Gas-cell atomic frequency standards (often referred to as Rubidium clocks) represent a well-established type of secondary frequency references, that offers competitive frequency stabilities up to medium-term timescales (~days) in compact volumes around 0.25 to 2 liters. Industrial realizations of such clocks find applications in telecommunications, as local frequency references, and in space applications like satellite navigation systems [1, 2]. During the past years a number of studies [3, 4, 5] have been conducted on laser-pumped gas-cell frequency standards with the aim of improved frequency stability performance compared to their lamp-pumped counterparts. The narrow and precisely controllable emission spectrum of laser diodes guarantees highly efficient optical pumping, and full separation of different effects that limit the clock performance. Laser optical pumping can therefore offer superior short-term clock stabilities ≤ 3·10-13 τ -1/2 [3, 4], as well as high medium and long-term stabilities  equalling or surpassing lamp pumping technology when drifts due to thermal or light shift effects are controlled [6, 7]. It thus offers the potential to realize improved high-performance gas-cell clocks while maintaining the advantageous compact design. Here we report on the demonstration of a compact and high-performance laser-pumped Rb clock with a frequency stability reaching 1.5·10-12 τ -1/2 down to < 1·10-14 at τ > 104 seconds, and the potential to reach a goal of ≤ 6·10-13 τ -1/2 and 1·10-14 at integration times τ ≥ 104 seconds. Such frequency stabilities from an instrument with a volume ≤ 2 litres, mass ≤ 2 kg, and power consumption ≤ 20 W are of high interest for, e.g., space applications such as satellite navigation systems.
In an alternative approach, the ultimate miniaturisation of gas-cell clocks has been advanced , aiming for clocks with low power-consumption and 1 to 10 cm3 volume, for use in portable end-user devices such as satellite navigation receivers, where moderate frequency stabilities around 10-11 over few hours are sufficient. Such clocks however require novel production techniques for miniaturized cells and mostly involve the coherent population trapping (CPT) interrogation scheme to avoid the need for a microwave cavity which inhibits to reduce the dimensions of the physics package to below the wavelength of the clock transition (≈ few centimetres). In our studies we evaluated the practical implementation of a novel excitation scheme aiming to overcome stability limitations in standard CPT clocks due to the lower signal contrast compared to the optical pumping approach .
HIGH-PERFORMANCE RB GAS-CELL CLOCKS
For the realisation of our compact high-performance clock demonstrator two main issues had to be addressed: the realization of a laser pump light source showing sufficiently good frequency and intensity stability for the short-term stability goal, and the mastering of long-term frequency drifts of the atomic reference. Such long-term drifts arise mainly from the temperature coefficient of the resonance cell and light shift effects under conditions of laser pumping; both can be controlled by fine-tuning of the cell’s buffer gas content. The phase noise properties of the microwave local oscillator also affect the short-term stability, but were not addressed in this study.
The clock is composed of a modified industrial Rb clock and a separate laser head as pump light source, while bearing in mind later integration of the laser head into the clock. The laser head contains a compact laser module and frequency stabilization to Rb absorption lines from a small reference spectroscopy setup. The laser frequency is stabilized to one of the 87Rb D2 (5S1/2→5P3/2) transition line components, for efficient optical pumping of the 5S1/2 ground state population of 87Rb atoms contained in the clock module’s resonance cell. In the clock module, the hyperfine ground-state “clock” transition at 6.8 GHz is probed by applying a microwave field to the clock cell via a microwave resonator cavity. A 10 MHz quartz local oscillator (LO) is stabilized to the center of this double-resonance signal using frequency modulation of the microwave and lock-in detection techniques (Fig. 1).
For the clock module we use an industrial Rb atomic clock (Temex Neuchâtel Time, RAFS type), showing lamp-pumped short-term stabilities of 3·10-12 τ-1/2 . From this clock the discharge lamp was removed and the quartz LO was exchanged to allow for a wider tuning range during clock optimization. Furthermore, the resonance cell’s buffer gas content was optimized, in order to adopt to the laser pumping conditions. Fig. 2 shows a photograph of the demonstrator clock comprised of its two sub-units.
Stabilized Laser Source
The laser head  has an overall physics package volume of 200 cm3 (upper part on the left hand side in Fig. 2) and contains a compact (54 cm3) external-cavity diode laser (ECDL) in Littrow configuration. It also includes a compact saturated-absorption set-up using a simple retro-reflected beam geometry, for laser frequency stabilization to a temperature-controlled and magnetically shielded Rb reference cell (2 cm3 volume). The laser head emits about 2 mW of output power within a spectral width FWHM < 500 kHz. The stabilised laser has a frequency noise of 2 kHz·Hz -1/2 and intensity noise RIN≈10-13/Hz (at about 300 Hz), and shows a frequency stability of 2·10-12 τ -1/2 up to 100 s and < 2·10-12 between 102 and 105 s. These values fulfil the requirements to reach short-term clock stabilities around 2·10-13 τ-1/2 . Passive drifts of the laser intensity amount to around 2·10-4 at 104 seconds, probably due to thermal gradients and instabilities in the laser head. Here improvements can be expected from optimized thermal design, active intensity stabilization, or further miniaturization of the laser head by the implementation of advanced single-mode laser diodes such as distributed feed-back (DFB) or distributed Bragg-reflector (DBR) laser diodes. Due to the moving grating, the ECDL-based laser head shows some mechanical sensitivity, which is ideally to be avoided in an envisaged space instrument. The availability of space-worthy DFB or DBR lasers at the required wavelengths thus presents an important development issues for future space atomic clocks and other laser-based instruments.
We also evaluated a DFB laser diode emitting at 780 nm in the same laser head, by omitting the diffraction grating of the ECDL. The larger linewidth around 7 MHz of the DFB laser results in slightly increased width of the observed reference lines (≈ 30 MHz instead of ≈ 20 MHz with the ECDL), which merely degrades the short-term laser frequency stability (to around 4·10-12 τ-1/2) that remains compatible with the requirements for a high-performance gas-cell clock. Because the stabilisation loop acts on the DFB current only, larger drifts of the laser output power can occur than for the grating-stabilised ECDL, but these can be compensated by an additional intensity stabilisation loop acting on the laser temperature . Both the ECDL-based and DFB laser head were successfully used in our Rb clock demonstrator. A detailed characterisation of different types of diode lasers in view of their potential application to gas-cell Rb clocks can be found in .
Clock resonance cell properties
In this section we discuss the main relevant properties of the clock resonance cell which affect the clock stability under laser optical pumping. While the obtained signal contrast and noise levels limit the short-term frequency stability, limitations arising from the light shift are small there and become significant only for the long-term stability, as is the case for the temperature coefficient of the buffer-gas cell. We control clock instabilities arising from this temperature coefficient and the intensity-related light shift effects by choosing an appropriate mixture and absolute pressure of buffer gases for the resonance cell.
Fig. 3 shows the double resonance signal contrast for selected cell temperatures. At typical light intensities around 30 – 60 μW/cm2, signal contrasts around 15 to 20 % and linewidths between 0.5 and 1.5 kHz are obtained, depending on microwave power levels. This results in a higher signal-to-noise ratio and thus improved short-term clock stability compared to lamp-pumped Rb clocks, that reach typical values around 1% and 1-2 kHz respectively, at their best. From the measured double-resonance signals at the low pump light powers used, we derive a shot-noise limit for the short-term stability to be around 2·10-13 τ-1/2  and an overall stability limit around 1·10-12 τ-1/2  Still better signal contrast up to 60% and thus improved short-term stability can be reached at higher light intensities or using schemes for still higher signal contrast 
The AC Stark shift or “light shift” of the clock transition induced by the pump light field constitutes a major source of instabilities in optically pumped atomic clocks . As a consequence, in optically pumped gas-cell clocks the clock transition frequency fC exhibits a dispersive shape as function of the pump light laser frequency vL, where the amplitude depends linearly on the total light intensity (see Fig. 4). Fluctuations of the pump light intensity or frequency will thus be translated into clock instabilities. We quantify such shifts of clock frequency due to changes in laser intensity or frequency by the proportionality parameters α (corresponding to the splitting of the light-shift curves for different light intensities) and β (slope of the light-shift curves), respectively.
In our clock realisation we minimize the intensity light shift by precise control of the buffer gas pressure in the clock resonance cell , such as to make the point of α ≈ 0 (downward arrow in Fig. 4) coincide with the stabilised pump-laser frequency (upward arrow in Fig. 4), which avoids the need for active stabilization of the pump light intensity. In this approach, minimisation of the frequency-dependent light-shift parameter β is not possible at the same time, making necessary a well-stabilised pump-laser frequency. Fig. 5 shows the measured intensity related shifts of the clock frequency for different cells. For typical pump light levels (≈ 40 μW/cm2) and with α, β expressed in fractional stability of fC we find α ≈ 2·10-10 ΔI/I and β ≈ 3·10-17/Hz.
From the measured laser stability, limitations to the short-term clock stability arising from the light shift are estimated to ≤ 1·10-13 τ-1/2 for both the intensity and frequency-related contributions. At 104 s, the measured laser intensity and frequency stabilities result in clock frequency stability limits around 4·10-14 and 3·10-14, respectively. Further optimisation of these limits down to around 10-14 at 104-105 seconds can be expected from fine adjustments of the clock cell’s buffer gas content, of the pump light intensity and its fluctuations, as well as from improved laser frequency stabilization or the implementation of schemes for light shift suppression [15, 7].
The use of buffer gases causes a linear shift of the atomic clock transition frequency with cell temperature, typically amounting to some 10-9/K for a pure gas, which contributes to the final stability limit of the clock. In order to reduce this temperature coefficient, we thus use an appropriate mixture of two buffer gases, that cancels out the linear temperature dependence on temperature and results in a strongly reduced temperature coefficient of second order only . Fig. 6 shows the measured temperature shift for the realized cell no. 2. With the cell temperature set around 57°C, the temperature coefficient is reduced to about 10-11/K, resulting in a clock stability limit around 10-14 for cell temperature control at the millikelvin level. Refined high-precision control of the buffer gas’ mixing ratio and total pressure in the cell is required in order to obtain both a low temperature coefficient at the operating cell temperature and low intensity light shift at the same time.
The stability of the laser pumped clock was evaluated for both the laser head with the ECDL and the DFB laser implemented, and using resonance cells with a buffer gas filling adopted for laser pumping (Fig. 7). With cell no. 2 (filled circles) the temperature coefficient is greatly improved and the medium-term stability reaches 4·10-14 at 104 seconds, consistent with the measured light shift coefficients and laser stability. At 104 seconds, the stability of our compact (≈ 2 liter, without laser electronics) clock also reproduces the performance of a much larger (≈ 27 liter) laser-pumped Cs gas-cell clock . Thus our clock demonstrator today represents the most compact laser-pumped gas-cell atomic frequency standard reaching this stability level.
Using the DFB laser head and cell no. 3 (diamonds in Fig. 7) improved short-term stability of 1.5·10-12 τ -1/2 is reached, while the medium-term stability is slightly degraded due to a higher temperature coefficient. Under standard laboratory conditions, the frequency drift of the clock typically lies between 2·10-13 and 1·10-12/day, already comparable to or lower than those for lamp-pumped Rb clocks under the same conditions, which indicates a reduced environmental sensitivity. Continued optimization on the signal-to-noise ratio and buffer gas control is required in order to reach a state-of-the-art stability goal of 1·10-14 over 4’000 to 105 seconds integration time (dashed line in Fig. 7).
HIGH-CONTRAST SCHEMES FOR MINIATURE ATOMIC CLOCKS
The main factor which limits the performance of CPT-based atomic clocks is the small amplitude of the CPT signal, which penalizes their short-term stability. This is largely due to the fact that the widely applied CPT interaction scheme using a two-frequency circularly polarized laser light field, has the disadvantage of putting most of the atoms into a “trap state” that does not contribute to the clock signal. In order to improve the frequency stability of CPT-based chip-scale clocks, it is thus necessary to increase the signal contrast and obtain a better signal-to-noise ratio . Among other approaches, a so-called “pseudo-resonance” scheme has been proposed , that combines the advantages of avoiding trap states and providing low magnetic sensitivity of the reference transition. This pseudo-resonance mechanism is based on signal discrimination at the maximum of absorption between two CPT resonances. We have experimentally evaluated the potential of this scheme for improved CPT gas-cell clocks. We use a VCSEL laser diode emitting at the Rb D1 line (795 nm) and modulated at 3.4 GHz via the injection current, and obtain pseudo-resonance contrasts of up to 1.2%, compared to 5% predicted by theory for the experimental conditions (, see Fig. 8). With the measured detection noise levels we estimate a short-term stability limit for the atomic clock of 3·10-11τ-1/2, to be compared to a numerically calculated shot-noise limit of 10-12 τ-1/2. This discrepancy can be explained by the detection noise being dominated not by shot noise but by laser noise (including AM-FM conversion) and additional noise arising from the applied 3.4 GHz modulation of the laser current. In order to demonstrate the numerically predicted clock stability limits of 10-14 τ-1/2 for this scheme under ideal conditions, not only shot-noise limited detection needs to be realised but also comparably “high-power” lasers (up to 1 mW output) with narrow (< 10 MHz) emission linewidth and sufficiently high modulation efficiency at 6.8 GHz have to be available. While these specifications are still relatively easy to obtain from an elaborate laboratory setup, their realisation within a cm-scale atomic clock presents a yet unsolved challenge that remains to be tackled.
Our demonstration and evaluation of a compact laser-pumped Rb gas-cell clock underlines the potential of laser optical pumping for the realisation of state-of-the-art Rb gas-cell clocks with stabilities of 10-14 over few hours up to one day, while maintaining a highly compact physics package occupying a volume of less than one litre. Such frequency standards are of high interest for ground and space applications such as telecommunication or satellite navigation. Additional effort is however still needed in order to refine the key technologies involved to the required performance level, notably the refined control of buffer gas cell production, light shift control, and compact low-noise microwave sources. The availability of reliable, space-worthy, and intrinsically single-mode laser diodes (e.g. DFB or DBR lasers) also presents a critical prerequisite for the realisation of this type of clocks and needs to be guaranteed. With the increasing availability of such suitable laser diode prototypes , further miniaturization of the stabilized laser source and thus of the overall clock are expected.
In the field of miniaturized “chip-scale” clocks based on CPT schemes, progress in improving the stability beyond 10-11 τ–1/2 appears to be a challenging task. With the existing approaches for reasonably simple and compact clock realisations, this is mainly due to the typically low signal contrast and high detection noise levels, as well as to spectral limitations of the VCSEL laser diodes to be used for achieving GHz modulation. However, such cm-size clocks can still be of interest where small volume and low power consumption are required and stabilities around 10-10 to 10-11 over few hours are sufficient.
We thank Temex Neuchâtel Time SA, Ferdinand-Braun-Institut für Höchstfrequenztechnik, S. Cartaleva, C. Andreeva, D. Slavov, G. Kazakov, B. Matisov, I. Mazets, and S. Jaquet for fruitful cooperation and their contributions to the work. We acknowledge financial support by the European Space Agency (ESTEC contracts 15280/01/NL/US and 19392/05/NL/CP), the Swiss National Science Foundation (projects 200020-105624, R'Equip 2160-067498, and SCOPES VI JRPBUPJ062412 and IB7620-106115), the Canton of Neuchâtel, the Swiss Confederation (art. 16), and the Swiss University Conference (Project CIMENT).
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