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Superfluid Droplets on a Solid Surface (1990) techniques available at kilohertz repetition 28. C. Kan and N. H. Burnett, unpublished results. 30. L. Xu et al., Opt. Lett. 21, 2008 (1996). rates offer the potential for attosecond- 29. The electric field of a light pulse can be described in 31. We are indebted to A. J. Schmidt for his encourage- terms of a carrier of frequency v and a time-varying ment and T. Brabec for useful discussions. K. Fe- resolution atomic spectroscopy and nonlin- 0 envelope of amplitude A(t ): E(t ) 5 A(t )exp[2i(v0t 1 rencz (Research Institute for Solid State Physics, ear optics in the x-ray regime. c)]. This decomposition can be used to pulse dura- Budapest, Hungary) is gratefully acknowledged for tions down to the carrier oscillation cycle [T. Brabec manufacturing the silver foils. This research was sup- REFERENCES AND NOTES and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997)]. ported by the Austrian Science Foundation under ___________________________ The parameter c is the relative carrier phase. It de- grants P-11109 and Y44-PHY. 1. J. C. Solem and G. C. Baldwin, Science 218, 229 termines the position of the carrier with respect to the (1982); M. Howells et al., ibid. 238, 514 (1987); J. E. envelope. 21 May 1997; accepted 9 September 1997 Trebes et al., ibid., p. 517. 2. D. Attwood, K. Halbach, K.-J. Kim, ibid. 228, 1265 (1985). 3. B. J. Macgowan et al., Phys. Rev. Lett. 65, 420 Superfluid Droplets on a Solid Surface (1990). 4. Flash x-ray sources such as those demonstrated in (3) would be ideal for the avoidance of image blur- D. Ross, J. E. Rutledge, P. Taborek* ring due to, for example, object motion during ex- posure [R. A. London et al., Appl. Opt. 28, 3397 (1989)]; however, the spatial coherence of the Photographs are presented of isolated superfluid helium-4 droplets prepared on a sources demonstrated in the water window so far cesium surface, the only material known that is not wetted by superfluid helium. Although are far from being sufficient for single-shot biologi- cal holography. thermodynamic measurements show that the cesium surface is highly uniform, the 5. A. McPherson et al., J. Opt. Soc. Am. B 4, 595 contact angle of the droplets is extremely hysteretic and depends on whether the contact (1987); X. F. Li et al., Phys. Rev. A 39, 5751 (1989). line is advancing or receding. Superfluid helium-4 droplets on an inclined surface do not 6. A. L’Huillier and Ph. Balcou, Phys. Rev. Lett. 70, 774 (1993); J. J. Macklin et al., ibid., p. 766. flow downhill but rather are strongly pinned to the surface. 7. J. L. Krause et al., ibid. 68, 3535 (1992). 8. P. B. Corkum, ibid. 71, 1995 (1993). 9. M. Lewenstein et al., Phys. Rev. A 49, 2117 (1994). 10. K. C. Kulander et al.,inProceedings of the Work- shop on Super-Intense Laser Atom Physics (SILAP) Superfluid He has unusual thermal and dows that provide an edge-on view of the III, P. Piraux, Ed. (Plenum, New York, 1993). mechanical properties (1) and is well substrate as well as a view from above at 11. K. Miyazaki and H. Takada, Phys. Rev. A 52, 3007 known for its ability to spread over surfac- an angle of 60° from the normal. The (1995). 12. I. P. Christov et al., Phys. Rev. Lett. 77, 1743 (1996); es and to flow without dissipation through substrate is a quartz microbalance with K. J. Schafer and K. C. Kulander, ibid. 78, 638 even microscopic holes. Virtually all of gold electrodes similar to those used in our (1997). the walls and surfaces used in earlier dis- earlier thermodynamic studies (5, 6). Fifty 13. J. Zhou et al., ibid. 76, 752 (1996). 14. Z. Chang et al.,inApplications of High Field and sipationless flow experiments were ob- atomic layers of Cs were vapor-deposited Short Wavelength Sources VII (OSA Tech. Digest served to be wetted by superfluid He. This onto the quartz and gold surfaces of the Ser., vol. 7, Optical Society of America, Washington, effect means that droplets on these sub- microbalance at a rate of 0.01 layer per DC, 1997), p. 187. 15. R. Haight and P. F. Seidler, Appl. Phys. Lett. 65, 517 strates are unstable and immediately second. During the evaporation, the tem- (1994). spread to form a smooth continuous film perature of the substrate and the walls of 16. S. Sartania et al., Opt. Lett. 22, 1562 (1997). over the entire surface so that vapor and the container were maintained below 6 K 17. M. Nisoli et al., ibid., p. 522. substrate are never in contact. Recent to maintain ultrahigh vacuum conditions. 18. Given the finite tube wall thickness of 0.05 mm, the actual target thickness is estimated as 100 to 200 mm. work (2) has shown that alkali metals are We used the microbalance to monitor the The coherence length related to the phase error intro- a special class of materials not completely deposition and to perform thermodynamic duced by the tight focusing of the fundamental (11)ison wetted by superfluid He. In particular, Cs characterizations of the surface; the wet- the order of 10 mm for wavelengths shorter than 10 nm. The target thickness has been minimized in an attempt substrates can be used to prepare super- ting temperature was measured to be Tw 5 to keep the interaction length as close as possible to this fluid samples with a distinctly different 2.04 K. A capillary tube (0.04 cm, outside “geometric” coherence length. It is this geometric co- topology consisting of a droplet with an diameter) attached to a source of room- herence length limitation that dictates the necessity of the high pressures applied. edge where substrate, superfluid, and va- temperature gas through a mass-flow con- 19. Note that this peak irradiance is reached only on the por meet at a three-phase contact line (3). troller provided a means of putting drops propagation axis in an infinitesimally small fraction of We present here direct observations of of superfluid on the surface. We main- the cross section of the Gaussian beam. The majority of the helium atoms in the interaction volume are isolated droplets of superfluid on a sub- tained the system at liquid-vapor coexist- exposed to somewhat lower irradiances. strate (4). Both the static and the dynamic ence by filling the bottom of the container 20. The pressure in the interaction region has been esti- behaviors of the droplets were unusual. with bulk liquid 4He. The drops were ob- mated as follows. The gas flow from the target region We found that the contact angle was an served with a long-focal-distance micro- into the chamber is calculated from the known pumping speed and the measured background extremely hysteretic function of the vol- scope that provided a magnification of pressure in the target chamber. Gas flow and back- ume of the drop. Perhaps most remarkable, ;330. ground pressure then determine uniquely the pres- superfluid droplets would not move across Figures 1 and 2 show a sequence of sure in the target. 21. I. P. Christov et al., Phys. Rev. Lett. 78, 1251 (1997). the surface until considerable force was photos of superfluid drops on a Cs sub- 22. C. Kan et al., ibid. 79, 2971 (1997). applied to them. This result is surprising strate at T 5 1.16 K. Pictures taken with 23. We used a detector quantum efficiency of 2%, an because solid surfaces are well known not the microscope looking down on the sub- electron multiplication gain of 5 3 106, and a grating diffraction efficiency of 10% (data provided by the to exert transverse forces on bulk super- strate at an angle of 30° above the hori- manufacturers) for this estimation. fluid or superfluid films without edges. zontal are shown in Fig. 1. The dark bar at 24. M. Schnu¨ rer et al., unpublished results. Our apparatus consisted of a substrate the top of the pictures is the capillary 25. M. V. Ammosov et al., Zh. Eksp. Teor. Fiz. 91, 2008 that can be rotated about a horizontal axis tube, and the lower bar is its shadow. The (1986) [Sov. Phys. JETP 64, 1191 (1986)]. 26. Siegman et al., IEEE J. Quantum Electron. 27, 1098 mounted in an optical cryostat with win- tube was left in contact with the superfluid (1991). drop so that fluid could be added and 27. Measurement of the x-ray beam profile at different Department of Physics and Astronomy, University of Cal- withdrawn. This geometry is conventional positions or direct interferometric measurement of ifornia, Irvine, CA 92697, USA. its spatial coherence will obviate the need for this for contact-angle measurements and typi- assumption. *To whom correspondence should be addressed. cally yields the advancing and receding 664 SCIENCE z VOL. 278 z 24 OCTOBER 1997 z www.sciencemag.org REPORTS contact angle (7). The drops appear oval was about 32° (8) and independent of the wetting transition that we have explored because of the viewing angle. The edge of volume of the drop; Fig. 2, A and B, show in previous work (5, 6). In order to ex- the planar gold electrode can be seen in snapshots of the same drop as fluid was added plain a receding contact angle of zero, the extreme and upper left; the Cs film is (the corresponding top view of the growing standard models based on consideration of too thin to provide appreciable optical drop is shown in Fig. 1, A and B).
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