Additive manufacturing (AM) of passive microwave components is of high interest for the cost-effective and rapid prototyping or manufacture of devices with complex geometries. Here, we present an experimental study on the properties of recently demonstrated microwave resonator cavities manufactured by AM, in view of their applications to high-performance compact atomic clocks. The microwave cavities employ a loop-gap geometry using six electrodes. The critical electrode structures were manufactured monolithically using two different approaches: Stereolithography (SLA) of a polymer followed by metal coating and Selective Laser Melting (SLM) of aluminum. The tested microwave cavities show the desired TE011-like resonant mode at the Rb clock frequency of ≈6.835 GHz, with a microwave magnetic field highly parallel to the quantization axis across the vapor cell. When operated in an atomic clock setup, the measured atomic Rabi oscillations are comparable to those observed for conventionally manufactured cavities and indicate a good uniformity of the field amplitude across the vapor cell. Employing a time-domain Ramsey scheme on one of the SLA cavities, high-contrast (34%) Ramsey fringes are observed for the Rb clock transition, along with a narrow (166 Hz linewidth) central fringe. The measured clock stability of 2.2 × 10−13 τ−1/2 up to the integration time of 30 s is comparable to the current state-of-the-art stabilities of compact vapor-cell clocks based on conventional microwave cavities and thus demonstrates the feasibility of the approach.
Compact microwave atomic clocks1 based on alkali vapor cells2,3 are widely employed as stable frequency references in numerous applications, ranging from telecommunication networks4 to onboard clocks in satellite navigation systems.5,6 In such atomic clocks, the frequency of a quartz local oscillator is stabilized to an inherently stable microwave transition in an alkali atom vapor held in a vapor cell. This greatly suppresses the quartz's fractional frequency instabilities to the 10−12 to <10−14 range (timing accuracies of 0.1 μs to <1 ns, respectively) over timescales up to one day. During the last decade, thanks to the employment of laser optical pumping, important advances were made in vapor-cell Rb atomic clocks based on the double-resonance (DR) scheme, using both the continuous-wave (CW)7 and the pulsed optical pumping (POP) interrogation (Ramsey scheme),8,9 where the pulsed Ramsey scheme is of particular interest for highly compact and high-performance Rb cell clocks. In all types of DR atomic clocks, the microwave resonator cavity is a critical component for applying the microwave field to the atoms in a well-controlled geometry. In view of practical applications, this microwave cavity should be small and light-weight and feature simple and fast assembly. In DR atomic clocks, such cavities are generally manufactured by conventional subtractive precision machining of metals, often followed by time-consuming assembly steps requiring precise positioning or alignment of the cavity components.
During the past few years, tremendous progress has been made in the field of additive manufacturing (AM), with several AM techniques nowadays available for manufacturing of microwave components.10 Two AM techniques are especially suitable for the fabrication of microwave cavities: Stereolithography (SLA) and Selective Laser Melting (SLM). Recently, complex waveguide-based microwave components made by SLA of polymers followed by metal coating were reported,11 and first simple microwave resonator structures made by SLM of aluminum were demonstrated.12 It is of interest to exploit AM of microwave cavities for atomic clocks that exhibit more complex geometries,13 to simplify manufacture and assembly, and—in the case of SLA of polymers—reduce the cavity mass. Recently, we reported on the proof-of-principle realization of a compact microwave cavity for CW-DR atomic clocks using SLA of a polymer.14 Here, we report on the detailed characterization of such AM cavities, manufactured by either SLA of a polymer or SLM of aluminum, and their implementation to high-performance Rb atomic clocks in the Ramsey scheme.8
In a Rb vapor-cell atomic clock,2,3 the reference “clock” transition is given by the 5S1/2 magnetic dipole transition at ≈6.835 GHz. Shifting only in second order with an external static magnetic field, the clock transition is conveniently isolated from the other mF Zeeman transitions by applying such a field (field vector Bdc) that defines the quantization axis. Driving the clock transition requires the microwave magnetic field vector H to be parallel to the quantization axis, which in Rb atomic clocks generally is collinear with the laser propagation vector k (see Fig. 1). In practical realizations, the vapor cell and microwave cavity often have cylindrical geometry.13,15 Two main requirements apply to the cavity field mode: first, in order to obtain a strong clock transition signal, H should be perfectly parallel to the quantization axis (Bdc) throughout the vapor cell; second, in particular for the POP clock mode,8,9 the microwave field amplitude should be as homogeneous as possible throughout the cell such that for a given microwave pulse duration, as many atoms as possible undergo an ideal π/2-pulse on the clock transition.
Our cavity is based on the so-called loop-gap structure13,16 which, for the used TE011-like mode, has a magnetic field distribution favorable for clock operation [Fig. 1(a)]. In a simplified way, it can be modelled via its equivalent lumped elements where the equivalent capacitance (reactance) can be considered as mainly dependent on the gap geometry, such as the gap width and thickness, as well as electrode height [Fig. 1(b)], while the equivalent inductance is mainly attributed to the cavity radius [see Eq. (1) in Ref. 13] The two parameters being geometrically decoupled allows us to significantly reduce the cavity radius, for a given frequency, by compensating the change in the reactance with the gap size. The result is a compact device with approximately three times lower volume compared to a simple cylindrical geometry.15 The field homogeneity of such cavities was previously studied experimentally17 and theoretically,18 where the loop-gap approach was found to perform on a par with the standard cylindrical geometry. The quality of field orientation can be evaluated by the Field Orientation Factor (FOF),13 obtained by numerical simulations as FOF ≈ 0.9, over the whole cell volume. Obviously, a high FOF can be achieved if the regions where the field lines turn are located outside the active volume of the Rb cell [see Fig. 1(a)]. Simulated Q-factors for the cavity are typically Q ≈ 150, dominated by losses in the dielectric cell walls.
Manufactured AM cavity cylinders are shown in Fig. 2. Both prototype cylinders are monolithic, combining the cylindrical shield and the electrode structure, thereby eliminating the need for time-consuming assembly and adjustments. Both cavity realizations are compatible with the same Rb cell and cavity endcaps equipped with the excitation loop. The aluminum cylinder (AlSi10Mg alloy, left-hand side of Fig. 2) is made using SLM and passivated with Alodine 1200s. No actions were taken to reduce the surface roughness of the cylinder (≈4–5 times larger for SLM compared to SLA) because RF losses are dominated by the dielectric cell walls and not by the roughness or bulk conductivity of the material. The polymer cylinder14 (right-hand side of Fig. 2) is made using SLA. In order to become RF-functional, the cylinder body was metal-coated with copper using a proprietary electroless plating process of SWISSto12. This copper layer is homogeneous and sufficiently thick (>7 skin-depths) on all surfaces of the polymer body. A thin silver layer added on top of the copper layer ensures passivation. The masses of the aluminum and polymer cylinders are 86 g and 60 g, respectively. The polymer cylinder also benefits from a slightly better manufacturing precision of SLA (≈40 μm). One possible drawback of the SLA cylinder could be its lower thermal conductivity, with impact on cell temperature control. Inserts (SLA) and threads (SLM) serve for attaching the cavity bottom and could become obsolete in a future fully monolithic AM cavity.
The S11 parameter (return loss) was measured using a Vector Network Analyzer for the fully assembled SLA and SLM prototypes, see Fig. 3. The measured S11 parameters show that both realizations meet the required 6.835 GHz frequency, confirming well the simulations. Potential small frequency shifts, due to fabrication tolerances in the AM process or of the vapor cell, can be compensated by frequency tuning, mainly achieved using a set of prototypes with gap sizes varied in 50 μm steps. The use of this main design parameter is limited, however, by the presence of a nearby unwanted mode which can couple closer to the TE011-like mode. Fine tuning of each cavity's resonance frequency is achieved by varying the dielectric loading of the cavity via adjusting the cell position. A sufficiently large tuning range is found, allowing us to meet the resonance condition for both cavity types (see Fig. 3). The measured Q-factors are ≈70 for the SLM and ≈60 for the SLA cavity, which are sufficient for our application. The difference to the simulated Q ≈ 150 is mainly attributed to manufacturing tolerances of the vapor cell (causing higher losses) as well as production uncertainties on the feeding loop, which can lead to increased coupling of the unwanted mode. The temperature-dependent shift of the cavity resonance frequency is measured as ≈– 250 kHz/K, reasonably small for limiting clock instability contributions arising from cavity temperature fluctuations via cavity pulling.1
For testing in an experimental Rb clock,9 the SLA cavity is heated to ≈57 °C and a dc coil placed around the cavity generates a field Bdc collinear with the symmetry axis of the cavity (z in Fig. 1). The openings at both ends of the cavity allow the laser light, provided by a compact laser head emitting at 780 nm (Rb D2 line),19 to travel through the cell, with k also parallel to the symmetry axis z. For all measurements presented here, the laser frequency was stabilized to the Fg = 2 ↔ Fe = 3 Doppler-free resonance obtained from an auxiliary evacuated Rb vapor cell integrated in the laser head. The whole cavity assembly is placed inside a mu-metal enclosure. The quality of the microwave magnetic field orientation (H parallel to Bdc) is evaluated in terms of the FOF (see Refs. 13 and 20 for the definition). Figure 4 shows a measurement of all seven Zeeman transitions in the ground state. The barely distinguishable sigma transitions induced by components of H perpendicular to Bdc21 testify a highly uniform magnetic field, with an experimentally measured FOF = 0.98. The nearby presence of the unwanted mode (Fig. 3) thus does not degrade the field uniformity. The homogeneity of the longitudinal component Hz of H throughout the cell can be experimentally assessed via the damping of the atomic population's Rabi oscillations.9 Figure 5 shows a comparison of Rabi oscillations measured for the SLA cavity and for a classically machined aluminum cavity, in terms of the normalized change in absorption R.9 The slower damping observed for the SLA cavity demonstrates a better microwave field homogeneity across the cell. In both cases, data were taken using a Ramsey-type pulse sequence with a Ramsey time of TR = 3.0 ms, and the microwave pulse area indicated refers to the total pulse area of the two nominal π/2 microwave pulses together.
For further evaluation, we operate the Rb atomic clock prototype in the POP scheme.8,9 The duration of each pulse is set as follows: both optical pumping time and microwave pulse time: 0.4 ms, Ramsey time: 3 ms, and optical detection time: 0.9 ms. The total cycle period is 5.22 ms (including dead times). The quartz oscillator is frequency stabilized to the central fringe of the detected high-contrast Ramsey pattern shown in Fig. 6.
From the measured detection noise during the detection phase (see the inset in Fig. 7), we estimate a signal-to-noise limit for the clock stability of 1.1 × 10−13 τ−1/2.22 The shot-noise instability limit is estimated to be 2.7 × 10−14 τ−1/2. An additional instability contribution of 7 × 10−14 τ−1/2 (Ref. 8) arises from the microwave synthesizer used7 due to the Dick effect23 for our modulation frequency of ≈ 200 Hz. Taking into account both the signal-to-noise limit and the Dick effect, an overall clock stability of 1.3 × 10−13 τ−1/2 is expected. The measured clock frequency stability is 2.2 × 10−13 τ−1/2 up to an integration time of 30 s, in good agreement with the expected stability (Fig. 7). This result is more than four times better than the one previously demonstrated using continuous-wave interrogation14 and is comparable to the state-of-the-art clock stabilities reported for Rb DR atomic clocks operating in the pulsed8 or CW9 scheme.
In conclusion, we presented a detailed study of a compact loop-gap microwave resonator cavity realized by AM techniques, in view of its applications to high-performance vapor-cell atomic clocks. In spite of the somewhat limited spatial resolution of the AM processes, a good reproducibility of the critical cavity structures is obtained. The high FOF and clear Rabi oscillations measured demonstrate the good performances of the AM cavity in view of both the desired high degrees of uniformity and the homogeneity of the microwave magnetic field. The clock stability of 2.2 × 10−13 τ−1/2 measured in the pulsed Ramsey mode shows that AM microwave cavities can fulfill the stringent requirements for high-performance Rb vapor-cell clocks based on Ramsey operation, including for space applications.
This work was supported by Space Positioning Measures of the Swiss Space Office of the State Secretariat for Education, Research and Innovation of the Swiss Confederation (SERI/SSO), call 2016. The authors also acknowledge support of the Swiss National Science Foundation, Grant Nos. 156621 and 162346, as well as previous support of the European Space Agency (ESA) and the European Metrology Research Programme (EMRP Project IND55-Mclocks). The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union. C.A., W.M., M.P., and G.M. thank C. E. Calosso (INRIM, Italy) for providing and support on the microwave local oscillator and F. Gruet and P. Scherler (both LTF, University of Neuchâtel, Switzerland) for support on the laser source and clock physics package.