We have developed a nozzle source that delivers a continuous beam of atomic helium or molecular hydrogen having a high degree of transverse coherence and with adequate optical brightness to enable new kinds of experiments. Using this source we have measured single slit diffraction patterns and the first ever speckle-diffraction patterns using atomic and molecular de Broglie waves. Our results suggest fruitful application of coherent matter beams in dynamic scattering and diffractive imaging at short wavelength and with extreme surface sensitivity

Deponte, Daniel P.

Elliott, Gregory S.

Kevan, Stephen D.

Patton, Forest S.

English

Sound Ideas

University of Puget SoundSound IdeasAll Faculty Scholarship Faculty Scholarship7-1-2006Speckle Patterns With Atomic And Molecular DeBroglie WavesForest S. PattonDepartment of Physics, University of Oregon, Eugene, Oregon 97403-1274, USADaniel P. DeponteDepartment of Physics, University of Oregon, Eugene, Oregon 97403-1274, USAGregory S. ElliottUniversity of Puget Sound, gelliott@pugetsound.eduStephen D. KevanDepartment of Physics, University of Oregon, Eugene, Oregon 97403-1274, USAFollow this and additional works at: http://soundideas.pugetsound.edu/faculty_pubsThis Article is brought to you for free and open access by the Faculty Scholarship at Sound Ideas. It has been accepted for inclusion in All FacultyScholarship by an authorized administrator of Sound Ideas. For more information, please contact soundideas@pugetsound.edu.CitationPatton, Forest S., Daniel P. Deponte, Gregory S. Elliott, and Stephen D. Kevan. 2006. "Speckle patterns with atomic and molecular deBroglie waves." Physical Review Letters 97(1): 013202-013202.Speckle Patterns with Atomic and Molecular de Broglie WavesForest S. Patton,1 Daniel P. Deponte,1 Greg S. Elliott,2 and Stephen D. Kevan11Department of Physics, University of Oregon, Eugene, Oregon 97403-1274, USA2Department of Physics, University of Puget Sound, Tacoma, Washington 98416, USA(Received 26 January 2006; revised manuscript received 17 April 2006; published 7 July 2006)We have developed a nozzle source that delivers a continuous beam of atomic helium or molecularhydrogen having a high degree of transverse coherence and with adequate optical brightness to enable newkinds of experiments. Using this source we have measured single slit diffraction patterns and the first everspeckle-diffraction patterns using atomic and molecular de Broglie waves. Our results suggest fruitfulapplication of coherent matter beams in dynamic scattering and diffractive imaging at short wavelengthand with extreme surface sensitivity.DOI: 10.1103/PhysRevLett.97.013202 PACS numbers: 39.10.+j, 03.75.Dg, 39.20.+qAfter de Broglie first postulated [1] and others verified[2–4] the wave nature of massive particles, applicationsusing matter waves expanded quickly into a diverse arrayof mainstream scientific instruments, including many elec-tron microscopies and a host of scattering and diffractiontechniques. Later, invention of the laser vastly facilitatedexploration and exploitation of wave coherence. The inter-section of these two developments has been slow to de-velop, largely due to the lack of sources with high coherentflux. A notable exception is the field of atom optics [5],which has produced a dazzling array of results relying onatom coherence in the long wavelength limit. There re-mains a keen interest in developing short wavelength co-herent sources to enable diffractive imaging and coherentscattering techniques with higher resolution than is avail-able in the optical regime. Much progress along these lineshas been accomplished by extracting the coherent fractionfrom field emission cathodes in electron microscopy [6,7].The high brightness available at third generation synchro-tron radiation sources has spawned efforts to use coherencein the soft and hard x-ray regimes [8–10]. High flux heliumbeams have been developed to study surface dynamicalphenomena [11], and collimating these to achieve highcoherence in one dimension has led to several pioneeringexperiments [12–14]. Here we describe a new apparatusthat produces continuous beams of thermal energy heliumatoms and hydrogen molecules having a high degree oftransverse coherence in two dimensions and a coherent fluxthat will be useful for a variety of new kinds of experi-ments. The particles have de Broglie wavelengths compa-rable to x rays, are neutral and nondamaging, and arescattered with high surface selectivity. We report the re-sults of preliminary tests in which we have used thisapparatus to measure single slit diffraction patterns and aspeckle-diffraction pattern of an irregularly shaped object.Figure 1 shows a schematic of our experimental setup. Akey ingredient of any experiment utilizing wave coherenceis source brightness (B), as measured by particle flux perunit area and solid angle, since this is directly related to theavailable coherent flux (Fcoh) by [8]: Fcoh  B 22; (1)where  is the de Broglie wavelength. Our He or H2 sourceis a glass capillary which has been drawn into a 2 mdiameter nozzle [15]. Gaseous He or H2 at variable stag-nation temperature T0 and pressure P0 expands freelythrough the nozzle into vacuum. Using a small nozzlediameter and high P0 will produce a beam of high bright-ness [15]. The resulting gas jet passes through a conicalskimmer with an opening diameter of 300 m into adifferential pumping region, and then into an ultrahighvacuum chamber and through a spatial filter consisting of5 m and 1 m diameter pinholes separated by 8 cm. Fora surface scattering experiment, the spatially filtered co-herent beam would be incident on a scattering sample.Scattered atoms or molecules are field ionized with nearlyunit efficiency using a tungsten tip having a nominal radiusof 100 nm held at a temperature of 100 K and avoltage of typically 10 kV. Field ionization detectionof molecular beams has been used for some time, and arecent article describes the current state of the pursuit[16,17]. The resulting ions are detected with a channelFIG. 1. Schematic representation of our apparatus. Shown arethe glass capillary nozzle mounted in a metal high-pressurechamber, two spatial filter pinholes, the micropositioning stagesthat hold the second pinhole and the detector consisting of atungsten field ionization tip and the channel electron multiplier(CEM), and a calibrated residual gas analyzer (RGA) used foralignment and to measure the coherent flux.PRL 97, 013202 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending7 JULY 20060031-9007=06=97(1)=013202(4) 013202-1 © 2006 The American Physical Societyelectron multiplier (CEM). The advantage of using fieldionization is that diffraction patterns can be measured withthe spatial resolution necessary to resolve interferencefringes by scanning the tip with piezoelectric actuatedstages. The very small ionization volume of the tip alsoeffectively discriminates against the ambient gas.Coherence is the property of waves that leads to inter-ference; that is, if coherent waves are overlapped in spaceand time, there will be coherent addition of wave ampli-tudes rather than incoherent addition of wave intensities[18]. Longitudinal coherence pertains to the monochroma-ticity or degree of regularity of the wave fronts in thedirection of propagation. For a free-jet expansion, thelongitudinal coherence length lL can be expressed in termsof the speed ratio, S [19]: lL  S    2; (2)where  is the average speed. By extrapolating previousresults [11] for our nozzle parameters we estimate S30–40 for H2 and S 100–110 for He at T0  100 K.Combining this with the de Broglie wavelengths deter-mined below, we determine lL to be several nanometers.High diffraction fringe contrast will be observed if thescattering path length difference is less than the longitudi-nal coherence length. lL does not limit contrast in theresults presented below, but it does provide a fundamentallimit on our ultimate spatial resolution.Transverse coherence refers to the degree of regularityof wave fronts perpendicular to the propagation direction[18] and in molecular beams is related to the less-well-studied perpendicular velocity distribution [15,20]. To im-prove the limited transverse coherence of a free-jet source,we insert a spatial filter composed of two pinholes that setthe transverse phase space acceptance at the level of theHeisenberg Uncertainty Principle. The correlation of waveamplitudes at two points in an observation plane willdiminish over a scale given by the transverse coherencelength lT , which can be predicted using the Zernicke–vanCittert theorem [18] to be lT  R2d1; (3)where d1 is the first pinhole size and R is the distancebetween the pinhole and the plane. A wave field with anaverage degree of coherence of 90% will fill the secondpinhole in the spatial filter if its diameter d2 is smaller thanthe transverse coherence length lT , leading to the constraint 2d1d2R< : (4)To test our approach, we diffracted He and H2 beams offseveral different apertures fabricated in 100 nm thick sili-con nitride membranes using a focused ion beam. The insetin Fig. 2 shows a micrograph of a 0:7 m wide slit thatreplaced the second spatial filter pinhole. The resultingdiffraction patterns shown in Fig. 2 exhibit fringes to atleast seventh order before they become lost in the back-ground produced by ionization of ambient gas. We havefitted our results to an ideal single slit diffraction patternconvoluted with a Gaussian distribution of transverse wavevectors of width kT  =lT [21], with addition of aconstant background. The resulting fits and derived valuesof  and lT are shown in the figure. We cannot accuratelymeasure the nozzle temperature T0, and therefore assumeconversion of stagnation gas enthalpy into directed kineticenergy [19] to infer the nozzle temperatures shown. Thederived values kT actually correspond to the width of thetransverse wave vector distribution projected onto the de-tector plane convoluted with the unknown size of thedetector ionization region and the amplitude of any resid-ual vibrations of the apparatus. The true transverse coher-ence lengths, therefore, are larger than those reported inFig. 2.The results in Fig. 2 provide a good characterization ofbeam properties but do not require coherence in bothtransverse directions. They also are not fundamentallynew, since researchers have produced thermal energy par-ticle waves with good coherence in one transverse direc-tion and have used these in single slit geometries toperform various precision measurements [12–14,22–24].A beam approaching full transverse coherence will allowqualitatively new classes of scattering experiments, whilealso further reducing the signal by factor of >104 due toincreased collimation. To demonstrate good transversecoherence requires that we measure the diffraction patternof an object that is small in both dimensions. We havemeasured Airy fringes from single pinholes, but a resultthat is closer to our planned experiments is to produce aspeckle-diffraction pattern of a random structure.Mechanical limitations precluded scattering the beam offFIG. 2 (color). Measured and fitted single slit diffraction pat-terns using hydrogen gas at P0  700 kPa and T0  120 K and240 K (calculated). Each scan took20min to record. The insetshows a scanning electron micrograph of our single slit producedin a silicon nitride membrane.PRL 97, 013202 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending7 JULY 2006013202-2an imperfect surface. Instead, we measured a specklepattern produced in transmission through the random pin-hole pattern shown in Fig. 3(a). In Fig. 3(b) we show theexpected speckle amplitude, which is the magnitude of theFourier transform of Fig. 3(a). The raw speckle amplitude,measured reproducibly using a raster scan, is shown inFig. 3(c). The diffraction pattern of a real object musthave inversion symmetry, and aside from uncertainty inthe measurement, our pattern does indeed exhibit thissymmetry, as evidenced by the similarity of the image inFig. 3(c) to its symmetrized version in Fig. 3(d). Theobserved and predicted speckle patterns have similar fea-tures, although finite coherence again diminishes the visi-bility of the measured fringes. The quality of these data isnot sufficient to extract a coherence length as was done forthe single slit results in Fig. 2. Instead, Fig. 3(e) shows theresult of convoluting the ideal diffraction pattern in panel(b) with a two-dimensional distribution of transverse wavevectors having an isotropic width equal to that deduced inFig. 2. The predicted fringe contrast in panel (e) is com-parable to that in the symmetrized experimental pattern inpanel (d), and the similarity between measured and pre-dicted fringe patterns is clear.These results constitute the first speckle-diffraction pat-tern collected with atomic or molecular de Broglie waves.More importantly, we have achieved a brightness andcoherent flux high enough to enable several future researchdirections. Table I summarizes the typical brightness,wavelength, and coherent flux of this and other shortwavelength particle and photon sources. We have shownelsewhere how to produce a source brightness in excess of1028 atoms= sec m2 rad2 [15], which is a few orders ofmagnitude below the average brightness of undulators atthird generation synchrotron radiation facilities. Given itssimplicity, relative low cost, continuous availability, andthe unit probability for helium scattering from surfaces, oursource will be very competitive in some applications. Forexample, we have adapted an existing theory for diffuse x-ray and neutron surface reflectivity [25] to estimate theaverage flux of coherent helium atoms scattered into asingle speckle from a surface with typical roughness char-acteristics. Atoms scatter diffusely with unit efficiency intoa distribution that is roughly the Fourier transform of thesurface height-height correlation function. For an opti-mized apparatus, the predicted average flux/speckle is 3–4 orders of magnitude below the incident flux—a substan-tial signal that could be used to measure surface fluctua-tions or to do diffractive imaging.A remaining instrumentation issue that is crucial to thelong-term application of coherent atomic and molecularbeams is the detector. With a dwell time of a few sec=pixel,2000 pixels, and a duty cycle of <50%, the image inFig. 3 required a total accumulation time of several hours.A larger momentum range was not accumulated due pri-marily to the thermal stability of our apparatus. Diffractiveimaging, where 106 pixels are required, is not possibleusing a single channel detector. This atom optical experi-ment would benefit from developing an ‘‘atom camera’’that would measure the entire speckle pattern in one expo-sure. Field emission and ionization tip arrays have beendeveloped and used in various sensor and display applica-tions [26,27], and integrating these with the necessary ionoptics and area detector would provide a sound approachfor such a development. If such an atom camera wereFIG. 3 (color). (a) Scanning electron micrograph of the random pinhole structure produced in a silicon nitride membrane;(b) expected speckle-diffraction amplitude, which is simply the magnitude of the Fourier transform of the structure in panel (a);(c) the measured speckle-diffraction amplitudes from the structure in panel (a); (d) inversion-symmetrized speckle-diffraction pattern;(e) expected speckle-diffraction amplitude corrected for finite coherence as explained in the text. Amplitudes rather than intensities areplotted to make the weaker fringes more easily visible.PRL 97, 013202 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending7 JULY 2006013202-3employed, a full diffraction pattern could be produced in afew minutes with adequate signal to provide a real-spaceresolution, limited by longitudinal coherence, of a fewnanometers. Such a detector would also benefit the atomicanalog of dynamic light scattering to measure soft, diffu-sive modes at surfaces on time scales longer than a micro-second or on energy scales less than a nanovolt. Finally,our source and such a detector would also facilitate severalexperiments at the interface of quantum optics and quan-tum physics. Our degeneracy parameter [28]—the numberof particles per coherence volume, Vcoh  lT2lL—is pres-ently  104, and will increase to 103 with a next-generation source design [15]. While this is small com-pared to liquid helium and Bose-Einstein condensates,where  1, and to lasers, where  is macroscopicallylarge, Hanbury Brown and Twiss [29] accomplished pio-neering quantum optical experiments 50 years ago usingmercury lamps with degeneracy parameters comparable toours.This work was carried out at the University of Oregonwith financial support provided by the National ScienceFoundation under Grant No. DMR-0506241 and theDepartment of Education GAANN GrantNo. P200A010820.[1] L. de Broglie, Ph.D. thesis, Universite De Paris, 1924.[2] C. Davisson and L. H. Germer, Phys. Rev. 30, 705 (1927).[3] I. Estermann and A. Stern, Z. Phys. 61, 95 (1930).[4] G. P. Thomson and A. Reid, Nature (London) 119, 890(1927).[5] P. Meystre, Atom Optics (Springer-Verlag, Berlin, 2001).[6] L. J. Wu, Y. M. Zhu, and J. Tafto, Phys. Rev. Lett. 85, 5126(2000).[7] J. M. Cowley, Phys. Rev. Lett. 84, 3618 (2000).[8] D. Attwood, K. Halbach, and K. J. Kim, Science 228, 1265(1985).[9] J. Miao, P. Charalambous, J. Kirz, and D. Sayre, Nature(London) 400, 342 (1999).[10] S. Brauer, G. B. Stephenson, M. Sutton, R. Bruning,E. Dufresne, S. G. J. Mochrie, G. Grubel, J. Als-Nielsen,and D. L. Abernathy, Phys. Rev. Lett. 74, 2010 (1995).[11] J. P. Toennies, in Surface Phonons, edited by W. Kress andF. W. de Wette (Springer-Verlag, Berlin, 1991), p. 111.[12] W. Schollkopf and J. P. Toennies, Science 266, 1345(1994).[13] R. E. Grisenti, W. Schollkopf, J. P. Toennies, G. C.Hegerfeldt, T. Kohler, and M. Stoll, Phys. Rev. Lett. 85,2284 (2000).[14] A. Kalinin, O. Kornilov, L. Rusin, J. P. Toennies, andG. Vladimirov, Phys. Rev. Lett. 93, 163402 (2004).[15] D. DePonte, F. S. Patton, and S. D. Kevan, Rev. Sci.Instrum. 77, 055107 (2006).[16] R. B. Doak, J. Phys. Condens. Matter 16, S2863 (2004).[17] D. Deponte, S. D. Kevan, and G. S. Elliott, Rev. Sci.Instrum. (to be published).[18] M. Born and E. Wolf, Principles of Optics (Pergamon,New York, 1975).[19] D. Miller, in Atomic and Molecular Beam Methods, editedby G. Scoles (Oxford University Press, New York, 1988),Vol. 1, p. 14.[20] H. C. W. Beijerinck and N. F. Verster, Physica B & C 111,327 (1981).[21] A. Zeilinger, R. Gahler, C. G. Shull, W. Treimer, andW. Mampe, Rev. Mod. Phys. 60, 1067 (1988).[22] O. Carnal and J. Mlynek, Phys. Rev. Lett. 66, 2689 (1991).[23] M. S. Chapman, C. R. Ekstrom, T. D. Hammond,J. Schmiedmayer, S. Wehinger, and D. E. Pritchard,Phys. Rev. Lett. 74, 4783 (1995).[24] M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van derZouw, and A. Zeilinger, Nature (London) 401, 680(1999).[25] S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley,Phys. Rev. B 38, 2297 (1988).[26] C. A. Spindt, Surf. Sci. 266, 145 (1992).[27] I. Brodie and C. A. Spindt, in Advances in Electronics andElectron Physics (Academic, New York, 1992), Vol. 83.pp. 1–106.[28] J. Goodman, Statistical Optics (Wiley, New York, 1985).[29] R. Hanbury Brown and R. Q. Twiss, Proc. R. Soc. A 242,300 (1957).TABLE I. Typical brightness, wavelength, and coherent flux of various short wavelength particle and photon sources. Coherent fluxvalues are derived from Eq. (1) and assume no monochromatization beyond the natural bandwidth of the source.Brightness (particles= sec m2 rad2) Wavelength (nm) Coherent flux (particles= sec)Helium micronozzleThis study 3 1027 0.1 1 107Optimized [15] 3 1028 0.1 1 108X-ray undulator 1032 0.1 2 1011Field emission tip 1032 0.004 4 108PRL 97, 013202 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending7 JULY 2006013202-4

Speckle Patterns With Atomic And Molecular De Broglie Waves

https://soundideas.pugetsound.edu/cgi/viewcontent.cgi?article=3744&amp;context=faculty_pubs

Speckle Patterns With Atomic And Molecular De Broglie Waves

Abstract

Similar works

Full text

Available Versions

Sound Ideas