We report the first observation of the annihilation of positronium from the 2S state. Positronium (Ps) is excited with a two-photon transition from the 1S to the 2S state where its lifetime is increased by a factor of eight compared to the ground state due to the decrease in the overlap of the positron electron wave-function. The yield of delayed annihilation photons detected as a function of laser frequency is used as a new method of detecting laser-excited Ps in the 2S state. This can be considered the first step towards a new high precision measurement of the 1S-2S Ps line

Alnis, J.

Antognini, A.

Brown, B.

Cooke, D.

Crivelli, P.

Friedreich, S.

Gabard, A.

Haensch, T.

Kirch, K.

Rubbia, A.

Vrankovic, V.

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Hyperfine Interact (2015) 233:67–73DOI 10.1007/s10751-015-1158-4Observation of positronium annihilation in the 2S state:towards a new measurement of the 1S-2S transitionfrequencyD. A. Cooke1 ·P. Crivelli1 ·J. Alnis2,6 ·A. Antognini1 ·B. Brown3 ·S. Friedreich1 ·A. Gabard5 ·T. W. Haensch4 ·K. Kirch1,5 ·A. Rubbia1 ·V. Vrankovic5Published online: 26 March 2015© Springer International Publishing Switzerland 2015Abstract We report the first observation of the annihilation of positronium from the 2Sstate. Positronium (Ps) is excited with a two-photon transition from the 1S to the 2S statewhere its lifetime is increased by a factor of eight compared to the ground state due tothe decrease in the overlap of the positron electron wave-function. The yield of delayedannihilation photons detected as a function of laser frequency is used as a new method ofdetecting laser-excited Ps in the 2S state. This can be considered the first step towards a newhigh precision measurement of the 1S–2S Ps line.Keywords Positronium · Spectroscopy · Bound state QED1 IntroductionPositronium (Ps) is the bound state of the positron and electron. Free from the finite-sizeeffects that become increasingly significant in high-precision spectroscopy of H [1], PsProceedings of the International Conference on Exotic Atoms and Related Topics (EXA 2014), Vienna,Austria, 15-19 September 2014. P. Crivellipaolo.crivelli@cern.ch1 ETH Zurich, Institute for Particle Physics, 8093 Zürich, Switzerland2 Max-Planck-Institute of Quantum Optics, 85741 Garching, Germany3 Marquette University, Milwaukee, WI 53233, USA4 Max-Planck-Institute of Quantum Optics, 85741 Garching, Germany5 Paul Scherrer Institute, 5232 Villigen, Switzerland6 Present address: University of Latvia, Riga, Latvia68 D. A. Cooke et al.is a purely leptonic atom for which weak interaction effects are negligible at the currentlevel of experimental accuracy, and thus provides an excellent testing ground for bound-state QED [2]. The energy levels of Ps can be calculated perturbatively as an expansionof the fine structure constant α with very high precision only limited by the complexity ofthe calculations and the knowledge of the fundamental constants. This is not the case, forinstance, for the hydrogen atom where the main source of the uncertainty in the predic-tions (involving S-states) are limited by the finite size of the proton. In comparison to otherhydrogen-like atoms, however, annihilation must be taken into account and recoil effectsare not suppressed by the m/M factor. The same theoretical tools could also be appliedin the field of quantum chromodynamics (QCD) for the calculation of the energy levelsof quarkonium (the bound state of 2 quarks) [3]. High-precision spectroscopy of Ps alsoallows the positron/electron mass ratio to be determined. This, together with other precisionexperiments with Ps such as searches for ‘invisible’ decays, which may indicate a hiddenmirror particle sector (e.g. [4] and references therein), could shed some light on the apparentmatter/antimatter asymmetry in the Universe, and perhaps on the nature of dark matter.Positronium has two ground states: the triplet (13S1, ortho-positronium) and the singlet(11S0, para-positronium) spin states. Due to the odd-parity under C-transformation, ortho-positronium decays predominantly into three photons with a lifetime in vacuum of τops =142.05 ns [5, 6]. Para-positronium decays predominantly into two photons with a lifetime invacuum of τpps = 125 ps [7, 8]. In the following, we will solely consider ortho-positronium(Ps) that, because of its longer lifetime (due to the phase-space and additional α suppressionfactors), allows us to perform the proposed studies.This paper reports on the first detection of laser-excited 2S state Ps by using the differ-ence in lifetime between the ground and excited states. This can be considered as the firststep towards a new high precision measurement of the 1S–2S Ps line. This quantity has pre-viously been measured using a pulsed laser [9] and then by using a continuous wave (CW)laser [10]. These measurements used an additional laser to photoionize the resulting excited-state Ps in order to detect the 2S state. Reaching a precision of 2.6 ppb, they provided thecurrent limit on the electron/positron mass ratio and tested bound-state QED calculationsup to O(α4), as calculated by [11]. The most recent calculations are up to O(α7) [12, 13],so an updated experimental determination is timely.2 Experimental methodThe measurement utilizes the ETHZ positron beam, which has been described previously[14], with modifications. Briefly, the positrons are derived from a 22Na source coupled toa solid rare gas moderator system. Positrons with energy of 200 eV are magnetically trans-ported around a 90◦ bend (to reduce contamination from fast particles and remove the directline-of-sight between the source and the detectors) to the target region. The target is formedby a 4 μg/m2 (about 20 nm thick) carbon foil with a porous silica thin-film positron–positronium converter 3 mm behind it. The whole assembly is biased at −5 kV, so positronsare implanted with slightly less than 5 keV kinetic energy (owing to energy loss in the win-dow). Secondary electrons from the C-foil are accelerated by this voltage back along thebeamline where they are detected on a multichannel plate, allowing the implanted positronsto be time-tagged. A significant fraction of the positrons implanted in the porous film arere-emitted into vacuum, bound as Ps, with near thermal energies [15, 16]. The target is fixednear the centre of a high-finesse (F ∼ 2.25 × 105) Fabry-Perot laser enhancement cavitysuch that the laser passes between the window and silica converter (as shown in Fig. 1).Observation of positronium annihilation in the 2S state 69Fig. 1 Target geometryThe laser itself is a frequency-doubled diode laser system from Toptica producing upto ∼ 750 mW of 486 nm light. In order for spectroscopy to be feasible the laser power mustbe enhanced to ∼ 1000 W to achieve intensities of the order of 1 MW/cm2. To reach thisvalue, approximately 500 mW of 486 nm light is injected into the high-finesse cavity withan in-coupling efficiency of ∼ 15 %. The enhancement cavity comprises two supermirrors(curvature radius 2 m and infinite for output and input mirrors respectively, transmissionand absorption both 7 ppm) separated by 30 cm, which leads to an enhancement factorof ∼ 1 × 104. Since, the beam waist at the centre of the cavity is σ = 370μm, the sep-aration between the laser beam axis and the target is therefore approximately 5 times thebeam waist, so that the enhancement factor of the cavity is unaffected by the loss of powerdue to the laser touching the e+/Ps converter. Although the advertised damage threshold ofthese mirror should have allowed a circulating power of 1500 W, degradation of cavity per-formance was observed already at 700 W. The circulating power was therefore deliberatelylimited to 500 W to avoid further damage to the mirrors.To compensate for the power limitation of the mirrors, a new kind of target geometrywas designed and implemented (see Fig. 1). The intention is to confine Ps spatially so thatthe Ps atoms could be redirected from the walls into the laser beam. In fact as Ps is verylight, even at room temperature it is very fast (v ≈ 104 m s−1), so the interaction timewith the laser is correspondingly short (on the order of 10 ns). Spatial confinement resultsin an estimated enhancement of a factor of five. To assess the effect of the collisions of Psin its ground state with the walls of the tube, we measured the lifetime and intensity of thePs emitted into vacuum for three target–window separations (3 mm, 5 mm and 9 mm) andobserved no variation in either property with distance. Destructive processes which mayoccur at the walls are limited to annihilation, as there is insufficient kinetic energy for Psbreak-up. The annihilation of the positron in the Ps atom with an electron which is not itsbound partner (so called pick-off effect) is proportional to the local electron density, thus,the cross-section for this process will be proportional to the time spent in the locality of thewall, or inversely proportional to the velocity. Our measurements suggest that the process isnegligible at these energies.For this measurement, the frequency is stabilized using the locking scheme shown inFig. 2, that is, with the laser locked to the enhancement cavity. The medium-term stabilityof 10 MHz precision was achieved by controlling the length of the enhancement cavityvia a HighFinesse WS7 wavemeter. Long term stability can be monitored by Te2 saturatedspectroscopy, using a line close to the Ps line [17].Detection of 2S Ps is achieved by exploiting the greatly increased lifetime of ortho-Ps inthe 2S state compared to the ground state (1.1 μs vs 142 ns). Two large solid angle BGOscintillator arrays (comprising four 20 × 6 cm crystals each), placed above and below thecavity, are used to detect the annihilation quanta from positronium formed in the converter.A signal event is defined as the detection of an energy deposition between 100 keV–60070 D. A. Cooke et al.Fig. 2 Laser frequency stabilization schemekeV within 10 ns in two BGO crystals in a time window of 2–4 μs after the tagging time.This time window is chosen to maximize the signal to background ratio, since the decay ofground state positronium after 2 μs are suppressed to a level below 1 ppm (e−2μs/0.142μs).The other sources of background are events that are not correlated with the tagged positron.A beam-related background arises in the case that a positron which is not the tagged one pro-duces annihilation photons detected within the signal window. This effect is greatly reducedby biasing off the positron beam with 220 V on an electrode (the beam energy is 200 eV),following the detection of secondary electrons. Accidental background not related to thebeam is generated by cosmic rays, environmental radioactivity and photomultiplier noiseand is reduced by requiring that the energy and time cuts described previously. To reducethe effect of internal radioactivity, the BGO crystals are shielded from each other by 25 mmof lead. These measures reduce the accidental rate to a level of < 10 events per 107 trig-gers. For comparison, simulations of expected signal rate yield a value of 28 events per 107triggers, assuming a 10 % positron-to-positronium conversion efficiency and for 500 W oflaser power on resonance.3 Resonance curveFigure 3 shows the resonance curve for laser excitation of Ps 1S → 2S, as measured usingthe lifetime method described above. The peak of the curve is 28 events on a backgroundlevel of 8, in reasonable agreement with the expected signal rate for the laser power achievedduring the measurement— ∼ 500 W—using a positron-to-Ps conversion efficiencyof ∼ 10 %. The position of the maximum of the resonance is arbitrary as reported by theWS7 wavemeter: this is not an absolute frequency measurement. Time-of-flight broadeningof approximately 30 MHz is evident. The measurements were recorded in a time period ofapproximately four hours, and a calibration check against a Te2 reference was performedbefore and after, to ensure that the laser frequency had not drifted significantly over themeasurement.The broad agreement between the peak signal rate and the prediction from simulationsuggests that 2S Ps also survives collisions with the walls of the tube. The simulation wasObservation of positronium annihilation in the 2S state 71-40 -20 0 20 40 60Frequency (arb, MHz)5101520253035CountsFig. 3 Number of observed events in 107 triggers vs. wavemeter frequencyperformed assuming 100 % (diffuse) reflection from the surfaces. In addition to pick-offannihilation, 2S Ps may also be expected to undergo collisional de-excitation, mainly bymixing with the 2P state (which subsequently decays rapidly by emission of a photon).That simulation and experiment agree without the inclusion of this effect implies that theenergy scale where collisional de-excitation becomes significant is below that typical ofroom temperature.The observation that thermal energy Ps appears to survive such collisions largelyunscathed suggests this technique for Ps confinement could be used in other relevant exper-iments, for example in Ps production for the GBar collaboration [18], or for studies ofPs–surface interactions. It is also in broad agreement with the calculations of [19] forexcited-state Ps–atom interaction cross-sections, where the lowest energy cross-section forcollisions with atomic Ar are < 1 × 10−16 cm2 (below 0.5 eV). That slow Ps can survivemultiple collisions with silica surfaces is perhaps not surprising. In order to escape from theporous silica target, the Ps must diffuse through the pore network, undergoing numerouscollisions at roughly the same energy, so the very fact that Ps can be emitted into vacuumfrom these materials suggest a high collision survival rate.At 5 keV implantation energy, the implantation depth is such that positronium has ther-malized within the material prior to emission. A conductive window is required to shieldthe spectroscopy volume from electric field penetration, for this measurement, 20 nm car-bon foils were used. These foils are extremely delicate, however, and it is planned that thewindow material be replaced by gold-coated silicon nitride for greater structural integrity.The energy loss spectrum of positrons transmitted through an uncoated 3 × 3 mm, 30 nmthickness silicon nitride window was measured to ensure that the positrons retain enoughkinetic energy to be sufficiently implanted. Above approximately 2 keV impact energy thetransmitted fraction reaches a saturation value, with the energy loss peaked at 100–200 eV.4 OutlookThis measurement constitutes a preliminary step towards a new determination of the Ps 1S-2S transition frequency, using the long lifetime of 2S Ps to detect excited Ps atoms. The72 D. A. Cooke et al.experimental set-up is currently being reconfigured to allow to reach the aimed precision of5×10−10 in order to check the recent QED calculations [12, 13]. This involves moving fromusing a time-tagged, continuous positron beam, to using the pulsed (and possibly bunched,i.e. with the pulses time-compressed) output from a two-stage buffer gas trap [20]. Pulsed-beam operation will effectively eliminate the background arising from untagged positronsand accidentals, thus improving the S/N ratio of our method by two orders of magnitude.With sufficient events, the Ps 2S lifetime could be determined, which would serve as ameasure of the stray electric field in the target tube (which should be < 10 Vcm−1). Fur-thermore, the lower background will give us the possibility to use simultaneously a secondmethod (already implemented in our set-up but not used due to the high beam related back-ground) for the detection of the 2S states based on three photons resonant ionization of thePs atoms in the same excitation laser. This technique can potentially yield additional infor-mation about the kinetic energy of the Ps atom, allowing for correction of the resultinglineshape for the 2nd-order Doppler shift.Significant improvements in the precision of the 1S→2S spectroscopy measurementusing Ps emitted from silica thin-films used as is are unlikely as even at thermal energiesthe velocity of Ps is large. Possibilities for lowering the energy further are laser cooling andStark deceleration of Rydberg Ps atoms, which are variously discussed in [21, 22] and withspecific reference to spectroscopy in [23, 24]. Stark deceleration of Rydberg Ps, followedby de-excitation back to the ground state could, in principle, allow the production of 1S Psat rest and therefore allow for a much higher accuracy that might result in a independentdetermination of the Rydberg constant free from finite size effects.Acknowledgments This work was supported by the Swiss National Science Foundation under theAmbizione grant PZ00P2 132059 and ETH Zurich Research Grant ETH-47-12-1. We would like to thank theIPP institute and ETH Zurich for their support, A. Gendotti, M. Wymann and the IPP workshop for their helpwith construction, S. Haas for assistance with data acquisition, and the PSI Magnet group for constructionand characterization of the cavity coils.References1. Beyer, A., Parthey, C.G., Kolachevsky, N., Alnis, J., Khabarova, K., Pohl, R., Peters, E., Yost, D.C.,Matveev, A., Predehl, K., Droste, S., Wilken, T., Holzwarth, R., Hänsch, T.W., Abgrall, M., Rovera, D.,Salomon, C., Laurent, P., Udem, T.: J. Phys. Conf. Ser. 467, 012003 (2013)2. Karshenboim, S.G.: Phys. Rep. 422, 1 (2005)3. Czarnecki, A., Melnikov, K.: Phys. Lett. B 519, 212 (2001)4. Crivelli, P., Belov, A., Gendotti, U., Gninenko, S., Rubbia, A.: J. Instrum. 5, P08001 (2010)5. Adkins, G.S., Fell, R.N., Sapirstein, J.R.: Annals Phys. 295, 136 (2002)6. Kataoka, Y., Asai, S., Kobayashi, T.: Phys. Lett. B 671, 219 (2009)7. Czarnicki, A., Melnikov, K., Yelkhovsky, A.: Phys. Rev. Lett. 83, 1135 (1999)8. Al-Ramadhan, A.H., Gidley, D.W.: Phys. Rev. Lett. 72, 1632 (1994)9. Chu, S., Mills, A.P., Hall, J.L.: Phys. Rev. Lett. 52, 1689 (1984)10. Fee, M.S., Chu, S., Mills, A.P., Chichester, R.J., Zuckerman, D.M., Shaw, E.D., Danzmann, K.: Phys.Rev. A: At., Mol., Opt. Phys 48, 192 (1993)11. Fell, R.N.: Phys. Rev. Lett. 68, 25 (1992)12. Melnikov, K., Yekhovsky, A.: Phys. Lett. B 458, 143 (1999)13. Pachucki, K., Karshenboim, S.G.: Phys. Rev. A 60, 2792 (1999)14. Alberola, N., Anthonioz, T., Badertscher, A., Bas, C., Belov, A.S., Crivelli, P., Gninenko, S.N., Golubev,N.A., Kirsanov, M.M., Rubbia, A., Sillou, D.: Nucl. Instrum. Meth. A 560, 224 (2006)15. Crivelli, P., Gendotti, U., Rubbia, A., Liszkay, L., Perez, P., Corbel, C.: Phys. Rev. A 81, 052703 (2010)16. Cassidy, D.B., Crivelli, P., Hisakado, T.H., Liszkay, L., Meligne, V.E., Perez, P., Tom, H.W.K., Mills,A.P.: Phys. Rev. A 81, 012715 (2010)Observation of positronium annihilation in the 2S state 7317. McIntyre, D.H., Hänsch, T.W.: Phys. Rev. A 34, 4504 (1986)18. Perez, P., Sacquin, Y.: Class. Quantum Grav. 29, 184008 (2012)19. Starrett, C., Walters, H.J.R.: Nucl. Instrum. Meth. B 266, 3221 (2008)20. Surko, C.M., Greaves, R.G., Iwata, K., Gilbert, S.J.: Nucl. Instrum. Meth. B 171, 2 (2000)21. Liang, E.P., Dermer, C.D.: Optics Comm. 65, 419 (1988)22. Hogan, S.D.: Phys. Rev. A 87, 063423 (2013)23. Crivelli, P., Cooke, D.A., Friedreich, S.: Int. J. Mod. Phys.: Conf. Ser. 30, 1460257 (2014)24. Crivelli, P., Nesvizhevsky, V.V., Voronin, A.Y.: Advances in High Energy Physics, arXiv:1408.7051(2014)

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Observation of positronium annihilation in the 2S state: towards a new measurement of the 1S-2S transition frequency

Observation of positronium annihilation in the 2S state: towards a new measurement of the 1S-2S transition frequency

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