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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 16 — Aug. 3, 2009
  • pp: 14109–14114
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Integrated magneto-optical traps on a chip using silicon pyramid structures

S. Pollock, J. P. Cotter, A. Laliotis, and E. A. Hinds  »View Author Affiliations


Optics Express, Vol. 17, Issue 16, pp. 14109-14114 (2009)
http://dx.doi.org/10.1364/OE.17.014109


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Abstract

We have integrated magneto-optical traps (MOTs) into an atom chip by etching pyramids into a silicon wafer. These have been used to trap atoms on the chip, directly from a room temperature vapor of rubidium. This new atom trapping method provides a simple way to integrate several atom sources on the same chip. It represents a substantial advance in atom chip technology and offers new possibilities for atom chip applications such as integrated single atom or photon sources and molecules on a chip.

© 2009 Optical Society of America

1. Introduction

Atom chips are microfabricated devices that control electric, magnetic and optical fields in order to trap and manipulate cold atom clouds [1

1. E. A. Hinds and I. G. Hughes, “A pyramidal magneto-optical trap as a source of slow atoms,” J.Phys. D 18, R119–R146 (1999). [CrossRef]

, 2

2. R. Folman, P. Kruger, J. Schmiedmayer, J. Denschlag, and C. Henkel, “Microscopic atom optics: from wires to an atom chip,” Adv. At., Mol. Opt. Phys. 48, 263–356 (2002).

, 3

3. J. Fortágh and C. Zimmermann, “Magnetic microtraps for ultracold atoms,” Rev. Mod. Phys. 79, 235–289 (2007). [CrossRef]

], and to form Bose-Einstein condensates [4

4. W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, “Bose-Einstein condensation on a microelectronic chip,” Nature 413, 498–501 (2001). [CrossRef] [PubMed]

, 5

5. H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, “Bose-Einstein ondensation in a surface microtrap,” Phys. Rev. Lett. 87, 230,401 (2001). [CrossRef]

, 6

6. C. D. J. Sinclair, E. A. Curtis, I. Llorente-Garcia, J. A. Retter, B. V. Hall, S. Eriksson, B. E. Sauer, and E. A. Hinds, “Bose-Einstein Condensation on a permanent-magnet atom chip,” Phys. Rev. A 72, 03,160(R) (2005). [CrossRef]

]. Prospective applications include atomic clocks, atom interferometers, and quantum information processors. Despite enormous progress in the development of atom chips over recent years, the method of loading them has continued to be quite inconvenient. Atoms are first collected in a macroscopic magneto-optical trap (MOT) far from the surface, which requires several laser beams. The magnetic field can be made using macroscopic coils external to the chip or using integrated wires to form a U-MOT [7

7. J. Reichel, W. Hänsel, and T. W. Hänsch, “Atomic Micromanipulation with Magnetic Surface Traps,” Phys. Rev. Lett. 83(17), 3398–3401 (1999). [CrossRef]

, 8

8. A. Grabowski and T. Pfau, “A lattice of magneto-optical and magnetic traps for cold atoms,” Eur. Phys. J. D 22, 347–354 (2003).

]. The atoms are then loaded into a magnetic trap, which finally has to be moved very accurately to transport them to the small structures on the chip. A simple alternative has been proposed [9

9. M. Trupke, F. Ramirez-Martinez, E. A. Curtis, J. P. Ashmore, S. Eriksson, E. A. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. V. Prakash, and J. J. Baumberg, “Pyramidal micromirrors for microsystems and atom chips,” App. Phys. Letts. 88, 071,116 (2006).

], in which the silicon wafer of the chip is processed to make pyramidal hollows wherever atoms are required. A single incident light beam is then multiply reflected in each pyramid to form the set of appropriately-polarized light beams needed for magneto-optical trapping [10

10. K. I. Lee, J. A. Kim, H. R. Noh, and W. Jhe, “Single-beam atom trap in a pyramidal and conical hollow mirror,” Opt. Letts. 21, 1177 (1996). [CrossRef]

]. This has the virtue that atoms are cooled and collected directly on the chip at the locations of interest. References [9

9. M. Trupke, F. Ramirez-Martinez, E. A. Curtis, J. P. Ashmore, S. Eriksson, E. A. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. V. Prakash, and J. J. Baumberg, “Pyramidal micromirrors for microsystems and atom chips,” App. Phys. Letts. 88, 071,116 (2006).

, 11

11. G. N. Lewis, Z. Moktdir, C. Gollasch, M. Kraft, S. Pollock, F. Ramirez-Martinez, J. Ashmore, A. Laliotis, M. Trupke, and E. A. Hinds, “Fabrication of Magnetooptical Atom Traps on a Chip,” J. MEMS 18, 347 (2009).

] report some technical aspects of fabricating integrated MOTs on a chip, but such a source has never previously been demonstrated.

In this article we present the successful operation of an integrated atom source using a pyramid MOT, lithographically fabricated in silicon, which collects atoms from a background vapor and cools and traps them on the chip. We outline the micro-fabrication process required to produce deep pyramidal structures in silicon, and the steps needed to achieve adequate optical quality of the pyramid facets. We present data for three different MOTs to establish how the atom number scales with the size of the MOT and we discuss possible future applications.

2. Fabrication

In order to fabricate deep pyramids, we start with silicon wafers of 3 mm thickness, cut on the [100] plane. These are coated on both sides with a thick (350nm) protective layer of low stress silicon nitride, applied by low pressure chemical vapor deposition. We use photo-lithography with reactive ion etching to open square apertures in one of the layers, thereby exposing the silicon. Etching in a solution of KOH (40% by weight in water) at a temperature of 80° C, then removes the exposed silicon at a rate of 60μm/hour in the direction perpendicular to the surface. The etch rate is anisotropic, exposing the {111} planes to create square pyramidal pits in the surface of the silicon wafer, as shown in Fig. 1(a). The length of one side of the base is √2 times the depth of the pyramid. A temperature-stabilized water bath and re-condenser are used because the etch rate is extremely sensitive to small variations in the concentration and temperature of the etchant. We have produced a number of pyramids in this way, ranging in depth from 0.9mm to 3 mm. At the longest etching times, of ~ 50 hours, we found that the chips were damaged from the back where the etchant had managed to penetrate the silicon nitride, probably through scratches produced during handling and mounting. This problem was solved by covering the back side with a PTFE disk during etching.

Fig. 1. Pyramids after various stages of processing. Top row: photographs. Bottom row: optical microscope images of an internal pyramid face. (a, d) Array of pyramids 2.8mm deep, etched without agitation. (b, e) Single pyramid 2.1mm deep, formed with air bubbling through etchant. (c, f) Pyramid 2.8mm deep, etched with agitation, then polished by 30 minutes of ICP etching. This particular wafer was diced to make the individual pyramid shown.

Figure 1(a) is a photograph of a 2.8mm-deep pyramid. We have added white lines to the image (here and in Figure 1(b)) in order to delineate the structure more clearly. The pyramid is perfectly formed except for the surface quality of the facets, which are locally smooth but exhibit roughness that is correlated over very long distances. This can be seen on the illuminated facet in Fig. 1(a) and is even more obvious in the optical microscope image of Fig. 1(d). This roughness is thought to be due to hydrogen bubbles, formed in the reaction between KOH and silicon, which modify the local silicon etch rate [12

12. A. S. Louro and J. R. Senna, “Real-time, in-situ microscopic observation of bubbles and roughening in KOH etching of silicon,” in Micromachining and Microfabrication Process Technology VII (2001).

] causing craters. The structures we see are large because the etch time is long. A pyramid in this condition does not work as a MOT.

We tried a number of approaches to reduce the formation of this roughness during the etching. Adding a small amount of isopropanol as a surfactant produced no evident improvement in the surface quality. It has been suggested that bubbling air through the etchant can improve the surface because the increased oxygen concentration may help to remove the hydrogen [12

12. A. S. Louro and J. R. Senna, “Real-time, in-situ microscopic observation of bubbles and roughening in KOH etching of silicon,” in Micromachining and Microfabrication Process Technology VII (2001).

]. We tried this and found that it does indeed improve the surface quality. Figure 1(b) shows a pyramid that was made in this way, and the microscope image in Figure 1(e) shows the improvement in surface quality. The same improvement is found when we agitate the etchant with a magnetic stirrer or shake the sample to remove the hydrogen bubbles as they form. It is possible therefore that the effect of bubbling the air is primarily mechanical rather than chemical. Despite the improvement, this smoother pyramid is still not able to operate as a MOT.

Faced with this persistent long-range roughness, we considered how the surface might be smoothed by a second stage of processing. Small-scale roughness can be covered up by coating the surface with amorphous silicon dioxide, which becomes smooth after annealing [13

13. K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 26(23), 1888–1890 (2001). [CrossRef]

]. However, this approach does not solve our problem because the thickness of the covering would need to be many tens of μm in order to become comparable with the correlation length of the roughness. A better approach is to etch the rough surfaces isotropically. We explored two isotropic etching techniques, (i) a wet etch using a mixture of hydrofluoric and nitric acids dissolved in acetic acid (HNA) and (ii) an inductively coupled plasma (ICP) etch using sulphur hexaflouride (SF6).

The nitric acid in HNA reacts with silicon to produce SiO2, which is then removed by reaction with the hydrofluoric acid. This polishing process produces a highly reflecting surface with no trace of roughness, but unfortunately it leaves the surfaces very rounded so that we no longer have the required pyramid geometry. We nevertheless tried these pyramids in our apparatus and established empirically that they do not work to produce a MOT. Two different HNA solutions were tried, in the ratios vol% (30:43:27) and (8:66:26), with etch rates differing by almost an order of magnitude. These both produced the same results, suggesting that the rounding is characteristic of the method and therefore that HNA polishing may not be suitable for our purposes.

We had more success with ICP etching, using a low-power plasma in pure SF6 to produce fluorine radicals that attack the silicon surface. We followed “recipe ID 2” of Ref. [14

14. K. P. Larsen, J. Ravnkilde, and O. Hansen, “Investigations of the isotropic etch of an ICP source for silicon microlens mold fabrication,” J. Micromech. Microeng. 15, 873–882 (2005). [CrossRef]

], which Larsen et al. used to reduce the roughness of silicon micro-lens moulds. We measure the rate of the ICP etch to be 3 μm/min perpendicular to the surface. After 30 min of etching, the surfaces are very much smoother and pyramids still retain their shape. Despite the large amount of material removed the faces remain flat and the edges are still sharp, as one can see in Figs. 1(c) and 1(f). The quality of the surface continues to improve with ICP etching time, but we did not study this beyond 60 min.

3. Experimental

In order to test whether a pyramid can operate as a MOT for ultra-cold atoms, we sputter-coat it with 25 nm of aluminum. This has a reflectivity of 0.8 at the operating wavelength, which allows the MOT to work without masking any part of the surface [11

11. G. N. Lewis, Z. Moktdir, C. Gollasch, M. Kraft, S. Pollock, F. Ramirez-Martinez, J. Ashmore, A. Laliotis, M. Trupke, and E. A. Hinds, “Fabrication of Magnetooptical Atom Traps on a Chip,” J. MEMS 18, 347 (2009).

]. We were unable to obtain MOT operation with the unpolished pyramids, with or without agitation during the etching process. We believe this is due to the large scale roughness of the surface, which creates a coarse texture of the light intensity in the trapping region, having feature sizes comparable with the size of the atom cloud. Pyramids that were polished in HNA do not work, even though the mirror surfaces are smooth, because the facets are curved. However, pyramids polished by ICP etching work well because the facets are flat with small scale surface roughness.

The experiment uses three diode lasers at 780 nm. A frequency-reference laser is locked by polarization spectroscopy to the 5S12(F=2)5P32(F=3) transition of 87Rb [15

15. C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35(24), 5141–5151 (2002). [CrossRef]

]. The MOT laser is frequency-locked 12MHz below the 85Rb transition 5S12(F=3)5P32(F=4), 1.1 GHz to the blue of the reference laser, using the “side of filter” technique [16

16. G. Ritt, G. Cennini, C. Geckeler, and M. Weitz, “Laser frequency offset locking using a side of filter technique,” App. Phys. B 79, 363–365 (2004). [CrossRef]

]. Atoms that fall into the F = 2 ground state are re-pumped by a DAVLL-stabilized laser tuned to the 5S12(F=2)5P32(F=3) 85Rb transition [17

17. K. L. Corwin, Z.-T. Lu, C. F. Hand, R. J. Epstein, and C. E. Wieman, “Frequency-Stabilized Diode Laser with the Zeeman Shift in an Atomic Vapor,” App. Opt. 37, 3295–3298 (1998). [CrossRef]

]. Each pyramid is illuminated with ~ 1mW of circularly polarized MOT light and ~ 50 μW of re-pump light.

Fig. 2. The complete chip package consisting of a 3 × 3 array of silicon pyramid MOTs mounted in a rectangular PEEK holder 25 × 30 mm2. The necessary magnetic fields are generated using a copper zig-zag array, which forms part of the package, above and below the chip.

4. Results

When cold atoms are trapped in a pyramid, they scatter enough MOT light to be detected by a CCD camera. Light is also scattered from the surfaces of the pyramid, but this background can be subtracted by taking images with and without atoms. Figure 3 shows such a difference image obtained with a 2.5mm-deep pyramid. In addition to the direct view of the cloud, one can see weaker images reflected from the sides of the pyramid. The light power detected by the camera can be converted to a number of atoms because we know the scattering rate per atom. In this case we measure 2000 ±400 atoms. The density distribution is roughly Gaussian with a standard deviation of 80 μm in the two visible directions, parallel to the surface of the chip. The vertical size is 1√2 of this, giving a peak density of 4 × 1014 atoms/m3. A larger, 2.8mm-deep pyramid yields 7000 ± 500 atoms in a cloud of the same size, while a smaller 2.1 mm-deep pyramid has a cloud of 1000 ± 300 atoms and a similar radius. These MOTs all have a temperature of approximately 100μK. In the rougher pyramids, where we could not detect a MOT, it is possible that there were some atoms, but the number would have had to be less then 300 in order to escape detection

It is expected that the number of atoms should scale as N ~ L 2 vc 4 [18

18. K. Lindquist, M. Stephens, and C. Wieman, “Experimental and Theoretical-Study of the Vapor-Cell Zeeman Optical Trap,” Phys. Rev. A 46(7), 4082–4090 (1992). [CrossRef] [PubMed]

], where L is the size of the pyramid and vc is the maximum velocity of atoms that can be captured. Because these MOTs are small, the capture velocity is limited by the capture distance, which scales as L. The friction force -αv has a coefficient α that is almost constant over the capture region. Consequently vc ~ L and therefore N ~ L 6. Our observations are consistent with this scaling and inconsistent with the theory for larger MOTs, where the stopping distance is not the limiting factor and N ~ L 3.6 [18

18. K. Lindquist, M. Stephens, and C. Wieman, “Experimental and Theoretical-Study of the Vapor-Cell Zeeman Optical Trap,” Phys. Rev. A 46(7), 4082–4090 (1992). [CrossRef] [PubMed]

]. With L 6 scaling, we expect a pyramid 1mm deep to capture approximately 10 atoms, which is below the detection limit of our current measurement scheme. We aim to work with such clouds by integrating optical micro-cavities into the same chip [19

19. M. Trupke, J. Goldwin, B. Darquié, G. Dutier, S. Eriksson, J. Ashmore, and E. A. Hinds, “Atom Detection and Photon Production in a Scalable, Open, Optical Microcavity,” Phys. Rev. Lett. 99, 063,601 (2007). [CrossRef]

] and to use them as a deterministic source of single atoms and photons. There is also currently considerable interest in producing and trapping ultracold molecules on a chip. The integrated pyramid MOT offers an ideal starting point for this project since atoms are readily photo-associated in a MOT [20

20. K. M. Jones, E. Tiesinga, P. D. Lett, and P. S. Julienne, “Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering,” Reviews of Modern Physics 78(2), 483 (2006). [CrossRef]

].

Fig. 3. Fluorescence image of 2000 cold 85Rb atoms in a 2.5mm-deep pyramid. Reflections of the MOT are just visible in two of the internal faces.

5. Conclusion

To summarize, we have shown how a pyramid MOT can be integrated into a silicon chip by a process of anisotropic wet etching, followed by polishing in an ICP etch. We have demonstrated that the integrated MOT works and have compared a range of sizes to test the scaling law. This new atom trapping method operates with just one input beam of light and provides a simple way to integrate several atom sources on the same chip. It represents a substantial advance in atom chip technology and opens the way to new functionality for atom chips including integrated single atom or photon sources and molecules on a chip.

Acknowledgments

We are indebted to M. Trupke for many useful discussions, to M. Tarbutt for suggesting the photoassociation of molecules in a pyramid MOT, and to S. Etienne & T. Matsuura at the London Centre for Nanotechnology (LCN) for fabrication assistance. This work is supported by the EC Seventh Framework project 216744 (CHIMONO), the UK EPSRC and QIPIRC, and the Royal Society.

References and links

1.

E. A. Hinds and I. G. Hughes, “A pyramidal magneto-optical trap as a source of slow atoms,” J.Phys. D 18, R119–R146 (1999). [CrossRef]

2.

R. Folman, P. Kruger, J. Schmiedmayer, J. Denschlag, and C. Henkel, “Microscopic atom optics: from wires to an atom chip,” Adv. At., Mol. Opt. Phys. 48, 263–356 (2002).

3.

J. Fortágh and C. Zimmermann, “Magnetic microtraps for ultracold atoms,” Rev. Mod. Phys. 79, 235–289 (2007). [CrossRef]

4.

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, “Bose-Einstein condensation on a microelectronic chip,” Nature 413, 498–501 (2001). [CrossRef] [PubMed]

5.

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, “Bose-Einstein ondensation in a surface microtrap,” Phys. Rev. Lett. 87, 230,401 (2001). [CrossRef]

6.

C. D. J. Sinclair, E. A. Curtis, I. Llorente-Garcia, J. A. Retter, B. V. Hall, S. Eriksson, B. E. Sauer, and E. A. Hinds, “Bose-Einstein Condensation on a permanent-magnet atom chip,” Phys. Rev. A 72, 03,160(R) (2005). [CrossRef]

7.

J. Reichel, W. Hänsel, and T. W. Hänsch, “Atomic Micromanipulation with Magnetic Surface Traps,” Phys. Rev. Lett. 83(17), 3398–3401 (1999). [CrossRef]

8.

A. Grabowski and T. Pfau, “A lattice of magneto-optical and magnetic traps for cold atoms,” Eur. Phys. J. D 22, 347–354 (2003).

9.

M. Trupke, F. Ramirez-Martinez, E. A. Curtis, J. P. Ashmore, S. Eriksson, E. A. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. V. Prakash, and J. J. Baumberg, “Pyramidal micromirrors for microsystems and atom chips,” App. Phys. Letts. 88, 071,116 (2006).

10.

K. I. Lee, J. A. Kim, H. R. Noh, and W. Jhe, “Single-beam atom trap in a pyramidal and conical hollow mirror,” Opt. Letts. 21, 1177 (1996). [CrossRef]

11.

G. N. Lewis, Z. Moktdir, C. Gollasch, M. Kraft, S. Pollock, F. Ramirez-Martinez, J. Ashmore, A. Laliotis, M. Trupke, and E. A. Hinds, “Fabrication of Magnetooptical Atom Traps on a Chip,” J. MEMS 18, 347 (2009).

12.

A. S. Louro and J. R. Senna, “Real-time, in-situ microscopic observation of bubbles and roughening in KOH etching of silicon,” in Micromachining and Microfabrication Process Technology VII (2001).

13.

K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 26(23), 1888–1890 (2001). [CrossRef]

14.

K. P. Larsen, J. Ravnkilde, and O. Hansen, “Investigations of the isotropic etch of an ICP source for silicon microlens mold fabrication,” J. Micromech. Microeng. 15, 873–882 (2005). [CrossRef]

15.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35(24), 5141–5151 (2002). [CrossRef]

16.

G. Ritt, G. Cennini, C. Geckeler, and M. Weitz, “Laser frequency offset locking using a side of filter technique,” App. Phys. B 79, 363–365 (2004). [CrossRef]

17.

K. L. Corwin, Z.-T. Lu, C. F. Hand, R. J. Epstein, and C. E. Wieman, “Frequency-Stabilized Diode Laser with the Zeeman Shift in an Atomic Vapor,” App. Opt. 37, 3295–3298 (1998). [CrossRef]

18.

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and Theoretical-Study of the Vapor-Cell Zeeman Optical Trap,” Phys. Rev. A 46(7), 4082–4090 (1992). [CrossRef] [PubMed]

19.

M. Trupke, J. Goldwin, B. Darquié, G. Dutier, S. Eriksson, J. Ashmore, and E. A. Hinds, “Atom Detection and Photon Production in a Scalable, Open, Optical Microcavity,” Phys. Rev. Lett. 99, 063,601 (2007). [CrossRef]

20.

K. M. Jones, E. Tiesinga, P. D. Lett, and P. S. Julienne, “Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering,” Reviews of Modern Physics 78(2), 483 (2006). [CrossRef]

OCIS Codes
(020.7010) Atomic and molecular physics : Laser trapping
(130.3120) Integrated optics : Integrated optics devices
(020.3320) Atomic and molecular physics : Laser cooling

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: July 2, 2009
Revised Manuscript: July 24, 2009
Manuscript Accepted: July 28, 2009
Published: July 29, 2009

Citation
S. Pollock, J. P. Cotter, A. Laliotis, and E. A. Hinds, "Integrated magneto-optical traps on a chip using silicon pyramid structures," Opt. Express 17, 14109-14114 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-14109


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References

  1. E. A. Hinds and I. G. Hughes, "A pyramidal magneto-optical trap as a source of slow atoms," J. Phys. D 18, R119-R146 (1999). [CrossRef]
  2. R. Folman, P. Kruger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. Mol. Opt. Phys. 48, 263-356 (2002).
  3. J. Fortágh and C. Zimmermann, "Magnetic microtraps for ultracold atoms," Rev. Mod. Phys. 79, 235-289 (2007). [CrossRef]
  4. W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, "Bose-Einstein condensation on a microelectronic chip," Nature 413, 498-501 (2001). [CrossRef] [PubMed]
  5. H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, "Bose-Einstein condensation in a surface microtrap," Phys. Rev. Lett. 87, 230,401 (2001). [CrossRef]
  6. C. D. J. Sinclair, E. A. Curtis, I. Llorente-Garcia, J. A. Retter, B. V. Hall, S. Eriksson, B. E. Sauer, and E. A. Hinds, "Bose-Einstein Condensation on a permanent-magnet atom chip," Phys. Rev. A 72, 03,160(R) (2005). [CrossRef]
  7. J. Reichel, W. Hänsel, and T. W. Hänsch, "Atomic Micromanipulation with Magnetic Surface Traps," Phys. Rev. Lett. 83(17), 3398-3401 (1999). [CrossRef]
  8. A. Grabowski and T. Pfau, "A lattice of magneto-optical and magnetic traps for cold atoms," Eur. Phys. J. D 22, 347-354 (2003).
  9. M. Trupke, F. Ramirez-Martinez, E. A. Curtis, J. P. Ashmore, S. Eriksson, E. A. Hinds, Z. Moktadir, C. Gollasch, M. Kraft, G. V. Prakash, and J. J. Baumberg, "Pyramidal micromirrors for microsystems and atom chips," App. Phys. Lett. 88, 071,116 (2006).
  10. K. I. Lee, J. A. Kim, H. R. Noh, and W. Jhe, "Single-beam atom trap in a pyramidal and conical hollow mirror," Opt. Lett. 21, 1177 (1996). [CrossRef]
  11. G. N. Lewis, Z. Moktdir, C. Gollasch, M. Kraft, S. Pollock, F. Ramirez-Martinez, J. Ashmore, A. Laliotis, M. Trupke, and E. A. Hinds, "Fabrication of Magnetooptical Atom Traps on a Chip," J. MEMS 18, 347 (2009).
  12. A. S. Louro and J. R. Senna, "Real-time, in-situ microscopic observation of bubbles and roughening in KOH etching of silicon," in Micromachining and Microfabrication Process Technology VII (2001).
  13. K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, "Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction," Opt. Lett. 26(23), 1888-1890 (2001). [CrossRef]
  14. K. P. Larsen, J. Ravnkilde, and O. Hansen, "Investigations of the isotropic etch of an ICP source for silicon microlens mold fabrication," J. Micromech. Microeng. 15, 873-882 (2005). [CrossRef]
  15. C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, "Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking," J. Phys. B 35(24), 5141-5151 (2002). [CrossRef]
  16. G. Ritt, G. Cennini, C. Geckeler, and M. Weitz, "Laser frequency offset locking using a side of filter technique," App. Phys. B 79, 363-365 (2004). [CrossRef]
  17. K. L. Corwin, Z.-T. Lu, C. F. Hand, R. J. Epstein, and C. E. Wieman, "Frequency-Stabilized Diode Laser with the Zeeman Shift in an Atomic Vapor," Appl. Opt. 37, 3295-3298 (1998). [CrossRef]
  18. K. Lindquist, M. Stephens, and C. Wieman, "Experimental and Theoretical-Study of the Vapor-Cell Zeeman Optical Trap," Phys. Rev. A 46(7), 4082-4090 (1992). [CrossRef] [PubMed]
  19. M. Trupke, J. Goldwin, B. Darquié, G. Dutier, S. Eriksson, J. Ashmore, and E. A. Hinds, "Atom Detection and Photon Production in a Scalable, Open, Optical Microcavity," Phys. Rev. Lett. 99, 063,601 (2007). [CrossRef]
  20. K. M. Jones, E. Tiesinga, P. D. Lett, and P. S. Julienne, "Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering," Rev. Mod. Phys. 78(2), 483 (2006). [CrossRef]

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