Einstein is reported to have once said that time is what a clock measures. Some say that what we experience as time is really our experience of the phenomenon of entropy, the second law of thermodynamics. Entropy, loosely explained, is the tendency for things to become disorganized. Hot coffee always goes cold. It never reheats itself. Eggs don’t unscramble themselves. Your room gets messy and you have to expend energy to clean it, until it gets messy again.
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Here at NIST, we don’t worry about any of these philosophical notions of time. For us, time is the interval between two events. That could be the rising and setting of the sun, the swing of a pendulum from one side to another, or the back-and-forth vibration of a small piece of quartz. For the most precise measurement of the second, we look at the resonant frequencies of atoms.
James Clerk Maxwell, the father of electromagnetic theory, was the first person to suggest that we might use the frequencies of atomic radiation as a kind of invariant natural pendulum, but he was talking about this in the mid-19th century, long before we could exert any kind of control over individual atoms. We would have to wait a century for NIST’s Harold Lyons to build the world’s first atomic clock.
Lyons’ atomic clock, which he and his team debuted in , was actually based on the ammonia molecule, but the principle is essentially the same. Inside a chamber, a gas of atoms or molecules fly into a device that emits microwave radiation with a narrow range of frequencies. When the emitter hits the right frequency, it causes a maximum number of atoms to change state, enabling scientists measure the duration of a certain number of cycles and define a second.
Lyons’ clock, while revolutionary, wasn’t any better at keeping time than doing so by astronomical observations. The first clock that used cesium and was accurate enough to be used as a time standard was built by NIST’s counterpart in the U.K., the National Physical Laboratory, in . NIST’s first cesium clock accurate enough to be used as a time standard, NBS-2, was built a few years later in and went into service as the U.S. official time standard on January 1, . It had an uncertainty of one second in every 3,000 years, meaning that it kept time to within 1/3,000 of a second per year, pretty good compared to an average quartz watch, which might gain or lose a second every month.
The atomic second based on the cesium clock was defined in the International System of Units as the duration of 9,192,631,770 cycles of radiation in . It remains so defined to this day.
While the definition has stayed the same, atomic clocks sure haven’t. Atomic clocks have been continually improved, becoming more and more stable and accurate until the hot clock design reached its peak with the NIST-7, which would neither gain nor lose one second in 6 million years.
Why do we say “hot” clock? That’s because until the s, the temperature of the cesium inside these clocks was a little more than room temperature. At those temperatures, cesium atoms move at around 130 meters per second, pretty fast. So fast, in fact, that it was hard to get a read on them. The clocks simply didn’t have much time to maximize their fluorescence and get a more accurate and stable signal. What we needed to do was give our detectors more time to get the best signal by slowing down the atoms. But how do you slow down an atom? With laser cooling, of course.
But how can lasers cause something to cool down? Aren’t lasers hot? The answer is: It depends. The science of slowing down atoms with lasers was pioneered by Bill Phillips and his colleagues, a feat for which they shared the Nobel Prize in Physics. Very basically what they did was use a specially tuned array of lasers to bombard the atoms with photons from all angles. These photons are like pingpong balls compared to the bowling-ball-like atoms, but if you have enough of them, they can arrest the motion of the cesium atoms, slowing them from about 130 meters per second to a few centimeters per second, giving the clock plenty of time to get a good read on their signal and vastly improving the accuracy and precision of the clock.
The first clock to use this new technology, NIST-F1, called a fountain clock, was put into service in and originally offered a threefold improvement over its predecessor, keeping time to within 1/20,000,000 of a second per year. NIST continued to enhance the design of NIST-F1 and subsequent fountain clocks until the accuracies approached one second every 100,000,000 years.
Not ones to rest on our laurels, NIST and its partner institutions, including JILA, are also working on a series of experimental clocks that operate at optical frequencies with trillions of clock “ticks” per second. One of these clocks, the strontium atomic clock, is accurate to within 1/15,000,000,000 of a second per year. This is so accurate that it would not have gained or lost a second if the clock had started running at the dawn of the universe.
But why do we need such accurate clocks? One thing that wouldn’t exist without such accurate time is the Global Positioning System, or GPS. Each satellite in the GPS network has atomic clocks aboard that beam signals to users below about their position and the time they sent the signal. By measuring the amount of time it takes for the signal to get to you from four different satellites, the receiver in your car or in your can figure out where you are to within a few meters or less.
Such accurate time is also used to timestamp financial transactions so that we know exactly when trades are happening, which can mean the difference between making a fortune and going broke. Accurate time is also necessary for synchronizing communications signals so that, for instance, your call isn’t lost as you travel between cellphone towers.
And as new, even more accurate clocks are invented, it’s assured that we will find uses for them. In the meantime, you’ll have to settle for knowing where you are anywhere on Earth at any given time while talking on your cellphone on your way to an appointment. Even if you arrive a few millionths of a second late, we won’t give you a hard time about it.
*Edited 5/12/
The passively pumped atom beam device is fabricated from a multi-layer stack of Si and glass wafers as shown in Fig. 1. The layers are anodically bonded to form a hermetically sealed vacuum cell with dimensions of 25 mm × 23 mm × 5 mm and ≈0.4 cm3 of internal volume. Internal components include Rb molybdate Zr/Al pill-type dispensers for generating Rb vapor in an internal source cavity20 as well as graphite and Zr/V/Fe non-evaporable getters (NEGs) in a separate drift cavity which maintain the vacuum environment. A series of microcapillaries connect the two internal cavities and produce atomic beams which freely propagate for 15 mm in the drift cavity. The device is heated to generate Rb vapor in the source cavity, and the atomic beam flux and divergence are defined by the capillary geometry21. Microfabrication allows for arbitrary modification of the shape, continuity, and divergence of the capillaries to control the atomic beam properties18,19.
The arrangement of alternating glass and Si layers and internal components which comprise the beam device are shown in Fig. 1b. The features etched in Si are created using deep reactive ion etching (DRIE), and the cavity in the central glass layer is conventionally machined. The two transparent encapsulating glass layers are low-He-permeation aluminosilicate glass22 with 700 µm thickness. The microcapillary array is etched into a 2 mm-thick Si layer which houses the internal components used for passive pumping and sourcing Rb. Two additional layers, a 600 µm-thick Si layer, and a 1 mm-thick borosilicate glass layer, act as a spacer to position the microcapillary array near the center of the device thickness and provide volume into which the atomic beam can expand in the drift cavity. The device is assembled by first anodically bonding the four upper layers under ambient conditions (see Methods) to create a preform structure. The four-layer preform is populated with the getters and Rb pill dispensers and topped with the final glass wafer. The stack is placed in an ultra-high vacuum (UHV) chamber and baked at 520 K for 20 h to degas the components, and the NEGs are thermally activated using laser heating to remove their passivation layer before sealing the device. The final interface is then anodically bonded to hermetically seal the vacuum device (see Fig. 1d).
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Rb atomic beams are generated in the drift cavity as vapor from the source cavity flows through the microcapillary array18. The atomic flux is determined by the source region Rb density and the geometry of the capillary array, which consists of 10 straight capillaries with 100 µm × 100 µm square cross section, 50 µm spacing, and 3 mm length. The flux through the capillaries and angular profile of the atomic beam are well described by analytic molecular flow models based on the capillary’s aspect ratio L/a, where L is the capillary length and a is its width21. The near-axis flux is similar to that of a “cosine” emitter for angles θ less than a/L from normal. The total flux through the capillary array \({F}_{n}=\frac{1}{4}{{w\; n}}_{{{{{{\rm{Rb}}}}}},1}\bar{v}{A}_{c}\), where \({w}=\,1/(1\,+\,3L/4a)\) is the transmission probability of the channel, \({n}_{{{{{{\rm{Rb}}}}}},1}\) is the Rb density in the source region, \(\bar{v}\) is the mean thermal speed of the atoms, and \({A}_{c}\) is the cross-sectional area of the capillary array (here \(10{a}^{2}\)). More complex capillary geometries such as the non-parallel or cascaded collimators can be used to further engineer the beam profile or reduce off-axis flux18,19.
The performance of the atomic beam device is measured using optical spectroscopy on the Rb D2 line at ~780 nm. The atoms are probed using a 5 µW elliptical laser beam with wy ≈ µm, wz ≈ 350 µm (1/e2 radius) normally incident on the device surface (propagating along the x axis). The total density nRb,1 of 85Rb and 87Rb (including all spin states) in the source cavity is measured using absorption spectroscopy with device temperature varying between 330 K and 385 K. A representative spectrum measured in the source cavity at 363 K (Fig. 2a) shows a Doppler broadened spectrum consistent with thermal Rb vapor (\(\bar{v}\) ≈ 300 m/s) and a density of nRb,1 ≈ 2.4 × m−3. The measured \({n}_{{{{{{\rm{Rb}}}}}},1}\) is consistent within experimental uncertainty with published values for the vapor pressure of liquid Rb metal across the temperature range probed.
The flux and angular divergence of the atomic beams are measured using fluorescence spectroscopy in the drift cavity. Fluorescence is collected using a 1:1 imaging system with ≈1.9% collection efficiency mounted at 45° from the beam axis in the x-z plane. The imaged area corresponds to a 1 mm × 1.4 mm region in the x-y plane. Fluorescence spectra scanning around the 85Rb F = 3 → F’ = 4 transition (labeled as zero optical detuning) are measured at varying distances along z from the capillary array. Example spectra at z = 1 mm and z = 11 mm at 363 K (shown in Fig. 2a, b) demonstrate narrow spectral features corresponding to the atomic beam signal and broader features arising from thermal background Rb vapor. The measured atomic beam flux is calculated from the number of detected atoms in the imaged volume Ndet (see methods) as \({F}_{{{{{{\rm{meas}}}}}}}={N}_{{{{{{\rm{det }}}}}}}{v}_{{{{{{\rm{beam}}}}}}}/L,\) where \({v}_{{{{{{\rm{beam}}}}}}}\) is the most probable longitudinal velocity of the atomic beam and L is the length over which the atoms interact with the probe beam. At 363 K and z = 1 mm, \({F}_{{{{{{\rm{meas}}}}}}}\) = 5 × s−1 and the FWHM of the fluorescence lines is ≈150 MHz, corresponding to a transverse velocity FWHM of ≈120 m/s. At this distance, ≈65% of the total capillary array is probed and the total atomic beam flux is estimated to be \({F}_{{{{{{\rm{tot}}}}}}}\) = 7.7 × s−1, consistent with the measured density in the source cavity and molecular flow predictions through the capillaries (see Fig. 2c inset).
Near the end of the drift cavity (z = 10 mm) Fmeas = 3.0 × s−1 or ≈3.9% of the total flux due to the divergence of the atomic beam. This value matches the theoretical expectation (Fig. 2c dashed black line) of 3.2 × s−1 based on \({n}_{{{{{{\rm{Rb}}}}}},1}\), the detected area of ≈1.4 mm2, and the angular distribution function of our capillaries under molecular flow21. This agreement indicates that atomic beam loss due to collisions is consistent with zero within our level of systematic uncertainty. We note that the relatively strong divergence of this beam is typical of microcapillary collimation due to the presence of two atomic flux components, one that is direct (line-of-sight to the source) and the other indirect (diffuse scatter from capillary walls). For measurements of direct atoms (\(\theta < a/L\)), the atomic flux within this range is \(\approx {{{{{{\rm{sin }}}}}}}^{2}\left(\theta \right){F}_{{{{{{\rm{tot}}}}}}}/w\) or ≈ 2.6% of \({F}_{{{{{{\rm{tot}}}}}}}\) for the presented capillary geometry. The beam fluorescence FWHM is ≈40 MHz at this distance, set primarily by the range of x-velocities collected in the imaging system. At \({F}_{{{{{{\rm{tot}}}}}}}\) = 7.7 × s−1, 10 years of sustained operation would require 20 mm3 of metallic Rb. Reported flux and density values have an estimated statistical uncertainty of 15% and systematic uncertainty of 30%.
From the lack of measured collisional loss over a 10 mm distance in the drift cavity, we estimate an upper bound on the background pressure of ~1 Pa. For collisional loss to be significant given our systematic uncertainty in the absolute value of the atomic flux, the transport mean free path of Rb would need to be <1 cm, and this would require partial pressures of >12 Pa of H2 or >3 Pa of N2, which are common vacuum contaminants23. The true background pressure may be significantly lower due to the high gettering efficiency of the NEGs for most common background gases including H2, N2, O2, CO, and CO2. The pumping speeds are estimated to be ≈1.4 L/s for H2 and ≈0.14 L/s for CO at room temperature24. He is not pumped by the passive getters and the steady state He partial pressure will approach the ambient value of ≈0.5 Pa. However, this equilibration may be slowed by our use of low-He-permeation aluminosilicate glass22. Operation of the atomic beam device over many months indicates the rate of oxidation of deposited Rb is negligible.
Fluorescence from thermal background Rb vapor in the drift cavity is evident in all measured spectra, and the measured background Rb density is estimated as \({n}_{{{{{{\rm{Rb}}}}}},2}\) = 3.7 × m−3 at z ≈ 11 mm (see Fig. 2b), equivalent to a partial pressure of ≈ 2 × 10−6 Pa. This density is ≈ × lower than the Rb density in the source cavity due to differential pumping from the microcapillary array and passive pumping primarily from the graphite getters. Graphite getters are commonly used in atomic clocks due to graphite’s affinity for intercalating alkali vapor, and the pressure differential implies a Rb pumping speed of ≈2 L/s for the ≈0.9 cm2 of graphite surface area used. The graphite getters used (Entegris CZR-2) have high porosity and low strength relative to other commonly available graphites25,26. Recent work has demonstrated that graphite can also act as a solid-state reservoir for alkali-metal27,28 and highly oriented pyrolytic graphite (HOPG) can serve both as an alkali getter and source depending on the operating temperature29.
The beam device has been operated intermittently (≈ operation hours) over a period of 15 months without observed degradation of the vacuum environment. The deposited Rb metal in the source cavity is slowly consumed during normal device operation, and partial laser-thermal activation of the pill dispensers has been performed 9 times to deposit additional Rb metal in this cavity. Normal operation of the beam device is observed within minutes after activation and thermal equilibration of the device, and no period of excessive background pressure is observed. Complete activation of the pill dispensers in a single process is likely achievable but has not been attempted in this device. Saturation of the NEGs or graphite has not been observed, indicating that any real or virtual leaks are small, although absolute measurements of the pressure in the presented device have not been made.
The potential utility of the chip-scale atomic beam device is demonstrated using CPT Ramsey spectroscopy of the 87Rb ground state hyperfine splitting (\({\nu }_{{HF}}\) ≈ 6.835 GHz) over a 10 mm distance, similar to previous laboratory CPT atomic beam clocks15,30,31. We address the D1 F = 1,2 → F’ = 2 Λ-system (Fig. 3a) using two circularly polarized, ≈250 µW laser beams propagating along the x-direction (wy ≈ 550 µm, wz ≈ 150 µm). The laser light is phase modulated at \({\nu }_{{{{{{\rm{mod}}}}}}}\) using a fiber-based electro-optical modulator, and the carrier frequency and a 1st order sideband address the CPT Λ-system with approximately equal optical powers. The modulated light is split into two equal-length, parallel paths which intersect the atomic beam at z = 1 mm and z = 11 mm to perform two-zone Ramsey spectroscopy. Fluorescence from atoms in the 2nd zone (1.4 mm2 imaged area) is collected on a Si photodiode with ≈1.9% efficiency. A magnetic field of ≈2.8 × 10−4 T is applied along the x-direction and separates the Zeeman-state dependent transitions.
CPT spectra measured in the second Ramsey zone at 363 K (Fig. 3c) demonstrate three, MHz-wide CPT resonances corresponding to mF = −1, 0, and 1 Λ-systems from ≈1 μs long interaction with the optical fields in the 2nd Ramsey zone. At the center of each of these resonances (Rabi pedestals) are narrower Ramsey fringes arising from interaction with light in both Ramsey zones. The central Ramsey fringe (Fig. 3d) serves as our clock signal and has a fringe width of ≈15 kHz arising from the 30 μs transit time between the two zones. The signal height is ≈3.6 pW and the contrast relative to the one-photon fluorescence is ≈15%. Contrast is limited in our probing scheme by the spread of atoms among mF levels and optical pumping out of the Λ-system. Other probing schemes involving pumping with both circular polarizations can reduce loss outside of the desired mF level and increase fringe contrast32,33,34. The clock fringe is offset by ≈4.5 kHz from the vacuum value of \({\nu }_{{HF}}\) due to the second-order Zeeman effect. Optical path length uncertainty of 0.5 mm between the two Ramsey zones limits comparison to the vacuum value of \({\nu }_{{HF}}\) at the ≈400 Hz level.
An atomic beam clock is realized using the central Ramsey fringe to stabilize the CPT microwave modulation frequency. For this measurement, the beam device is heated to 392 K and the observed peak-to-valley height of the clock Ramsey fringe signal is ≈16 pW using 200 μW of optical power in each Ramsey zone. An error signal is formed using 150 Hz square wave modulation of the clock frequency at an amplitude of 11 kHz, and feedback is used to steer the microwave synthesizer’s center frequency \({\nu }_{{{{{{\rm{clock}}}}}}}\) with a bandwidth of ≈1 Hz. The synthesizer is referenced to a hydrogen maser, and a time series of \({\nu }_{{{{{{\rm{clock}}}}}}}\) is recorded. The measured overlapping Allan deviation (ADEV) of the fractional frequency stability of \({\nu }_{{{{{{\rm{clock}}}}}}}\) (Fig. 4) demonstrates a short-term stability of ≈ 1.2 × 10−9 /\(\sqrt{\tau }\) from 1 s to 250 s, limited by the signal height and the ≈13.5 fW/\(\sqrt{{{{{{\rm{Hz}}}}}}}\) noise equivalent power of the amplified Si detector used. Straightforward improvement in fluorescence collection efficiency and fringe contrast could improve the short-term stability below 1 × 10−10 /\(\sqrt{\tau }\), similar to the performance of existing chip-scale atomic clocks1. Quantum projection noise limits the potential stability of the presented measurement to ≈9 × 10−12 /\(\sqrt{\tau }\), assuming a thermal 87Rb beam at 392 K, a detectable flux of 1.8 × s−1, and a fringe contrast of 25%.
We have demonstrated a chip-scale atomic clock based on miniaturized atomic beams. The key components of the passively pumped atomic beam device are planar, lithographically defined structures etched in Si and glass wafers, compatible with volume microfabrication. The 10-channel microcapillary array etched into one of the Si device layers provides a total atomic flux of ≈7.7 × s−1 at 363 K, and ≈3.9% of the atoms pass through a 1.4 mm2 detection area 10 mm downstream. The measured performance of the atomic beam matches expectations based on molecular flow through the collimator array with no free parameters, indicating that collisions with background gases are minimal and the background pressure is ~1 Pa or lower. Passive and differential pumping of the Rb vapor supports the ≈ × Rb partial pressure differential between the source and drift cavities and enables high beam flux while minimizing the background Rb pressure in the drift cavity. The presented beam system has been operated intermittently for 15 months without degradation of the vacuum environment or saturation of the passive pumps.
The realization of a microwave Ramsey CPT beam clock demonstrates the potential utility of the atomic beam device. CPT Ramsey fringes are measured using the atomic beam over a 10 mm distance, demonstrating atomic coherence across the drift cavity. A clock signal is formed using the magnetically insensitive, mF = 0 transitions between the 87Rb hyperfine ground states, and Ramsey fringes at an operating temperature of 392 K are measured to be 15 kHz-wide with 16 pW of CPT signal. This clock signal is used to stabilize the microwave oscillator driving the CPT transitions, and the clock demonstrates a short-term fractional frequency stability of ≈ 1.2 × 10−9 /\(\sqrt{\tau }\) from 1 s to 250 s. The presented short-term stability is limited by the available signal-to-noise ratio (SNR) of ≈ at 1 s, and improvement of the short-term stability below 1 × 10−10 /\(\sqrt{\tau }\) appears feasible, competitive with existing buffer gas-based miniature atomic clocks, by straightforward improvement to the collection optics and use of a higher contrast pumping scheme32,33,35.
The presented beam clock approach has the potential to exceed existing chip-scale atomic clocks in both long-term stability and accuracy36. Commercial atomic beam clocks based on microwave excitation of the clock transition using a Ramsey length of ≈15 cm achieve a stability at 5 days of 10−14 and an accuracy of 5 × 10−13. Many of the key systematics in beam clocks scale with the clock transition linewidth, and hence inversely with the Ramsey distance, implying that a 15 mm beam clock could achieve stability at the 10−13 level. Work on CPT atomic beam clocks using Na and a 15 cm Ramsey length achieved a stability of 1.5 × 10−11 at s without evidence of a flicker floor31,37. Projected to Cs with a Ramsey length of 15 mm implies an achievable stability at the level of 1.0 × 10−11 at s, equivalent to less than 100 ns timing error at 1 day of integration. Realization of this stability will depend on managing drift in the optical, vacuum, and atomic environments in a fully miniaturized beam clock system.
The leading systematic shifts that will impact a compact beam clock include Doppler shifts, Zeeman shifts, end-to-end cavity phase shifts, collisional shifts, and light shifts. Each of these shifts has been studied extensively in conventional microwave atomic beam frequency standards13,38 and in CPT beam clocks31. We evaluate these requirements assuming a stability goal of 10−12, equivalent to ≈6.8 mHz stability of \({\nu }_{{{{{{\rm{clock}}}}}}}\), for a 1.5 cm Ramsey length. Optical path length instability of the CPT laser beam can lead to both Doppler shifts and end-to-end cavity phase shifts. Doppler shifts arise from CPT laser beam pointing drift (thermal or aging) along the atomic beam axis and shifts the clock frequency at ≈7.5 kHz rad−1, requiring µrad beam pointing stability to reach 10−12 frequency stability. Optical path length stability at the 10 nm level is needed to minimize end-to-end cavity phase shifts. This shift can be minimized using symmetrical Ramsey beam paths, which make thermal expansion common mode along the two Ramsey arms and largely eliminates the bias. Asymmetrical path length variation can arise from thermal gradients along the beam paths and will induce clock shifts. For 15 mm beam paths fabricated using glass or Si substrates, 100 mK temperature uniformity is sufficient to achieve the desired stability.
Collisional shifts place limits on the vacuum stability required in the atomic beam device. Common background gases such as H2 and He induce collisional shifts of \({\nu }_{{{{{{\rm{HF}}}}}}}\) at the level of 5 Hz Pa−1, and 1 mPa pressure stability is needed to achieve 10−12 fractional frequency stability23,39. Given the inferred pressure of ~1 Pa in our device at 363 K, 100 mK temperature stability is sufficient assuming zero background pressure variation. Stabilizing the He partial pressure in passively pumped devices is challenging due to the high He diffusivity in many materials and insufficient getter material for He. We use low-He-permeation aluminosilicate glass to reduce the rate of He ingress, stabilizing He partial pressure variations22,40,41,42. Collisions with background Rb atoms along the drift cavity generate spin-exchange shifts of \({\nu }_{{{{{{\rm{HF}}}}}}}\), and the magnitude of the Rb-Rb collisional shift depends on the occupancy ratio between ground state hyperfine levels before CPT interrogation. Assuming optical pumping into the F = 2 ground state, \({\nu }_{{{{{{\rm{HF}}}}}}}\) shifts at ≈ Hz Pa−1. The total clock shift is estimated to be ≈6.8 mHz for our demonstrated ≈2 × 10−6 Pa Rb background partial pressure43 and places lax requirements on the background pressure stability. Intra-beam collisional shifts also exist at approximately the same level and can be reduced using cascaded collimators to reduce the atomic beam density18.
Light shifts are another significant source of clock instability and can arise from both the ac-Stark effect44 as well as incomplete optical pumping into the CPT dark state45,46. The magnitude and sign of the light shifts can depend strongly on the intensity ratio of the CPT driving fields and the pumping scheme used47, and the shift scales inversely with the Ramsey time. We estimate the light shift sensitivity in the proposed geometry at the level of 1 × 10−12 for a 0.1% change in the CPT field intensity ratio based on measured light shifts in a cold-atom clock using \({\sigma }_{+}\)/\({\sigma }_{-}\) optical pumping, nominally equal CPT field intensities, and a 4 ms Ramsey time47. This level of stability may require use of active monitoring of the optical modulation used to generate the CPT fields42,48,49. Several methods have been developed to manage light shifts in atomic clocks using multiple measurements of the clock frequency, such as auto-balanced Ramsey spectroscopy50,51 or power-modulation spectroscopy52,53. Zeeman shifts arise from variations in the quantization magnetic field, and at a field of ≈10−4 T (sufficient to separate the magnetically sensitive mF ≠ 0 transitions from the clock transition), the Zeeman effect shifts \({\nu }_{{HF}}\) by ≈575 Hz. This dictates a field stability at six parts-per-million (ppm), which can be achieved using intermittent interrogation of a mF ≠ 0 transition to correct the field strength.
Considering each of the common sources of drift summarized in Table 1, an ultimate fractional frequency stability at or below the level of 10−12 appears feasible in a chip-scale atomic beam clock. The presented beam clock presents a path for realizing low size, weight, and power (low-SWaP) atomic clocks. Future efforts will focus on realizing this long-term clock stability goal using integration with micro-optical and thermal packaging to produce a fully integrated device at the size- and power-scale of existing CSACs. Such a device should achieve sub-µs timing error at a week of integration and would contribute to low-SWaP timing holdover applications. The chip-scale beam device presented here is a general platform for quantum sensing, and future work using this system could explore applications including inertial sensing using atom interferometry, electrometry using Rydberg spectroscopy, and higher-performance compact clocks using optical transitions.
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