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

Physics Colloquium MuTACIIT Review 29 AugustFermilab 2013 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 IIT#Physics#Colloquium######8/29/13 2/43 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 IIT#Physics#Colloquium######8/29/13 3/43 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 ... ∓ ∓ Antimatte∓ Leptons : e , µ , τ , ν’s • And, don’t forget: antimatter and matter annihilate on contact

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 3/43 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 IIT#Physics#Colloquium######8/29/13 4/43 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 IIT#Physics#Colloquium######8/29/13 4/43 Our story begins with...

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 5/43 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 IIT#Physics#Colloquium######8/29/13 6/43 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 IIT#Physics#Colloquium######8/29/13 7/43 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 IIT#Physics#Colloquium######8/29/13 8/43 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 IIT#Physics#Colloquium######8/29/13 9/43 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 K0̄ 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 • hot particle-physics topic (LHCb/Belle/LBNE...) the discovery of 1violations of 2 of fundamental symmetry principles in the decay of neutral K-mesons" 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 IIT#Physics#Colloquium######8/29/13 MLA style: "The10 Nobel/43 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 IIT#Physics#Colloquium######8/29/13 11/43 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 K0̄ 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 hot particle-physics topic (LHCb/Belle/LBNE...) the discovery of 1violations of 2 of fundamental symmetry principles in the decay of neutral K-mesons" 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 IIT#Physics#Colloquium######8/29/13 MLA style: "The12 Nobel/43 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 IIT#Physics#Colloquium######8/29/13 13/43 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 IIT#Physics#Colloquium######8/29/13 14/43 Three Cosmological Puzzles 1. Baryon asymmetry ‣ as we’ve seen, believed to be due to CPV, but insufficient CPV seen experimentally to support this 2. Expansion of universeDark appears Matter? to be accelerating Evidence‣ believed for Darkto be Matterdue to “comesdark fromenergy,”http://www.astro.umd.edu/~ssm/mond/fit_compare.html comprising 70% http://astroweb.case.edu/ssm/mond/ motionof attotal large – but scales: no direct not enough observational gravity fit_compare.html fromevidence visible matter. as to its nature or existence 3. Galactic rotation curves ‣ suggest existence of large amounts of “dark matter” (5NASA x normal matter) – but dark matter particles have yet to be found Alternative is to modify gravity: Might there be a simpler explanation??? ModifiedD.#M.#Kaplan,#IIT NewtonianIIT#Physics#Colloquium######8/29/13 Dynamics (MOND). 15/43 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 no need [A. Benoit-Lévy and G. Chardin, “Introducing the ⇒ Dirac-Milne universe,” Astron. & Astrophys. 537 (2012) 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] - 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 IIT#Physics#Colloquium######8/29/13 16/43 Studying Antimatter Gravity

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 17/43 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 gravitationalFamous 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 only➢measured 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 IIT#Physics#Colloquium######8/29/13 17/43 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 IIT#Physics#Colloquium######8/29/13 18/43 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+

p—

~ 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 Uofnive rsgravityity (scalar5 + vector + tensor), or add “5th force” to the known 4 D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 19/43 Studying Antimatter Gravity

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

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 20/43 NATURE PHYSICS DOI: 10.1038/NPHYS2025 ARTICLES Studying AntimatterNATURE PHYSICS DOI: 10.1038/NPHYS2025 Gravity ARTICLES a Mirror coils d Aarhus Univ, Simon Fraser Univ, Berkeley, Swansea 40 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, ElectrodesUniv of British Columbia, Univ of e+ Tokyo, Stockholm Univ, YorkVacuum Univ, wallUnivCryostat of Liverpool, wall 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 y yˆ _ p zˆ ¬40 yˆ — + _ They make antihydrogen from p and e in a p • zˆ xˆ 3-layer Si detector ¬40 ¬40 ¬20 0 20 40 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

5#%#$%'& (T) (mm)

y [G. B. Andresen et al., “Confinement of antihydrogen  2 0 B  (T) (mm) for 1,000 seconds,” Nature Phys. 7 (2011) 558] y

 2

¬60 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 and an octupole its magnetic-field magnet (not configuration. shown) anda, mirror A schematic magnets, view respectively. of the ALPHA Penning trap. Radial trap electrodes and axial confinementare held at of9 K, and have Figure 1. Aschematic,cut-awaydiagramoftheantihydrogenproductionand ⇤ then shutFigure off 1: (left) the 3D schematicmagnetantihydrogenan| inner of ALPHAatoms diameter currents is provided of trap 44.5 [7];by mm. an (right) A octupole three-layer& on-axissee magnet silicon (not magnetic vertex shown) detector and field mirror surrounds vs magnets,z [5]. the respectively.magnets and Penning the cryostat. trap electrodes A 1 T base are field held is providedat 9 K, and by 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 isbrought provided in from by an the external left. b, The magnets and the annihilation detector.solenoid Themagnetic-field (not trap shown). wall strength An is antiprotonon the in the innery beam–z plane radius is introduced (z is along from the trap the right, axis, withwhereasz 0 positrons at the centre from anofthe accumulator magnetic are trap). brought Green in dashed from the lines left. inb, this The and other figures whether more H ̅ annihilate [C. Amole et al., “Description and first= application of of the electrodes. Not shown is the solenoid,magnetic-fielddepict which the strength locations makes in a theof uniform they–z innerplane field walls (z is inof alongzˆ the. the electrodes. trap axis,c, with Thez axial0 fieldat the profile, centre with of the an magnetic effective trap). trap length Green of dashed270 lines mm. ind, this The and field other strength figures in the x–y a new technique to measure the= gravitational mass ⇤ The components are not drawn to scale.depictplane. the locationse, The field-strength of the inner walls profile of the along electrodes. the x axis.c, The axial field profile, with an effective trap length of 270 mm. d, The field strength in the x–y of antihydrogen,” Nature Comm. 4 (2013) 1785] ⇤ on the top or on theplane. e,bottom The field-strength profile along the x axis. D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13efficient injection of antiprotons into the positrons with21/43 very to our previous work16. Knowledge of annihilation positions 1. Introduction efficientlow kineticinjection energies. of antiprotons into the positrons with very to ouralso previous provides work sensitivity16. Knowledge to the antihydrogen of annihilation energy positions distribution, low kineticAbout energies. 6 103 antihydrogen atoms are produced by enablingalso providesas we shall sensitivity show. to the antihydrogen energy distribution, Recently, antihydrogen (H)¯ atoms were trapped inAbout the ALPHA 6 103⇥antihydrogen apparatus at atoms CERN are produced by enabling as we shall show. 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 plasmasthe antihydrogen trap to walls interact32, whereas and for 1 incidentally s. a Most small of fraction the atoms are trapped. annihilate A on series ofIn Tablemeasurements, 1 and Fig. wherein 2, we present the confinement the results time for was a seriesvaried of from 0.4 s 32 trapped antiprotons was crucial to proving thatthe antihydrogen trapfast walls electric, whereas wasfield actually pulses a small is trappedfraction then applied are trapped. to clear A any series remaining of measurements,to 2,000 s. wherein These data, the confinement collected under time similar was varied conditions, from 0.4 contained s [1, 2, 3]. The antihydrogen was trapped in a magneticfast electriccharged minimum field particles. pulses [4] After is created then a specified applied by an to confinement clear any remaining time for eachto 2,000112 s. These detected data, annihilation collected under events similar out conditions, of 201 trapping contained attempts. chargedexperimental particles. cycle, After the a specified superconducting confinement magnets time for for the each magnetic112 detectedAnnihilation annihilation patterns events in both out of time 201 and trapping position attempts. (Fig. 3) agree octupole magnet which produced fields of 1.53 Texperimental at the trap cycle, wall the at R superconductingW = 22.28 mm, magnets for the magnetic Annihilation patterns in both time and position (Fig. 3) agree and two mirror coils which produced fields of 1 T attrap their are centers shut down at withz = a 9138 ms time mm. constant. Antihydrogen, when well with those predicted by simulation (see below). Our cosmic trap arereleased shut down from with the magnetic a 9 ms time± trap, constant. annihilates Antihydrogen, on the Penning-trap when well withbackground those predicted rejection by36 simulationenables us (see to establish, below). Our with cosmic high statistical The relative orientation of these coils and the trap boundaries are shown in Figure 1. 36 releasedelectrodes. from the The magnetic antiproton trap, annihilation annihilates on events the Penning-trapare registered usingbackgroundsignificance, rejection theenables observation us to establish, of trapped with antihydrogen high statistical 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 silicon vertex detector33,34 (see Methods). For most of the data confinement times (Fig. 2b). At 1,000 s, the probability that the increased from about 1.06 T at the trap centera (r silicon= z = vertex 0 mm), detector to 2 T(see at the Methods). trap For most of the data 1 confinement times (Fig. 2b). At 1,000 s, the probability that the 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 presented1.062applied+1 here,.53 during2 T=1 a static the.86 axial confinement T on electric the trap bias and field shutdown of 500 V stages m was to deflectannihilationin the events cosmic observed ray background are due to (that a statistical is, the Poisson fluctuation probability, ± applied during the confinement and shutdown stages to deflect in the cosmic ray background (that is, the Poisson probability, 4 wall at (r = RW, z =0mm). Antihydrogen was trappedbare antiprotons in this minimum that may have because been trapped through the magnetic p, of the observed events assuming cosmic background4 only ) is ‡ bare antiprotons that16 may have been trapped through the magnetic p, of the observed events15 assuming cosmic background only ) is of the interaction of its magnetic moment with the inhomogeneousmirror effect16 . (Deflectionfield. Ground of antiprotons state by the bias field has been less than15 10 , corresponding to a statistical significance of 8.0 . mirror effect . (Deflection of antiprotons by the bias field has been 16less than 10 , corresponding to a statistical significance of 8.0 . antihydrogen with a properly aligned spin is a low fieldexperimentally seeker; as verified its motion using is intentionally slow trapped antiprotons16 .) Even at 2,000 s, we have an indication of antihydrogen survival experimentally verified using intentionally trapped antiprotons .) Even at 2,000 s, we have an indication3 of antihydrogen survival This bias field ensured that annihilation events could only be with a p value of 43 10 or a statistical significance of 2.6 . The enough that its spin does not flip, the antihydrogenThis is bias pushed field ensured back towards that annihilation the trap events could only be with a p value of 4 10 or a statistical significance of 2.6 . The produced by neutral antihydrogen. 1,000 s observation⇥ constitutes a more than a 5,000-fold increase center by a force DRAFTproduced by neutral antihydrogen. 1,000 s observation⇥ constitutes a more than a 5,000-fold increase The silicon vertex detector, surrounding the mixing trap in measured confinement time relative to the previously reported § The silicon vertex detector, surrounding the mixing trap in measured confinement time relative to the previously reported F = (µH¯ B), in threein three layers layers (Fig. 1a), (Fig. enables 1a), enables position-sensitive(1) position-sensitive detection detection of lower of limitlower of limit 172 ms of 172 (ref. ms 16). (ref. 16). · antihydrogen annihilations even in the presence of a large amount Possible mechanisms for antihydrogen loss from the trap include where B is the total magnetic field, and µ ¯ isantihydrogen the antihydrogen annihilations magnetic even moment. in the presence of a large amount 35 Possible mechanisms for antihydrogen loss from the trap include H of scattering material (superconducting magnets and cryostat)35 , annihilations on background gas, heating through elastic collisions of scattering material (superconducting magnets and cryostat) , annihilations on background gas, heating through elastic collisions 21 Unfortunately, the magneticFigure 2: moment (left) Magnetic for ground field state (inand antihydrogen tesla) is one on of axis the is dueunique small; to featuresmirror the trap coils of ALPHA in ALPHA (see Methods). vs distance The (inwith mm) background gas and the loss of a quasi-trapped population21 and is one of the unique features of ALPHA (see Methods). The with background gas and the loss of a quasi-trapped population 20 depth in the ALPHAfrom apparatus center ofis only trap; (right)Trap =0z-derivative.54capability K, where of of K magnetic vertexis used detection as field an at energy to left efficiently (tesla/mm) distinguish [6]. between (see below). Spin-changing collisions between trapped20 atoms E capability of vertex detection to efficiently distinguish36 between (see below). Spin-changing collisions between trapped atoms unit. cosmic rays and antiproton annihilations36 , as well as the fast are negligible because of the low antihydrogen density. The main cosmic rays and antiproton annihilations25 , as well as the fast are negligible because of the low antihydrogen density. The main Trapped antihydrogen was identified by quicklyshutdownshutdown turning capability o capability↵ the of superconducting our of trap our25 trap, provide, provide background background counts countsbackgroundbackground gases in gases our cryogenicin our cryogenic vacuum vacuum are expected are expected to be He to be He 3 per trapping attempt of 1.4 3 10 . This is six orders of and H . Our theoretical analysis of antihydrogen collisions indicates octupole and mirror magnetic field coils. Any antihydrogenper trapping presentattempt inof the 1.4 trap10⇥ was. This is six orders of and H2. Our theoretical2 analysis of antihydrogen collisions indicates magnitudemagnitude smaller smaller than than was obtained was⇥ obtained in ref. in 37 ref. (on 37 the (on basis the basisthat trapthat losses trap due losses to due gas collisions to gas collisions give a lifetime give a lifetime in the range in the range then released onto the trap walls, where it annihilated. The temporal and spatial 1 5 of the reported 1 min shutdown time and1 20 s background of 3005 to 10 s, depending on the temperature of the gas (see coordinates of such annihilations were recorded byof thea vertex reported imaging 1 min particle2 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 inincrease 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. NATURENATURE PHYSICS PHYSICSVOL 7 VOLJULY 7 2011JULYwww.nature.com/naturephysics 2011 www.nature.com/naturephysics 559 559 | | | | | | 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

−20 =100 40 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- [ALPHA Collaboration, 2013] ¼ ¼ 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 NATURE COMMUNICATIONS | 4:1785 | DOI: 10.1038/ncomms2787 | www.nature.com/naturecommunications 3 May take 5 years...? [C. Amole et al., “Description and first application of • & 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 IIT#Physics#Colloquium######8/29/13 22/43 Studying Antimatter Gravity

• How else might it be done?

• Many H ̅ 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 IIT#Physics#Colloquium######8/29/13 23/43 Studying Antimatter Gravity • Besides antihydrogen, 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 – would be the first gravitational measurement of a lepton, and of a 2nd-generation particle

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 24/43 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 P readily produced when µ stop in matter 3/2 F=2 74 MHz - F=1 2 2 S 10922 MHz 1/2 F=1 558 MHz 1047 MHz F=0 F=1 chemically, almost identical to hydrogen 187 MHz - F=0 λ= 244 nm 2 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 for microwavenew or laser forces, spectroscopy. 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 etc. carrying constituents inside the proton are not known to sufficient accuracy. D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 High energy scattering25 experiments/43 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 IIT#Physics#Colloquium######8/29/13 26/43 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 therePACS would numbers: 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, 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%, theof muons the to extreme M atoms in di superfluidfficulty helium to suat orffi belowciently shield the inter- antimatter. An interesting feature is that M atoms are 0.5 K in which they thermalize and from which they get SourceInterferometer Detection 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 eventuallypartiallyIIT#Physics#Colloquium######8/29/13 traverses themalized, interferometer hydrogen-like, and reaches M atom.27/43 However, up to until re- tocompare obtain an almost with monochromatic positrons beam was of never M atoms realized.the detection Not region affected on the right handcently, side. The a gravitational dimensions experiment with muonium would (∆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 ≈ (correspondingby these to problems 270 K or a wavelength are neutralλ 5. systems6A)˚ and likethan the antihydrogen divergence. 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 itation on neutral particles is via a phase acquired in the2π 2 periment. The principle with the source, the three grat- Φg = g τ first0.003. test of the(3) gravitational interaction of antimatter d ≈ inggravitational interferometer and potential the detection in region a suitably is sketched built interferometer, with matter. It would also be the first and probably in Fig. 1. We assume here three identical gratings and This is rather small but still an order of magnitude larger 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 to apply5.6mrad. 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 andfar 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 measurementstabiliza- (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 areatoms 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 = 25 pm! 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 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] a Mach-Zehnder is (using the notation of [9]) type interferometer should be used inHow the muonium might ex- it be done? • 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 the interference pattern D.#M.#Kaplan,#IIT than the phaseIIT#Physics#Colloquium######8/29/13 shift due to the acceleration induced 28/43 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 M production method: - need monoenergetic M so as to have uniform flight time - otherwise the interference patterns of different atoms will have differing relative phases, and the signal will be washed out

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 29/43 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 M 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 IIT#Physics#Colloquium######8/29/13 30/43 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 use the first two for setting up the interference pattern 2 than the phase shift due to the acceleration induced between the first and second gratings and an interferometric phase shift Φ = 2π gτ /d ≈ 0.003 if d 2 = 100 nm grating pitch is used, with ≈14% M survivalwhich and ≈10% is transmission scanned to bythe detector moving. the third grating. The setup by the rotation of the earth (Sagnac effect: 4πτ v/d The necessary gratings can be fabricated using state-of-the-art nanolithography, including −4 × is rather short, because the decay length of the M atoms ωearth 3 10 ). Other accelerations of the system electron beam lithography and pattern transfer into a free-standing film by reactive ion etching. ≈ × 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 as a whole, e.g. from environmental noise, mainly af- suppress background. 12 Measuring Φ to 10% requiresfrom grating source fabrication to detection fidelity, and may be 4 decay lengths long, interferometer stabilization and alignment, at the few-picometer level; this is within the current fect the contrast and must therefore be suppressed. The state of the art.13 At the anticipated rate of 105 M atoms/sand, and without taking decays further and inefficiencies collimation the source illuminates a — same is true for misalignments of the gratings and their into account, the measurement precision is 0.3g per √n, where n is the exposure time in days.7 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 are detected, theA interference “ship in a patternbottle!” has a reduced con- cm 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]yieldsthestatisticalM detector Sensitivity estimate fect alignment of the three identical, equidistant, parallel sensitivity of the experiment:@ 100 kHz: gratings can be obtained. The relatively small size of the interferometer is a SFHe 1 d 1 S = (1) major advantage for the stabilization. As in previous C√N 2π τ 2 Incoming (Not to scale) 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 M beam emerging from SFHe surface into the horizontal

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 31/43 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 use the first two for setting up the interference pattern 2 than the phase shift due to the acceleration induced between the first and second gratings and an interferometric phase shift Φ = 2π gτ /d ≈ 0.003 if d 2 = 100 nm grating pitch is used, with ≈14% M survivalwhich and ≈10% is transmission scanned to bythe detector moving. the third grating. The setup by the rotation of the earth (Sagnac effect: 4πτ v/d The necessary gratings can be fabricated using state-of-the-art nanolithography, including −4 × is rather short, because the decay length of the M atoms ωearth 3 10 ). Other accelerations of the system electron beam lithography and pattern transfer into a free-standing film by reactive ion etching. ≈ × 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 as a whole, e.g. from environmental noise, mainly af- suppress background. 12 Measuring Φ to 10% requiresfrom grating source fabrication to detection fidelity, and may be 4 decay lengths long, interferometer stabilization and alignment, at the few-picometer level; this is within the current fect the contrast and must therefore be suppressed. The state of the art.13 At the anticipated rate of 105 M atoms/sand, and without taking decays further and inefficiencies collimation the source illuminates a — same is true for misalignments of the gratings and their into account, the measurement precision is 0.3g per √n, where n is the exposure time in days.7 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 are detected, theA interference “ship in a patternbottle!” has a reduced con- cm 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]yieldsthestatisticalM detector Sensitivity estimate fect alignment of the three identical, equidistant, parallel sensitivity of the experiment:@ 100 kHz: gratings can be obtained. The relatively small size of the interferometer is a SFHe 1 d 1 S = (1) major advantage for the stabilization. As in previous C√N 2π τ 2 Incoming (Not to scale) 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! and!is!reflected!into!the!horizontal!off!of!the!thin!SFHe!film!coating!whichthe!cryostat!interior. means' thatwhere the sign ofg ¯ is fixed after one day and tion. The gratings for the laser interferometry are ideally 3% accuracy canC be = achieved0.3 (est. aftercontrast) 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 the alignment and stability of the inter- for positioning the gratings and for scanning of the third ! 3 d = 100 nm (grating pitch) τ = M lifetime

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 31/43 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

SFHe

Incoming (Not to scale) surface-muon beam ! 1. Figure'Can2:'' sufficientlyConcept!sketch!of!muonium!interferometer!setup!(many!details!omitted).!!A!≈micron precise diffraction gratings be2thick!layer!of! fabricated? 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 IIT#Physics#Colloquium######8/29/13 32/43 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 IIT#Physics#Colloquium######8/29/13 33/43 Answering the Questions: 1. Can sufficiently precise diffraction gratings be fabricated? - our collaborator, Derrick Mancini of the ANL Center for Nanoscale Materials (CNM) thinks so – proposal submitted to CNM to try it 2. Can interferometer and detector be aligned to a few pm and stabilized against vibration? - needs R&D, but LIGO does much 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 (can M detector detect x-rays?) 5. Does Taqqu’s scheme work? - needs R&D; PSI working on it D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 34/43 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 Could use 2 Michelson Each!diffraction!grating!is!a!50%!open!structure!with!a!slit!pitch!of!100!nm.!!The!assumed!grating!separation!splitter corresponds!to!one!muon!lifetime.! photo- • laser detector ! interferometers per grating !

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

SFHe

“natural” sensitivity ~ λ/2 ~ 300 nm; need ~ 3 pm (Not to scale) - Incoming –5 surface-muon 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 ofand!is!reflected!into!the!horizontal!off!of! the intensity, usingthe!thin!SFHe!film!coating! SAW the!cryostat!interior.' modulation, etc.

o still lots of details to work out!! 3

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 35/43 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 - tripling → x 1.2 improvement – diminishing returns ‣ but 9 x bigger signal ⇒ easier calibration, alignment, & stabilization

• Need simulation study to identify optimum, taking all effects into account

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 36/43 Additional Considerations

• Alternate solutions: - different M production scheme? o “monochromate” the beam by chopping? - laser interferometry instead of gratings?

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 37/43 Alternate Solutions

• Different M production scheme? - muonium production often employs SiO2 powder or silica aerogel - thermal energy spectrum, not monochromatic - can monochromate using choppers - drawbacks: o flux reduction M o rotating shaft & bearings in vacuum

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 38/43 Selected for a Viewpoint in Physics week ending PRL 108, 090402 (2012) PHYSICAL REVIEW LETTERS 2 MARCH 2012

Influence of the Coriolis Force in Atom Interferometry

Shau-Yu Lan,1,* Pei-Chen Kuan,1 Brian Estey,1 Philipp Haslinger,2 and Holger Mu¨ller1,3 1Department of Physics, University of California, Berkeley, California 94720, USA 2VCQ, Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria 3Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, California 94720, USA (Received 31 October 2011; published 27 February 2012) In a light-pulse atom interferometer, we use a tip-tilt mirror to remove the influence of the Coriolis force from Earth’s rotation and to characterize configuration space wave packets. For interferometers with a large momentum transfer and large pulse separation time, we improve the contrast by up to 350% and suppress systematic effects. We also reach what is to our knowledge the largest space-time area enclosed in any atom interferometer to date. We discuss implications for future high-performance instruments.

DOI: 10.1103/PhysRevLett.108.090402 PACS numbers: 03.75.Dg, 06.30.Gv, 37.25.+k, 67.85. d À

Light-pulse atom interferometers use atom-photon in- a particular output of the interferometer is given by teractions to coherently split, guide, and recombine freely cos2 Á=2 , where Á is the phase difference accumu- falling matter-waves [1]. They are important in measure- latedð by theÞ matter wave between the two paths. It can be 2 2 ments of local gravity [2], the gravity gradient [3], the calculated to be ÁÆ 8n k =2m T nkgT T T0 , Sagnac effect [4], Newton’s gravitational constant [5], the sum of a recoil-induced¼ ð@ term 8nÞ2 Æk2=2m ðT,þ andÞ a ð Þ the fine structure constant [6], and tests of fundamental gravity-induced one, nkgT T T0 , where@ g is the accel- laws of physics [7–9]. Recent progress in increased mo- eration of free fall and correspondð þ Þ to the upper and lower Alternate Solutions Æ mentum transfer led to larger areas enclosed between the interferometer, respectively (Fig. 1)[14]. Atomic-beaminterferometer arms laser [10–12] and,interferometry: combined with common- gravimetryBecause of Earth’s rotation, however, the interferometer • mode noise rejection between simultaneous interferome- does not close precisely. We adopt Cartesian coordinates in “goldters standard” [13,14], to strongly increased sensitivity. With these an inertial frame, one that does not rotate with Earth. We Selected for a Viewpoint in Physics advances, what used to be a minuscule systematic effect take the x axis horizontalweek ending pointing west, the y axis pointing PRL 108, 090402 (2012)now impacts interferometerPHYSICAL performance: REVIEW The LETTERS Coriolis south, and the z axis2 MARCH such that 2012 the laser, pointing vertically force caused by Earth’s rotation has long been known to upwards, coincides with it at t1, see Fig. 2. Later, at t2, t3, cause systematic effects [2]. In this Letter, we not only and t , the laser is rotated relative to the inertial frame, Influence of the Coriolis Force in Atom Interferometry4 demonstrate that it causes severe loss of contrast in large changing the direction of the momentum transfer. As a Shau-Yuspace-time Lan,1,* atomPei-Chen interferometers, Kuan,1 Brian Estey, but also1 Philipp use Haslinger, a tip-tilt2 andresult, Holger the Mu¨ller wave1,3 packet’s relative velocities during the mirror1 [15] to compensate for it, improving contrast (by intervals [t , t ], [t , t ], [t , t ], and [t , ] are, to first Department of Physics, University of California, Berkeley, California 94720, USA 1 2 2 3 3 4 4 1 2upVCQ, to Faculty 350%), of pulsePhysics, separation University of time, Vienna, and Boltzmanngasse sensitivity, and5, A-1090order Vienna, in Austria , È 3Lawrencecharacterize Berkeley the National configuration Laboratory, space One Cyclotron wave packets. Road, Berkeley, In ad- California 94720, USA (Received 31 October 2011; published 27 February 2012) dition, we remove the systematic shift arising from the v12 2nvr 0; 0; 1 ;v23 2nvr T cos#;0; 0 ; In aSagnac light-pulse effect atom interferometer, [16]. This leads we use to a tip-tilt the largestmirror to space-timeremove the influence of the¼ Coriolisð force Þ ¼ ð È Þ from Earth’s rotation and to characterize configuration space wave packets. For interferometersv34 2nvr with a2T T0 cos#;0; 1 ;v4 0; area enclosed in any atom interferometer yet demonstrated, ¼ ð Èð þ Þ À Þ 1 ¼ large momentumgiven by transfer a momentum and large transfer pulse separation of 10 time,k, where we improvek is the the contrast by up to 350% and (1) suppressmomentum systematic effects. of one We photon, also reach and what a pulse is to@ our separation knowledge@ time the largest of space-time area enclosed in any250 atom ms. interferometer to date. We discuss implications for future high-performance instruments. DOI: 10.1103/PhysRevLett.108.090402Figure 1 shows the atom’s trajectoriesPACS in our numbers: apparatus. 03.75.Dg, 06.30.Gv, 37.25.+k, 67.85. d –9 À techniqueWe first consider good the upper to two∆g paths:/g ~ At 10 a time t0, an atom - of mass m in free fall is illuminated by a laser pulse of Light-pulse atomwave interferometers number k use. Atom-photon atom-photon in- interactionsa particular coherently output of the interferometer is given by teractions- to coherentlytimedtransfer split, laser the guide, momentum pulses and recombine of amake number freely superposition2ncosof2 photonsÁ=2 ,to where the Á is the phase difference accumu- falling matter-wavesatom [1]. with They about are important 50% probability, in measure- placinglated theð by atom theÞ matter into a wave between the two paths. It can be of atomic hyperfine states, which interfere2 2 ments of local gravitycoherent [2], superposition the gravity gradient of two [3 quantum], the statescalculated that toseparate be ÁÆ 8n k =2m T nkgT T T0 , D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 ¼ ð 39Þ/432 Æ2 ð þ Þ Sagnac effect [4],with Newton’s a relative gravitational velocity constantof 2nv , [ where5], thev sumk=m of ais recoil-induced the @ term 8n k =2m T, and a r r FIG. 1 (color online).ð Þ Simultaneous conjugate Ramsey-Borde´ the fine structure constant [6], and tests of fundamental gravity-induced¼ one, nkgT T T0 , where@ g is the accel- recoil velocity. An interval T later, a second@ pulse stops interferometers.ð þ Þ Left: atomic trajectories. Beam splitters (=2 laws of physics [7that–9]. relativeRecent progress motion in and increased another mo- intervalerationT later, of free a fall third and correspond to the upper and lower mentum transfer led to larger areas enclosed between the interferometer,0 respectivelyÆpulses) (Fig. split1)[ and14]. recombine the wave packets. Right: plotting the pulse directs the wave packets towards each other. The interferometer arms [10–12] and, combined with common- Because of Earth’s rotation,populations however,A through the interferometerD at the outputs of the interferometers mode noise rejectionpackets between meet simultaneous again at t4 interferome-t1 2T T0doeswhen not a finalclose pulse precisely. Weversus adopt each Cartesian other yields coordinates an ellipse in whose shape is determined by overlaps the atoms. The probability¼ þ þ of detecting an atom in Á Á 16n2 k2=2m T. ters [13,14], to strongly increased sensitivity. With these an inertial frame, one that doesþ À not rotateÀ ¼ withð Earth. WeÞ advances, what used to be a minuscule systematic effect take the x axis horizontal pointing west, the y axis@ pointing now impacts interferometer0031-9007 performance:=12=108(9)=090402(5) The Coriolis south, and the z axis 090402-1 such that the laser, pointing verticallyÓ 2012 American Physical Society force caused by Earth’s rotation has long been known to upwards, coincides with it at t1, see Fig. 2. Later, at t2, t3, cause systematic effects [2]. In this Letter, we not only and t4, the laser is rotated relative to the inertial frame, demonstrate that it causes severe loss of contrast in large changing the direction of the momentum transfer. As a space-time atom interferometers, but also use a tip-tilt result, the wave packet’s relative velocities during the mirror [15] to compensate for it, improving contrast (by intervals [t1, t2], [t2, t3], [t3, t4], and [t4, ] are, to first up to 350%), pulse separation time, and sensitivity, and order in , 1 characterize the configuration space wave packets. In ad- È dition, we remove the systematic shift arising from the v12 2nvr 0; 0; 1 ;v23 2nvr T cos#;0; 0 ; Sagnac effect [16]. This leads to the largest space-time ¼ ð Þ ¼ ð È Þ v34 2nvr 2T T0 cos#;0; 1 ;v4 0; area enclosed in any atom interferometer yet demonstrated, ¼ ð Èð þ Þ À Þ 1 ¼ given by a momentum transfer of 10 k, where k is the (1) momentum of one photon, and a pulse@ separation@ time of 250 ms. Figure 1 shows the atom’s trajectories in our apparatus. We first consider the upper two paths: At a time t0, an atom of mass m in free fall is illuminated by a laser pulse of wave number k. Atom-photon interactions coherently transfer the momentum of a number 2n of photons to the atom with about 50% probability, placing the atom into a coherent superposition of two quantum states that separate with a relative velocity of 2nv , where v k=m is the r r ¼ FIG. 1 (color online). Simultaneous conjugate Ramsey-Borde´ recoil velocity. An interval T later, a second@ pulse stops interferometers. Left: atomic trajectories. Beam splitters (=2 that relative motion and another interval T0 later, a third pulses) split and recombine the wave packets. Right: plotting the pulse directs the wave packets towards each other. The populations A through D at the outputs of the interferometers packets meet again at t4 t1 2T T0 when a final pulse versus each other yields an ellipse whose shape is determined by ¼ þ þ 2 2 overlaps the atoms. The probability of detecting an atom in Áþ ÁÀ 16n k =2m T. À ¼ ð@ Þ 0031-9007=12=108(9)=090402(5) 090402-1 Ó 2012 American Physical Society Alternate Solutions • Atomic-beam laser interferometry: gravimetry “gold standard” • Evaluating feasibility for muonium will take some effort - many variables to consider, e.g.: - use ground-state muonium? o requires difficult “Lyman-alpha” VUV laser o likely impractical to get laser beams into cryostat without windows - or n = 2 muonium? o what fraction are produced in that state? D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 40/43 R&D Status • Still early days... IIT-CAPP-13-6 arXiv:1308.0878 [physics.ins-det] • Seeking funding, Measuring Antimatter Gravity with Muonium Daniel M. Kaplan,* Derrick C. Mancini,† Thomas J. Phillips, Thomas J. Roberts,‡ Jeffrey Terry students, and Illinois Institute of Technology, Chicago, IL 60616, USA

Richard Gustafson collaborators University of Michigan, Ann Arbor, MI!48109 USA A0 Target & C Dipoles for 300 MeV/c ’s Klaus Kirch π collaboration so far: Paul Scherrer Institute and ETH Zürich, Switzerland - M. Popovic presentation at NuFact 2013 Seeking venue at ABSTRACT 300MeV/c pions! • We consider a measurement of the gravitational acceleration of antimatter, g̅ , using muonium. A monoenergetic, low-velocity, horizontal muonium beam will be formed Fermilab from a surface-muon beam using a novel technique and directed at an atom interferometer. The measurement requires a precision three-grating interferometer: the first grating pair creates an interference pattern which is analyzed by scanning the third grating vertically using piezo actuators. State-of-the-art nanofabrication3100MeV/c can pionsproduce thefor g-2! - e.g., proposed new needed membrane grating structure in silicon nitride or ultrananoscrystalline diamond. With 100 nm grating pitch, a 10% measurement of g̅ can be made using some months of surface-muon beam time. This will be the first gravitational measurement of leptonic low-energy muon matter, of 2nd-generation matter and, possibly, the first measurement of the gravitational beam at AP0 acceleration of antimatter.

INTRODUCTION

The gravitational acceleration of antimatter has never been directly measured.1 A measurement D.#M.#Kaplan,#IIT could IIT#Physics#Colloquium######8/29/13bear importantly on the formulation of a quantum theory41 /43 of gravity and on our understanding of the early history and current configuration of the universe. It may be viewed as a test of General5 Relativity, or as a search for new, as-yet-unseen, forces, and is of great interest from either perspective.

General Relativity (GR), the accepted theory of gravity, predicts no difference between the gravitational behavior of antimatter and that of matter. This follows from the equivalence principle—a key assumption of GR—implying that the gravitational force on an object is independent of its composition. While well established experimentally, GR is fundamentally incompatible with quantum mechanics, and development of a quantum alternative has been a longstanding quest. Since all available experimental evidence on which to base a quantum theory of gravity concerns matter–matter interactions, matter–antimatter measurements could play a key role in this quest. Indeed, the most general candidate theories include the possibility that the force between matter and antimatter will be different—perhaps even of opposite sign—from that of matter on matter.2

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! * Email: [email protected] † Also at Argonne National Laboratory, Argonne, IL 60439, USA ‡ Also at Muons, Inc.

! 1 R&D Status • Still early days... IIT-CAPP-13-6 arXiv:1308.0878 [physics.ins-det] • Seeking funding, Measuring Antimatter Gravity with Muonium Daniel M. Kaplan,* Derrick C. Mancini,† Thomas J. Phillips, Thomas J. Roberts,‡ Jeffrey Terry students, and Illinois Institute of Technology, Chicago, IL 60616, USA

Richard Gustafson collaborators University of Michigan, Ann Arbor, MI!48109 USA A0 Target & C Dipoles for 300 MeV/c ’s Klaus Kirch π collaboration so far: Paul Scherrer Institute and ETH Zürich, Switzerland - M. Popovic presentation at NuFact 2013 The ProjectABSTRACT X Accelerator:300MeV/c pions! Seeking venue at Concept and Capabilities • We consider a measurement of the gravitational acceleration of antimatter, g̅ , using muonium. A monoenergetic, low-velocity, horizontal muonium beam will be formed Fermilab from a surface-muon beam using a novel technique and directed at an atom interferometer. The measurement requires a precision three-grating interferometer: the first grating pair creates an interference pattern which is analyzed by scanning the third grating vertically using piezo actuators. State-of-the-art nanofabrication3100MeV/c can pionsproduce thefor g-2! - e.g., proposed new needed membrane grating structure in silicon nitride or ultrananoscrystalline diamond. With 100 nm grating pitch, a 10% measurement of g̅ can be made using some months of surface-muon beam time. This will be the first gravitational measurement of leptonic low-energy muon matter, of 2nd-generation matter and, possibly, the first measurement of the gravitational acceleration of antimatter. beam at AP0 Steve Holmes DPF Community Summer Study July 30, 2013 ultimately, Project X INTRODUCTION - 1 The gravitational acceleration of antimatter has never been directly measured. A measurement D.#M.#Kaplan,#IIT could IIT#Physics#Colloquium######8/29/13bear importantly on the formulation of a quantum theory41 /43 of gravity and on our understanding of the early history and current configuration of the universe. It may be viewed as a test of General5 Relativity, or as a search for new, as-yet-unseen, forces, and is of great interest from either perspective.

General Relativity (GR), the accepted theory of gravity, predicts no difference between the gravitational behavior of antimatter and that of matter. This follows from the equivalence principle—a key assumption of GR—implying that the gravitational force on an object is independent of its composition. While well established experimentally, GR is fundamentally incompatible with quantum mechanics, and development of a quantum alternative has been a longstanding quest. Since all available experimental evidence on which to base a quantum theory of gravity concerns matter–matter interactions, matter–antimatter measurements could play a key role in this quest. Indeed, the most general candidate theories include the possibility that the force between matter and antimatter will be different—perhaps even of opposite sign—from that of matter on matter.2

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! * Email: [email protected] † Also at Argonne National Laboratory, Argonne, IL 60439, USA ‡ Also at Muons, Inc.

! 1 Conclusions • Antigravity hypothesis might neatly solve several vexing problems in physics and cosmology • In principle, testable with antihydrogen or muonium - if possible, both should be measured ➡First measurement of muonium gravity would be a milestone! • But first we must determine feasibility

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 42 /43 Final Remarks

• These measurements are an obligatory homework assignment from Mother Nature!

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

D.#M.#Kaplan,#IIT IIT#Physics#Colloquium######8/29/13 43/43