Antimatter Gravity MICE-U.S. Plans withDaniel Muons M. Kaplan US Spokesperson, MICE Collaboration Daniel M. Kaplan

Physics Seminar WichitaMuTAC State Review Univ. June Fermilab16, 2017 16–17 March, 2006 Outline • Dramatis Personae • A Bit of History - antimatter, the baryon asymmetry of the universe, and all that... • The Ideas, The Issues, The Opportunities • Required R&D • Conclusions Our story’s a bit complicated, so please bear with me! ...and stop me if you have a question! D. M. Kaplan, IIT An#ma&er Gravity Seminar 2/41 Matter & Energy

• After many decades of experimentation with subatomic particles, we now know whatDramatis everything is made of... Personae

Baryons & antibaryons : p== uud & p uud ΛΛ==uds & uds ... Mesons : K00== ds & K ds B00== db & B db B+ == ub & B− ub ... Leptons : e∓, µ∓, τ∓, ν’s

D. M. Kaplan, IIT An#ma&er Gravity Seminar 3/41 Matter & Energy

• After many decades of experimentation with subatomic particles, we now know whatDramatis everything is made of... Personae “Imperfect mirror” Baryons & antibaryons : Antip== uud & p uud ΛΛ==uds & uds ... Mesons : Anti K00== ds & K ds B00== db & B db

Anti B+ == ub & B− ub ... Antimatter Leptons : e∓, µ∓, τ∓, ν’s • And, don’t forget: antimatter and matter annihilate on contact

D. M. Kaplan, IIT An#ma&er Gravity Seminar 3/41 Outline • Dramatis Personae ➡ • A Bit of History - antimatter, the baryon asymmetry of the universe, and all that... • The Ideas, The Issues, The Opportunities • Muonium Gravity Experiment • Required R&D • Conclusions

D. M. Kaplan, IIT An#ma&er Gravity Seminar 4/41 Our story begins with...

D. M. Kaplan, IIT An#ma&er Gravity Seminar 5/41 Antimatter! [photo credits: Nobelprize.org] • Introduced by Dirac in 1928 Dirac equation (QM + relativity) - Paul A. M. Dirac described positrons in addition to electrons positron discovered by Anderson in 1932 - Carl Anderson - antiproton discovered by Chamberlain & Segrè in 1955 - now well established that

o all charged particles (and many types of neutrals) Owen Chamberlain have antiparticles, of opposite electric charge o Big Bang produced exactly equal amounts of matter and antimatter Emilio Segrè

D. M. Kaplan, IIT An#ma&er Gravity Seminar 6/41 Antimatter! o Big Bang produced exactly equal amounts of matter and antimatter – a puzzle!

D. M. Kaplan, IIT An#ma&er Gravity Seminar 7/41 Baryon Asymmetry o Big Bang produced exactly equal amounts of matter and antimatter – a puzzle! • Already in 1956, M. Goldhaber noted the “baryon [M. Goldhaber, “Speculations on Cosmogeny,” asymmetry of the universe” (BAU) Science 124 (1956) 218] - universe seems to contain lots of mass in the form of baryons – protons and neutrons – but almost no antimatter! How could this be consistent with the BB? - now generally believed BAU arose through CP violation (discovered in 1964) - but, pre-1964, more plausible to postulate gravitational repulsion between matter and antimatter – “antigravity”!

D. M. Kaplan, IIT An#ma&er Gravity Seminar 7/41 Am. J. Phys. 26 (1958) 358

. . . [...]

[...] [...] • Note: Eqivalence Principle is fundamental to General Relativity ‣ if it doesn’t apply to antimatter, at the very least, our understanding of GR must be modified D. M. Kaplan, IIT An#ma&er Gravity Seminar 8/41 Baryon Asymmetry o Big Bang produced exactly equal amounts of matter and antimatter – a puzzle! • Already in 1956, M. Goldhaber noted the baryon [M. Goldhaber, “Speculations on Cosmogeny,” asymmetry of the universe (BAU) Science 124 (1956) 218] - universe seems to contain lots of mass in the form of baryons – protons and neutrons – but almost no antimatter! How could this be consistent with the BB? - now generally believed BAU arose through CP violation (discovered in 1964) - but, pre-1964, more plausible to postulate gravitational repulsion between matter and antimatter – “antigravity”!

D. M. Kaplan, IIT An#ma&er Gravity Seminar 9/41 The Nobel Prize in Physics 1980 http://www.nobelprize.org/nobel_prizes/physics/laureates/1980/

The Nobel Prize in Physics 1980 James Cronin, Val Fitch The Nobel Prize in Physics 1980

Baryon AsymmetryThe Nobel Prize in Physics 1980 http://www.nobelprize.org/nobel_prizes/physics/laureates/1980/

now generally believed BAU arose through CP Theviolation Nobel Prize in Physics 1980 - James Cronin, Val Fitch (discovered in 1964) The Nobel JamesPrize Watson inCronin Physics 1980 • But – where’s the needed CP violation? - CPV discovery [Cronin, Fitch, et al., PRL 13 (1964) 138]: ~10–3 asymmetry in decays of K0 vs K̄0 meson

allows distinguishing matter from antimatter James Watson Cronin Val Logsdon Fitch ‣ [photo credits: The Nobel Prize in Physics 1980 was awarded jointly to James Watson Cronin and Val Logsdon Fitch "for in an absolute sense (“annihilating an alien”) Nobelprize.org] the discovery of violations of fundamental symmetry principles in the decay of neutral K-mesons"

Photos: Copyright © The Nobel Foundation - but too weak by orders of magnitude to 8 To cite this page account for observed ~1-in-10 BAU MLA style: "The Nobel Prize in Physics 1980". Nobelprize.org. Nobel Media AB 2013. Web. 22 Aug 2013.

‣ more CP violation to be discovered?? Val Logsdon Fitch The Nobel Prize in Physics 1980 was awarded jointly to James Watson Cronin and Val Logsdon Fitch "for the discovery of violations of fundamental symmetry principles in the decay of neutral K-mesons" • hot particle-physics topic (LHCb/Belle/LBNE...) 1 of 2 8/22/13 8:11 PM – but, so far, no experimental evidence for it Photos: Copyright © The Nobel Foundation

To cite this page D. M. Kaplan, IIT An#ma&er Gravity Seminar MLA style: "The10 Nobel/41 Prize in Physics 1980". Nobelprize.org. Nobel Media AB 2013. Web. 22 Aug 2013.

1 of 2 8/22/13 8:11 PM CPV and Alien Annihilation • Imagine you’re an alien from another galaxy approaching Earth in a spaceship. • Is it safe to land or will you be annihilated on contact??? • Just radio Earth and ask: ‣ “In the decay of the long-lived neutral kaon, is the more common lepton matter or antimatter?” ‣ If you agree with their answer, it’s safe to land!

D. M. Kaplan, IIT An#ma&er Gravity Seminar 11/41 The Nobel Prize in Physics 1980 http://www.nobelprize.org/nobel_prizes/physics/laureates/1980/

The Nobel Prize in Physics 1980 James Cronin, Val Fitch The Nobel Prize in Physics 1980

Baryon AsymmetryThe Nobel Prize in Physics 1980 http://www.nobelprize.org/nobel_prizes/physics/laureates/1980/

now generally believed BAU arose through CP Theviolation Nobel Prize in Physics 1980 - James Cronin, Val Fitch (discovered in 1964) The Nobel JamesPrize Watson inCronin Physics 1980 • But – where’s the needed CP violation? - CPV discovery [Cronin, Fitch, et al., PRL 13 (1964) 138]: ~10–3 asymmetry in decays of K0 vs K̄0 meson

‣ allows distinguishing matter from antimatter James Watson Cronin Val Logsdon Fitch [photo credits: The Nobel Prize in Physics 1980 was awarded jointly to James Watson Cronin and Val Logsdon Fitch "for in an absolute sense (“annihilating an alien”) Nobelprize.org] the discovery of violations of fundamental symmetry principles in the decay of neutral K-mesons" - but too weak by orders of magnitude to Photos: Copyright © The Nobel Foundation 8 account for observed ~1-in-10 BAU! To cite this page MLA style: "The Nobel Prize in Physics 1980". Nobelprize.org. Nobel Media AB 2013. Web. 22 Aug 2013.

‣ more CP violation to be discovered?? Val Logsdon Fitch The Nobel Prize in Physics 1980 was awarded jointly to James Watson Cronin and Val Logsdon Fitch "for the discovery of violations of fundamental symmetry principles in the decay of neutral K-mesons" hot question: LHCb/Belle II/T2K/NOvA/DUNE… 1 of 2 8/22/13 8:11 PM – but, so far, no experimental evidence for it Photos: Copyright © The Nobel Foundation

LHCb To cite this page D. M. Kaplan, IIT An#ma&er Gravity Seminar MLA style: "The12 Nobel/41 Prize in Physics 1980". Nobelprize.org. Nobel Media AB 2013. Web. 22 Aug 2013.

1 of 2 8/22/13 8:11 PM But there’s more...

D. M. Kaplan, IIT An#ma&er Gravity Seminar 13/41 Outline • Dramatis Personae • A Bit of History - antimatter, the baryon asymmetry of the universe, and all that... ➡ • The Ideas, The Issues, The Opportunities • Muonium Gravity Experiment • Required R&D • Conclusions

D. M. Kaplan, IIT An#ma&er Gravity Seminar 14/41 Four Cosmological Puzzles 1. Baryon asymmetry (at least) • as we’ve seen, believed to be due to CPV, but insufficient CPV seen experimentallyDark to support thisMatter? 2. Expansion of universe appears to be accelerating Evidence •forbelieved Dark to Matter be due to comes “dark energy from,” comprisinghttp://www.astro.umd.edu/~ssm/mond/fit_compare.html 70% of total – but no motion at largedirect scales:observational not evidence enough as gravityto its nature or existence from visible matter. http://astroweb.case.edu/ssm/mond/ 3. Galactic rotation curves and clusters fit_compare.html • suggest existence of large amounts of “dark matter” (5 x normal matter) – but dark matter particles yet to be found

4. Flatness and HorizonNASA problems • Universe has same temperature in all directions Alternative– but isphotons to modifyjust arriving fromgravity: opposite directions are from regions that have not yet had time to communicate or equilibrate→“inflation” Modified NewtonianMight there Dynamicsbe a simple r(MOND).explanation??? D. M. Kaplan, IIT An#ma&er Gravity Seminar 15/41 2 2 F = GMm/r = mµ(a/a0)a ~ (ma if a>>a0),(ma /a0 if a<

Thomas Phillips 16 of 59 Antigravity? • What if matter and antimatter repel gravitationally? - leads to universe with separated matter and antimatter regions, and makes gravitational dipoles possible

BAU is local, not global [A. Benoit-Lévy and G. Chardin, “Introducing the Dirac-Milne universe,” Astron. & Astrophys. 537 (2012) ⇒ no need for new sources of CPV A78] - repulsion changes the expansion rate of the universe

possible explanation for apparent [D. Hajdukovic, “Quantum vacuum and virtual gravitational dipoles: the solution to the dark energy acceleration – without dark energy problem?,” Astrophys. Space Sci. 339 (2012) 1]

all regions of early universe causally [A. Benoit-Lévy and G. Chardin, ibid.] connected - virtual gravitational dipoles can modify gravity at long distances [L. Blanchet, “Gravitational polarization and the phenomenology of MOND,” Class. Quant. Grav. 24, possible explanation for rotation 3529 (2007); curves – without dark matter L. Blanchet & A.L. Tiec, “Model of dark matter and dark energy based on gravitational polarization,” PRD 78, 024031 (2008)] D. M. Kaplan, IIT An#ma&er Gravity Seminar 16/41 Studying Antimatter Gravity

D. M. Kaplan, IIT An#ma&er Gravity Seminar 17/41 Whitteborn & Fairbanks Expt

[F. C. Witteborn & W. M. Fairbank, “Experimental Comparison of the First attempt to address the question! Gravitational Force on Freely • Falling Electrons and Metallic Whitteborn & FairbanksElectrons,” Phys.Expt Rev. Lett. • Famous experiment, intended to 19,1049 (1967)] measure Famousgravitational experiment force on attempted positrons to measure gravitational force • Started withon electrons positrons. in copper drift tube; measured➢electrons maximum in copper time drift of flight tube ➢ • Managed onlymeasured to set an maximum upper TOFlimit:

Only managed to set a limit on F < 0.09 mg ⇒ electrical levitation? electrons: F < 0.09mg • Indicated difficulty of a (never published) measurementNever with published positrons (made?) measurement with positrons PRL 19,1049 (1967)

D. M. Kaplan, IIT An#ma&er Gravity Seminar 17/41 Thomas Phillips Friday, October 26, 2012 25 Next Attempt • Los Alamos-led team proposed (1986) to measure gravitational force on antiprotons at the CERN Low Energy Antiproton Ring (LEAR) • Similar approach to Witteborn & Fairbank, but with 2000x greater m/q ratio • Project ended inconclusively ‣ Generally taken as evidence that gravitational measurements on charged antimatter are hopeless ➡ need to work with neutral antimatter

D. M. Kaplan, IIT An#ma&er Gravity Seminar 18/41 Studying Antimatter Gravity • Experimentally, still unknown even whether antimatter falls up or down! Or whether g – g ̄ = 0 or ε - in principle a simple interferometric measurement with slow antihydrogen beam [T. Phillips, Hyp. Int. 109 (1997) 357]:

Mask Time- de Broglie grating

waves of- !"=#

interfere Flight Detector

3 v ~ 10 m/s 2 H̅ ½ gt = 5??? µm e+

p̅

~ 1 m ~ 1 m In either case, if g = – g, antigravity as discussed above Equivalence Principle - ̄ must be modified! Thomas Phillips Preliminary Draft - if g ̄ = g ± ε, need to modify theory Duke ofUniv ergravitysity (scalar5 + vector + tensor), or add “5th force” to the known 4 D. M. Kaplan, IIT An#ma&er Gravity Seminar 19/41 Studying Antimatter Gravity

But that’s not how anybody’s doing it!

D. M. Kaplan, IIT An#ma&er Gravity Seminar 20/41 NATURE PHYSICS DOI: 10.1038/NPHYS2025 ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS2025 ARTICLES Studying Antimattera GravityMirror coils d 40 Aarhus Univ, Simon Fraser Univ, Berkeley, Swansea a Electrodes d Univ, CERN,Mirror Univ coils Federal do Rio de Janeiro, Univ of World leader: ALPHA* at e+ Vacuum wall 40 • Calgary, TRIUMF, UnivElectrodes of British Columbia, Univ of Cryostat wall e+ Tokyo, Stockholm Univ, YorkVacuum Univ, wallUniv of Liverpool, 0

Univ of Victoria, Auburn Univ, NRCN-Nuclear (mm) CERN Antiproton Decelerator y Cryostat wall Research Center Negev, RIKEN 0 (mm) * Antihydrogen Laser Physics Apparatus yˆ _ y p zˆ ¬40 yˆ _ p They make antihydrogen fromˆ xˆp̄ and 3-layere+ Si detectorin a ¬40 ¬40 ¬20 0 20 40 • z x (mm) Antihydrogen and mirror-trapped antiproton discrimination xˆ 3-layer Si3 detector ¬40 ¬20 0 20 40 Penning trap and trap it withb an60 octupole winding e 3 x (mm)

.$%/0'"# b 60 e 3 122+3+"4%+'2 0 (T)

5#%#$%'& (mm)

y [G. B. Andresen et al., “Confinement of antihydrogen ⎥ 2 B

0 ⎥ (T) (mm) for 1,000 seconds,” Nature Phys. 7 (2011) 558] y ¬60 ⎥ 2 B ¬200¬1000 100 200 ⎥ ¬60 1 ¬200¬1000 z (mm) 100 200 ¬40 ¬20 0 20 40 1 c z (mm) ¬40 ¬20 0 20x (mm) 40 c 2 x (mm) (T) ⎥

2 B

!"#$%&'(#) ⎥ 123 (T) ⎥ B ⎥ 1 123B (T) ¬200¬1000 100 200 *+&&'&,-'+") 1 B (T) ! " ¬200¬1000 z (mm) 100 200 # z (mm) Figure 1 The ALPHA antihydrogen trap and its magnetic-field configuration. a, A schematic view of the ALPHA trap. Radial and axial confinement of Figureantihydrogen 1 The| ALPHA atoms antihydrogen is provided trap by andan octupole its magnetic-field magnet (not configuration. shown) anda mirror, A schematic magnets, view respectively. of the ALPHA Penning trap. trap Radial electrodes and axial are confinement held at 9 of K, and have Figure 1. FigureAschematic,cut-awaydiagramoftheantihydrogenproductionand 1: (left) 3D schematic| of ALPHA trap [7]; (right) on-axis magnetic field vs z [5]. ⇤ Shutting off the magnets,antihydrogenan inner atoms diameter they is provided of 44.5 then mm.by an A octupole three-layer studied magnet silicon (not vertex shown) detector and mirror surrounds magnets, the magnets respectively. and Penning the cryostat. trap electrodes A 1 T base are field held is provided at 9 K, andby an have external • trapping region of the ALPHA apparatus, showing the relative positions of the ⇤ cryogenically cooled Penning-Malmbergan inner trapsolenoid diameter electrodes, (not of shown). 44.5 the mm. An minimum-B A antiproton three-layer beam trap silicon is vertex introduced detector from surrounds the right, the whereas magnets positrons and the from cryostat. an accumulator A 1 T base field are brought is provided in from by an the external left. b, The whethermagnets and themore annihilation H detector.̅ annihilatesolenoidmagnetic-field The (not trap shown). wall strength An is antiprotonon thein the[C. innery beam– Amolez plane radius is introduced (etz isal., along “Description from the trap theright, axis, and with whereas firstz application0 positrons at the centre from of of an the accumulator magnetic are trap). brought Green in dashed from the lines left. inb this, The and other figures of the electrodes. Not shown is the solenoid,magnetic-field which strength makes in a the uniformy–z planea new field (z techniqueis in alongzˆ. the to trap measure axis, with thez 0gravitational at the= centre ofmass the magnetic trap). Green dashed lines in this and other figures depict the locations of the inner walls of the electrodes. c, The axial= field profile, with an effective trap length of 270 mm. d, The field strength in the x–y The components are not drawn to scale.depict the locations of the inner wallsof antihydrogen,” of the electrodes. Naturec, The axial Comm. field profile, 4 (2013) with 1785] an effective trap length of 270 mm.⇤ d, The field strength in the x–y plane. e, The field-strength profile along the x axis. ⇤ on the top or on theplane. ebottom, The field-strength profile along the x axis. D. M. Kaplan, IIT An#ma&er Gravity Seminar 21/41 16 efficient injection of antiprotons into the positrons with very to our previous16 work . Knowledge of annihilation positions 1. Introduction efficientlow kinetic injection energies. of antiprotons into the positrons with very to ouralso previous provides work sensitivity. Knowledge to the antihydrogen of annihilation energy positions distribution, low kinetic energies. 3 also provides sensitivity to the antihydrogen energy distribution, ¯ About 63 10 antihydrogen atoms are produced by enabling as we shall show. Recently, antihydrogen (H) atoms were trapped inAbout thethe ALPHA plasmas 6 10 ⇥ toantihydrogen apparatus interact for at atoms 1 CERN s. Most are produced of the atoms by enabling annihilateas on we shallIn show. Table 1 and Fig. 2, we present the results for a series of the plasmas⇥ to interact for 1 s. Most of the atoms annihilate on In Table 1 and Fig. 2, we present the results for a series of [1, 2]. The ability to discriminate between trappedthe antihydrogen trap walls32, whereas and incidentally a small fraction are trapped. A series of measurements, wherein the confinement time was varied from 0.4 s the trap walls32, whereas a small fraction are trapped. A series of measurements, wherein the confinement time was varied from 0.4 s trapped antiprotons was crucial to proving that antihydrogenfast electric fieldwas actually pulses is thentrapped applied to clear any remaining to 2,000 s. These data, collected under similar conditions, contained fast electric field pulses is then applied to clear any remaining to 2,000 s. These data, collected under similar conditions, contained [1, 2, 3]. The antihydrogen was trapped in a magneticcharged minimum particles. [4] After created a specified by an confinement time for each 112 detected annihilation events out of 201 trapping attempts. charged particles. After a specified confinement time for each 112 detected annihilation events out of 201 trapping attempts. octupole magnet which produced fields of 1.53 Texperimental at theexperimental trap cycle, wall cycle, the at R superconducting theW = superconducting 22.28 mm, magnets magnets for the for magnetic the magneticAnnihilationAnnihilation patterns patterns in both in time both and time position and position (Fig. 3) (Fig. agree 3) agree and two mirror coils which produced fields of 1trap T at aretrap their shut are downcenters shut down with at a withz 9 ms= a time 9 ms138 constant. time mm. constant. Antihydrogen, Antihydrogen, when whenwell withwell those with predicted those predicted by simulation by simulation (see below). (see below). Our cosmic Our cosmic ± 36 The relative orientation of these coils and the trapreleased boundariesreleased from from the are magnetic the shown magnetic trap, in Figure trap,annihilates annihilates 1. on the on Penning-trap the Penning-trapbackgroundbackground rejection rejection36 enablesenables us to establish, us to establish, with high with statistical high statistical electrodes. The antiproton annihilation events are registered using significance, the observation of trapped antihydrogen after long These fields were superimposed on a uniform axialelectrodes. field of The 1 T antiproton [5, 6]. The annihilation33,34 fields thus events are registered using significance, the observation of trapped antihydrogen after long a silicona silicon vertex vertex detector detector33,34 (see Methods).(see Methods). For most For ofmost the of data the dataconfinementconfinement times (Fig. times 2b). (Fig. At 2b). 1,000 At s, 1,000 the probability s, the probability that the that the increased from about 1.06 T at the trap center (r = z = 0 mm), to 2 T at the trap 1 presented here, a static axial electric bias field of 5001 V m was annihilation events observed are due to a statistical fluctuation axial ends (r =0mm,z = 138 mm), and to presented1.062 +1 here,.532 T=1 a static.86 axial T on electric the trap bias field of 500 V m was annihilation events observed are due to a statistical fluctuation ± appliedapplied during during the confinement the confinement and shutdown and shutdown stages stages to deflect to deflectin thein cosmic the cosmic ray background ray background (that is, (that the is, Poisson the Poisson probability, probability, wall at (r = R , z =0mm). Antihydrogen was trapped in this minimum because 4 W ‡ bare antiprotonsbare antiprotons that may that have may been have trapped been trapped through through the magnetic the magneticp, of thep, of observed the observed events events assuming assuming cosmic cosmic background background only4) is only ) is of the interaction of its magnetic moment with the inhomogeneous16 16 field. Ground state 15 15 mirrormirror effect effect. (Deflection. (Deflection of antiprotons of antiprotons by the by bias the field bias has field been has beenless thanless 10 than , 10corresponding , corresponding to a statistical to a statistical significance significance of 8.0 of. 8.0 . antihydrogen with a properly aligned spin is a lowexperimentally fieldexperimentally seeker; verified as verified its using motion using intentionally isintentionally slow trapped trapped antiprotons antiprotons16.) 16Even.) atEven 2,000 at s, 2,000 we have s, we an have indication an indication of antihydrogen of antihydrogen survival survival 3 3 enough that its spin does not flip, the antihydrogenThisThis is bias pushed biasfield field ensured back ensured towards that annihilation that the annihilation trap events events could could only be onlywith be awithp value a p ofvalue 4 10 of 4 or10 a statisticalor a statistical significance significance of 2.6 of. The 2.6 . The ⇥ center by a force DRAFTproducedproduced by neutral by neutral antihydrogen. antihydrogen. 1,000 s1,000 observation s observation⇥ constitutes constitutes a more a than more a than 5,000-fold a 5,000-fold increase increase § TheThe silicon silicon vertex vertex detector, detector, surrounding surrounding the mixing the mixing trap trapin measuredin measured confinement confinement time relative time relative to the previously to the previously reported reported F = (µ ¯ B), (1) H · in threein three layers layers (Fig. 1a),(Fig. enables 1a), enables position-sensitive position-sensitive detection detection of lower of limitlower of limit 172 msof 172 (ref. ms 16). (ref. 16). where B is the total magnetic field, and µ ¯ isantihydrogen theantihydrogen annihilations annihilations magnetic even moment. in even the in presence the presence of a large of a amount large amountPossiblePossible mechanisms mechanisms for antihydrogen for antihydrogen loss from loss the from trap the include trap include H 35 35 Unfortunately, the magneticFigure 2: moment (left) Magnetic for ground fieldof state scattering (inof antihydrogen tesla) scattering material on axis material (superconducting is due small; (superconducting to mirror the trap coils magnets in magnets ALPHA and cryostat) and vs cryostat) distance, annihilations, (inannihilations mm) on background on background gas, heating gas, heating through through elastic collisions elastic collisions and isand one is of one the of unique the unique features features of ALPHA of ALPHA (see Methods). (see Methods). The Thewith backgroundwith background gas and gas the and loss the of loss a quasi-trapped of a quasi-trapped population population21 21 depth in the ALPHAfrom apparatus center ofis only trap; (right)Trap =0z-derivative.54 K, where of K magnetic is used as field an at energy left (tesla/mm) [6]. 20 E capabilitycapability of vertex of vertex detection detection to efficiently to efficiently distinguish distinguish between between(see below).(see below). Spin-changing Spin-changing collisions collisions between between trapped trapped atoms atoms20 unit. 36 cosmiccosmic rays rays and antiproton and antiproton annihilations annihilations, as36 well, as as well the as fast the fastare negligibleare negligible because because of the lowof the antihydrogen low antihydrogen density. density. The main The main Trapped antihydrogen was identified by quicklyshutdownshutdown turning capability o capability↵ the of superconducting our of trap our25 trap, provide25, provide background background counts countsbackgroundbackground gases in gases our in cryogenic our cryogenic vacuum vacuum are expected are expected to be He to be He 3 octupole and mirror magnetic field coils. Any antihydrogenper trapping presentattempt inof the 1.4 trap10 was. This3 is six orders of and H . Our theoretical analysis of antihydrogen collisions indicates per trapping attempt of⇥ 1.4 10 . This is six orders of 2and H2. Our theoretical analysis of antihydrogen collisions indicates then released onto the trap walls, where it annihilated.magnitudemagnitude smaller The smaller temporal than than was and obtained was spatial obtained⇥ in ref. in 37 ref. (on 37 the (on basis the basisthat trapthat losses trap duelosses to due gas to collisions gas collisions give a lifetime give a lifetime in the range in the range 1 5 of the reported 1 min shutdown time and 20 s background1 of 300 to 10 s, depending5 on the temperature of the gas (see coordinates of such annihilations were recorded by aof vertex the reported imaging 1 particle2 min shutdown detector time and 20 s background⇤ of 300 to 10 s, depending on the temperature of the gas (see rate).rate). Improvements Improvements in annihilation-event in annihilation-event identification identification have also have alsoMethods).Methods).⇤ The observed The observed confinement confinement of antihydrogen of antihydrogen for 1,000 for s 1,000 s Note that 0.06 T is field from the mirrors at z =0mm.resultedresulted in an in increase an increase in detection in detection efficiency efficiency (see Methods) (see Methods) relative relativeis consistentis consistent with these with estimates. these estimates. Note that Note trapping that trapping lifetimes lifetimes of of ‡ Because of the interaction between the mirror and octupole fields, the magnetic field minimum is actually§ slightly radially displaced from the trap center, not at the trap center itself. NATURE PHYSICS VOL 7 JULY 2011 www.nature.com/naturephysics 559 NATURE PHYSICS| VOL| 7 JULY| 2011 www.nature.com/naturephysics 559 | | | NATURE COMMUNICATIONS | DOI: 10.1038/ncomms2787 ARTICLE

correspondence between the escape time of an anti-atom and its gravitational effects late in time when the magnetic restoring initial energy because it can take some time for an anti-atom to force is relatively weak, and the remaining particles are those with find the ‘hole’ in the trap potential. Computer simulations of this the lowest energy. We note that while the number of late anni- process, described in ref. 38, show that anti-atoms of a given hilating anti-atoms is dependent on the exact energy distribution initial energy escape over a temporal range of at least 10 ms. The used to initialize the simulations, the annihilation locations of simulations discussed in ref. 38 did not include a gravitational these anti-atoms are not; for the purposes of this paper, the exact force; to aid in our interpretation of the current experimental distribution is unimportant. data, we extended these simulations to include gravity by the addition of a gravitational term to the equation of motion: Reverse cumulative average analysis. To determine an experi- d2q mental limit on F, we compare our data set of 434 observed M 2 lH B q; t Mgg^y; 1 antihydrogen annihilation events to computer simulations at dt ¼ rð Á ð ÞÞ À ð Þ various F’s. Our statistics suffer from the fact that escaping anti- where q is the centre-of-mass position of the anti-atom, and g is atoms are most sensitive to gravitational forces at late times, but the local gravitational acceleration. Previous measurements39 on relatively few of the events occur at late times. For example, even ALPHA established that the magnitude of the magnetic moment with the cooling due to the adiabatic expansion that occurs as the lH equals that of hydrogen to the accuracy required in this paper; trap depth is lowered, only 23 anti-atoms out of the 434 anni- its direction is assumed to adiabatically track the external hilate after 20 ms. Moreover, inspection of the simulation data in magnetic field. Fig. 2 shows that even when there is a pronounced tendency for the anti-atoms to fall down, some still annihilate near the top of Simulation studies. To model the experiment, we simulated the the trap. To obtain a qualitative understanding of the data, we use effects of gravity on an ensemble of ground-state antihydrogen the reverse cumulative average /y|tS: the average of the y atoms randomly selected from the pe energy distribution positions of all the annihilations that occur at time t or later (see described above. These anti-atoms are first propagated for 50 ms Methods). This reverse cumulative average highlights the more in the full-strength trap fields to effectivelyffiffi randomize their informative late-time events while still including as many events positions, and then propagated in the post-shutdown decaying as possible into the average. Figure 4 plots /y|tS for the events fields until they annihilate on the trap wall. The results of a typical and the simulations at several values of F. These plots suggest that simulation are shown in Fig. 2 for F 100, which exaggerates the an upper bound on F can be established from the data, at a value ¼ somewhere between F 60 and 150. effects of gravity relative to the baseline of F 1 expected from ¼ the equivalence principle. As can be seen in¼ Fig. 2, there is a tendency for the anti-atoms to annihilate in the bottom half Monte Carlo analysis. Although the visual approach taken in (yo0) of the trap. This tendency is pronounced for anti-atoms Fig. 4 is striking, a more sophisticated analysis is necessary for a annihilating at later times. This is because, as shown in Fig. 3 and quantitative assessment of F. Specifically, our problem is this: in Table 1, the confining potential well associated with the given our event set of experimental annihilations {(y,t)}Ev, where Studying Antimattermagnetic and gravitational Gravity forces in equation 1 is most skewed by y is the observed position of a given annihilation and t is the time of this annihilation, and given a family of similar sets of simulated • simulation o data – sim avg – – data avg pseudo-annihilations {(y,t)}F at various F, how can we determine 20

The first published limit: 600 • 10 (mm)

y 300 0 ms 0 Let F = mgrav./minert. of H̅ 0 • 120 −10 Annihilation 80 10 ms 40 −20 =100 Then F • 0 0 5 10 15 20 25 30 15 Time (ms) 10

Potential (mK) 20 ms Figure 2 | Annihilation locations. The times and vertical (y) annihilation 5 –65 ≤ F ≤ 110 @ 90% C.L. locations (green dots) of 10,000 simulated antihydrogen atoms in the 0 decaying magnetic fields, as found by simulations of equation 1 with 6 F 100. Because F 100 in this simulation, there is a tendency for the anti- ¼ ¼ [ALPHA Collaboration, 2013] atoms to annihilate in the bottom half (yo0) of the trap, as shown by the 3 30 ms black solid line, which plots the average annihilation locations binned in 0 1 ms intervals. The average was taken by simulating approximately −3 900,000 anti-atoms; the green points are the annihilation locations of a −20 −10 0 10 20 They propose improving sub-sample of these simulated anti-atoms. The blue dotted line includes the y (mm) • effects of detector azimuthal smearing on the average; the smearing reduces the effect of gravity observed in the data. The red circles are the Figure 3 | Potential well. The potential well, for F 100, at the indicated ¼ sensitivity to ∆F ~ 0.5 annihilation times and locations for 434 real anti-atoms, as measured by times and at z 0. The flat-bottomed appearance of the well at early times ¼ 3 our particle detector. Also shown (black dashed line) is the average results from the quadratic addition of the solenoidal field to the r annihilation location for B840,000 simulated anti-atoms for F 1. dependent octupole field. (Here, r is the transverse radius r x2 y2.) ¼ ¼ þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi May take another 5 years...? NATURE[C. Amole COMMUNICATIONS et al., “Description| 4:1785 | DOI: 10.1038/ncomms2787 and first application | www.nature.com/naturecommunications of 3 • & 2013 Macmillan Publishers Limited. All rights reserved. a new technique to measure the gravitational mass of antihydrogen,” Nature Comm. 4 (2013) 1785]

D. M. Kaplan, IIT An#ma&er Gravity Seminar 22/41 Studying Antimatter Gravity

• How else might it be done?

• Many H̅ efforts in progress at CERN AD (ALPHA, ATRAP, ASACUSA, AEgIS, GBAR) - too various to describe here... • All require antiprotons, so possible only at AD

• BUT – another approach may also be feasible...

D. M. Kaplan, IIT An#ma&er Gravity Seminar 23/41 Studying Antimatter Gravity • Besides antihydrogen (and maybe positronium?), only one other antimatter system conceivably amenable to gravitational measurement: • Muonium (M or Mu) – ‣ a hydrogenic atom with a positive (anti)muon replacing the proton

(an object of study for more than 50 years) • Measuring muonium gravity – if feasible – could be the first gravitational measurement of a lepton, and of a 2nd-generation particle

D. M. Kaplan, IIT An#ma&er Gravity Seminar 24/41 Muonium • Much is known about muonium...

- a purely leptonic atom, [V. W. Hughes et al., “Formation of Muonium and Observation discovered in 1960 of its Larmor Precession,” Phys. Rev. Lett. 5, 63 (1960)] February4,2008 14:21 ProceedingsTrimSize: 9inx6in hughes˙mem˙KJ˙muonium

τM = τµ = 2.2 µs 2

2 2 P3/2 F=2 + 74 MHz readily produced when µ stop in matter 2 F=1 - 2 S 10922 MHz 1/2 F=1 558 MHz 1047 MHz F=0 F=1 chemically, almost identical to hydrogen 187 MHz - λ= 244 nm 2 F=0 2 P1/2 atomic spectroscopy well studied 2 455 THz - λ= 244 nm forms certain compounds (MuCl, NaMu,...) F=1 - 2 4463 MHz 1 S1/2 F=0 Figure 1. Energy levels of the hydrogen-like muonium atom for states with principal quantum numbers n=1 and n=2. The indicated transitions couldbeinducedtodateby “ideal testbed” for QED, the search formicrowave new or laser spectroscopy.forces, High accuracy has been achieved for the transitions - which involve the ground state. The atoms can be produced mostefficiently for n=1.

precision measurement of muon properties,charge and spin carryingetc. constituents inside the proton are not known to sufficient accuracy. D. M. Kaplan, IIT An#ma&er Gravity Seminar High energy scattering experiments25/41 have shown for leptons nostructure down to dimensions of 10−18 m. They may therefore be considered ”point- like”. As a consequence, complications as those arising fromthestructure of the nucleus in natural atoms and such artificial systems that contain hadrons are absent in the muonium atom (M = µ+e−), which is the bound state of two leptons, a positive muon (µ+)andanelectron(e) 1,2.Itmay be considered a light hydrogen isotope. The dominant interaction within the muonium atom (see Fig. 1)iselec- tromagnetic. In the framework of bound state Quantum Electrodynamics (QED) the electromagnetic part of the binding can be calculated to suffi- ciently high accuracy for modern high precision spectroscopy experiments. There are also contributions from weak interactions arisingthroughZ0- boson exchange and from strong interactions owing to vacuum polarization Outline • Dramatis Personae • A Bit of History - antimatter, the baryon asymmetry of the universe, and all that... • The Ideas, The Issues, The Opportunities ➡ • Muonium Gravity Experiment • Required R&D • Conclusions

D. M. Kaplan, IIT An#ma&er Gravity Seminar 26/41 Studying Muonium Gravity

arXiv:physics/0702143v1 [physics.atom-ph] Testing Gravity with Muonium

K. Kirch∗ Paul Scherrer Institut (PSI), CH-5232 Villigen PSI, Switzerland (Dated: February 2, 2008) − Recently a new technique for the production of muon (µ+)andmuonium(µ+e )beamsofun- precedented brightness has been proposed. As one consequence and using a highly stable Mach- Zehnder type interferometer, a measurement of the gravitational accelerationg ¯ of muonium atoms at the few percent level of precision appears feasible within100daysofrunningtime.Theinertial mass of muonium is dominated by the mass of the positively charged - antimatter - muon. The measurement ofg ¯ would be the first test of the gravitational interaction of antimatter, of a purely leptonic system, and of particles of the second generation. 2 ity experiment, then there would be no telling what ex- PACS numbers: citing physics could follow.” L ~ 1.4 cm x The muonium experiment appears feasible now be- cause of two recent inventions: (i) a new technique to ~ 43 mrad stop, extractThe and gravitational compress a high acceleration intensity beam of pos- of antimatter has notΘ Matomscomesfromthefactthattheinertialmassof itive muons, to reaccelerate the muons to 10 keV and fo- w<100 µ m cusbeen them into measured a beam spot so of far. 100 µmdiameteroreven An experiment with antiprotons the muon is some 207 times larger than the one of the d~100 nm less(see [14]; and [1] (ii) and a new references technique to therein) efficiently convert did not succeed because electron, thus, muonium is almost completey, to 99.5%, the muons to M atoms in superfluid helium at or below 0.5of K in the which extreme they thermalize diffi andculty from to which suffi theyciently get Source shield theInterferometer inter- antimatter. Detection An interesting feature is that M atoms are boostedaction by 270K region perpendicular from to electromagnetic the surface when they fields. For a simi- almost exclusively produced at thermal energies by stop- leave into vacuum [15]. lar reason, results of measurements withFIG. electrons 1: Scheme of [2] the experimental are ping setup:µ the+ Min beam matter comes which they often leave again as ther- Assuming an existing surface muon beam of highest from the cryogenic µ+ beam target on the left hand side, intensitydiscussed as input, very see e.g. controversial [16],D. M. Kaplan, IIT it should be and possible the planenters to and eventuallypartiallyAn#ma&er Gravity traverses themalized, interferometerSeminar hydrogen-like, and reaches M atom.27/41 However, up to until re- to obtain an almost monochromatic beam of M atoms the detection region on the right hand side. The dimensions (∆E/Ecompare0.5/270) with with positrons a velocity of was about never 6300 m/s realized.are not to Not scale a andffected the diffractioncently, angle θ is in a reality gravitational smaller experiment with muonium would (corresponding≈ to 270 K or a wavelength λ 5.6A)˚ and than the divergence. by these problems are neutral≈ systems like antihydrogen have been science fiction. The reason for this publication a1-dimensionaldivergenceof!∆E/E 43 mrad at a and, consequently,− considerable effort today is devoted is, that there is now the real chance to perform such an rate of about 105 s 1 Matoms[15].Thisisamanyorders≈ of magnitudeto the preparation brighter beam than of available suitable up to samples now. ferometer. of antihydrogen The gravitational phaseexperiment shift to be observed within the next few years. Following(compare the approach [1]). A of possibility [5, 6, 8, 9] a Mach-Zehnder to measureis the (using effect the notation of grav- of [9]) type interferometer should be used in the muonium ex- An experiment with M atoms would constitute the 2π 2 periment.itation The on principle neutral with particles the source, the is three via grat- a phase acquired inΦg = the g τ first0.003. test of the(3) gravitational interaction of antimatter inggravitational interferometer and potential the detection in region a suitably is sketched built interferometer,d ≈ in Fig. 1. We assume here three identical gratings and This is rather small but still an orderwith of magnitudematter. larger It would also be the first and probably usedemonstrated the first two for setting in the up the classic interference Colella–Overhauser–Werner pattern than the phase shift due to theunique acceleration test induced of particles of the second generation. While which(COW) is scanned experiment by moving the third [3]. grating. In case The setup of limitedby the rotation source of the per- earth (Sagnac effect: 4πτ2v/d is rather short, because the decay length of the M atoms −4 it would also be× the first test in a purely leptonic system formance, when one has to deal with extendedωearth 3 10 sources,). Other accelerations of the system is about 1.4 cm only (τµ =2.2 µs). The whole system as a whole,≈ × e.g. from environmentalone should noise, mainly note af- that tests of the equivalence principle fromcomparatively source to detection large may be beam 4 decay lengths divergence long, fect and the poor contrast energy and must thereforeproving be suppressed. at a high The level of precision that the gravitational anddefinition, without further Mach-Zehnder collimation the source type illuminates interferometers a same is true have for misalignments strik- of the gratings and their cross section of less than 5 mm over the length of the drifts. The effects must be keptinteraction below the phase is shift, independent of composition of test masses interferometer.ing advantages The three [4]. free-standing Their gratings performance can be for has example, been for demon- an unwanted translationalso in∆ principlex of the third prove (to still impressive precision) that madestrated, sufficiently among large with others, existing, with proven neutronstechnology [5](scanning) and atoms grating perpendicular [6]. to the M beam and the with a period of 100 nm [17, 18] resulting in a diffrac- lines of the grating one requireselectrons fall in the same way as the rest of the material. tionThe angle ideaθ = λ/d to5 apply.6mrad. interferometry The optimum distance to the measurement For a recent review on tests of the equivalence principle L between two gratings≈ is slightly larger than one decay ∆x of an antimatter system was inspired by the COW-2π Φg (4) length; however, for simplicity here L =1.4cm. Assum- d ≤ see [10]. ingexperiments another length L each, and for dates distances back, of the source as and far as I know, to the and consequently As a first measurement, the determination of the sign the1980s detector [7]to the but nearest was interferometer put into grating, print, result withs explicit mention- in 4 decay lenghts. Decay and transmission loss by the ∆x<0.5 A=50pm˚ of interaction. could(5) be already interesting (for a discus- threeing 50% of open antihydrogen, ratio gratings reduces positronium the initial M rate and antineutrons, first −3 −1 sion of antigravity see [11], but also, e.g, [12]), however, a byin a factor 1997 2 [8].10 Common,yieldingN0 problems=200s detected of the M. speciesRotational are misalignment the qual- of the gratings around the M Because only× the indicated first order diffraction carries reasonable first goal for such an experiment would be to ity of the particle beams and the availabilitybeam must of besuitable, much less than the period over beam the desired information but essentially all transmitted M height ratio, 100 nm/5 mm, or 20determineµrad and correspondingg ¯ to better than 10%. One should add here, aresu detected,fficiently the interference large gratings. pattern has a The reduced case con- ofdrifts positronium must not exceed was 20 nrad. In a similar way, limits trast of somewhat below 4/9. Assuming a contrast of that it is not at all obvious that there could be a dis- further elaborated suggesting the usefor of all standing other static light or dynamic deviations from the per- C =0.3andusingeqn.(3)of[9]yieldsthestatistical fect alignment of the three identical,crepancy equidistant, between parallel the gravitational interaction of matter sensitivitywaves of as the di experiment:ffraction gratings [9] but thegratings realization can be obtained. of an The relatively small size ofand the interferometer antimatter, is a see [13]. But the universality of [13] has experiment appears1 d still1 very challenging. In the mean- S = 2 (1) major advantage for the stabilization.been disputed As in previous and possible scenarios have been sketched time also otherC√N experimental0 2π τ approachesmatter to measure interferometry the experiments [5, 6] the muonium arXiv:physics/0702143v1 [physics.atom-ph] 16 Feb 2007 in [11]. Anyhow, an experimentalist will probably favor gravitational0 interaction.3g per!#days have been (2) proposedexperiment for must antihy- use (multiple) laser interferometry for ≈ alignment, monitoring and feedbackthe direct position measurement stabiliza- (and this, again, not only with whichdrogen means that and the positronium, sign ofg ¯ is fixed after see one [1] day for and an overview.tion. The gratings for the laser interferometry are ideally 3% accuracy can be achieved after 100 days of running. integrated in the M atom gratingsrespect as perfect to alignment antimatter but also to a lepton of the second WithNo the discussion quite satisfactory about statistics, a gravity the next impor- experimentis required. using State muo- of the art piezogeneration) systems can be over used the discussion of models. The follow- tantnium issues are atoms the alignment (M = andµ+ stabilitye−)appearedintheliteratureyet of the inter- for positioning the gratings anding for scanning quote of from the third [11] for antiprotons holds equally well for and the original idea of using M atoms for testing anti- muonium atoms:“Itwouldbethefirsttestofgravity,i.e. matter gravity is again by Simons [7]. The suitability of general relativity, in the realm of antimatter. Even if the experiment finds exactly what one expects, namely that antimatter falls toward the earth just as matter does, it would be, ’A classic, one for the text books.’ .... Of ∗[email protected] course, if a new effect were found in the antiproton grav- Studying Muonium Gravity

• Adaptation of Phillips’ interferometry idea

to an antiatom with a 2.2 µs lifetime!2 ity experiment, then there would be no telling what ex-

citing physics could follow.” L ~ 1.4 cm x The muonium experiment appears feasible now be- cause of two recent inventions: (i) a new technique to ~ 43 mrad stop, extract and compress a high intensityv ~ beam 6300 of pos- m/s Θ ½ gt2 = ???24 pm! itive muons, to reaccelerate the muonsMu to 10 keV and fo- w<100 µ m cus them into a beam spot of 100 µmdiameteroreven d~100 nm less [14]; and (ii) a new technique to efficiently convert the muons to M atoms in superfluid helium at or below Smaller than 0.5 K in which they thermalize and from which they get SourceInterferometer Detection an atom! boosted by 270K perpendicular to the surface when they leave into vacuum [15]. FIG. 1: Scheme of the experimental setup: the M beam comes Assuming an existing surface muon beam of highest from the cryogenic µ+ beam target on the left hand side, intensity as input, see e.g. [16], it should“Same be possible experiment”enters and partially traverses theas interferometer Phillips and reac hesproposed – to obtain an almost monochromatic• beam of M atoms the detection region on the right hand side. The dimensions (∆E/E 0.5/270) with a velocity of about 6300 m/s are not to scale and the diffraction angle θ is in reality smaller (corresponding≈ to 270 K or a wavelength λ 5.6A)˚ and than the divergence. only≈ harder?! a1-dimensionaldivergenceof!∆E/E 43 mrad at a rate of about 105 s−1 Matoms[15].Thisisamanyorders≈ of magnitude brighter beam than available up to now. ferometer. The gravitational phase shift to be observed Following the approach of [5, 6, 8, 9]How a Mach-Zehnder mightis (using it the be notation done? of [9]) type interferometer should be used• in the muonium ex- 2π 2 periment. The principle with the source, the three grat- Φg = g τ 0.003. (3) ing interferometer and the detection region is sketched d ≈ in Fig. 1. We assume here three identical gratings and This is rather small but still an order of magnitude larger use the first two for setting up theD. M. Kaplan, IIT interference pattern than the phaseAn#ma&er Gravity shift due to theSeminar acceleration induced 28/41 which is scanned by moving the third grating. The setup by the rotation of the earth (Sagnac effect: 4πτ2v/d −4 × is rather short, because the decay length of the M atoms ωearth 3 10 ). Other accelerations of the system is about 1.4 cm only (τµ =2.2 µs). The whole system as a whole,≈ × e.g. from environmental noise, mainly af- from source to detection may be 4 decay lengths long, fect the contrast and must therefore be suppressed. The and without further collimation the source illuminates a same is true for misalignments of the gratings and their cross section of less than 5 mm over the length of the drifts. The effects must be kept below the phase shift, interferometer. The three free-standing gratings can be for example, for an unwanted translation ∆x of the third made sufficiently large with existing, proven technology (scanning) grating perpendicular to the M beam and the with a period of 100 nm [17, 18] resulting in a diffrac- lines of the grating one requires tion angle θ = λ/d 5.6mrad. The optimum distance L between two gratings≈ is slightly larger than one decay ∆x 2π Φg (4) length; however, for simplicity here L =1.4cm. Assum- d ≤ ing another length L each, for distances of the source and the detector to the nearest interferometer grating, results and consequently in 4 decay lenghts. Decay and transmission loss by the ∆x<0.5 A=50pm˚ . (5) three 50% open ratio gratings reduces the initial M rate −3 −1 by a factor 2 10 ,yieldingN0 =200s detected M. × Rotational misalignment of the gratings around the M Because only the indicated first order diffraction carries beam must be much less than the period over beam the desired information but essentially all transmitted M height ratio, 100 nm/5 mm, or 20 µrad and corresponding are detected, the interference pattern has a reduced con- drifts must not exceed 20 nrad. In a similar way, limits trast of somewhat below 4/9. Assuming a contrast of for all other static or dynamic deviations from the per- C =0.3andusingeqn.(3)of[9]yieldsthestatistical fect alignment of the three identical, equidistant, parallel sensitivity of the experiment: gratings can be obtained. The relatively small size of the interferometer is a 1 d 1 S = 2 (1) major advantage for the stabilization. As in previous C√N0 2π τ matter interferometry experiments [5, 6] the muonium 0.3g per!#days (2) experiment must use (multiple) laser interferometry for ≈ alignment, monitoring and feedback position stabiliza- which means that the sign ofg ¯ is fixed after one day and tion. The gratings for the laser interferometry are ideally 3% accuracy can be achieved after 100 days of running. integrated in the M atom gratings as perfect alignment With the quite satisfactory statistics, the next impor- is required. State of the art piezo systems can be used tant issues are the alignment and stability of the inter- for positioning the gratings and for scanning of the third Studying Muonium Gravity

• Part of the challenge is the Mu production method: - want monoenergetic Mu so as to have uniform flight time - otherwise the interference patterns of different atoms would have differing relative phases, and the signal could be washed out

D. M. Kaplan, IIT An#ma&er Gravity Seminar 29/41 Monoenergetic Muonium?

[D. Taqqu, “Ultraslow Muonium for a Muon Proposal by D. Taqqu of Paul beam of ultra high quality,” Phys. Procedia • 17 (2011) 216] Scherrer Institute (Switzerland): - stop slow muons in µm-thick layer of superfluid He (SFHe) - chemical potential of hydrogen in SFHe will eject Mu atoms at 6,300 m/s, perpendicular to SFHe surface o makes ~ “monochromatic” beam (in the beam- physics jargon): ∆E/E ≈ 0.2%

D. M. Kaplan, IIT An#ma&er Gravity Seminar 30/41 2

ity experiment, then there would be no telling what ex-

citing physics could follow.” L ~ 1.4 cm x The muonium experiment appears feasible now be- cause of two recent inventions: (i) a new technique to ~ 43 mrad stop, extract and compress a high intensity beam of pos- Θ itive muons, to reaccelerate the muons to 10 keV and fo- w<100 µ m cus them into a beam spot of 100 µmdiameteroreven d~100 nm less [14]; and (ii) a new technique to efficiently convert the muons to M atoms in superfluid helium at or below 0.5 K in which they thermalize and from which they get SourceInterferometer Detection boosted by 270K perpendicular to the surface when they leave into vacuum [15]. FIG. 1: Scheme of the experimental setup: the M beam comes Assuming an existing surface muon beam of highest from the cryogenic µ+ beam target on the left hand side, intensity as input, see e.g. [16], it should be possible enters and partially traverses the interferometer and reaches to obtain an almost monochromatic beam of M atoms the detection region on the right hand side. The dimensions (∆E/E 0.5/270) with a velocity of about 6300 m/s are not to scale and the diffraction angle θ is in reality smaller (corresponding≈ to 270 K or a wavelength λ 5.6A)˚ and than the divergence. ≈ a1-dimensionaldivergenceof!∆E/E 43 mrad at a rate of about 105 s−1 Matoms[15].Thisisamanyorders≈ of magnitude brighter beam than available up to now. ferometer. The gravitational phase shift to be observed Following the approach of [5, 6, 8, 9] a Mach-Zehnder is (using the notation of [9]) type interferometer should be used in the muonium ex- 2π 2 periment. The principle with the source, the three grat- Φg = g τ 0.003. (3) ing interferometer and the detection region is sketched d ≈ in Fig. 1. We assume here three identical gratings and This is rather small but still an order of magnitude larger between the first and second gratings and an interferometricuse phase the s firsthift Φ = two2π gτ2/d for ≈ 0.003 setting if d up the interference pattern than the phase shift due to the acceleration induced = 100 nm grating pitch is used, with ≈14% M survivalwhich and ≈10% is transmission scanned to by the detector moving. the third grating. The setup 2 The necessary gratings can be fabricated using state-of-the-art nanolithography, including by the rotation of the earth (Sagnac effect: 4πτ v/d −4 × electron beam lithography and pattern transfer into ais free rather-standing film short, by reactive because ion etching. the decay length of the M atoms ωearth 3 10 ). Other accelerations of the system Detection is straightforward using the coincident positronis about-annihilation 1.4 and cm electron only signals (τ µ to =2.2 µs). The whole system ≈ × suppress background. 12 Measuring Φ to 10% requires grating fabrication fidelity, and as a whole, e.g. from environmental noise, mainly af- interferometer stabilization and alignment, at the fewfrom-picometer source level; this tois within detection the current may be 4 decay lengths long, fect the contrast and must therefore be suppressed. The state of the art.13 At the anticipated rate of 105 M atoms/s, and taking decays and inefficiencies — into account, the measurement precision is 0.3g per √nand, where without n is the exposure further time in days. collimation7 the source illuminates a same is true for misalignments of the gratings and their cross section of less than 5 mm over the length of the drifts. The effects must be kept below the phase shift, interferometer. The three free-standing gratings can be for example, for an unwanted translation ∆x of the third made sufficiently large with existing, proven technology (scanning) grating perpendicular to the M beam and the with a period of 100 nm [17, 18] resulting in a diffrac- lines of the grating one requires tion angle θ = λ/d 5.6mrad. The optimum distance L between two gratings≈ is slightly larger than one decay ∆x 2π Φg (4) length; however, for simplicity here L =1.4cm. Assum- d ≤ ing another length L each, for distances of the source and and consequently the detector to the nearest interferometer grating, results Figure' 1:''Principle! of! Mach! Zehnder! three2grating! atom! interferometer.!!The!de!Broglie!waves!due!to!each!in 4 decay lenghts. Decay and transmission loss by the Muoniumincident!atom!all!contribute!to!the!same!interference!pattern!over!a!range!of!incident!beam!angles!and!positions.!! Gravity Experiment ∆x<0.5 A=50pm˚ . (5) Each!diffraction!grating!is!a!50%!open!structure!with!a!slit!pitch!of!100!nm.!!The!assumed!grating!separation!three 50% open ratio gratings reduces the initial M rate corresponds!to!one!muon!lifetime.! −3 −1 by a factor 2 10 ,yieldingN0 =200s detected M. One! can then imagine the following× apparatus: Rotational misalignment of the gratings around the M • ! Because only the indicated first order diffraction carries beam must be much less than the period over beam the desiredCryostat information but essentially all transmitted M height ratio, 100 nm/5 mm, or 20 µrad and corresponding 1.4 A “ship in a bottle!” cm are detected, the interference pattern has a reduced con- drifts must not exceed 20 nrad. In a similar way, limits trast of somewhat below 4/9. Assuming a contrast of Sensitivity estimate for all other static or dynamic deviations from the per- C =0.3andusingeqn.(3)of[9]yieldsthestatisticalMuM detector Mu @ 100 kHz: fect alignment of the three identical, equidistant, parallel sensitivity of the experiment: gratings can be obtained. The relatively small size of the interferometer is a SFHe 1 d 1 S = 2 (1) major advantage for the stabilization. As in previous (Not to scale) C√N 2π τ Incoming 0 matter interferometry experiments [5, 6] the muonium surface-muon beam 0.3g per!#days (2) experiment must use (multiple) laser interferometry for ! ≈ Figure'2:''Concept!sketch!of!muonium!interferometer!setup!(many!details!omitted).!!A!≈micron2thick!layer!of! alignment, monitoring and feedback position stabiliza- SFHe!(possibly!with!a!small!3He!admixture)!stops!the!muon!beam!and!forms!muonium!(M)!which!exits!vertically! • Welland!is!reflected!into!the!horizontal!off!of! known propertythe!thin!SFHe!film!coating! whichofthe! cryostat!interior.SFHe means' thatto coat the sign surface ofg ¯ is fixed after one day and tion. The gratings for the laser interferometry are ideally 3% accuracy can be achieved after 100 days of running. integrated in the M atom gratings as perfect alignment of its container With the quite satisfactory statistics, the next impor- is required. State of the art piezo systems can be used tant issues are the alignment and stability of the inter- for positioning the gratings and for scanning of the third • 45°! section of cryostat3 thus serves as reflector to turn vertical Mu beam emerging from SFHe surface into the horizontal

D. M. Kaplan, IIT An#ma&er Gravity Seminar 31/41 2

ity experiment, then there would be no telling what ex-

citing physics could follow.” L ~ 1.4 cm x The muonium experiment appears feasible now be- cause of two recent inventions: (i) a new technique to ~ 43 mrad stop, extract and compress a high intensity beam of pos- Θ itive muons, to reaccelerate the muons to 10 keV and fo- w<100 µ m cus them into a beam spot of 100 µmdiameteroreven d~100 nm less [14]; and (ii) a new technique to efficiently convert the muons to M atoms in superfluid helium at or below 0.5 K in which they thermalize and from which they get SourceInterferometer Detection boosted by 270K perpendicular to the surface when they leave into vacuum [15]. FIG. 1: Scheme of the experimental setup: the M beam comes Assuming an existing surface muon beam of highest from the cryogenic µ+ beam target on the left hand side, intensity as input, see e.g. [16], it should be possible enters and partially traverses the interferometer and reaches to obtain an almost monochromatic beam of M atoms the detection region on the right hand side. The dimensions (∆E/E 0.5/270) with a velocity of about 6300 m/s are not to scale and the diffraction angle θ is in reality smaller (corresponding≈ to 270 K or a wavelength λ 5.6A)˚ and than the divergence. ≈ a1-dimensionaldivergenceof!∆E/E 43 mrad at a rate of about 105 s−1 Matoms[15].Thisisamanyorders≈ of magnitude brighter beam than available up to now. ferometer. The gravitational phase shift to be observed Following the approach of [5, 6, 8, 9] a Mach-Zehnder is (using the notation of [9]) type interferometer should be used in the muonium ex- 2π 2 periment. The principle with the source, the three grat- Φg = g τ 0.003. (3) ing interferometer and the detection region is sketched d ≈ in Fig. 1. We assume here three identical gratings and This is rather small but still an order of magnitude larger between the first and second gratings and an interferometricuse phase the s firsthift Φ = two2π gτ2/d for ≈ 0.003 setting if d up the interference pattern than the phase shift due to the acceleration induced = 100 nm grating pitch is used, with ≈14% M survivalwhich and ≈10% is transmission scanned to by the detector moving. the third grating. The setup 2 The necessary gratings can be fabricated using state-of-the-art nanolithography, including by the rotation of the earth (Sagnac effect: 4πτ v/d −4 × electron beam lithography and pattern transfer into ais free rather-standing film short, by reactive because ion etching. the decay length of the M atoms ωearth 3 10 ). Other accelerations of the system Detection is straightforward using the coincident positronis about-annihilation 1.4 and cm electron only signals (τ µ to =2.2 µs). The whole system ≈ × suppress background. 12 Measuring Φ to 10% requires grating fabrication fidelity, and as a whole, e.g. from environmental noise, mainly af- interferometer stabilization and alignment, at the fewfrom-picometer source level; this tois within detection the current may be 4 decay lengths long, fect the contrast and must therefore be suppressed. The state of the art.13 At the anticipated rate of 105 M atoms/s, and taking decays and inefficiencies — into account, the measurement precision is 0.3g per √nand, where without n is the exposure further time in days. collimation7 the source illuminates a same is true for misalignments of the gratings and their cross section of less than 5 mm over the length of the drifts. The effects must be kept below the phase shift, interferometer. The three free-standing gratings can be for example, for an unwanted translation ∆x of the third made sufficiently large with existing, proven technology (scanning) grating perpendicular to the M beam and the with a period of 100 nm [17, 18] resulting in a diffrac- lines of the grating one requires tion angle θ = λ/d 5.6mrad. The optimum distance L between two gratings≈ is slightly larger than one decay ∆x 2π Φg (4) length; however, for simplicity here L =1.4cm. Assum- d ≤ ing another length L each, for distances of the source and and consequently the detector to the nearest interferometer grating, results Figure' 1:''Principle! of! Mach! Zehnder! three2grating! atom! interferometer.!!The!de!Broglie!waves!due!to!each!in 4 decay lenghts. Decay and transmission loss by the Muoniumincident!atom!all!contribute!to!the!same!interference!pattern!over!a!range!of!incident!beam!angles!and!positions.!! Gravity Experiment ∆x<0.5 A=50pm˚ . (5) Each!diffraction!grating!is!a!50%!open!structure!with!a!slit!pitch!of!100!nm.!!The!assumed!grating!separation!three 50% open ratio gratings reduces the initial M rate corresponds!to!one!muon!lifetime.! −3 −1 by a factor 2 10 ,yieldingN0 =200s detected M. One! can then imagine the following× apparatus: Rotational misalignment of the gratings around the M • ! Because only the indicated first order diffraction carries beam must be much less than the period over beam the desiredCryostat information but essentially all transmitted M height ratio, 100 nm/5 mm, or 20 µrad and corresponding 1.4 A “ship in a bottle!” cm are detected, the interference pattern has a reduced con- drifts must not exceed 20 nrad. In a similar way, limits trast of somewhat below 4/9. Assuming a contrast of Sensitivity estimate for all other static or dynamic deviations from the per- C =0.3andusingeqn.(3)of[9]yieldsthestatisticalMuM detector Mu @ 100 kHz: fect alignment of the three identical, equidistant, parallel sensitivity of the experiment: gratings can be obtained. The relatively small size of the interferometer is a SFHe 1 d 1 S = 2 (1) major advantage for the stabilization. As in previous (Not to scale) C√N 2π τ Incoming 0 matter interferometry experiments [5, 6] the muonium surface-muon beam 0.3g per!#days (2) experiment must use (multiple) laser interferometry for ! ≈ Figure'2:''Concept!sketch!of!muonium!interferometer!setup!(many!details!omitted).!!A!≈micron2thick!layer!of! alignment, monitoring and feedback position stabiliza- SFHe!(possibly!with!a!small!3He!admixture)!stops!the!muon!beam!and!forms!muonium!(M)!which!exits!vertically!where and!is!reflected!into!the!horizontal!off!of!the!thin!SFHe!film!coating!whichthe!cryostat!interior. means' thatC the= 0.3 sign (est. of g ¯contrast)is fixed after one day and tion. The gratings for the laser interferometry are ideally 3% accuracy can be achieved after 100 days of running. integrated in the M atom gratings as perfect alignment With the quiteN satisfactory0 = # of events statistics, the next impor- is required. State of the art piezo systems can be used tant issues are thed = alignment 100 nm (grating and stability pitch) of the inter- for positioning the gratings and for scanning of the third ! 3 τ = M lifetime

D. M. Kaplan, IIT An#ma&er Gravity Seminar 31/41 VOLUME 71, NUMBER 15 PH YSICAL REVIEW LETTERS 11 OcToBER 1993

Focusing a Beam of Ultracold Spin-Polarized Hydrogen Atoms with a Helium-Film-Coated Quasiparabolic Mirror

U. G. Luppov Randall Laboratory of Physics, University of Michigan, Ann Arbor, Michigan $8109 112-0 and Joint Institute for Nuclear Research, Dubna, Russia

W. A. Kaufman, K. M. Hill, * R. S. Raymond, and A. D. Krisch Randall Laboratory of Physics, University of Michigan, Ann Arbor, Michigan $8109 112-0 (Received 7 January 1993)

We formed the first "atomic-optics" beam of electron-spin-polarized hydrogen atoms using a quasi- parabolic polished copper mirror coated with a hydrogen-atom-reflecting film of superAuid He. The mirror was located in the gradient of an 8-T solenoidal magnetic Beld and mounted on an ultracold cell at 350 mK. After the focusing by the mirror surface, the beam was again focused with a sextupole magnet. The mirror, which was especially designed for operation in the magnetic field gradient of our solenoid, increasedVOLUMEthe focused71, NUMBERbeam intensity15 by a factor PHYSICALof about 7.5. REVIEW LETTERS 11 OCTOBER 1993 PACSSFHenumbers: H29. 25.mirrorpj, 34.30. +n,an67. established70.+n technique • — 2 5 I I I I I I Teflon coated Instrumentation OI. HC copper I Teflon copper nozzle Grooves tubing mll t of Many high energy spin physics experiments require wardsBaf our goal of 10i7 H s Heat a high intensity spin-polarized atomic hydrogen source, The Michigan prototype jet [2] using the no- which is either accelerated as a high energy polarized pro- microwave-extraction method [6] is shown in Fig. 1. The H Beam 1.5 ton beam, or used as a polarized internal target placed in atomic hydrogen was produced in a room temperature rf a stored high energy beam [1]. We are developing an ul- dissociator and guided to an ultracold stabilization cell 1.0 tracold high density jet target [2] ofBraidproton-spin-polarized through3He/4H,a Teflon Polishedtube with a Tefion-coated copper nozzle He AAAAMIKAAMAAAA% mixture surface hydrogen atoms for the experiments42 NEPTUN-AK [3] and held at about 20 K. The double walls of the cell formed NEPTUN [4] at the 400 GeV to 3 TeV UNK proton ac- the horizontal mixing chamber of the0.5dilution refrigera- 0 30 celerator in Protvino, Russia. This relatively new ultra- (mm) tor; its cooling power was about 20 mW at 300 mK. A cold method uses a cell coated with superfIuid 4He and bafne near the cell's exit aperture thermalized0.0 I theI I out-I I I I I I ! I I I I I 1 I I I I FIG. 2. Schematic diagram of the stabilization cell and 0 3 4 a high magnetic field to produce electron-spin-polarized going atoms. The cell's entrance and exit apertures were z(cm) atomic hydrogen [5]. Depolarizationmirror. TheandTeAon-coatedrecombinationcopper respectivelynozzle is alsolocatedshown.at 95'Fo and 65% of the central field into molecular D. M. Kaplan, IIThydrogen are strongly suppressed An#ma&er Gravity because ofSeminarthe 8-T superconducting solenoid.32FIG./41The3.cellThewascalculatedcom- and manufactured mirror shapes. the average thermal energy is much too small to flip the pletely covered with a superfiuid The4Hedot-dashedfilm; it typicallycurve is the calculated parabolic mirror. The electron spin. Using the Michigansurfaces. ultracoldThe atomsprototypein the twooperatedhigherfor energyabout 3hyper-h at a temperaturedotted curveof 350is mK.the calculated field gradient mirror while the jet [2], we recently investigatedfine states"no microwave"(low fieldextrac-seekers) wereAfterrepelledthe hydrogentowardatomsthe were solidsufficientlycurve isthermalizedthe manufactured four-coned mirror. field gra- tion, which uses a steep magneticlow Geldfieldregions,gradientwhereto sep-they collectedby collisionsandwiththenthee8'usedcell surfaces, the magnetic dient separated the atoms according to their arate the cold hydrogen atomsfromofthedifferent5-mm-diamelectron-spinexit aperture. Afterphysicallyemerging from states This method yielded about the same dc flow two different electron-spin states. The atoms in the two [6, 7]. the exit aperture, the electron-spin-polarized atoms were of almost 10 ~ electron-spin-polarized hydrogen atoms lowest hyperfine states (high field seekers) were attracted magnetically accelerated by the remaining Geld gradient. to maintain a low-temperature 4He film on the surfaces. per sec (H s into a compression tube (CT) detector [6] toward the high field region. Most of these atoms even- ) We measured the extracted atomic hydrogen beam as our earlier "microwave" extraction method [2). tually escaped from the cell throughUsingthethe50-mm2uncoatedannu-cell as a recombination detector, the The quantum refIection ofAux,coldusinghydrogena compressionatoms from tube lardetectorgap aroundmountedthe entrancedown- nozzle.atomicThesehydrogenatoms thenfeed rate to the cell was determined a helium-film-covered surfacestreamwas firstof demonstratedboth the cellbyand therecombinedsextupoleon baremagnetsurfaces;as the calorimetricallyresulting molecularto behy- about 2x10i7 Hs de- Berkhout et al [8]. They shownm. easuredin aboutFig. 1.80%Thespecu-hydrogendrogenatomswasenteredpumped theaway by cryopanelsWe firstandmadeother baselinecold measurements with no mirror; lar refIectivity for normal incidencetector throughon a hemisphericala 5 mmx10 mm rectangular slit, which the measured CT signal was plotted versus the sextupole optical quality concave quartzwasmirrorthe onlycoatedopeningwith a 100-and was rotated for alignment current at several diferent solenoid fields [10]. The max- Storage cell mK saturated He film. Thewithquantumthe beam.reHectionTheoccursatomic hydrogen quickly r recom- imum was — signal observed at a central solenoid field of Teflon coated Mixing chamber Sex tu pole because each hydrogen atom is light and interacts very nozzle Nitrogen Shield bined into molecular hydrogen on thecopperdetector's roomBaff le 7.3 this gave the largest gradient which increased T; Compression Teflon I weakly with the helium film. /- MI ror tube detector temperature inner surfaces. Thetubingincoming atomic hy- both the electron-spin separation inside the cell and the I 'I We now report the first formation of an external beam H f drogen flow was determined from the measured pressure solenoid focusing outside. The measured CT signal at of ultracold electron-spin-polarized hydrogen atoms us- diKerence between the inside and outside of the CT vol- the optimumCryopanelsextupole current for each solenoid field is ing a highly polished quasiparabolic copper mirror coated Shield ume; both pressures wereim- measured with cold cathode later shown4K in Fig. 5 as the no-mirror baseline [11]. with a He film. This mirror focusing significantly 0 10 20 30 Thermal detector proved our jet's beam transportmagnetronefIiciencygaugesand thus[9]. Thein- detector was calibratedcm by To rnatch our geometry, we first designed 8 parabolic creased the detected beam intensitybleeding bymoleculara factor ofhydrogenabout intoI IG.the1.CTSchematicvolume diagramat a of themirrorMichiganwithprototypea focal ul-length of 2.5 mm and a length of (7.5 to 3.7)x10i5 Hs . Thisknownis anrate.important step to- tracold spin-polarized atomic hydrogen43 mm,jet. as shown in Fig. 3. With no magnetic field gra- A 30-cm-long water-cooled sextupole with a 7.5-cm- dient, this parabolic mirror would intercept about 80%%uo diam bore and003 1-9007/9a 3.8-kG3/71pole-tip(15)/2405field(4)at$06.20000 A focused of the atoms excusing240S from a point source at the focus; the atomic beam1993intoThe theAmericanCT. ThePhysicalliquid-helium-cooledSociety the remaining 20%%uo would miss the inirror. We then 5-crn i.d. transport tube through the sextupole reduced manufactured two mirrors that were single-coned and the radiation heat load to the cell. Cryosorption panels double-coned approximations to this parabola; however, located along the beam decreased the residual gas pres- at a solenoid Beld of 7.3 T, both these mirrors increased sure, and thereby reduced the beam-gas scattering. The the CT signal by only about 40%%uo. Unfortunately, in a apparatus is described in more detail in Ref. [6]. solenoid field gradient, a parabolic mirror is not exactly We designed a "parabolic" mirror to use specular re- correct for producing a parallel atomic beam. With no flection [8) as an "atomic-optics" focusing technique in Geld gradient, each atom's trajectory would be straight, our ultracold spin-polarized atomic hydrogen jet tar- and would be reflected parallel to the parabolic mirror's get. Assuming specular reBection and a point source, axis. However, the field gradient accelerated each atom a parabolic mirror should form a parallel beam of atomic and bent its trajectory; thus each atom was reflected at hydrogen. Such a mirror could significantly increase the some angle to the mirror axis. beam available for focusing by a sextupole magnet. We, To obtain a more parallel reBected beam, we then de- therefore, made three diferent somewhat parabolic mir- signed a quasiparabolic "field gradient mirror"; by as- rors and mounted each mirror with its focus at the cell suming that the magnetic Geld decreases linearly along exit aperture as shown in Fig. 2. We then measured the the axis, one obtains parabolic trajectories in the gradi- intensity of the beam focused into the CT detector by ent region. This mirror should reflect all monochromatic each mirror. Each mirror was made of oxygen-free elec- atoms emitted by a point source into a parallel beam. trolytic copper whose high thermal conductivity helped The mirror shape is given in cylindrical coordinates by

2406 between the first and second gratings and an interferometric phase shift Φ = 2π gτ2/d ≈ 0.003 if d = 100 nm grating pitch is used, with ≈14% M survival and ≈10% transmission to the detector. The necessary gratings can be fabricated using state-of-the-art nanolithography, including electron beam lithography and pattern transfer into a free-standing film by reactive ion etching. Detection is straightforward using the coincident positron-annihilation and electron signals to suppress background. 12 Measuring Φ to 10% requires grating fabrication fidelity, and interferometer stabilization and alignment, at the few-picometer level; this is within the current state of the art.13 At the anticipated rate of 105 M atoms/s, and taking decays and inefficiencies — into account, the measurement precision is 0.3g per √n, where n is the exposure time in days.7

Figure' 1:''Principle! of! Mach! Zehnder! three2grating! atom! interferometer.!!The!de!Broglie!waves!due!to!each! Muoniumincident!atom!all!contribute!to!the!same!interference!pattern!over!a!range!of!incident!beam!angles!and!positions.!! Gravity Experiment Each!diffraction!grating!is!a!50%!open!structure!with!a!slit!pitch!of!100!nm.!!The!assumed!grating!separation! corresponds!to!one!muon!lifetime.! Some! important questions: • ! Cryostat 1.4 cm A “ship in a bottle!”

M detector Mu

SFHe

Incoming (Not to scale) surface-muon beam ! Figure'Can2:'' sufficientlyConcept!sketch!of!muonium!interferometer!setup!(many!details!omitted).!!A!≈micron precise diffraction gratings be2thick!layer!of! fabricated? 1. SFHe!(possibly!with!a!small!3He!admixture)!stops!the!muon!beam!and!forms!muonium!(M)!which!exits!vertically! and!is!reflected!into!the!horizontal!off!of!the!thin!SFHe!film!coating!the!cryostat!interior.'

2. Can interferometer and detector be aligned to a few pm and stabilized against vibration?

3. !Can interferometer and detector3 be operated at cryogenic temperature? 4. How determine zero-degree line? 5. Does Taqqu’s scheme work? D. M. Kaplan, IIT An#ma&er Gravity Seminar 33/41 Outline • Dramatis Personae • A Bit of History - antimatter, the baryon asymmetry of the universe, and all that... • The Ideas, The Issues, The Opportunities • Muonium Gravity Experiment ➡ • Required R&D • Conclusions

D. M. Kaplan, IIT An#ma&er Gravity Seminar 34/41 Answering the Questions: 1. Can sufficiently precise diffraction gratings be fabricated? - our collaborator, D. Mancini, ex-ANL Center for Nanoscale Materials (CNM) director, thinks so – fabrication proposal approved at CNM (in progress with undergrad teams) 2. Can interferometer and detector be aligned to a few pm and stabilized against vibration? - R&D ongoing, looks OK (LIGO does better than we need) 3. Can interferometer and detector be operated at cryogenic temperature? - needs R&D; work at IPN Orsay implies at least piezos OK 4. How determine zero-degree line? - use cotemporal x-ray beam (Mu detector can detect x-rays) 5. Does Taqqu’s scheme work? - needs R&D; PSI working on it with our collaborator T. Phillips D. M. Kaplan, IIT An#ma&er Gravity Seminar 35/41 between the first and second gratings and an interferometric phase shift Φ = 2π gτ2/d ≈ 0.003 if d = 100 nm grating pitch is used, with ≈14% M survival and ≈10% transmission to the detector. The necessary gratings can be fabricated using state-of-the-art nanolithography, including electron beam lithography and pattern transfer into a free-standing film by reactive ion etching. Detection is straightforward using the coincident positron-annihilation and electron signals to suppress background. 12 Measuring Φ to 10% requires grating fabrication fidelity, and interferometer stabilization and alignment, at the few-picometer level; this is within the current state of the art.13 At the anticipated rate of 105 M atoms/s, and taking decays and inefficiencies — into account, the measurement precision is 0.3g per √n, where n is the exposure time in days.7

Interferometer Alignment

mirror Figure' 1:''Principle! of! Mach! Zehnder! three2grating! atom! interferometer.!!The!de!Broglie!waves!due!to!each! incident!atom!all!contribute!to!the!same!interference!pattern!over!a!range!of!incident!beam!angles!and!positions.!!beam Simplified concept: 2 MichelsonEach!diffraction!grating!is!a!50%!open!structure!with!a!slit!pitch!of!100!nm.!!The!assumed!grating!separation! splitter photo- • corresponds!to!one!muon!lifetime.laser ! detector ! interferometers per grating !

Cryostat send laser beams in through cryostat lid - Mu/x-ray detector o keeps instrumentation & heat external M detector to cryostat & Mu detection path open SFHe

“natural” sensitivity ~ λ/2 ~ 600 nm; need ~ 3 pm (Not to scale) - Incoming ⇒ surface-muon –5 beam 10 enhancement ! Figure'2:''Concept!sketch!of!muonium!interferometer!setup!(many!details!omitted).!!A!≈micron2thick!layer!of! SFHe!(possibly!with!a!small!3He!admixture)!stops!the!muon!beam!and!forms!muonium!(M)!which!exits!vertically! o enhance by sitting at a zero of and!is!reflected!into!the!horizontal!off!of!the intensity, usingthe!thi n!SFHe!film!coating!the!cryostat!interior.'

heterodyne detection etc. → Laser Tracking Frequency Gauge

[R. Thapa et al., “Subpicometer length measurement using semiconductor o still some details to work out! ! laser tracking frequency3 gauge,” Opt. Lett. 36, 3759 (2011)]

D. M. Kaplan, IIT An#ma&er Gravity Seminar 36/41 between the first and second gratings and an interferometric phase shift Φ = 2π gτ2/d ≈ 0.003 if d = 100 nm grating pitch is used, with ≈14% M survival and ≈10% transmission to the detector. The necessary gratings can be fabricated using state-of-the-art nanolithography, including electron beam lithography and pattern transfer into a free-standing film by reactive ion etching. Detection is straightforward using the coincident positron-annihilation and electron signals to suppress background. 12 Measuring Φ to 10% requires grating fabrication fidelity, and interferometer stabilization and alignment, at the few-picometer level; this is within the current state of the art.13 At the anticipated rate of 105 M atoms/s, and taking decays and inefficiencies — into account, the measurement precision is 0.3g per √n, where n is the exposure time in days.7

Interferometer Alignment

mirror Figure' 1:''Principle! of! Mach! Zehnder! three2grating! atom! interferometer.!!The!de!Broglie!waves!due!to!each! incident!atom!all!contribute!to!the!same!interference!pattern!over!a!range!of!incident!beam!angles!and!positions.!!beam Simplified concept: 2 MichelsonEach!diffraction!grating!is!a!50%!open!structure!with!a!slit!pitch!of!100!nm.!!The!assumed!grating!separation! splitter photo- • corresponds!to!one!muon!lifetime.laser ! detector ! interferometers per grating !

Cryostat send laser beams in through cryostat lid - Mu/x-ray detector o keeps instrumentation & heat external M detector to cryostat & Mu detection path open SFHe

“natural” sensitivity ~ λ/2 ~ 600 nm; need ~ 3 pm (Not to scale) - Incoming ⇒ surface-muon –5 beam 10 enhancement ! Figure'2:''Concept!sketch!of!muonium!interferometer!setup!(many!details!omitted).!!A!≈micron2thick!layer!of! SFHe!(possibly!with!a!small!3He!admixture)!stops!the!muon!beam!and!forms!muonium!(M)!which!exits!vertically! o enhance by sitting at a zero of and!is!reflected!into!the!horizontal!off!of!the intensity, usingthe!thi n!SFHe!film!coating!the!cryostat!interior.' heterodyne detection etc.→ Laser Tracking Frequency Gauge [R. Thapa et al., “Subpicometer length more measurement using semiconductor o still some details to work out!! 3 miniaturized laser tracking frequency gauge,” version Opt. Lett. 36, 3759 (2011)] D. M. Kaplan, IIT An#ma&er Gravity Seminar 36/41

Figure 4: Optical layout concept of the two TFG measurement interferometers that observe the position of grating 3: orthogonal views of one of many possibleconfihgurations.Lightfromafiber end is approximately collimated by the objective which, with matching lens I, produces a beam of the correct size and convergence. Matching lens II produces the converging beam needed at the 1 cavity entry port (cavity mirror I). The cavity is bent and of low finesse (say 30 to 100). The ⁄4- wave plate and polarizing beam splitter (PBS) sendthereturninglighttothedetector,suppressing light returning back to the fiber. Red arrows show direction of light.

silicon bench, and Cavity Mirror II. Thus, it measures the height of Cavity Mirror II with respect to the silicon bench. The detector is shown in blue (upper left). It may be replaced by a fiber coupler, fiber, and a detector located outside the cryostat. For absolute alignment, we propose a unique approach that exploits the interferometer’s ability to use soft X-rays, produced at a synchrotron radiation source (or, in the final experiment, using a bench-top source), of similar wavelength as anticipated for the Mu beams (0.6nm). These mea- surements, which can be interleaved with the Mu measurement for real-time alignment tracking, determine the absolute, zero-deflection, phase since the traversal time, hence gravitational phase shift, of X-rays through the interferometer is negligibly small. Changes in the absolute phase monitor the system’s drift. For measurement of the Mu gravitational phase shift, the stability requirement is that these drifts be slow on the time scale needed to measure the absolute phase with X-rays. In the final experiment, the TFG measures short-term variations and the X-rays pro- vide long-term calibration. During development, X-ray and TFG measurements will be compared to learn whether there are any significant structural distortions not measured by a small number of TFGs. We do not expect any, but if there are, remedies include adding TFGs to monitor the additional degrees of freedom. The TFGs will track any mechanical drifts in the support structure but not drifts or distortions of the gratings within their frames. While the X-ray interference pattern will measure and track these, it will be important to minimize them. Heating from muon decays, piezo actuation, and the X-ray beam will all be negligible (the X-ray intensity will be limited to a sub-microwatt level in order to avoid excessive detector deadtime).

10 Additional Considerations • What’s the optimal muonium pathlength? - say muonium interferometer baseline doubled: –2 costs e = 1/7.4 in event rate, but gains x 4 in deflection ‣ a net win by 4 e–1 ≈ 1.5 → Statistically optimal - tripling → only x1.2 improvement – diminishing returns ‣ but 9x bigger signal ⇒ easier calibration, alignment, & stabilization

• Need simulation study to identify optimum, taking all effects into account – gearing up for it (with undergrad teams)

D. M. Kaplan, IIT An#ma&er Gravity Seminar 37/41 Additional Considerations

• Alternate solutions: - different M production scheme? o thick-film SFHe production → x100 or more higher rate! o proposed for R&D @ PSI along with thin-film scheme

D. M. Kaplan, IIT An#ma&er Gravity Seminar 38/41 Picture Gallery

D. M. Kaplan, IIT An#ma&er Gravity Seminar 39/41 Picture Gallery Our Optics Lab at IIT

Our Optics Lab at IIT

August 2016, TJR IIT Gravity Group 8

August 2016, TJR IIT Gravity Group 9

D. M. Kaplan, IIT An#ma&er Gravity Seminar 39/41 G-POEM MotionPicture System Gallery Installation at IIT Our Optics Lab at IIT The support is prepared … and the granite way is installed.

Our Optics Lab at IIT

August 2016, TJR IIT Gravity Group 8

August 2016, TJR IIT Gravity Group 9

D. M. Kaplan, IIT An#ma&er Gravity EquivalenceSeminar Principle, Exoplanets, 39/41 J. Phillips, 10/27/2016 12 Picometer laser gauge G-POEM MotionPicture System Gallery Installation at IIT Our Optics Lab at IIT The support is prepared … and the granite way is installed.

Our Optics Lab at IIT

August 2016, TJR IIT Gravity Group 8

August 2016, TJR IIT Gravity Group 9

D. M. Kaplan, IIT An#ma&er Gravity EquivalenceSeminar Principle, Exoplanets, 39/41 J. Phillips, 10/27/2016 12 Picometer laser gauge Conclusions • Antigravity hypothesis might neatly solve several vexing problems in physics and cosmology

- or g ̄ = g ± ε may point the way to a deeper theory • In principle, testable with antihydrogen or muonium - if possible, both should be measured ➡ First measurement of muonium gravity would be a milestone! • But first must determine feasibility D. M. Kaplan, IIT An#ma&er Gravity Seminar 40/41 Final Remarks

• These measurements are a required homework assignment from Mother Nature!

• Whether g ̄ = – g or not, if successfully carried out, the results will certainly appear in future textbooks.

D. M. Kaplan, IIT An#ma&er Gravity Seminar 41/41 Acknowledgments Thanks to my collaborators: IIT: • Derrick Mancini Jeff Terry Tom Roberts Jim Phillips Tom Phillips UCSD: Bob Reasenberg • …our ≈100 IPRO and BSMP undergrad students, and the IIT administration D. M. Kaplan, IIT An#ma&er Gravity Seminar 42/41 Backups

D. M. Kaplan, IIT An#ma&er Gravity Seminar 43/41 Do we need to test the POE? • Many argue not – Eötvös/Eöt-Wash, earth-moon-sun system,…“set limits O(10–[7–9])”* • But these arguments all rest on untested assumptions – e.g. [Alves, Jankowiak, Saraswat, arXiv:0907.4110v1]

“We then make the assumption that any deviation of gH from gH̅ would manifest itself as a violation of the equivalence principle in these forms of energy† at the same level.” • Aren’t such assumptions worth testing??? ‣ especially when doing so costs ⋘ LHC? ‣ and so much is potentially at stake? * in any case, these don’t apply to muons † i.e., fermion loops and sea antiquarks

D. M. Kaplan, IIT An#ma&er Gravity Seminar 44/41