Abstract
Atomic beams are a longstanding technology for atom-based sensors and clocks with widespread use in commercial frequency standards. Here, we report the demonstration of a chip-scale microwave atomic beam clock using coherent population trapping (CPT) interrogation in a passively pumped atomic beam device. The beam device consists of a hermetically sealed vacuum cell fabricated from an anodically bonded stack of glass and Si wafers in which lithographically defined capillaries produce Rb atomic beams and passive pumps maintain the vacuum environment. A prototype chip-scale clock is realized using Ramsey CPT spectroscopy of the atomic beam over a 10âmm distance and demonstrates a fractional frequency stability of â1.2âÃâ10â9/\(\sqrt{\tau }\) for integration times, Ï, from 1âs to 250âs, limited by detection noise. Optimized atomic beam clocks based on this approach may exceed the long-term stability of existing chip-scale clocks, and leading long-term systematics are predicted to limit the ultimate fractional frequency stability below 10â12.
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Introduction
The development of low-power, chip-scale atomic devices including clocks and magnetometers has been enabled by advances in the optical interrogation of atoms confined in microfabricated vapor cells1. These miniaturized devices commonly use coherent population trapping (CPT) resonances in alkali atoms, which generate a coherent dark state between hyperfine atomic ground states using two optical fields in a Î-scheme2. Optical probing of the microwave transition avoids the need for bulky microwave cavities, providing a compact and low-power method for probing the atoms and enabling battery-powered operation3,4. Buffer gases are commonly used to reduce the decoherence rate from wall collisions and narrow the atomic line. As a result, devices such as the chip-scale atomic clock (CSAC) can realize â10â11 fractional frequency stability at 1000âs of averaging while consuming only 120âmW of power5. Thermal drifts and aging of the buffer gas environment, along with light shifts and other systematics, contribute to the long-term instability of buffer gas systems and degrades clock performance in existing CSACs beyond 1000âs of averaging with a drift rate of ~10â9 per month.
Clocks based on atomic beams and laser-cooled gases operate in ultra-high vacuum (UHV) environments and avoid shifts from buffer gases, allowing for higher frequency stability and continuous averaging over periods of days or weeks. Laser-cooling technology underpins the most advanced atomic clocks6, and while recent efforts in photonic integration7,8 and vacuum technology9,10,11 have advanced the state of the art, significant hurdles to miniaturization and low-power operation remain12. Atomic beams have played a significant role throughout the history of frequency metrology, serving as commercial frequency standards since the 1960s and as national frequency standards for realization of the SI second13,14. Miniaturized atomic beams15,16,17,18,19 offer a path for exceeding the long-term stability of existing chip-scale devices while circumventing the complexity and power needs of more advanced laser-cooled schemes.
In this work, we demonstrate a chip-scale atomic beam clock built using a passively pumped Rb atomic beam device as shown in Fig. 1. The beam device contains a Rb reservoir that feeds a microcapillary array and generates Rb atomic beams in an internal, evacuated cavity. Fabrication of the device is realized using a stack of lithographically defined planar structures which are anodically bonded to form a hermetic package. Spectroscopic measurements of the atomic flux and beam collimation are presented to demonstrate the successful realization of the atomic beam device. The atom beam device presents a pathway for realizing low-power, low-drift atomic sensors using microfabricated components and supports further integration with advanced thermal and photonic packaging to realize highly manufacturable quantum sensors.
a Image of atomic beam device with labeled components (peanut for scale). Rb vapor in the source cavity feeds a buried microcapillary array and forms an atomic beam (indicated by a red-to-blue arrow) in the drift cavity. Non-evaporable getters (NEGs) and graphite maintain the vacuum environment in the device. b Expanded view of the beam device showing component layers as well as Rb pill dispensers, graphite rods, and NEG pumps. c Schematic of the microcapillary array etched in a Si wafer. Each capillary has a 100âµmâÃâ100âµm square cross-section. The array collimates the atomic beam and provides differential pumping between the source and drift regions. d The final anodic bond which hermetically seals the device occurs in an ultra-high vacuum (UHV) chamber.
The microwave atomic beam clock is demonstrated using Ramsey CPT interrogation in the atomic beam device. Ramsey spectroscopy of the 87Rb ground-state hyperfine transitions is measured across a 10âmm distance and demonstrates quantum coherence across the device. The magnetically insensitive mFâ=â0 hyperfine transition is used to realize the atomic beam clock signal, and a clock short-term fractional frequency stability of â1.2âÃâ10â9 is achieved at 1âs of integration in this prototype device. The performance of this beam clock is limited by technical noise, and an optimized cm-scale device is expected to achieve stability better than 10â10 at 1âs of integration with a stability floor below 10â12, supported by a detailed analysis of the sources of drift in atomic beam clocks.
Results
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 25âmmâÃâ23âmmâÃâ5âmm and â0.4âcm3 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 15âmm 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 700âµm thickness. The microcapillary array is etched into a 2âmm-thick Si layer which houses the internal components used for passive pumping and sourcing Rb. Two additional layers, a 600âµm-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 520âK for 20âh 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).
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 100âµmâÃâ100âµm square cross section, 50âµm spacing, and 3âmm length. The flux through the capillaries and angular profile of the atomic beam are well described by analytic molecular flow models based on the capillaryâs 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 âcosineâ 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 ~780ânm. The atoms are probed using a 5âµW elliptical laser beam with wyâââ2100âµm, wzâââ350âµm (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 330âK and 385âK. A representative spectrum measured in the source cavity at 363âK (Fig. 2a) shows a Doppler broadened spectrum consistent with thermal Rb vapor (\(\bar{v}\)âââ300âm/s) and a density of nRb,1âââ2.4âÃâ1018âmâ3. 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.
a Source cavity absorption (gray) and drift cavity fluorescence at zâ=â1âmm (red) and zâ=â11âmm (blue) measures the Rb number density, flux, and the velocity distribution normal to the device surface at 363âK. b Fluorescence at zâ=â11âmm includes narrow peaks from the atomic beam signal as well as a broad signal corresponding to background Rb vapor (light blue curve). Passive and differential pumping generates a large (â6500Ã) Rb partial pressure differential between the source and drift cavities. c The measured atomic beam flux Fmeas and spectral FWHM are plotted versus distance from the capillary array at 363âK. Flux prediction based on nRb,1 (black dashed lines) and the geometrical FWHM limit set by the fluorescence imaging (red dotted line) are shown. Inset shows the estimated total capillary flux Ftot versus device temperature and comparison to the total expected capillary array flux \({F}_{n}\) (dashed line). Error bars represent 68% confidence intervals.
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 â1.9% collection efficiency mounted at 45° from the beam axis in the x-z plane. The imaged area corresponds to a 1âmmâÃâ1.4âmm region in the x-y plane. Fluorescence spectra scanning around the 85Rb Fâ=â3âââFââ=â4 transition (labeled as zero optical detuning) are measured at varying distances along z from the capillary array. Example spectra at zâ=â1âmm and zâ=â11âmm at 363âK (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 363âK and zâ=â1âmm, \({F}_{{{{{{\rm{meas}}}}}}}\)â=â5âÃâ1011âsâ1 and the FWHM of the fluorescence lines is â150âMHz, corresponding to a transverse velocity FWHM of â120âm/s. At this distance, â65% of the total capillary array is probed and the total atomic beam flux is estimated to be \({F}_{{{{{{\rm{tot}}}}}}}\)â=â7.7âÃâ1011âsâ1, 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 (zâ=â10âmm) Fmeasâ=â3.0âÃâ1010âsâ1 or â3.9% of the total flux due to the divergence of the atomic beam. This value matches the theoretical expectation (Fig. 2c dashed black line) of 3.2âÃâ1010âsâ1 based on \({n}_{{{{{{\rm{Rb}}}}}},1}\), the detected area of â1.4âmm2, 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 \(\approx {{{{{{\rm{sin }}}}}}}^{2}\left(\theta \right){F}_{{{{{{\rm{tot}}}}}}}/w\) orâââ2.6% of \({F}_{{{{{{\rm{tot}}}}}}}\) for the presented capillary geometry. The beam fluorescence FWHM is â40âMHz at this distance, set primarily by the range of x-velocities collected in the imaging system. At \({F}_{{{{{{\rm{tot}}}}}}}\)â=â7.7âÃâ1011âsâ1, 10 years of sustained operation would require 20âmm3 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 10âmm distance in the drift cavity, we estimate an upper bound on the background pressure of ~1âPa. 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 <1âcm, and this would require partial pressures of >12âPa of H2 or >3âPa 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 â1.4âL/s for H2 and â0.14âL/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 â0.5âPa. 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 \({n}_{{{{{{\rm{Rb}}}}}},2}\)â=â3.7âÃâ1014âmâ3 at zâââ11âmm (see Fig. 2b), equivalent to a partial pressure ofâââ2âÃâ10â6âPa. This density isâââ6500à 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 graphiteâs affinity for intercalating alkali vapor, and the pressure differential implies a Rb pumping speed of â2âL/s for the â0.9âcm2 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 (â1000 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 (\({\nu }_{{HF}}\)âââ6.835âGHz) over a 10âmm distance, similar to previous laboratory CPT atomic beam clocks15,30,31. We address the D1 Fâ=â1,2âââFââ=â2 Î-system (Fig. 3a) using two circularly polarized, â250âµW laser beams propagating along the x-direction (wyâââ550âµm, wzâââ150âµm). 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 Î-system with approximately equal optical powers. The modulated light is split into two equal-length, parallel paths which intersect the atomic beam at zâ=â1âmm and zâ=â11âmm to perform two-zone Ramsey spectroscopy. Fluorescence from atoms in the 2nd zone (1.4âmm2 imaged area) is collected on a Si photodiode with â1.9% efficiency. A magnetic field of â2.8âÃâ10â4âT is applied along the x-direction and separates the Zeeman-state dependent transitions.
a Schematic of two-zone Ramsey interrogation of the atomic beam. b Level diagram illustrating the CPT Î-systems. c Spectroscopic signal observed in 2nd Ramsey zone shows three, MHz-width CPT features. d The central CPT feature contains the clock signal Ramsey fringe with â15âkHz width and â15% fluorescence contrast.
CPT spectra measured in the second Ramsey zone at 363âK (Fig. 3c) demonstrate three, MHz-wide CPT resonances corresponding to mFâ=ââ1, 0, and 1 Î-systems from â1âμs 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 â15âkHz arising from the 30âμs transit time between the two zones. The signal height is â3.6âpW and the contrast relative to the one-photon fluorescence is â15%. Contrast is limited in our probing scheme by the spread of atoms among mF levels and optical pumping out of the Î-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 â4.5âkHz from the vacuum value of \({\nu }_{{HF}}\) due to the second-order Zeeman effect. Optical path length uncertainty of 0.5âmm between the two Ramsey zones limits comparison to the vacuum value of \({\nu }_{{HF}}\) at the â400âHz 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 392âK and the observed peak-to-valley height of the clock Ramsey fringe signal is â16âpW using 200âμW of optical power in each Ramsey zone. An error signal is formed using 150âHz square wave modulation of the clock frequency at an amplitude of 11âkHz, and feedback is used to steer the microwave synthesizerâs center frequency \({\nu }_{{{{{{\rm{clock}}}}}}}\) with a bandwidth of â1âHz. 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 ofâââ1.2âÃâ10â9 /\(\sqrt{\tau }\) from 1âs to 250âs, limited by the signal height and the â13.5 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 1âÃâ10â10 /\(\sqrt{\tau }\), similar to the performance of existing chip-scale atomic clocks1. Quantum projection noise limits the potential stability of the presented measurement to â9âÃâ10â12 /\(\sqrt{\tau }\), assuming a thermal 87Rb beam at 392âK, a detectable flux of 1.8âÃâ1010âsâ1, and a fringe contrast of 25%.
The Allan deviation (ADEV) of the chip-scale atomic beam clock frequency (black points) is measured for integration times Ïâ<â250âs. The short-term fractional frequency stability Ïy(Ï) isâââ1.2âÃâ10â9 /\(\sqrt{\tau }\) (red line) over this range. Error bars represent 68% confidence intervals.
Discussion
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 â7.7âÃâ1011âsâ1 at 363âK, and â3.9% of the atoms pass through a 1.4âmm2 detection area 10âmm 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 ~1âPa or lower. Passive and differential pumping of the Rb vapor supports theâââ6500âÃâRb 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 10âmm distance, demonstrating atomic coherence across the drift cavity. A clock signal is formed using the magnetically insensitive, mFâ=â0 transitions between the 87Rb hyperfine ground states, and Ramsey fringes at an operating temperature of 392âK are measured to be 15 kHz-wide with 16âpW 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 ofâââ1.2âÃâ10â9 /\(\sqrt{\tau }\) from 1âs to 250âs. The presented short-term stability is limited by the available signal-to-noise ratio (SNR) ofâââ1200 at 1âs, and improvement of the short-term stability below 1âÃâ10â10 /\(\sqrt{\tau }\) 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 â15âcm achieve a stability at 5 days of 10â14 and an accuracy of 5âÃâ10â13. Many of the key systematics in beam clocks scale with the clock transition linewidth, and hence inversely with the Ramsey distance, implying that a 15âmm beam clock could achieve stability at the 10â13 level. Work on CPT atomic beam clocks using Na and a 15âcm Ramsey length achieved a stability of 1.5âÃâ10â11 at 1000âs without evidence of a flicker floor31,37. Projected to Cs with a Ramsey length of 15âmm implies an achievable stability at the level of 1.0âÃâ10â11 at 1000âs, equivalent to less than 100âns 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 10â12, equivalent to â6.8âmHz stability of \({\nu }_{{{{{{\rm{clock}}}}}}}\), for a 1.5âcm 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 â7.5âkHzâradâ1, requiring µrad beam pointing stability to reach 10â12 frequency stability. Optical path length stability at the 10ânm 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 15âmm beam paths fabricated using glass or Si substrates, 100âmK 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 5âHzâPaâ1, and 1âmPa pressure stability is needed to achieve 10â12 fractional frequency stability23,39. Given the inferred pressure of ~1âPa in our device at 363âK, 100âmK 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 Fâ=â2 ground state, \({\nu }_{{{{{{\rm{HF}}}}}}}\) shifts at â3400âHzâPaâ1. The total clock shift is estimated to be â6.8âmHz for our demonstrated â2âÃâ10â6âPa 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 1âÃâ10â12 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 4âms 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 â10â4âT (sufficient to separate the magnetically sensitive mFââ â0 transitions from the clock transition), the Zeeman effect shifts \({\nu }_{{HF}}\) by â575âHz. This dictates a field stability at six parts-per-million (ppm), which can be achieved using intermittent interrogation of a mFââ â0 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 10â12 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.
Methods
Fabrication of atom beam device
Features including two internal cavities and the microcapillary array are etched into Si wafers using DRIE. The beam cell is assembled by first anodically bonding the Si layers, intermediate glass layer, and one encapsulating glass layer to create a preform structure. The preform bonds are performed in air at 623â673âK using a bonding voltage of 800â900âV for several hours. The Rb pills, graphite rods, and NEGs are loosely held in cavities etched in the 2-mm-thick Si wafer, leaving room for expansion during operation. The final bond, which hermetically seals the package, occurs in a UHV chamber using an electrode to press the final encapsulating glass layer onto the preform. The device is vacuum baked at â1âÃâ10â5âPa and 520âK for 20âh to reduce volatile contaminants, and the NEGs are thermally activated using a few W of 975ânm laser light focused onto each getter for â600âs. The NEGs are observed to glow a red color during activation, consistent with a temperature ~1170âK. After NEG activation, the final anodic bond hermetically seals the device. Pressure in the UHV chamber is maintained at â3.5âÃâ10â5âPa for the bond with the cell at â640âK and bonding voltage of â1800âV for 21âh. The sealed device is removed from the UHV bonding chamber and mounted on a temperature-controlled plate for operation in air. Pill dispensers (1âmm diameter, 0.6âmm thickness, 0.4âmg total Rb content) are activated using laser heating with a few W of 975ânm light to a temperature of â950âK until a stable Rb density is observed in the source cavity.
Atom beam flux characterization
The atomic beam flux is measured using fluorescence spectroscopy on the Rb D2 transitions as shown in Fig. 219,54. Spectroscopy is performed using a 5âµW elliptical laser beam traveling normal to the beam device surface with 1/e2 radii of wyâââ2100âµm and wzâââ350âµm. The peak intensity is â0.1âmW/cm2, and the low intensity limits optical pumping during transit through the probing beam. Atomic fluorescence is imaged using a 1:1 imaging system mounted at 45 degrees in the x-z plane to collect â1.9% of the atomic fluorescence onto a 1âmmâÃâ1âmm Si photodiode. The effective probed volume at constant interrogating intensity is â1âmmâÃâ1.4âmmâÃâ\({w}_{z}\sqrt{\pi /2}\) or â0.6âmm3, and this volume can be translated across the drift region. The factor \({{L}_{z}=w}_{z}\sqrt{\pi /2}\) accounts for the Gaussian intensity variation along the z-direction. The flux through this volume \({F}_{{{{{{\rm{meas}}}}}}}={N}_{{{{{{\rm{meas}}}}}}}{v}_{{{{{{\rm{beam}}}}}}}/{L}_{z}\) where \({N}_{{{{{{\rm{meas}}}}}}}\) is the number of atoms measured in the probed volume, \({v}_{{{{{{\rm{beam}}}}}}}=\sqrt{3{k}_{B}T/m}\) is the most probable longitudinal velocity, kB is Boltzmannâs constant, and m is the atomic mass. We measure Ndet using the integrated spectrum of radiated power \({\Phi }_{{{{{{\rm{Total}}}}}}}=\int P\left(\omega \right)d\omega\) across the 85Rb Fâ=â3â>âFââ=â4 transition where P(Ï) is the measured optical power at angular detuning Ï. At low saturation intensity the integrated spectral power per atom \({\Phi }_{0}=\frac{{hc}\pi }{4\lambda }s{\Gamma }^{2}\) and \({N}_{{{{{{\rm{meas}}}}}}}=\frac{{\Phi }_{{Total}}}{{\Phi }_{0}}\), where h is Plankâs constant, c is the speed of light, λ is the D2 transition wavelength, s is the transition saturation parameter, and \(\Gamma\)âââ2ÏâÃâ6.067âMHz is the natural linewidth of the D2 transition.
Data availability
Data underlying the results of this study are available from the authors upon request.
Code availability
The codes that support the findings of this study are available from the authors upon request.
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Acknowledgements
We acknowledge Andrew Ludlow and Ying-Ju Wang for their comments on this document. We acknowledge Elizabeth Donley and Azure Hansen for contributions to device design; Juniper Pollock for helpful discussions; and Susan Schima, Daron Westly, and Durga Gajula for support in device fabrication. Official contribution of the National Institute of Standards and Technology; not subject to copyright in the United States. Mention of commercial products is for information only and does not imply recommendation or endorsement by NIST. This work was supported by the NIST on a Chip program (G.D.M., A.S., J.K., and W.R.M.). Award 70NANB18H006 from U.S. Department of Commerce, NIST (G.D.M., A.S.), and award No. N00014-20-1-2429 from the Office of Naval Research (C.L., C.R.). A patent is pending (U.S. Patent Application No. 63/302,308).
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C.L., G.D.M., C.R., and J.K. contributed to the atomic beam device design. G.D.M., C.L., J.K., C.R., and W.R.M. contributed to the beam device development and fabrication. G.D.M., A.S., and W.R.M. performed measurements and data analysis of the atomic beam device and the atomic beam clock. All authors contributed to the CPT Ramsey protocol, interpretation of results, and writing of this manuscript.
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Martinez, G.D., Li, C., Staron, A. et al. A chip-scale atomic beam clock. Nat Commun 14, 3501 (2023). https://doi.org/10.1038/s41467-023-39166-1
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DOI: https://doi.org/10.1038/s41467-023-39166-1
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