and vector light-shift cancellation techniques. By introducing both an H-maser and a Global Positioning System (GPS) carrier phase link, the absolute frequency of the $^1S_0(F=9/2) - {}^3P_0(F=9/2)$ clock transition of the $^{87}$Sr optical lattice clock is determined as 429,228,004,229,875(4) Hz, where the uncertainty is mainly limited by that of the…
We perform spectroscopic observations of the 698-nm clock transition in $^{87}$Sr confined in an optical lattice using a laser linewidth transfer technique. A narrow-linewidth laser interrogating the clock transition is prepared by transferring the linewidth of a master laser (1064 nm) to that of a slave laser (698 nm) with a high-speed controllable fiber-based frequency comb. The Fourier-limited spectrum is observed for an 80-ms interrogating pulse. We determine that the absolute frequency of the 5s$^{2}$ $^{1}$S$_{0}$ - 5s5p $^{3}$P$_{0}$ clock transition in $^{87}$Sr is 429 228 004 229 872.…
We demonstrated for the first time the characterization of absolute frequency stability of three reference cavities by cross beating three laser beams which are independently locked to these reference cavities. This method shows the individual feature of each reference cavity, while conventional beatnote measurement between two cavities can only provide an upper bound. This method allows for numerous applications such as optimizing the performance of the reference cavity for optical clockwork.
Tests of local position invariance (LPI) made by comparing the relative redshift of atomic clocks based on different atoms have been carried out for a variety of pairs of atomic species. In most cases, several absolute frequency measurements per year are used to look for an annual signal, resulting in tests that can span on order of a decade. By using the output of continuously running clocks, we carry out LPI tests with comparable or higher precision after less than 1.5 years. These include new measurements of the difference in redshift anomalies β for hyperfine transitions in Rb87 and Cs133 …
This article describes the recent progress of optical lattice clocks with neutral strontium ($^{87}$Sr), ytterbium ($^{171}$Yb) and mercury ($^{199}$Hg) atoms. In particular, we present frequency comparison between the clocks locally via an optical frequency comb and between two Sr clocks at remote sites using a phase-stabilized fibre link. We first review cryogenic Sr optical lattice clocks that reduce the room-temperature blackbody radiation shift by two orders of magnitude and serve as a reference in the following clock comparisons. Similar physical properties of Sr and Yb atoms, such as tr…
With direct polarizability measurements we demonstrated extremely low sensitivity of the inner-shell clock transition at $1.14\,μ$m in Tm atoms to external dc electric fields and black-body radiation (BBR). We measured differential polarizabilities of clock levels in Tm at wavelengths of 810--860\,nm and at 1064\,nm and inferred the static scalar differential polarizability of the inner-shell clock transition of $-0.047(18)$ atomic units corresponding to only $2\times10^{-18}$ fractional frequency shift from BBR at the room temperature. This is a few orders of magnitude smaller compared to the…
The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg^+ and Ca optical standards with respect to the SI second as realized at NIST. We find the transition frequencies to be f_Hg=1 064 721 609 899 143(10) Hz and f_Ca=455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg^+ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of …
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 present a system of two independent strontium optical lattice standards probed with a single shared ultra-narrow laser. The absolute frequency of the clocks can be verified by the use of Er:fiber optical frequency comb with the GPS-disciplined Rb frequency standard. We report hertz-level spectroscopy of the clock line and measurements of frequency stability of the two strontium optical lattice clocks.
Absolute frequency measurement of the $^{40}$Ca$^{+}$ clock transition using a GNSS link to the SI second
Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften（奥地利科学院量子光学与量子信息研究所）；Universität Innsbruck, Institut für Experimentalphysik（因斯布鲁克大学实验物理研究所）；Alpine Quantum Technologies GmbH（阿尔卑斯量子技术有限公司）；Singapore University of Technology and Design（新加坡科技设计大学）；Qatar Center for Quantum Computing, College of Science and Engineering, Hamad Bin Khalifa University（哈马德·本·哈利法大学科学与工程学院卡塔尔量子计算中心）
The low-lying isomeric state of $^{229}$Th provides unique opportunities for high-resolution laser spectroscopy of the atomic nucleus. We determine the energy of this isomeric state by taking the absolute energy difference between the excitation energy required to populate the 29.2-keV state from the ground-state and the energy emitted in its decay to the isomeric excited state. A transition-edge sensor microcalorimeter was used to measure the absolute energy of the 29.2-keV $γ$-ray. Together with the cross-band transition energy (29.2 keV$\to$ground) and the branching ratio of the 29.2-keV st…
Sun's gravitation potential at earth varies during a year due to varying Earth-Sun distance. Comparing the results of very accurate measurements of atomic clock transitions performed at different time in the year allows us to study the dependence of the atomic frequencies on the gravitational potential. We examine the measurement data for the ratio of the frequencies in Hg$^+$ and Al$^+$ clock transitions and absolute frequency measurements (with respect to caesium frequency standard) for Dy, Sr, H, hyperfine transitions in Rb and H, and obtain significantly improved limits on the values of th…
Optical lattice clocks surpass primary Cs microwave clocks in frequency stability and accuracy, and are promising candidates for a redefinition of the second in the International System of Units (SI). However, the robustness of optical lattice clocks has not yet reached a level comparable to that of Cs fountain clocks which contribute to International Atomic Time (TAI) by the nearly continuous operation. In this paper, we report the long-term operation of an $^{171}$Yb optical lattice clock with a coverage of 80.3% for half a year including uptimes of 93.9% for the first 24 days and 92.6% for …
Precision saturation spectroscopy of the $^{88}{\rm Sr} ^1S_0-^3P_1$ is performed in a vapor cell filled with various rare gas including He, Ne, Ar, and Xe. By continuously calibrating the absolute frequency of the probe laser, buffer gas induced collision shifts of $\sim $kHz are detected with gas pressure of 1-20 mTorr. Helium gave the largest fractional shift of $1.6 \times 10^{-9} {\rm Torr}^{-1}$. Comparing with a simple impact calculation and a Doppler-limited experiment of Holtgrave and Wolf [Phys. Rev. A {\bf 72}, 012711 (2005)], our results show larger broadening and smaller shifting …
Optical frequency comparison of the 40Ca+ clock transition ν_{Ca} (2S1/2-2D5/2, 729nm) against the 87Sr optical lattice clock transition ν_{Sr}(1S0-3P0, 698nm) has resulted in a frequency ratio ν_{Ca} / ν_{Sr} = 0.957 631 202 358 049 9(2 3). The rapid nature of optical comparison allowed the statistical uncertainty of frequency ratio ν_{Ca} / ν_{Sr} to reach 1x10-15 in only 1000s and yielded a value consistent with that calculated from separate absolute frequency measurements of ν_{Ca} using the International Atomic Time (TAI) link. The total uncertainty of the frequency ratio using optical co…
We present absolute frequency measurement of the unperturbed P7 P7 O$_2$ B-band transition with relative standard uncertainty of $2\times10^{-11}$. We reached the level of accuracy typical for Doppler-free techniques, with Doppler-limited spectroscopy. The Doppler-limited shapes of the P7 P7 spectral line were measured with a frequency-stabilized cavity ring-down spectrometer referenced to an $^{88}$Sr optical atomic clock by an optical frequency comb.
The absolute frequencies of the hyperfine components of the R(26) 62-0 transition in molecular iodine at 501.7 nm are measured for the first time with an optical clockwork based on a femtosecond laser frequency comb generator. The set-up is composed of an Ar+ laser locked to a hyperfine component of the R(26) 62-0 transition detected in a continuously pumped low-pressure cell (0.33 Pa). The detected resonances show a linewidth of 45 kHz (half-width at half-maximum). The uncertainty of the frequency measurement is estimated to be 250 Hz.
Singly-ionized ytterbium, with ultra-narrow optical clock transitions at 467 nm and 436 nm, is a convenient system for the realization of optical atomic clocks and tests of present-day variation of fundamental constants. We present the first direct measurement of the frequency ratio of these two clock transitions, without reference to a cesium primary standard, and using the same single ion of 171Yb+. The absolute frequencies of both transitions are also presented, each with a relative standard uncertainty of $6\times 10^{-16}$. Combining our results with those from other experiments, we repor…
Transition frequencies were determined for transitions in Ra in an atomic beam and for reference lines in Te$_2$ molecules in a vapor cell. The absolute frequencies were calibrated against a GPS stabilized Rb-clock by means of an optical frequency comb. The 7s$^2\,^1$S$_0$(F = 1/2)-7s7p$\,^1$P$_1$(F = 3/2) transition in $^{225}$Ra was determined to be $621\,042\,124(2)\,$MHz. The measurements provide input for designing efficient and robust laser cooling of Ra atoms in preparation of a search for a permanent electric dipole moment in Ra isotopes.
We demonstrate a one-dimensional optical lattice clock with ultracold 171Yb atoms, which is free from the linear Zeeman effect. The absolute frequency of the 1S0(F = 1/2) - 3P0(F = 1/2) clock transition in 171Yb is determined to be 518 295 836 590 864(28) Hz with respect to the SI second.
The pursuit of ever more precise measures of time and frequency is likely to lead to the eventual redefinition of the second in terms of an optical atomic transition. To ensure continuity with the current definition, based on a microwave transition between hyperfine levels in ground-state $^{133}$Cs, it is necessary to measure the absolute frequency of candidate standards, which is done by comparing against a primary cesium reference. A key verification of this process can be achieved by performing a loop closure$-$comparing frequency ratios derived from absolute frequency measurements against…
We report the operation of a dual Rb/Cs atomic fountain clock. 133Cs and 87Rb 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 87Rb hyperfine frequency.
Aided by ultra-high resolution spectroscopy, the overall systematic uncertainty of the $^{1}S_{0}$-$^{3}P_{0}$ clock resonance for lattice-confined $^{87}$Sr has been characterized to $9\times10^{-16}$. This uncertainty is at a level similar to the Cs-fountain primary standard, while the potential stability for the lattice clocks exceeds that of Cs. The absolute frequency of the clock transition has been measured to be 429,228,004,229,874.0(1.1) Hz, where the $2.5\times10^{-15}$ fractional uncertainty represents the most accurate measurement of a neutral-atom-based optical transition frequency…
With ultracold $^{87}$Sr confined in a magic wavelength optical lattice, we present the most precise study (2.8 Hz statistical uncertainty) to-date of the $^1S_0$ - $^3P_0$ optical clock transition with a detailed analysis of systematic shifts (20 Hz uncertainty) in the absolute frequency measurement of 429 228 004 229 867 Hz. The high resolution permits an investigation of the optical lattice motional sideband structure. The local oscillator for this optical atomic clock is a stable diode laser with its Hz-level linewidth characterized across the optical spectrum using a femtosecond frequency…
The absolute frequency of the $^{87}{\rm Sr}$ lattice clock transition was evaluated with an uncertainty of $1.1\times 10^{-15}$ using a frequency link to the international atomic time (TAI). The frequency uncertainty of a hydrogen maser used as a transfer oscillator was reduced by homogeneously distributed intermittent measurement over a five-day grid of TAI. Three sets of four or five days measurements as well as systematic uncertainty of the clock at $8.6\times 10^{-17}$ have resulted in an absolute frequency of $^{87}{\rm Sr}\ {}^1S_0 - {}^3P_0$ clock transition to be 429 228 004 229 872.8…
We present and analyze four frequency measurements designed to characterize the performance of an optical frequency reference based on spectral hole burning in \EuYSO. The first frequency comparison, between a single unperturbed spectral hole and a hydrogen maser, demonstrates a fractional frequency drift rate of $5 \times 10^{-18}$ s$^{-1}$. Optical-frequency comparisons between a pattern of spectral holes, a Fabry-Pérot cavity, and an Al$^+$ optical atomic clock show a short-term fractional frequency stability of $1 \times10^{-15} τ^{-1/2}$ that averages down to $2.5^{+1.1}_{-0.5} \times 10^…
SI-traceable measurements of optical frequencies using International Atomic Time (TAI) do not require a local primary frequency reference, but suffer from an uncertainty in tracing to the SI second. For the measurement of the $^{87}$Sr lattice clock transition, we have reduced this uncertainty to low $10^{-16}$ level by averaging three sets of ten-day intermittent measurements, in which we operated the lattice clock for $10^4$ s on each day. Moreover, a combined oscillator of two hydrogen masers was employed as a local flywheel oscillator (LFO) in order to mitigate the impact of sporadic excur…
We present the first characterization of the spectral properties of superradiant light emitted from the ultra-narrow, 1 mHz linewidth optical clock transition in an ensemble of cold $^{87}$Sr atoms. Such a light source has been proposed as a next-generation active atomic frequency reference, with the potential to enable high-precision optical frequency references to be used outside laboratory environments. By comparing the frequency of our superradiant source to that of a state-of-the-art cavity-stabilized laser and optical lattice clock, we observe a fractional Allan deviation of $6.7(1)\time…
We describe Doppler spectroscopy of Bose-Einstein condensates of ytterbium atoms using a narrow optical transition. We address the optical clock transition around 578 nm between the ${^1}S_0$ and ${^3}P_0$ states with a laser system locked on a high-finesse cavity. We show how the absolute frequency of the cavity modes can be determined within a few tens of kHz using high-resolution spectroscopy on molecular iodine. We show that optical spectra reflect the velocity distribution of expanding condensates in free fall or after releasing them inside an optical waveguide. We demonstrate sub-kHz spe…
