We have performed spectroscopy on sodium atoms that are optically channeled in the single node of a laser standing wave set up across a parallel-plate cavity. Using this technique we have extended our previous measurement of the Lennard-Jones van der Waals energy-level shift [Sandoghdar et al., Phys. Rev. Lett. 68, 3432 (1992)] down to a cavity width of ~500 nm. We discuss the applications of this technique to the precise measurement of atom-surface distances

Haroche, S.

Hinds, E. A.

Sandoghar, V.

Sukenik, C. I.

English

Old Dominion University

Old Dominion UniversityODU Digital CommonsPhysics Faculty Publications Physics3-1996Spectroscopy of Atoms Confined to the SingleNode of a Standing Wave in a Parallel-Plate CavityV. SandogharC. I. SukenikOld Dominion University, csukenik@odu.eduS. HarocheE. A. HindsFollow this and additional works at: https://digitalcommons.odu.edu/physics_fac_pubsPart of the Atomic, Molecular and Optical Physics CommonsThis Article is brought to you for free and open access by the Physics at ODU Digital Commons. It has been accepted for inclusion in Physics FacultyPublications by an authorized administrator of ODU Digital Commons. For more information, please contact digitalcommons@odu.edu.Repository CitationSandoghar, V.; Sukenik, C. I.; Haroche, S.; and Hinds, E. A., "Spectroscopy of Atoms Confined to the Single Node of a Standing Wavein a Parallel-Plate Cavity" (1996). Physics Faculty Publications. 9.https://digitalcommons.odu.edu/physics_fac_pubs/9Original Publication CitationSandoghdar, V., Sukenik, C. I., Haroche, S., & Hinds, E. A. (1996). Spectroscopy of atoms confined to the single node of a standingwave in a parallel-plate cavity. Physical Review A, 53(3), 1919-1922. doi: 10.1103/PhysRevA.53.1919Spectroscopy of atoms confined to the single node of a standing wave in a parallel-plate cavityV. Sandoghdar,* C. I. Sukenik,† S. Haroche,* andE. A. Hinds‡Department of Physics, Yale Uniersity, New Haven, Connecticut 06520~Received 10 November 1995!We have performed spectroscopy on sodium atoms that are optically channeled in the single node of a laserstanding wave set up across a parallel-plate cavity. Using this technique we have extended our previousmeasurement of the Lennard-Jones van der Waals energy-level shift @Sandoghdar et al., Phys. Rev. Lett. 68,3432 ~1992!# down to a cavity width of ;500 nm. We discuss the applications of this technique to the precisemeasurement of atom-surface distances.PACS number~s!: 32.80.Pj; 03.65.Bz; 32.70.JzIn the past decade the field of atomic physics has wit-nessed impressive progress in the manipulation of neutralatoms using laser light. In particular, the optical dipole forcehas been used to trap or channel atoms in potentials createdin one-, two-, or three-dimensional standing wave patterns@2#. Atoms in these potentials offer a simple realization of thequantum-mechanical particle in a box, and several recent ex-periments have studied the mechanical motion of such atoms@3–6#. From an applied point of view there has also beenrecent interest in optical channeling for its promise in atomicbeam lithography with submicron resolution @7,8#. All theseexperiments however, involve thousands of channels or po-tential wells in typically millimeter-sized interaction regions.Here we study atoms in an isolated potential well.In order to study atoms in the single node or antinode of astanding wave, one requires either a detector with subwave-length resolution or a system in which the atoms occupy onlyone such potential well. While the advent of near-field opti-cal microscopes with nanometer resolution might bring uscloser to the first option, a simple realization of the secondpossibility is a laser-light standing wave between two paral-lel mirrors, separated by only one wavelength. In the absenceof the light a ground-state atom in such a cavity experiencescavity QED energy-level shifts due to the modification of theelectromagnetic field by the mirrors @9,10#. Curve a in Fig. 1is the potential calculated for the ground state of sodiumbetween two plates separated by 0.5 mm. Once the laser lightis turned on, the atom sees an additional optical dipole po-tential @11# approximated byUopt~z !5\d2 ln@11S~z !# , ~1!where d is the detuning from resonance, S is the saturationparameter, and z is the displacement from the center of thecavity. Curve b in Fig. 1 shows the total potential for theground-state atom in the presence of typical channeling light(d5152 MHz, S50.01 at the antinode!. In particular, onesees that the optical dipole force makes a channel at thecenter that can hold the atom in place against the atom-cavityforce. Anderson et al. @12# have already reported an increasein the number of atoms transmitted through the cavity as aresult of confinement in such a potential. In this paper wereport the first excitation spectra for channeled atoms.We use a two-step resonant optical transition to excite theatoms to a low-lying nS Rydberg state (n510,11,12) forwhich there is a very strong atom-cavity van der Waals in-teraction. This is well approximated by an unretardedLennard-Jones potential @13# because the coherence time ofthe electric dipole fluctuations is much longer than the propa-gation time for light crossing the cavity. The form of thepotential is @14#ULJ~z !52^nSud2unS&6p«0L3 (oddn S 1~n22z/L !3 1 1~n12z/L !3D ,~2!where L is the separation between the two mirrors and z isonce again the position of the atom inside the cavity. This isplotted in curve c of Fig. 1 for the 12S state of sodium.Whereas the ground-state shifts are in the kHz range, theRydberg levels of interest here are shifted downards by sev-eral hundred MHz, causing a strong redshift of the excitationspectrum.The experimental setup, shown in Fig. 2, is largely thesame as our previous spectroscopy experiment in wider cavi-ties where there was no optical manipulation of the atoms@1#. Ground-state sodium atoms from a thermal beam(;240°C! enter a cavity made from two plane gold-coatedmirrors that are 8 mm long in the atomic beam direction and3 cm high. They are arranged to form a wedge touching atthe bottom and separated at the top by about 3 mm. The newfeature of this experiment is the optical channeling light,which has a total power of about 3 mW and is detuned by152 MHz from the transition 3S1/2,F52!3P3/2,F53 . Thislight is coupled into the cavity through the partially transmit-ting gold-coated mirrors and is cylindrically focused to avertical waist of 600 mm and a horizontal waist of 9 mmalong the atomic beam axis, with its maximum at the exit ofthe cavity. The height of this laser beam is adjusted to coin-cide with the second Fizeau fringe in the wedge so that it is*Present address: Laboratoire Kastler-Brossel, 24 rue Lhomond,75231 Paris, France.†Present address: Department of Physics, University of Michigan,Ann Arbor, Michigan 48109.‡Present address: Physics and Astronomy, University of Sussex,Brighton BN1 9QH, EnglandPHYSICAL REVIEW A MARCH 1996VOLUME 53, NUMBER 3531050-2947/96/53~3!/1919~4!/$10.00 1919 © 1996 The American Physical Societyresonant with the cavity. Because the reflectivity of the goldcavity wall at 589 nm is 65%, the optical field is predomi-nantly a standing wave whose intensity gradient produces theoptical dipole channel. The smaller traveling wave compo-nent gives rise to a weak radiation pressure force and inducesa ground-state light shift of about 140 kHz ~included in Fig.1!, neither of which is significant in this experiment. Al-though the wavelength of the light is 589 nm, the width ofthe cavity at this point is ;504 nm because there is a phaseshift associated with the imperfect reflectivity of the goldwalls ~see Ref. @1#!.Approximately 200 mm before leaving the cavity, the at-oms encounter two superimposed laser beams, one yellow(l15589 nm! and one blue (l2'425 nm!, which excitethem to a Rydberg state nS (n510, 11, or 12! through thetwo-step resonant process 3S!3P!nS . These laser beamsare focused to a waist of 300 mm and are adjusted to be atright angles to the atomic beam so as to eliminate the first-order Doppler effect. Most of the excited atoms are stronglyattracted to the walls by the van der Waals force 2¹ULJ @seeEq. ~2! and Fig. 1, curve c# and are lost from the beam.However, those located within ;40 nm @15# of the centercan emerge from the cavity and enter a detector where theyare field ionized and counted using a channel electron mul-tiplier. An auxiliary atomic beam is used to lock the yellowlaser to the resonance line, while Rydberg excitation spectrafrom this same beam provide a reference line against whichto measure the cavity shifts.Figure 3 shows on the left a typical 11S excitation spec-trum for sodium atoms channeled at the center of the cavity,while on the right is the spectrum from unperturbed atoms inthe reference atomic beam. The shift between the two is dueprimarily to the interaction between the cavity and the Ryd-berg atoms at its center. In the absence of the channelinglight, no excitation signal could be detected because theground-state atoms were lost to the cavity walls before theycould reach the excitation region. The line from the atoms inthe cavity is inhomogeneously broadened by a stray electricfield due to the random patch potentials on the gold surfaces.The patch size is comparable with the 30-nm thickness of thegold coating and the patch potential is of order 100 mV @16#.Since the atoms at the center of the cavity ‘‘see’’ a region ofroughly 100 patches on each side, the typical potential dif-ference is of order 10 mV. The corresponding electric field isa few hundred V/cm, which varies randomly with a correla-tion length comparable to the 0.5 mm spacing of the mirrors.The Gaussian distribution of patch potentials leads to an ex-ponential distribution of Stark shifts over the 300-mm regionilluminated by the excitation light. The solid line in Fig. 3 isa convolution of Lorentzians with an exponential distributionof Stark shifts, chosen to fit our data. First, we find the ho-mogeneous linewidth ~typically 20 MHz due to power broad-ening! from the high-frequency edge of the excitation spec-trum. Next, the mean Stark shift is chosen to reproduce theshape of the rest of the line, and corresponds typically to apatch field of 250 V/cm. Although the patch fields producean appreciable tail on the red side of the line, there is verylittle shift of the peak because the most probable Stark shiftis zero. Finally, the van der Waals shift is adjusted to obtainthe correct position of the spectrum relative to the referenceeline. We estimate that the uncertainty in the van der Waalsshift determined by this procedure is about 610 MHz.In Fig. 4 we present the data from two sets of experimen-tal runs, series a and b . In both cases the cavity width L wasset close to 504 nm. The horizontal error bars are estimatedat 630 nm, mainly due to the uncertainty in positioning theFIG. 1. Energy-level shifts of a sodium atom in a 504-nm-widecavity. Curve a , ground state in an empty cavity. b , ground state inthe presence of channeling light with 152 MHz detuning and satu-ration parameter 0.01 at the antinodes. Positive shift at the center isdue to a small traveling-wave component of the light. c , muchlarger shift of the 12S state; shift displayed on the right verticalaxis.FIG. 2. Schematic view of the apparatus.FIG. 3. Typical excitation spectra for the 11S state. Left: atom incavity, with and without channeling. Right: atom in free space.1920 53BRIEF REPORTSspectroscopy laser beams on the center of the Fizeau fringe.We have also included our earlier data points obtained in avariety of larger cavity widths without any channeling. Thereis moderately good agreement between these new measure-ments ~labeled a and b) and the Lennard-Jones potential~solid curves! for an atom at the center of the cavity given byULJ~z !527z~3 !^nSud2unS&24p«0L3, ~3!where z is the Riemann function. The new results can thusbe regarded as an extension of our measurement of theLennard-Jones van der Waals interaction to the smaller atom-surface distance of 252 nm.An equally interesting point of view, however, is that wecan reasonably assume the validity of the Lennard-Jones po-tential, then instead of testing it we can use it as a tool tomeasure the cavity width L . For example, in Fig. 4 the shiftsof series a are systematically stronger than expected, whilethose of series b are weaker. We attribute this to differentcavity widths in the two sets of runs due to a small change inthe vertical placement of the spectroscopy laser beams ~seeFig. 2!. This results in a discrepancy of tens of MHz in themeasured shift because the gradient of the van der Waalspotential is so steep. Figure 5 shows the shifts measured inthis work as a function of the mean square electric dipolemoment ^nSud2unS& , together with least-squares straight-lines fits constrained to go through the origin. It is clear thatthe two series of runs belong to lines of different slope. Us-ing Eq. ~3!, we determine from these slopes that the cavitywidths were 456~7! and 527~7! nm in series a and b , respec-tively.It may be possible to extend this technique to study thedistribution of atoms in the optical channel and their distancefrom the walls if, instead of detecting the production ofRydberg atoms, we measure the loss of ground-state atomsdue to Rydberg excitation in the cavity. In that case the linewill be inhomogeneously broadened by the van der Waalsshift and the shape of the line will give direct informationabout the atomic wave function in the channel provided thepatch fields are sufficiently small. Similarly, a standing wavewith several nodes should then give rise to spectra with sev-eral features corresponding to atoms in different opticalchannels.This work was supported by the National Science Foun-dation. We thank M. G. Boshier for helpful discussions.@1# V. Sandoghdar, C. I. Sukenik, E. A. Hinds, and S. Haroche,Phys. Rev. Lett. 68, 3432 ~1992!.@2# C. Cohen-Tannoudji, Fundamental Systems in Quantum Op-tics, Les Houches Summer School. Session LIII ~North-Holland, Amsterdam, 1992!; H. Metcalf and P. van der Strat-ten, Phys. Rep. 244, 203 ~1994!.@3# C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, Phys. Rev. Lett. 59, 1659 ~1987!.@4# P. Verkerk, B. Lounis, C. Salomon, C. Cohen-Tannoudji, J.-Y.Courtois, and G. Grynberg, Phys. Rev. Lett. 68, 3861 ~1992!.@5# A. Hemmerich and T. W. Ha¨nsch, Phys. Rev. Lett. 70, 410~1993!.@6# A. Kastberg, W. D. Phillips, S. L. Rolston, J. C. Spreeuw, andP. S. Jessen, Phys. Rev. Lett. 74, 1542 ~1995!.FIG. 4. Measured energy level shifts for 10S , 11S , and 12Sstates as a function of cavity width. Labels a and b mark twodifferent runs at 504-nm cavity width. Data for larger cavity widthsare reproduced from our earlier publication @1#. Solid curves aretheoretical predictons of the Lennard-Jones theory for an atom atthe center of a parallel-plate cavity.FIG. 5. Energy-level shifts measured in this work plotted as afunction of mean square dipole moment ^nSud2unS&. Straight-linefits to the data yield cavity widths of 456~7! nm for series a and527~7! nm for series b .53 1921BRIEF REPORTS@7# G. Timp, R. E. Behringer, D. M. Tennant, J. E. Cunningham,M. Prentiss, and K. K. Berggren, Phys. Rev. Lett. 69, 1636~1992!.@8# J. J. McClelland, R. E. Scholten, E. C. Palm, and R. J. Celotta,Science 262, 877 ~1993!.@9# G. Barton, Proc. R. Soc. London A 410, 141 ~1987!.@10# C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E.A. Hinds, Phys. Rev. Lett. 70, 560 ~1993!.@11# A. Ashkin, Phys. Rev. Lett. 40, 729 ~1978!.@12# A. W. Anderson, M. G. Boshier, S. Haroche, E. A. Hinds, W.Jhe, and D. Meschede, At. Phys. 11, 626 ~1989!.@13# J. E. Lennard-Jones, Trans. Faraday Soc. 28, 333 ~1932!.@14# E. A. Hinds, Adv. At. Mol. Opt. Phys. 28, 275 ~1991!.@15# We have made detailed classical calculations of the atomiccenter-of-mass trajectories in the cavity. For example, atomsexcited to the 11S state at a distance of 200 mm from the cavityexit do not escape unless they are within 638 nm of the center.However, this value should be regarded only as an order-of-magnitude estimate: a precise result would require a wave-mechanical description of the atom’s motion.@16# J. B. Camp, T. W. Darling, and R. E. Brown, J. Appl. Phys. 69,7126 ~1991!.1922 53BRIEF REPORTS

Spectroscopy of Atoms Confined to the Single Node of a Standing Wave in a Parallel-Plate Cavity

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Spectroscopy of Atoms Confined to the Single Node of a Standing Wave in a Parallel-Plate Cavity

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