Abstract

Micro-fabricated (MEMS) alkali vapor cells are at the heart of the miniaturization of atomic devices such as atomic magnetometers, atomic gyroscopes and atomic clocks. Among the different techniques used to fill microfabricated alkali vapor cell, UV decomposition of rubidium azide (RbN3) into metallic Rb and nitrogen in Al2O3 coated cells is a very promising approach for low-cost wafer-level fabrication. Here we present a detailed lifetime study of such cells. The rubidium consumption being the main identified cell failure mode, it is monitored with an novel image analysis technique and with high temperature long term aging tests.

© 2017 Optical Society of America

1. Introduction

Micro-fabricated (MEMS) alkali vapor cells are at the heart of the miniaturization of atomic devices such as atomic magnetometers [1], atomic gyroscopes [2] and atomic clocks [3]. The efforts brought into this subject during the last decade in term of design, manufacturing processes and filing techniques have led to an increased complexity and more reliable devices as compared to the pioneering works cited above (see for example [4, 5]). More generally, atomic vapor cells also have applications, for example, in quantum memory [6], quantum light source [7], quantum precision measurement [8] and quantum imaging [9]. Among the different techniques used to fill micro-fabricated alkali vapor cells, the UV decomposition of Rubidium (or Cesium) azide (RbN3) into metallic Rb and gaseous N2 [10] is a very promising approach for low-cost wafer-level fabrication. A particular application of MEMS alkali vapor cells is the Chip Scale Atomic Clocks (CSAC) which has found an increased interest in telecommunication systems, global positioning and synchronization of communication networks [11]. A relevant example is the commercial device SA.45s of Microsemi [12] based on Coherent Population Trapping (CPT) [13].

Demonstrating the potential of a microcell technology for CSAC applications requires to overcome at least two main critical aspects: The first point is that a saturated vapor of alkali metal remains present in the cell for a time at least equivalent to its expected lifetime, the second is that the clock frequency remains within the specifications in term of short and long-term frequency stability. The present article focuses on the first point, the second being left to further study. In order to maintain the saturated atomic density needed for operation, a visible amount of condensed metallic alkali is required inside the cell. One of the main failure modes of MEMS atomic vapor cells filled with alkali metal azide was identified to be the disappearance of this metallic alkali over time [14]. In the case of cells filled with CsN3, the consumption of metallic alkali was attributed by Woetzel et al. [14] to the reduction of the sodium oxide contained in the glass or to the reduction of the glass’ silicon dioxide by the alkali metal. On the other hand, similar studies on cm-sized rubidium discharge lamps showed an alkali consumption which was attributed to diffusion of the rubidium in the glass envelope [15,16].

As a solution, Woetzel et al. [14] proposed an Al2O3 coating which showed a cell lifetime improvement by a factor of ≈ 100. We report here on a quantitative lifetime estimation of MEMS cells wall-coated with 20 nm Al2O3 and filled with RbN3. A novel technique, shortly presented in [17], is used to quantify the amount of metallic rubidium present in the cell and to monitor its consumption over time. Measurements done at different temperatures finally allow to extract an activation energy for the consumption process and to estimate the cell lifetime based on an initial rubidium quantity.

2. MEMS atomic vapor cells fabrication

The wafer-scale fabrication process used here was presented in [18] and is detailed in Fig. 1. A 100 mm diameter, 1000 μm thick n-type silicon wafer with a total thickness variation (TTV) E:\Aparna\January\25.1.17\xml< 10 μm is used as substrate. Cylindrical cavities with a diameter of 2 mm are etched in the wafer by DRIE. After this step, a 200 μm thick Borofloat® 33 wafer with a TTV below 10 μm is anodically bonded to the bottom of the Si wafer at 320°C under 2000 N pressure and 250 V voltage. A 20 nm layer of Al2O3 is then deposited on the top of this preform as well as on the bottom of a second Borofloat® 33 wafer by molecular vapor deposition (MVD). A small amount of RbN3 aqueous solution is then automatically pipetted into the cavities and dried in ambient atmosphere. The cavities are then hermetically sealed by anodic bonding of the second Borofloat® 33 wafer under controlled Argon atmosphere with the same parameters as above. A vacuum level of a few 10−5 mbar is typically reached before Ar backfilling. The Al2O3 layer did not prevent the bonding step as previously observed by Woetzel et al. [14]. Finally, the triple wafer stack is diced into individual vapor cells and metallic Rb and N2 buffer gas are created in situ by UV irradiation of the RbN3 following the decomposition reaction (see Fig. 2):

2RbN32Rb+3N2

 

Fig. 1 Fabrication process overview: (0) Si wafer of 1000 μm thickness as substrate, (1) DRIE etching of 2 mm wide through-holes, (2) anodic bonding of 200 μm thick Borofloat® 33 window wafer, (3–4) MVD deposition of 20 nm Al2O3 diffusion barrier, (5) micro-dispensing of RbN3 aqueous solution, (6) anodic bonding of second window, (7) dicing

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Fig. 2 MEMS atomic vapor cells before (left) and after (right) UV irradiation. Small droplets of metallic Rb can be seen after the irradiation.

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For this purpose, a low-pressure Hg lamp emitting at 254 nm was used. A five days exposition is necessary in order to observe an RbN3 decomposition yield of ≈90%.

This filling technique is compatible with conventional clean-room facilities, can be done in ambient atmosphere conditions and is low-cost since, as compared to direct dispensing, a smaller quantity of alkali metal is dispensed. The pipetting and the UV decomposition must, however, be well controlled as the N2 partial pressure must be adapted such that the Ar/N2 ratio matches a desired value. Indeed, in buffer gas atomic clocks, the inversion temperature, i.e., the temperature at which the first order dependency of the cell clock frequency to the temperature vanishes, depends on the ratio between the different buffer gas partial pressures [19]. Moreover, as the amount of buffer gas is linked to the rubidium quantity, the amount of alkali metal sealed in the cell is limited. Cells fabricated with this filling technique are therefore more sensitive to failure modes related to rubidium consumption. The technique presented here was especially developed to explore this issue.

3. Rb consumption monitoring

3.1. Consumption model

The rubidium consumption monitoring method presented here is based on the image analysis of the rubidium droplets at the surface of the MEMS atomic cells. Comparison between coated and uncoated cells confirmed the results of Woetzel et al. [14] (see Fig. 3). The following focuses therefore on cells with Al2O3 coating. Observations in cells filled with low RbN3 quantity showed that the rubidium is consumed in two steps: first an initial consumption occurs as the Rb is created by UV irradiation and no atomic signal can be measured by laser spectroscopy. After this initial consumption, metallic rubidium can be observed on the cell windows and an atomic absorption signal can be measured. However, this quantity decreases slowly over time, depending on the temperature. As the first consumption can be attributed to reaction of the rubidium with a contamination in the cell surface or volume (for example oxygen), the second consumption path is more difficult to determine. In the case of uncoated glass, two candidate for the consumption process were proposed: reduction of the sodium oxide contained in the glass or of the glass silicon dioxide by the rubidium [14] and diffusion of the rubidium in the bulk of the glass [15,16]. In the first case, the reaction rate is constant and the consumed mass is proportional to time t. In the second case however, due to diffusion laws, the consumed mass is proportional to t. For Al2O3 coated cells, the two consumption paths remain possible and the Rb consumption could be explained by diffusion through the membrane formed by the Al2O3, by an extremely slow reduction of the Al2O3 layer by the rubidium or by one of the two mentioned processes through pinholes in the the Al2O3 layer.

 

Fig. 3 Example of the evolution of the amount of rubidium for two cells with and without Al2O3 coating for cells heated at 180°C. The measurement is derived from the method presented below. The surface of glass covered by metallic rubidium is presented here instead of the Rb volume as the contact angle of Rb on uncoated glass was not calibrated.

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For the following, we chose to consider a consumption at a fixed rate k with a consumed mass proportional to t. This is justified by the fact that no evidence of an asymptotic deviation from a linear consumption was observed in our measurements (see Fig. 3). Moreover, a consumption model proportional to t would lead to an overestimation of the cell lifetime in the case of a non-diffusive process whereas a model proportional to t would lead to a less critical underestimation of the lifetime in the case of a reaction driven process. The total amount of rubidium at a time t during the cell lifetime can therefore be written as:

mmeas.(t)=mprod.minit.cons.kt
where mprod. is the amount of Rb produced by the UV decomposition of RbN3, minit.cons. is the initial Rb consumed mass.

3.2. Measurement of metallic rubidium amount

In order to monitor the two consumptions steps, an image analysis method was developed: the metallic rubidium present in cells is migrated on the cell window with the help of a thermal gradient (see Fig. 4 - left). The droplets are then imaged with a microscope and the droplets radius a are measured using an image recognition software (see Fig. 4 - right). Comparable imaging techniques were used by Zhao and Wu [20] to measure the desorption rate of Rb droplets. In that case however, no image recognition software as well as no thermal gradient were used. Figure 5 illustrate the evolution of the droplets size over time.

 

Fig. 4 Image recognition of Rb droplets size in MEMS atomic vapor cell: [left] Microscope image of a cell - [right] Extraction of drop radius by image recognition software

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Fig. 5 Example of the droplets evolution over time for a cell heated at 196°C. Small black dots can be observed on each drop. These particles of unknown composition are likely the nucleation sites of the droplets.

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From their diameter, the droplet volume can be estimated as the volume of a spherical cap with an unknown contact angle θ which depends on the wettability of the rubidium on the Al2O3 coating (see Fig. 6):

V=πh6(3a2+h2)
with h = a tan(θ/2).

 

Fig. 6 Spherical cap model used for Rb drop volume estimation

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3.3. Calibration of droplets volume and measurement of the initial consumption

In order to measure the contact angle, and at the same time the initial consumption (minit.cons.), the image recognition method is combined with micro-Raman spectroscopy to measure the N2 pressure inside the cells. The technique used here was shortly described in [17] and in more details in [21]. It consists in the extraction of the N2 pressure from the signal recorded when a confocal micro-Raman spectrometer is focalized inside the cell cavity.

A batch of cells was filled with different RbN3 quantities, UV decomposed and measured with the two methods. Due to the stoichiometric relation between N2 and Rb, the measure of the N2 pressure gives the produced amount of rubidium. For cells filled with the smallest quantities of RbN3, a small N2 pressure was measured but no metallic Rb detected, indicating a non negligible initial metallic Rb consumption. The observed Rb mass mmeas. can then be written as:

mmeas.={mprod.minit.cons.ifmprod.>minit.cons.0ifmprod.<minit.cons.
where mprod. is the the produced Rb mass calculated from the N2 measurement. Using (3) to calculate the measured mass (mmeas.) and (4) on the experimental data, the contact angle θ can be adjusted such that the slope between mmeas. and mprod. is 1 for the non-0 values of mmeas. (see Fig. 7). From this optimization, experimental values of θ = 57 ± 6° for the contact angle and minit.cons. = 0.50 ± 0.08 μg for the initial consumed mass were found.

 

Fig. 7 Estimation of Rb initial consumption: The contact angle θ is adapted such that the slope is 1 for the non-0 values of the measured Rb quantity

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3.4. Cell lifetime estimation

The rubidium consumption rate is supposed to be temperature dependent following an Arrhenius equation [22]:

k=AeEaRT
where k is the Rb consumption rate, A the prefactor with the same unit as k, R is the ideal gas constant in [J·mol−1·K−1], T the temperature in [K] and Ea the activation energy in [J mol−1].

The image recognition method was used together with the determined contact angle θ to monitor the rubidium quantity over time and to extract the cell lifetime. Three batches of 4 to 6 cells from the same wafer were placed in a thermoregulated oven at different temperatures (171, 180, and 196°C, measured with a class B Pt100 temperature sensor). The remaining amount of rubidium in the cells was measured at regular intervals for up to 7 months and the average consumption rates ki were extracted by linear fitting for each cell. The resulting values are plotted in an Arrhenius graph in Fig. 8. A linear fit is then realized on the ki in order to extract the activation energy and a value of Ea = 60 ± 24 kJ/mol was found.

 

Fig. 8 Estimation of the activation energy by fitting of the rubidium consumption rates of cells at different temperatures (k is given here in μg/s)

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4. Discussion

Based on the measured rubidium consumption values and assuming a desired lifetime of 10 years at 95°C, a quantity of 0.600.10+0.59 μg of metallic rubidium is required. This quantity corresponds to the creation of 8314+81 mbar N2 by the rubidium azide decomposition reaction. In order to reach an inversion temperature at the operation temperature (i.e. 95°C) and suppress the first order dependence of the cell frequency to the temperature, an Ar pressure of 10818+105 mbar is required [19]. This gives a total buffer gas pressure of 19132+186 mbar.

This pressure is above the value typically used in rubidium MEMS cells of about 150 mbar [23]. However, in MEMS atomic vapor cells, the limiting factor for the total buffer gas pressure is the overlapping between the optical absorption lines. Indeed, a high buffer gas pressure broadens the optical absorption lines. When they start to overlap, the CPT contrast considerably reduces, thus limiting clock performances. This is particularly the case for cells filled with natural rubidium where the two isotopes absorption lines overlap and for cells filled with isotopically enriched 85Rb where the two absorption lines are separated from each-other by only ≈ 3.035 GHz. In the case of cells filled with isotopically enriched 87Rb, the absorption lines are separated by ≈ 6.834 GHz which allows for a larger buffer gas pressure before overlapping occurs. Moreover, natural rubidium is commonly used due to its much cheaper price but in the case of RbN3 dispensing, isotopically enriched 87 Rb can be used because the dispensed Rb quantities are very limited. Determination of the ideal buffer gas pressure for 87Rb is not treated here and will be the subject of further investigations.

5. Conclusion

We measured the lifetime of MEMS atomic vapor cells for chip-scale atomic clocks with 20 nm Al2O3 wall coating deposited by MVD. These cells were filled with rubidium by UV decomposition of RbN3. The main cell failure mode was identified as the initial and the in-operation consumption of rubidium. For 1 mm thick and 2 mm diameter cavities, an initial consumption of 0.50 ± 0.08 μg of Rb was measured. The in-operation consumption was treated to be temperature dependent with a fixed rate following an Arrhenius law. The activation energy was measured and a value of 60±24 kJ/mol was found. To achieve a 10 year lifetime, an Rb quantity of 0.600.10+0.59 μg of metallic rubidium was calculated. The creation of this quantity of rubidium by RbN3 decomposition produces a higher pressure of buffer gas as compared to values typically used in rubidium MEMS cells but it does not preclude their implementation in chip-scale atomic clocks in the case of 87Rb. We can therefore conclude that the UV decomposition of 87RbN3 together with Al2O3 wall coating is a combination of technologies that enables the low-cost wafer-level fabrication of MEMS atomic vapor cells with a lifetime superior to 10 years. To confirm the full suitability of this cell technology for CSACs applications, the evolution of the cell frequency along time is nevertheless still to be investigated.

Funding

European Space Agency (ESA) under the Networking and Partnering Initiative (NPI) (ESA Contract No. 4000112650/14/NL/GLC); CSEM’s R&D activity financed by the canton of Neuchâtel and the cantons of Central Switzerland.

Acknowledgments

We gratefully acknowledge G. Mileti (Université de Neuchâtel, Switzerland), L. Balet and F. Droz (CSEM SA) for the fruitful discussions on the rubidium consumption mechanisms as well as A. Bionaz, M. Amine, P.-A. Clerc and T. Volden (CSEM SA) for their participation in the MEMS cell manufacturing.

References and links

1. P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L.-A. A. Liew, and J. Moreland, “Chip-scale atomic magnetometer,” Appl. Phys. Lett. 85, 6409–6411 (2004). [CrossRef]  

2. E. A. Donley, J. L. Long, T. C. Liebisch, E. R. Hodby, T. A. Fisher, and J. Kitching, “Nuclear quadrupole resonances in compact vapor cells: The crossover between the NMR and the nuclear quadrupole resonance interaction regimes,” Phys. Rev. A 79, 013420 (2009). [CrossRef]  

3. S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004). [CrossRef]  

4. R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015). [CrossRef]   [PubMed]  

5. S. Abdullah, C. Affolderbach, F. Gruet, and G. Mileti, “Aging studies on micro-fabricated alkali buffer-gas cells for miniature atomic clocks,” Appl. Phys. Lett. 106, 163505 (2015). [CrossRef]  

6. M. Hosseini, B. Sparkes, G. Campbell, P. Lam, and B. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011). [CrossRef]   [PubMed]  

7. C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178–180 (2007). [CrossRef]  

8. T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. SÃÿrensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 1–4 (2008). [CrossRef]  

9. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008). [CrossRef]   [PubMed]  

10. L.-A. Liew, J. Moreland, and V. Gerginov, “Wafer-level filling of microfabricated atomic vapor cells based on thin-film deposition and photolysis of cesium azide,” Appl. Phys. Lett. 90, 114106 (2007). [CrossRef]  

11. S. Knappe, “MEMS atomic clocks,” Compr. Microsyst. 3, 571–612 (2007).

12. Microsemi, “Quantum SA.45s Chip Scale Atomic Clock (CSAC),” www.microsemi.com/products/timing-synchronization-systems/embedded-timing-solutions/components/sa-45s-chip-scale-atomic-clock.

13. J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421–442 (2005). [CrossRef]  

14. S. Woetzel, F. Talkenberg, T. Scholtes, R. Ijsselsteijn, V. Schultze, and H. G. Meyer, “Lifetime improvement of micro-fabricated alkali vapor cells by atomic layer deposited wall coatings,” Surf. Coat. Technol. 221, 158–162 (2013). [CrossRef]  

15. C. Volk, R. Frueholz, T. English, T. Lynch, and W. Riley, “Lifetime and Reliability of Rubidium Discharge Lamps for Use in Atomic Frequency Standards,” in “38th Annual Symposium on Frequency Control,” (1984).

16. R. Cook and R. Frueholz, “An improved rubidium consumption model for discharge lamps used in rubidium frequency standards,” in “Proceedings of the 42nd Annual Frequency Control Symposium,” (1988), pp. 525–531.

17. S. Karlen, J. Gobet, T. Overstolz, and J. Haesler, “Non-destructive MEMS atomic vapor cells characterization by Raman spectroscopy and image analysis,” in “2016 European Frequency and Time Forum (EFTF),” (2016), pp. 1–3. [CrossRef]  

18. T. Overstolz, J. Haesler, G. Bergonzi, A. Pezous, P.-A. Clerc, S. Ischer, J. Kaufmann, and M. Despont, “Wafer scale fabrication of highly integrated rubidium vapor cells,” in “IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS),” (2014), pp. 552–555.

19. J. Vanier, R. Kunski, N. Cyr, J. Y. Savard, and M. Têtu, “On hyperfine frequency shifts caused by buffer gases: Application to the optically pumped passive rubidium frequency standard,” J. Appl. Phys. 53, 5387–5391 (1982). [CrossRef]  

20. K. Zhao and Z. Wu, “Atomic resonance behavior in laser-induced Rb atom desorption - The effect of ambient gas atoms and molecules,” Phys. Lett. A 299, 73–78 (2002). [CrossRef]  

21. S. Karlen, J. Gobet, T. Overstolz, J. Haesler, and S. Lecomte, “Quantitative micro-Raman spectroscopy for pressure measurement in small volumes,” Manuscript in preparation.

22. K. J. Laidler, “The development of the Arrhenius equation,” J. Chem. Educ. 61, 494–498 (1984). [CrossRef]  

23. R. Straessle, M. Pellaton, C. Affolderbach, Y. Pétremand, D. Briand, G. Mileti, and N. F. de Rooij, “Low-temperature indium-bonded alkali vapor cell for chip-scale atomic clocks,” J. Appl. Phys. 113, 064501 (2013). [CrossRef]  

References

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  1. P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L.-A. A. Liew, and J. Moreland, “Chip-scale atomic magnetometer,” Appl. Phys. Lett. 85, 6409–6411 (2004).
    [Crossref]
  2. E. A. Donley, J. L. Long, T. C. Liebisch, E. R. Hodby, T. A. Fisher, and J. Kitching, “Nuclear quadrupole resonances in compact vapor cells: The crossover between the NMR and the nuclear quadrupole resonance interaction regimes,” Phys. Rev. A 79, 013420 (2009).
    [Crossref]
  3. S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004).
    [Crossref]
  4. R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
    [Crossref] [PubMed]
  5. S. Abdullah, C. Affolderbach, F. Gruet, and G. Mileti, “Aging studies on micro-fabricated alkali buffer-gas cells for miniature atomic clocks,” Appl. Phys. Lett. 106, 163505 (2015).
    [Crossref]
  6. M. Hosseini, B. Sparkes, G. Campbell, P. Lam, and B. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
    [Crossref] [PubMed]
  7. C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178–180 (2007).
    [Crossref]
  8. T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. SÃÿrensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 1–4 (2008).
    [Crossref]
  9. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
    [Crossref] [PubMed]
  10. L.-A. Liew, J. Moreland, and V. Gerginov, “Wafer-level filling of microfabricated atomic vapor cells based on thin-film deposition and photolysis of cesium azide,” Appl. Phys. Lett. 90, 114106 (2007).
    [Crossref]
  11. S. Knappe, “MEMS atomic clocks,” Compr. Microsyst. 3, 571–612 (2007).
  12. Microsemi, “Quantum™ SA.45s Chip Scale Atomic Clock (CSAC),” www.microsemi.com/products/timing-synchronization-systems/embedded-timing-solutions/components/sa-45s-chip-scale-atomic-clock .
  13. J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421–442 (2005).
    [Crossref]
  14. S. Woetzel, F. Talkenberg, T. Scholtes, R. Ijsselsteijn, V. Schultze, and H. G. Meyer, “Lifetime improvement of micro-fabricated alkali vapor cells by atomic layer deposited wall coatings,” Surf. Coat. Technol. 221, 158–162 (2013).
    [Crossref]
  15. C. Volk, R. Frueholz, T. English, T. Lynch, and W. Riley, “Lifetime and Reliability of Rubidium Discharge Lamps for Use in Atomic Frequency Standards,” in “38th Annual Symposium on Frequency Control,” (1984).
  16. R. Cook and R. Frueholz, “An improved rubidium consumption model for discharge lamps used in rubidium frequency standards,” in “Proceedings of the 42nd Annual Frequency Control Symposium,” (1988), pp. 525–531.
  17. S. Karlen, J. Gobet, T. Overstolz, and J. Haesler, “Non-destructive MEMS atomic vapor cells characterization by Raman spectroscopy and image analysis,” in “2016 European Frequency and Time Forum (EFTF),” (2016), pp. 1–3.
    [Crossref]
  18. T. Overstolz, J. Haesler, G. Bergonzi, A. Pezous, P.-A. Clerc, S. Ischer, J. Kaufmann, and M. Despont, “Wafer scale fabrication of highly integrated rubidium vapor cells,” in “IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS),” (2014), pp. 552–555.
  19. J. Vanier, R. Kunski, N. Cyr, J. Y. Savard, and M. Têtu, “On hyperfine frequency shifts caused by buffer gases: Application to the optically pumped passive rubidium frequency standard,” J. Appl. Phys. 53, 5387–5391 (1982).
    [Crossref]
  20. K. Zhao and Z. Wu, “Atomic resonance behavior in laser-induced Rb atom desorption - The effect of ambient gas atoms and molecules,” Phys. Lett. A 299, 73–78 (2002).
    [Crossref]
  21. S. Karlen, J. Gobet, T. Overstolz, J. Haesler, and S. Lecomte, “Quantitative micro-Raman spectroscopy for pressure measurement in small volumes,” Manuscript in preparation.
  22. K. J. Laidler, “The development of the Arrhenius equation,” J. Chem. Educ. 61, 494–498 (1984).
    [Crossref]
  23. R. Straessle, M. Pellaton, C. Affolderbach, Y. Pétremand, D. Briand, G. Mileti, and N. F. de Rooij, “Low-temperature indium-bonded alkali vapor cell for chip-scale atomic clocks,” J. Appl. Phys. 113, 064501 (2013).
    [Crossref]

2015 (2)

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
[Crossref] [PubMed]

S. Abdullah, C. Affolderbach, F. Gruet, and G. Mileti, “Aging studies on micro-fabricated alkali buffer-gas cells for miniature atomic clocks,” Appl. Phys. Lett. 106, 163505 (2015).
[Crossref]

2013 (2)

S. Woetzel, F. Talkenberg, T. Scholtes, R. Ijsselsteijn, V. Schultze, and H. G. Meyer, “Lifetime improvement of micro-fabricated alkali vapor cells by atomic layer deposited wall coatings,” Surf. Coat. Technol. 221, 158–162 (2013).
[Crossref]

R. Straessle, M. Pellaton, C. Affolderbach, Y. Pétremand, D. Briand, G. Mileti, and N. F. de Rooij, “Low-temperature indium-bonded alkali vapor cell for chip-scale atomic clocks,” J. Appl. Phys. 113, 064501 (2013).
[Crossref]

2011 (1)

M. Hosseini, B. Sparkes, G. Campbell, P. Lam, and B. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

2009 (1)

E. A. Donley, J. L. Long, T. C. Liebisch, E. R. Hodby, T. A. Fisher, and J. Kitching, “Nuclear quadrupole resonances in compact vapor cells: The crossover between the NMR and the nuclear quadrupole resonance interaction regimes,” Phys. Rev. A 79, 013420 (2009).
[Crossref]

2008 (2)

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. SÃÿrensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 1–4 (2008).
[Crossref]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

2007 (3)

L.-A. Liew, J. Moreland, and V. Gerginov, “Wafer-level filling of microfabricated atomic vapor cells based on thin-film deposition and photolysis of cesium azide,” Appl. Phys. Lett. 90, 114106 (2007).
[Crossref]

S. Knappe, “MEMS atomic clocks,” Compr. Microsyst. 3, 571–612 (2007).

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178–180 (2007).
[Crossref]

2005 (1)

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421–442 (2005).
[Crossref]

2004 (2)

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004).
[Crossref]

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L.-A. A. Liew, and J. Moreland, “Chip-scale atomic magnetometer,” Appl. Phys. Lett. 85, 6409–6411 (2004).
[Crossref]

2002 (1)

K. Zhao and Z. Wu, “Atomic resonance behavior in laser-induced Rb atom desorption - The effect of ambient gas atoms and molecules,” Phys. Lett. A 299, 73–78 (2002).
[Crossref]

1984 (1)

K. J. Laidler, “The development of the Arrhenius equation,” J. Chem. Educ. 61, 494–498 (1984).
[Crossref]

1982 (1)

J. Vanier, R. Kunski, N. Cyr, J. Y. Savard, and M. Têtu, “On hyperfine frequency shifts caused by buffer gases: Application to the optically pumped passive rubidium frequency standard,” J. Appl. Phys. 53, 5387–5391 (1982).
[Crossref]

Abbé, P.

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
[Crossref] [PubMed]

AbdelHafiz, M.

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
[Crossref] [PubMed]

Abdullah, S.

S. Abdullah, C. Affolderbach, F. Gruet, and G. Mileti, “Aging studies on micro-fabricated alkali buffer-gas cells for miniature atomic clocks,” Appl. Phys. Lett. 106, 163505 (2015).
[Crossref]

Affolderbach, C.

S. Abdullah, C. Affolderbach, F. Gruet, and G. Mileti, “Aging studies on micro-fabricated alkali buffer-gas cells for miniature atomic clocks,” Appl. Phys. Lett. 106, 163505 (2015).
[Crossref]

R. Straessle, M. Pellaton, C. Affolderbach, Y. Pétremand, D. Briand, G. Mileti, and N. F. de Rooij, “Low-temperature indium-bonded alkali vapor cell for chip-scale atomic clocks,” J. Appl. Phys. 113, 064501 (2013).
[Crossref]

Arimondo, E.

Bergonzi, G.

T. Overstolz, J. Haesler, G. Bergonzi, A. Pezous, P.-A. Clerc, S. Ischer, J. Kaufmann, and M. Despont, “Wafer scale fabrication of highly integrated rubidium vapor cells,” in “IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS),” (2014), pp. 552–555.

Boudot, R.

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
[Crossref] [PubMed]

Boyer, V.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178–180 (2007).
[Crossref]

Briand, D.

R. Straessle, M. Pellaton, C. Affolderbach, Y. Pétremand, D. Briand, G. Mileti, and N. F. de Rooij, “Low-temperature indium-bonded alkali vapor cell for chip-scale atomic clocks,” J. Appl. Phys. 113, 064501 (2013).
[Crossref]

Buchler, B.

M. Hosseini, B. Sparkes, G. Campbell, P. Lam, and B. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Campbell, G.

M. Hosseini, B. Sparkes, G. Campbell, P. Lam, and B. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Chutani, R.

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
[Crossref] [PubMed]

Clerc, P.-A.

T. Overstolz, J. Haesler, G. Bergonzi, A. Pezous, P.-A. Clerc, S. Ischer, J. Kaufmann, and M. Despont, “Wafer scale fabrication of highly integrated rubidium vapor cells,” in “IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS),” (2014), pp. 552–555.

Cook, R.

R. Cook and R. Frueholz, “An improved rubidium consumption model for discharge lamps used in rubidium frequency standards,” in “Proceedings of the 42nd Annual Frequency Control Symposium,” (1988), pp. 525–531.

Cyr, N.

J. Vanier, R. Kunski, N. Cyr, J. Y. Savard, and M. Têtu, “On hyperfine frequency shifts caused by buffer gases: Application to the optically pumped passive rubidium frequency standard,” J. Appl. Phys. 53, 5387–5391 (1982).
[Crossref]

de Clercq, E.

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
[Crossref] [PubMed]

de Rooij, N. F.

R. Straessle, M. Pellaton, C. Affolderbach, Y. Pétremand, D. Briand, G. Mileti, and N. F. de Rooij, “Low-temperature indium-bonded alkali vapor cell for chip-scale atomic clocks,” J. Appl. Phys. 113, 064501 (2013).
[Crossref]

Despont, M.

T. Overstolz, J. Haesler, G. Bergonzi, A. Pezous, P.-A. Clerc, S. Ischer, J. Kaufmann, and M. Despont, “Wafer scale fabrication of highly integrated rubidium vapor cells,” in “IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS),” (2014), pp. 552–555.

Donley, E. A.

E. A. Donley, J. L. Long, T. C. Liebisch, E. R. Hodby, T. A. Fisher, and J. Kitching, “Nuclear quadrupole resonances in compact vapor cells: The crossover between the NMR and the nuclear quadrupole resonance interaction regimes,” Phys. Rev. A 79, 013420 (2009).
[Crossref]

English, T.

C. Volk, R. Frueholz, T. English, T. Lynch, and W. Riley, “Lifetime and Reliability of Rubidium Discharge Lamps for Use in Atomic Frequency Standards,” in “38th Annual Symposium on Frequency Control,” (1984).

Fernholz, T.

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. SÃÿrensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 1–4 (2008).
[Crossref]

Fisher, T. A.

E. A. Donley, J. L. Long, T. C. Liebisch, E. R. Hodby, T. A. Fisher, and J. Kitching, “Nuclear quadrupole resonances in compact vapor cells: The crossover between the NMR and the nuclear quadrupole resonance interaction regimes,” Phys. Rev. A 79, 013420 (2009).
[Crossref]

Frueholz, R.

C. Volk, R. Frueholz, T. English, T. Lynch, and W. Riley, “Lifetime and Reliability of Rubidium Discharge Lamps for Use in Atomic Frequency Standards,” in “38th Annual Symposium on Frequency Control,” (1984).

R. Cook and R. Frueholz, “An improved rubidium consumption model for discharge lamps used in rubidium frequency standards,” in “Proceedings of the 42nd Annual Frequency Control Symposium,” (1988), pp. 525–531.

Galliou, S.

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
[Crossref] [PubMed]

Gerginov, V.

L.-A. Liew, J. Moreland, and V. Gerginov, “Wafer-level filling of microfabricated atomic vapor cells based on thin-film deposition and photolysis of cesium azide,” Appl. Phys. Lett. 90, 114106 (2007).
[Crossref]

Gobet, J.

S. Karlen, J. Gobet, T. Overstolz, and J. Haesler, “Non-destructive MEMS atomic vapor cells characterization by Raman spectroscopy and image analysis,” in “2016 European Frequency and Time Forum (EFTF),” (2016), pp. 1–3.
[Crossref]

S. Karlen, J. Gobet, T. Overstolz, J. Haesler, and S. Lecomte, “Quantitative micro-Raman spectroscopy for pressure measurement in small volumes,” Manuscript in preparation.

Gorecki, C.

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
[Crossref] [PubMed]

Gruet, F.

S. Abdullah, C. Affolderbach, F. Gruet, and G. Mileti, “Aging studies on micro-fabricated alkali buffer-gas cells for miniature atomic clocks,” Appl. Phys. Lett. 106, 163505 (2015).
[Crossref]

Haesler, J.

S. Karlen, J. Gobet, T. Overstolz, J. Haesler, and S. Lecomte, “Quantitative micro-Raman spectroscopy for pressure measurement in small volumes,” Manuscript in preparation.

T. Overstolz, J. Haesler, G. Bergonzi, A. Pezous, P.-A. Clerc, S. Ischer, J. Kaufmann, and M. Despont, “Wafer scale fabrication of highly integrated rubidium vapor cells,” in “IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS),” (2014), pp. 552–555.

S. Karlen, J. Gobet, T. Overstolz, and J. Haesler, “Non-destructive MEMS atomic vapor cells characterization by Raman spectroscopy and image analysis,” in “2016 European Frequency and Time Forum (EFTF),” (2016), pp. 1–3.
[Crossref]

Hodby, E. R.

E. A. Donley, J. L. Long, T. C. Liebisch, E. R. Hodby, T. A. Fisher, and J. Kitching, “Nuclear quadrupole resonances in compact vapor cells: The crossover between the NMR and the nuclear quadrupole resonance interaction regimes,” Phys. Rev. A 79, 013420 (2009).
[Crossref]

Hollberg, L.

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L.-A. A. Liew, and J. Moreland, “Chip-scale atomic magnetometer,” Appl. Phys. Lett. 85, 6409–6411 (2004).
[Crossref]

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004).
[Crossref]

Hosseini, M.

M. Hosseini, B. Sparkes, G. Campbell, P. Lam, and B. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Ijsselsteijn, R.

S. Woetzel, F. Talkenberg, T. Scholtes, R. Ijsselsteijn, V. Schultze, and H. G. Meyer, “Lifetime improvement of micro-fabricated alkali vapor cells by atomic layer deposited wall coatings,” Surf. Coat. Technol. 221, 158–162 (2013).
[Crossref]

Ischer, S.

T. Overstolz, J. Haesler, G. Bergonzi, A. Pezous, P.-A. Clerc, S. Ischer, J. Kaufmann, and M. Despont, “Wafer scale fabrication of highly integrated rubidium vapor cells,” in “IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS),” (2014), pp. 552–555.

Jensen, K.

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. SÃÿrensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 1–4 (2008).
[Crossref]

Karlen, S.

S. Karlen, J. Gobet, T. Overstolz, and J. Haesler, “Non-destructive MEMS atomic vapor cells characterization by Raman spectroscopy and image analysis,” in “2016 European Frequency and Time Forum (EFTF),” (2016), pp. 1–3.
[Crossref]

S. Karlen, J. Gobet, T. Overstolz, J. Haesler, and S. Lecomte, “Quantitative micro-Raman spectroscopy for pressure measurement in small volumes,” Manuscript in preparation.

Kaufmann, J.

T. Overstolz, J. Haesler, G. Bergonzi, A. Pezous, P.-A. Clerc, S. Ischer, J. Kaufmann, and M. Despont, “Wafer scale fabrication of highly integrated rubidium vapor cells,” in “IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS),” (2014), pp. 552–555.

Kitching, J.

E. A. Donley, J. L. Long, T. C. Liebisch, E. R. Hodby, T. A. Fisher, and J. Kitching, “Nuclear quadrupole resonances in compact vapor cells: The crossover between the NMR and the nuclear quadrupole resonance interaction regimes,” Phys. Rev. A 79, 013420 (2009).
[Crossref]

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L.-A. A. Liew, and J. Moreland, “Chip-scale atomic magnetometer,” Appl. Phys. Lett. 85, 6409–6411 (2004).
[Crossref]

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004).
[Crossref]

Knappe, S.

S. Knappe, “MEMS atomic clocks,” Compr. Microsyst. 3, 571–612 (2007).

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L.-A. A. Liew, and J. Moreland, “Chip-scale atomic magnetometer,” Appl. Phys. Lett. 85, 6409–6411 (2004).
[Crossref]

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004).
[Crossref]

Krauter, H.

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. SÃÿrensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 1–4 (2008).
[Crossref]

Kunski, R.

J. Vanier, R. Kunski, N. Cyr, J. Y. Savard, and M. Têtu, “On hyperfine frequency shifts caused by buffer gases: Application to the optically pumped passive rubidium frequency standard,” J. Appl. Phys. 53, 5387–5391 (1982).
[Crossref]

Laidler, K. J.

K. J. Laidler, “The development of the Arrhenius equation,” J. Chem. Educ. 61, 494–498 (1984).
[Crossref]

Lam, P.

M. Hosseini, B. Sparkes, G. Campbell, P. Lam, and B. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Lecomte, S.

S. Karlen, J. Gobet, T. Overstolz, J. Haesler, and S. Lecomte, “Quantitative micro-Raman spectroscopy for pressure measurement in small volumes,” Manuscript in preparation.

Lett, P. D.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, “Strong relative intensity squeezing by four-wave mixing in rubidium vapor,” Opt. Lett. 32, 178–180 (2007).
[Crossref]

Liebisch, T. C.

E. A. Donley, J. L. Long, T. C. Liebisch, E. R. Hodby, T. A. Fisher, and J. Kitching, “Nuclear quadrupole resonances in compact vapor cells: The crossover between the NMR and the nuclear quadrupole resonance interaction regimes,” Phys. Rev. A 79, 013420 (2009).
[Crossref]

Liew, L.-A.

L.-A. Liew, J. Moreland, and V. Gerginov, “Wafer-level filling of microfabricated atomic vapor cells based on thin-film deposition and photolysis of cesium azide,” Appl. Phys. Lett. 90, 114106 (2007).
[Crossref]

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004).
[Crossref]

Liew, L.-A. A.

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L.-A. A. Liew, and J. Moreland, “Chip-scale atomic magnetometer,” Appl. Phys. Lett. 85, 6409–6411 (2004).
[Crossref]

Long, J. L.

E. A. Donley, J. L. Long, T. C. Liebisch, E. R. Hodby, T. A. Fisher, and J. Kitching, “Nuclear quadrupole resonances in compact vapor cells: The crossover between the NMR and the nuclear quadrupole resonance interaction regimes,” Phys. Rev. A 79, 013420 (2009).
[Crossref]

Lynch, T.

C. Volk, R. Frueholz, T. English, T. Lynch, and W. Riley, “Lifetime and Reliability of Rubidium Discharge Lamps for Use in Atomic Frequency Standards,” in “38th Annual Symposium on Frequency Control,” (1984).

Marino, A. M.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

Maurice, V.

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
[Crossref] [PubMed]

McCormick, C. F.

Meyer, H. G.

S. Woetzel, F. Talkenberg, T. Scholtes, R. Ijsselsteijn, V. Schultze, and H. G. Meyer, “Lifetime improvement of micro-fabricated alkali vapor cells by atomic layer deposited wall coatings,” Surf. Coat. Technol. 221, 158–162 (2013).
[Crossref]

Mileti, G.

S. Abdullah, C. Affolderbach, F. Gruet, and G. Mileti, “Aging studies on micro-fabricated alkali buffer-gas cells for miniature atomic clocks,” Appl. Phys. Lett. 106, 163505 (2015).
[Crossref]

R. Straessle, M. Pellaton, C. Affolderbach, Y. Pétremand, D. Briand, G. Mileti, and N. F. de Rooij, “Low-temperature indium-bonded alkali vapor cell for chip-scale atomic clocks,” J. Appl. Phys. 113, 064501 (2013).
[Crossref]

Moreland, J.

L.-A. Liew, J. Moreland, and V. Gerginov, “Wafer-level filling of microfabricated atomic vapor cells based on thin-film deposition and photolysis of cesium azide,” Appl. Phys. Lett. 90, 114106 (2007).
[Crossref]

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004).
[Crossref]

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L.-A. A. Liew, and J. Moreland, “Chip-scale atomic magnetometer,” Appl. Phys. Lett. 85, 6409–6411 (2004).
[Crossref]

Overstolz, T.

S. Karlen, J. Gobet, T. Overstolz, J. Haesler, and S. Lecomte, “Quantitative micro-Raman spectroscopy for pressure measurement in small volumes,” Manuscript in preparation.

S. Karlen, J. Gobet, T. Overstolz, and J. Haesler, “Non-destructive MEMS atomic vapor cells characterization by Raman spectroscopy and image analysis,” in “2016 European Frequency and Time Forum (EFTF),” (2016), pp. 1–3.
[Crossref]

T. Overstolz, J. Haesler, G. Bergonzi, A. Pezous, P.-A. Clerc, S. Ischer, J. Kaufmann, and M. Despont, “Wafer scale fabrication of highly integrated rubidium vapor cells,” in “IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS),” (2014), pp. 552–555.

Passilly, N.

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
[Crossref] [PubMed]

Pellaton, M.

R. Straessle, M. Pellaton, C. Affolderbach, Y. Pétremand, D. Briand, G. Mileti, and N. F. de Rooij, “Low-temperature indium-bonded alkali vapor cell for chip-scale atomic clocks,” J. Appl. Phys. 113, 064501 (2013).
[Crossref]

Pétremand, Y.

R. Straessle, M. Pellaton, C. Affolderbach, Y. Pétremand, D. Briand, G. Mileti, and N. F. de Rooij, “Low-temperature indium-bonded alkali vapor cell for chip-scale atomic clocks,” J. Appl. Phys. 113, 064501 (2013).
[Crossref]

Pezous, A.

T. Overstolz, J. Haesler, G. Bergonzi, A. Pezous, P.-A. Clerc, S. Ischer, J. Kaufmann, and M. Despont, “Wafer scale fabrication of highly integrated rubidium vapor cells,” in “IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS),” (2014), pp. 552–555.

Polzik, E. S.

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. SÃÿrensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 1–4 (2008).
[Crossref]

Pooser, R. C.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

Rauch, J.-Y.

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
[Crossref] [PubMed]

Riley, W.

C. Volk, R. Frueholz, T. English, T. Lynch, and W. Riley, “Lifetime and Reliability of Rubidium Discharge Lamps for Use in Atomic Frequency Standards,” in “38th Annual Symposium on Frequency Control,” (1984).

Savard, J. Y.

J. Vanier, R. Kunski, N. Cyr, J. Y. Savard, and M. Têtu, “On hyperfine frequency shifts caused by buffer gases: Application to the optically pumped passive rubidium frequency standard,” J. Appl. Phys. 53, 5387–5391 (1982).
[Crossref]

SÃÿrensen, A. S.

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. SÃÿrensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 1–4 (2008).
[Crossref]

Scholtes, T.

S. Woetzel, F. Talkenberg, T. Scholtes, R. Ijsselsteijn, V. Schultze, and H. G. Meyer, “Lifetime improvement of micro-fabricated alkali vapor cells by atomic layer deposited wall coatings,” Surf. Coat. Technol. 221, 158–162 (2013).
[Crossref]

Schultze, V.

S. Woetzel, F. Talkenberg, T. Scholtes, R. Ijsselsteijn, V. Schultze, and H. G. Meyer, “Lifetime improvement of micro-fabricated alkali vapor cells by atomic layer deposited wall coatings,” Surf. Coat. Technol. 221, 158–162 (2013).
[Crossref]

Schwindt, P. D. D.

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L.-A. A. Liew, and J. Moreland, “Chip-scale atomic magnetometer,” Appl. Phys. Lett. 85, 6409–6411 (2004).
[Crossref]

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004).
[Crossref]

Shah, V.

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004).
[Crossref]

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L.-A. A. Liew, and J. Moreland, “Chip-scale atomic magnetometer,” Appl. Phys. Lett. 85, 6409–6411 (2004).
[Crossref]

Sherson, J. F.

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. SÃÿrensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 1–4 (2008).
[Crossref]

Sparkes, B.

M. Hosseini, B. Sparkes, G. Campbell, P. Lam, and B. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Straessle, R.

R. Straessle, M. Pellaton, C. Affolderbach, Y. Pétremand, D. Briand, G. Mileti, and N. F. de Rooij, “Low-temperature indium-bonded alkali vapor cell for chip-scale atomic clocks,” J. Appl. Phys. 113, 064501 (2013).
[Crossref]

Talkenberg, F.

S. Woetzel, F. Talkenberg, T. Scholtes, R. Ijsselsteijn, V. Schultze, and H. G. Meyer, “Lifetime improvement of micro-fabricated alkali vapor cells by atomic layer deposited wall coatings,” Surf. Coat. Technol. 221, 158–162 (2013).
[Crossref]

Têtu, M.

J. Vanier, R. Kunski, N. Cyr, J. Y. Savard, and M. Têtu, “On hyperfine frequency shifts caused by buffer gases: Application to the optically pumped passive rubidium frequency standard,” J. Appl. Phys. 53, 5387–5391 (1982).
[Crossref]

Vanier, J.

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421–442 (2005).
[Crossref]

J. Vanier, R. Kunski, N. Cyr, J. Y. Savard, and M. Têtu, “On hyperfine frequency shifts caused by buffer gases: Application to the optically pumped passive rubidium frequency standard,” J. Appl. Phys. 53, 5387–5391 (1982).
[Crossref]

Volk, C.

C. Volk, R. Frueholz, T. English, T. Lynch, and W. Riley, “Lifetime and Reliability of Rubidium Discharge Lamps for Use in Atomic Frequency Standards,” in “38th Annual Symposium on Frequency Control,” (1984).

Woetzel, S.

S. Woetzel, F. Talkenberg, T. Scholtes, R. Ijsselsteijn, V. Schultze, and H. G. Meyer, “Lifetime improvement of micro-fabricated alkali vapor cells by atomic layer deposited wall coatings,” Surf. Coat. Technol. 221, 158–162 (2013).
[Crossref]

Wu, Z.

K. Zhao and Z. Wu, “Atomic resonance behavior in laser-induced Rb atom desorption - The effect of ambient gas atoms and molecules,” Phys. Lett. A 299, 73–78 (2002).
[Crossref]

Zhao, K.

K. Zhao and Z. Wu, “Atomic resonance behavior in laser-induced Rb atom desorption - The effect of ambient gas atoms and molecules,” Phys. Lett. A 299, 73–78 (2002).
[Crossref]

Appl. Phys. B (1)

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421–442 (2005).
[Crossref]

Appl. Phys. Lett. (4)

L.-A. Liew, J. Moreland, and V. Gerginov, “Wafer-level filling of microfabricated atomic vapor cells based on thin-film deposition and photolysis of cesium azide,” Appl. Phys. Lett. 90, 114106 (2007).
[Crossref]

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching, L.-A. A. Liew, and J. Moreland, “Chip-scale atomic magnetometer,” Appl. Phys. Lett. 85, 6409–6411 (2004).
[Crossref]

S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L.-A. Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys. Lett. 85, 1460–1462 (2004).
[Crossref]

S. Abdullah, C. Affolderbach, F. Gruet, and G. Mileti, “Aging studies on micro-fabricated alkali buffer-gas cells for miniature atomic clocks,” Appl. Phys. Lett. 106, 163505 (2015).
[Crossref]

Compr. Microsyst. (1)

S. Knappe, “MEMS atomic clocks,” Compr. Microsyst. 3, 571–612 (2007).

J. Appl. Phys. (2)

J. Vanier, R. Kunski, N. Cyr, J. Y. Savard, and M. Têtu, “On hyperfine frequency shifts caused by buffer gases: Application to the optically pumped passive rubidium frequency standard,” J. Appl. Phys. 53, 5387–5391 (1982).
[Crossref]

R. Straessle, M. Pellaton, C. Affolderbach, Y. Pétremand, D. Briand, G. Mileti, and N. F. de Rooij, “Low-temperature indium-bonded alkali vapor cell for chip-scale atomic clocks,” J. Appl. Phys. 113, 064501 (2013).
[Crossref]

J. Chem. Educ. (1)

K. J. Laidler, “The development of the Arrhenius equation,” J. Chem. Educ. 61, 494–498 (1984).
[Crossref]

Nat. Commun. (1)

M. Hosseini, B. Sparkes, G. Campbell, P. Lam, and B. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Lett. A (1)

K. Zhao and Z. Wu, “Atomic resonance behavior in laser-induced Rb atom desorption - The effect of ambient gas atoms and molecules,” Phys. Lett. A 299, 73–78 (2002).
[Crossref]

Phys. Rev. A (1)

E. A. Donley, J. L. Long, T. C. Liebisch, E. R. Hodby, T. A. Fisher, and J. Kitching, “Nuclear quadrupole resonances in compact vapor cells: The crossover between the NMR and the nuclear quadrupole resonance interaction regimes,” Phys. Rev. A 79, 013420 (2009).
[Crossref]

Phys. Rev. Lett. (1)

T. Fernholz, H. Krauter, K. Jensen, J. F. Sherson, A. S. SÃÿrensen, and E. S. Polzik, “Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement,” Phys. Rev. Lett. 101, 1–4 (2008).
[Crossref]

Sci. Rep. (1)

R. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. AbdelHafiz, P. Abbé, S. Galliou, J.-Y. Rauch, and E. de Clercq, “Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications,” Sci. Rep. 5, 14001 (2015).
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Science (1)

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref] [PubMed]

Surf. Coat. Technol. (1)

S. Woetzel, F. Talkenberg, T. Scholtes, R. Ijsselsteijn, V. Schultze, and H. G. Meyer, “Lifetime improvement of micro-fabricated alkali vapor cells by atomic layer deposited wall coatings,” Surf. Coat. Technol. 221, 158–162 (2013).
[Crossref]

Other (6)

C. Volk, R. Frueholz, T. English, T. Lynch, and W. Riley, “Lifetime and Reliability of Rubidium Discharge Lamps for Use in Atomic Frequency Standards,” in “38th Annual Symposium on Frequency Control,” (1984).

R. Cook and R. Frueholz, “An improved rubidium consumption model for discharge lamps used in rubidium frequency standards,” in “Proceedings of the 42nd Annual Frequency Control Symposium,” (1988), pp. 525–531.

S. Karlen, J. Gobet, T. Overstolz, and J. Haesler, “Non-destructive MEMS atomic vapor cells characterization by Raman spectroscopy and image analysis,” in “2016 European Frequency and Time Forum (EFTF),” (2016), pp. 1–3.
[Crossref]

T. Overstolz, J. Haesler, G. Bergonzi, A. Pezous, P.-A. Clerc, S. Ischer, J. Kaufmann, and M. Despont, “Wafer scale fabrication of highly integrated rubidium vapor cells,” in “IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS),” (2014), pp. 552–555.

S. Karlen, J. Gobet, T. Overstolz, J. Haesler, and S. Lecomte, “Quantitative micro-Raman spectroscopy for pressure measurement in small volumes,” Manuscript in preparation.

Microsemi, “Quantum™ SA.45s Chip Scale Atomic Clock (CSAC),” www.microsemi.com/products/timing-synchronization-systems/embedded-timing-solutions/components/sa-45s-chip-scale-atomic-clock .

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Figures (8)

Fig. 1
Fig. 1 Fabrication process overview: (0) Si wafer of 1000 μm thickness as substrate, (1) DRIE etching of 2 mm wide through-holes, (2) anodic bonding of 200 μm thick Borofloat® 33 window wafer, (3–4) MVD deposition of 20 nm Al2O3 diffusion barrier, (5) micro-dispensing of RbN3 aqueous solution, (6) anodic bonding of second window, (7) dicing
Fig. 2
Fig. 2 MEMS atomic vapor cells before (left) and after (right) UV irradiation. Small droplets of metallic Rb can be seen after the irradiation.
Fig. 3
Fig. 3 Example of the evolution of the amount of rubidium for two cells with and without Al2O3 coating for cells heated at 180°C. The measurement is derived from the method presented below. The surface of glass covered by metallic rubidium is presented here instead of the Rb volume as the contact angle of Rb on uncoated glass was not calibrated.
Fig. 4
Fig. 4 Image recognition of Rb droplets size in MEMS atomic vapor cell: [left] Microscope image of a cell - [right] Extraction of drop radius by image recognition software
Fig. 5
Fig. 5 Example of the droplets evolution over time for a cell heated at 196°C. Small black dots can be observed on each drop. These particles of unknown composition are likely the nucleation sites of the droplets.
Fig. 6
Fig. 6 Spherical cap model used for Rb drop volume estimation
Fig. 7
Fig. 7 Estimation of Rb initial consumption: The contact angle θ is adapted such that the slope is 1 for the non-0 values of the measured Rb quantity
Fig. 8
Fig. 8 Estimation of the activation energy by fitting of the rubidium consumption rates of cells at different temperatures (k is given here in μg/s)

Equations (5)

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2 RbN 3 2 Rb + 3 N 2
m m e a s . ( t ) = m p r o d . m i n i t . c o n s . k t
V = π h 6 ( 3 a 2 + h 2 )
m m e a s . = { m p r o d . m i n i t . c o n s . if m p r o d . > m i n i t . c o n s . 0 if m p r o d . < m i n i t . c o n s .
k = A e E a R T

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