the weak equivalence principle with antimatter: the aegis...

Davide PaganoUniversità degli Studi di Brescia & INFN Pavia

on behalf of the AEgIS collaboration

The Weak Equivalence Principle with antimatter: the AEgIS experiment at CERN

Rencontres de Moriond 2016, March 19 - 26, 2016

2The Weak Equivalence Principle

• Universality of free fall (UFF) established by Galileo and Newton

Weak equivalence principle (WEP)

• Unique behavior:

electric field vs. gravitational field

electric field: gravitational field:

F = q · E F = m · G

|E| � Q

r2|G| � M

r2

|a| � q |a| �= F(m) , a = const.

• For other forces, mass has only one function; as the measure of inertia. For

gravity, it also fulfills a second function; as source of acceleration.

clock will run faster as the gravitational field around it isreduced.”

In January 1960, Leonard Schiff3 showed that, as long as agravity field affects clocks and normal matter alike, the gravi-tational redshift can be derived from WEP and special relativ-ity and as such it is not a crucial test of GR. Measurements ofthe gravitational redshift are therefore tests of the underlyingWEP, but he argued that even with the best atomic clocks ofthe time they could not compete with the torsion balance testsreported by E€otv€os half a century earlier.

Recently, a proposal has been made for a new space mis-sion devoted to measuring the gravitational redshift andtesting WEP with cold atoms.4 A much better ground mea-surement of the gravitational redshift has been reported,based on free falling cold atoms.5 A strong scientific debateis ongoing and this has motivated the present work.

This paper is organized as follows. In Sec. II, we go backto UFF and the equivalence principle of Galileo, Newton,and E€otv€os to stress the advantages of null experiments. InSec. III, we recall how UFF and Newton’s equivalence prin-ciple (the “weak equivalence principle”) led Einstein to thestrong equivalence principle (or “Einstein equivalenceprinciple”) and to the formulation of general relativity, sothat a violation of UFF/WEP would either require that GR beamended or call for a new force of nature. This has led to thequest for UFF/WEP null experiments that are as accurateand precise as possible.

In Sec. IV, following Schiff,3 we derive the gravitationalredshift from the WEP and special relativity and show that—as long as clocks are affected by a gravitating body like nor-mal matter—its measurement is a test of UFF/WEP but it isby far less competitive than direct null tests. A suggestedstronger deviation from WEP of clocks as compared to ordi-nary bodies6 appears to be beyond the reach of current andplanned experiments. The best, so-far controversial, measure-ment of the gravitational redshift,5 based on free falling coldatoms in combination with a nearby absolute gravimeter, is atest of the WEP. As such it is in perfect agreement with theoriginal experimental result,7 but it is in no way competitivewith UFF/WEP null tests. In this analysis we frequently stepinto the “Schiff conjecture” as formulated in 1973 by Thorneet al.8 In consideration of the “vigorous argument” betweenSchiff and Thorne on this issue, we trace the conjecture backto Schiff’s original statement in Ref. 3 and report it. We alsoreport the results of the best experiment to date that has com-pared the effect of a gravitating body (the Sun) on the rate ofclocks of different internal structure and in different locationsas the solar potential changes over the year.9

Finally, in Sec. V, we compare UFF/WEP tests using mac-roscopic proof masses versus cold atoms to show that,although the experiments are completely different, there isno difference in the nature of the tests and one should pursuethe most promising ones, both in terms of sensitivity and interms of differences in the physical properties of the atomsbeing tested.

II. UNIVERSALITY OF FREE FALL AND THEEQUIVALENCE PRINCIPLE FROM GALILEO TONEWTON

In the Discorsi10 (pp. 128–129; pp. 84–85 of the Englishedition) Galileo describes his tests of the universality of freefall (UFF) made with two pendulums of different composi-tion. The book was published in Leiden in 1638 when

Galileo was 74, almost blind, and under house arrest by orderof the Pope, but he had made these experiments in the early1600s.11 The accuracy of the test was12 about 10!3.

In 1687, in the opening paragraph of the Principia,13

Newton wrote: “This quantity that I mean hereafter underthe name of…mass…is known by the weight…for it is pro-portional to the weight as I have found by experiments onpendulums, very accurately made….” If inertial and gravita-tional mass mi and mg are the same for all test bodies regard-less of their mass and composition, the equations of motionunder the gravitational attraction of a source mass M (e.g.,the Earth, assumed for simplicity to be spherically symmet-ric) state that they all fall with the same acceleration:

mi€~r ¼ !

GMmg

r3~r; so mi ¼ mg implies that

€~r ¼ !GM

r3~r: (1)

If inertial and gravitational mass are equivalent, UFF holds;should experiments invalidate UFF, they would invalidatethe equivalence of inertial and gravitational mass as well.

This was the “equivalence principle” from 1687 until1907. Note that Eq. (1) holds for any position vector~r , in thevicinity of the source body as well as very far away from it,e.g., it applies also to test bodies on Earth falling in the grav-itational field of the Sun (as tested by Dicke and his studentsin the early 1960s14), or in the case of the Earth and theMoon falling towards the Sun (as tested with lunar laserranging15).

E€otv€os and collaborators1 first coupled the test masses bysuspending them on a very sensitive torsion balance, andwere able to test UFF in the field of the Earth to about 10!8.Dicke’s torsion balance experiment was the first UFF test inthe field of the Sun (to ’10!11), followed by Braginsky andPanov16 (to ’10!12). More recent experiments with rotatingtorsion balances have tested UFF both in the field of theSun17 and in the field of the Earth18 yielding the best limitsto date (see Ref. 19, Table 3): UFF is confirmed to about10!12 in the field of the Sun and to about 10!13 in the field ofthe Earth.

It is worth stressing that UFF experiments can reach highaccuracy because they can be performed as null experiments.The physical quantity of interest in UFF experiments is therelative acceleration Da ¼ a1 ! a2 of the free falling proofmasses, from which the dimensionless E€otv€os parameter

g # Da

a(2)

is obtained (here a ¼ ða1 þ a2Þ=2 is the average free fallacceleration of the masses in the gravity field of the sourcebody). The g parameter quantifies a deviation from UFF. IfUFF holds, Da ¼ 0 and g ¼ 0; for a given value of a, thesmaller the differential acceleration measured, the smallerthe value of g, the more accurate the test.

If the experiment is designed to measure the differentialacceleration between the test masses, the experiment signalshould be zero in the absence of UFF violation (after classi-cal differential effects have been reduced to below the tar-get). In such null experiments no precise theoreticalprediction must be made which the measured signal shouldbe compared to in order to obtain the physical quantity ofinterest.

528 Am. J. Phys., Vol. 81, No. 7, July 2013 Nobili et al. 528

• Einstein Equivalence Principle: • WEP • Local Lorentz Invariance (LLI) • Local Position Invariance (LPI)

electric field vs. gravitational field

electric field: gravitational field:

F = q · E F = m · G

|E| � Q

r2|G| � M

r2

|a| � q |a| �= F(m) , a = const.

• For other forces, mass has only one function; as the measure of inertia. For

gravity, it also fulfills a second function; as source of acceleration.

= const∝

∝∝

3Test of the EEP

• EEP is the “heart and soul” of General Relativity (GR):

R. Dicke, Les Houches Summer School of Theoretical Physics: Relativity, Groups and Topology, pp. 165–313, CNUM: C63-07-01 (1964)

4

19001920

19401960

19701980

19902000

10-8

10-9

10-10

10-11

10-12

10-13

10-14

YEAR OF EXPERIMENT

Eotvos

Renner

Princeton

Moscow

Boulder

Eot-Wash

Eot-Wash

Free-fall

Fifth-force searches

LLR

a1 -a 2

(a1+a2)/2

2010

Matter waves

FIG. 1: Selected tests of the weak equivalence principle, showing bounds on η. The free-fall and Eot-Wash experiments wereoriginally performed to search for a fifth force (green region, representing many experiments). The blue band shows evolvingbounds on η for gravitating bodies from lunar laser ranging (LLR).

• tests of the independence of the speed of light of the velocity of the source, using both binary X-ray stellarsources and high-energy pions;

• tests of the isotropy of the speed of light.

In addition to these direct experiments, there was the Dirac equation of quantum mechanics and its prediction ofanti-particles and spin; later would come the stunningly successful relativistic theory of quantum electrodynamics.For a pedagogical review on the occasion of the 2005 centenary of special relativity, see [15].In 2015, on the 110th anniversary of special relativity, one might ask “what is there left to test?” Special relativity

has been so thoroughly integrated into the fabric of modern physics that its validity is rarely challenged, except bycranks and crackpots. It is ironic then, that during the past 15 years, a vigorous theoretical and experimental efforthas been launched to find violations of special relativity. The motivation for this effort is not a desire to repudiateEinstein, but to look for evidence of new physics “beyond” Einstein, such as apparent, or “effective” violations ofLorentz invariance that might result from certain models of quantum gravity. Quantum gravity asserts that thereis a fundamental length scale given by the Planck length, ℓPl = (!G/c3)1/2 = 1.6 × 10−33 cm, but since length isnot an invariant quantity (Lorentz–FitzGerald contraction), then there could be a violation of Lorentz invariance atsome level in quantum gravity. In brane world scenarios, while physics may be locally Lorentz invariant in the higherdimensional world, the confinement of the interactions of normal physics to our four-dimensional “brane” could induceapparent Lorentz violating effects. And in models such as string theory, the presence of additional vector and tensorlong-range fields that couple to matter of the standard model could induce effective violations of Lorentz symmetry.These and other ideas have motivated a serious reconsideration of how to test Lorentz invariance with better precisionand in new ways.A simple and useful way of interpreting some of these modern experiments, called the c2-formalism, is to suppose

that the electromagnetic interactions suffer a slight violation of Lorentz invariance, through a change in the speed ofelectromagnetic radiation c relative to the limiting speed of material test particles (c0, made to take the value unityvia a choice of units), in other words, c = 1. Such a violation necessarily selects a preferred universal rest frame,presumably that of the cosmic background radiation, through which we are moving at about 370 km s−1. Such aLorentz-non-invariant electromagnetic interaction would cause shifts in the energy levels of atoms and nuclei thatdepend on the orientation of the quantization axis of the state relative to our universal velocity vector, and on the

• EEP valid → gravity is governed by a“metric theory of gravity”

• EEP extensively tested experimentally:

Isotropy of atomic energy levels:LLI

� = |c�2 � 1| > 10-23

Torsion balance:

WEP

> 10-13⌘ =a1 � a2

(a1 + a2)/2

C. Will, Living Rev. Relativity 17 (2014)

Gravitational red shift:

LPI

�⌫

⌫= (1 + ↵)

�U

c2> 10-6

WEP

4WEP for antimatter: the current picture

• Some arguments would suggest the WEP holds for antimatter

• neutrinos detected from Supernova 1987A S. Pakvasa et al., Phys. Rev. Lett. D. 39, 6 (1989)

• Shapiro delay of relativistic particles not a test for the EEPG. T. Gillies, Class. Quantum Grav. 29 (2012)

• On the experimental side:

• p-p cyclotron frequency comparisons: G. Gabrielse et al., PRL 82 (3198) (1999)

!c � !c

!c< 9⇥ 10�11

• Strong theoretical arguments only apply to the idea of antigravity• Morrison (1958), Schiff (1958), Good (1961), etc…

• none of them necessarily requires mantimatteri = mmatter

g

• Model dependent, CPT assumption, absolute potentials, …

• and others…but none of them is conclusive

5WEP for antimatter: why to test it?

• Our attempts for a quantum theory of gravity typically result into new interactions which violate the WEP (ex. KK theory)

• Because it’s possible and no direct measurements are available

mg/mi• 2013: ALPHA experiment at CERN set limit on for HNature Communications 4, 1785 (2013)

> 110 excluded at 95% CL•

• 1989: PS-200 experiment at CERN tried to use (4 K) antiprotonsNucl. Instr. and Meth. B, 485 (1989)

• 1967: Fairbank and Witteborn tried to use positronsPhys. Rev. Lett. 19, 1049 (1967)

• Previous attempts:

• Both unsuccessful because of stray E and B fields

mg/mi

• Some open questions (like dark matter and baryogenesis) could benefit from a direct measurement Astrophys. Space Sci. 334, 219–223 (2011)

Int. J. Mod. Phys. D18, 251–273 (2009)

JHEP 1502, 076 (2015)

6The Antiproton Decelerator (AD)

• At CERN antimatter studies are possible thanks to the Antiproton Decelerator (AD)

• 26 GeV/c p from PS used to produced p

James Storey

Antiproton production

30

p + p → p + p + p + p

26 GeV/c p

p

p

pp 3.5 GeV/c

Air cooled Iridium target

• Approximately 3 x 107 p delivered each cycle

• AD slows down p to ~100 MeV/c in a 100 s cycle

7

• Goal: direct measurement of the Earth’s local gravitational acceleration g on H with a final precision of some percent

• How: by measuring the vertical displacement of the shadow image produced by an H beam though a Moiré deflectometer

The AEgIS experiment

The precise measurement of forces between objectsgives deep insight into the fundamental interactions andsymmetries of nature. A paradigm example is the

comparison of the motion of matter in the gravitational field,testing with high precision that the acceleration is material-independent, that is, the weak equivalence principle1–4. Althoughindirect experimental evidence suggests that the weak equivalenceprinciple also holds for antimatter5–7, a direct observation forantimatter is still missing. First attempts in this direction haverecently been reported by the ALPHA collaboration8, who usedthe release of antihydrogen from a magnetic trap to exclude theabsolute value of the gravitational acceleration of antihydrogen tobe 100 times larger than for matter. An alternative approach isfollowed by the GBAR collaboration9, which is based onsympathetic cooling of positive antihydrogen ions and theirsubsequent photodetachment. One of the specified goals ofthe AEgIS collaboration (antihydrogen experiment: gravity,interferometry, spectroscopy) is the direct detection of thegravitational acceleration using an antihydrogen beam10,11

combined with a moire deflectometer12, a device with highsensitivity for acceleration measurements.

Here, we present the successful realization of such a device forantiprotons. This has been achieved using slow antiprotons fromthe Antiproton Decelerator (AD) at CERN, the technology ofemulsion detectors developed for recent high-energy neutrinoexperiments13 and a novel referencing method employingTalbot–Lau interferometry14,15 with light. The observation isconsistent with a force at the 500 aN level acting on theantiprotons. This demonstration is an important prerequisitefor future studies of the gravitational acceleration of antimatterbuilding on an antihydrogen beam.

ResultsMoire deflectometer. The principle used in the experimentreported here is visualized in Fig. 1a. A divergent beam ofantiprotons enters the moire setup consisting of three equallyspaced elements: two gratings and a spatially resolving emulsiondetector. The two gratings with periodicity d define the classicaltrajectories leading to a fringe pattern with the same periodicity atthe position of the detector. If the transit time of the particlesthrough the device is known, absolute force measurementsare possible by employing Newton’s second law of mechanics16.

As indicated in Fig. 1b, the position of the moire pattern is shiftedin the presence of a force with respect to the geometric shadow by

Dy ¼ Fkm

t2 ¼ at2; ð1Þ

where F|| represents the force component along the gratingperiod, m is the inertial mass of the test particle, a is theacceleration and t is the time of flight between the two gratings. Itis important to note that the shift has two contributions. Thevelocity of the particle after the second grating in the direction ofthe acceleration is non-zero and the particle is also accelerated inthe second half of the moire deflectometer. The relevantparameter for precision measurements is the sensitivity, that is,the minimal detectable acceleration amin. This can be estimatedby considering the maximal signal S to noise ratio possible in thisscenario. Since the influence of a pattern shift is most sensitivelydetected at the steepest gradient of the pattern the visibilityu¼ (Smax$ Smin)/(Smaxþ Smin) should be maximized and theperiodicity minimized. The noise of the signal is intrinsicallylimited for classical particle sources to the shot noise which scalesas 1/

ffiffiffiffiNp

, where N is the number of detected particles.Consequently, the minimal detectable acceleration12 is given byamin ¼ d= 2put2

ffiffiffiffiNp" #

. It is important to note that this deviceworks even for a very divergent source of particles as shown inFig. 1a, and thus is an ideal device for the highly divergent beamof antihydrogen atoms that is expected in the AEgIS apparatus.

Talbot–Lau interferometry with light as absolute reference.To determine the magnitude of the fringe pattern shift,knowledge of the undeflected fringe position (indicated as greytrajectories in Fig. 1b) is required. Due to the neutrality and highspeed of photons, it is favourable to measure this position inde-pendently with light so that the action of forces is negligible.Unlike the case of classical particles described above, geometricpaths are not applicable for visible light as diffraction at thegratings has to be taken into account. Figure 1c depicts the cor-responding light field pattern where the distance between thegratings is given by the Talbot length LTalbot¼ 2d2/l. This con-figuration is known as Talbot–Lau interferometer14, which isbased on the near-field Talbot effect15—the rephasing of thepattern in discrete distances behind a grating illuminated withlight. The final pattern is not a classical distribution, but aninterference pattern and coincides with the pattern of the moire

Light interference

Matter moiréa b

c

40 µm

25 mm

25 mm

Moiré Contact

Figure 1 | Moire deflectometer for antiprotons. (a) A divergent antiproton beam impinges on two subsequent gratings that restrict the transmittedparticles to well-defined trajectories. This leads to a shadow fringe pattern as indicated in b, which is shifted in the presence of a force (blue trajectories).Finally, the antiprotons are detected with a spatially resolving emulsion detector. To infer the force, the shifted position of the moire pattern has to becompared with the expected pattern without force. (c) This is achieved using light and near-field interference, the shift of which is negligible. A grating indirect contact with the emulsion is used to reference the antimatter and the light measurements.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5538

2 NATURE COMMUNICATIONS | 5:4538 | DOI: 10.1038/ncomms5538 | www.nature.com/naturecommunications

& 2014 Macmillan Publishers Limited. All rights reserved.

H

8AEgIS collaboration

Stefan Meyer Institute

CERN Czech Technical University ETH Zurich

University of Genova

University of Milano

University of Padova

University of Pavia

University College London

Politecnico di Milano

Max-Planck Institute Heidelbert

Institute of Nuclear Research of the

Russian Academy of Science

University of Bergen

University of Bern

University of Brescia

Heidelberg University

University of Trento

University of Paris Sud

University of Oslo

University of Lyon 1

INFN sections of: Genova, Milano, Padova, Pavia,

Trento

21 Institutes and 80 people

9AEgIS apparatus

J.Storey on behalf of the AEgIS collaboration

!

The AEgIS apparatus

30

H

catching traps

H production traps

flight region


!

The AEgIS apparatus

30

H

catching traps

H production traps

flight region


!

The AEgIS apparatus

30

H

catching traps

H production traps

flight region5 T

1 T

p catching trap

p

e+

Moiré

H production trap

10Antihydrogen production strategy

• Rydberg H* atoms produced via charge exchange

• Temperature of H given by the temperature of p

• Rydberg H: strong dipole moment → Stark acceleration

Figure 1. Principle of antihydrogen production in AEgIS.

Antihydrogen production. Rydberg antihydrogen atoms H⇤are produced from cold antiprotons

(p) and Rydberg (ortho)positronium Ps⇤ via the charge exchange reaction Ps⇤ + p ! H⇤+

e� [4, 5]. This process has various advantages:

• The production cross section scales as � / n

4Ps where nPs is the principal quantum number

of orthopositronium. The cross section is around 10�9 cm2 for nPs = 20.

• The reaction can produce ultracold antihydrogen atoms if the antiprotons are cold enough.The antihydrogen temperature is 120 mK for Tp = 100 mK and nPs = 30.

• The antihydrogen atoms are pulsed. The temperature of the antihydrogen atoms must below enough (⇠100 mK) to reduce the beam spread (Maxwell-Boltzmann distribution withthe average speed of 50 m/s).

Antihydrogen beam formation. The antihydrogen atoms in excited Rydberg states have largeelectric dipole moments and can be accelerated by electric field gradients to several 100 m/stowards the moire deflectometer. This technique has already been demonstrated by acceleratingRydberg hydrogen atoms with n = 22, 23, 24 to velocities up to 2⇥ 108 m/s2 [6].

Gravity measurement. The gravity module, a classical moire deflectometer [7] coupled to anH detector, will measure the gravitational acceleration g of the antihydrogen beam. Thedeflectometer consists of two silicon gratings of 40 µm pitch with 12 µm slit widths. Thetwo gratings are 40 cm apart. Figure 2 shows that the two gratings produce a pattern on theH detector with the same period as the grating pitch. The intensity pattern can be measuredprecisely with emulsion detectors (see below).

The trajectory of the H atoms is a↵ected by gravity, which leads to a shift of the periodicpattern, depending on the strength of the gravitational force and the velocity of the beambetween the two gratings. The shift is determined by including a measurement of the time-of-flight between the production point and the detector. The gravitational acceleration g is given

Ps⇤ + p ! H⇤ + e�

• � / n4Ps n4

Ps ⇡ 20� 30

• determined by nH nPs

~ 20 - 30

11Antiproton capture and cooling

Elena Jordan IMPRS Seminar November 2013

Antiproton capture and cooling• Energy reduced by 50‐µm degrader foil

• Trapping sequence:1. Trap is prepared with plasma of

108 cold electrons2. Small fraction of antiprotons with

E < 9 keV is reflected3. Axial potential on entrance side is

raised to trap μ4. Antiprotons are sympathetically

cooled by electrons

• Trap cooled to 100 mK by a dilutionrefrigerator

• sympathetic coolingwith laser cooled negative ions

e-

degrader

t = 200 ns

t = 500 ns

t = few s

99.9% lost0.1%

E < 5 keV

solenoid magnet B = 5 T

z

z

z

el. p

oten

tial

el. p

oten

tial

el.

p

> 105 cold antiprotons

t = 200 ns

t = 500 ns

few s

el. potential

el. potential

z

z

z

99.9% lost

0.1%

B = 5T

e‐

p

5T solenoid

ep







cooled by electrons



e-

degrader

t = 200 ns

t = 500 ns

t = few s

99.9% lost0.1%

E < 5 keV


z

z

z

el. p

oten

tial

el. p

oten

tial

el.

p


t = 200 ns

t = 500 ns

few s

el. potential

el. potential

z

zz

99.9% lost

0.1%

B = 5T

e‐

p







cooled by electrons



e-

degrader

t = 200 ns

t = 500 ns

t = few s

99.9% lost0.1%

E < 5 keV


z

z

z

el. p

oten

tial

el. p

oten

tial

el.

p


t = 200 ns

t = 500 ns

few s

el. potential

el. potential

z

z

z

99.9% lost

0.1%

B = 5T

e‐

p







cooled by electrons



e-

degrader

t = 200 ns

t = 500 ns

t = few s

99.9% lost0.1%

E < 5 keV


z

z

z

el. p

oten

tial

el. p

oten

tial

el.

p


t = 200 ns

t = 500 ns

few s

el. potential

el. potential

z

z

z

99.9% lost

0.1%

B = 5T

e‐

p







cooled by electrons



e-

degrader

t = 200 ns

t = 500 ns

t = few s

99.9% lost0.1%

E < 5 keV


z

z

z

el. p

oten

tial

el. p

oten

tial

el.

p


t = 200 ns

t = 500 ns

few sel. potential

el. potential

z

z

z

99.9% lost

0.1%

B = 5T

e‐

p







cooled by electrons



e-

degrader

t = 200 ns

t = 500 ns

t = few s

99.9% lost0.1%

E < 5 keV


z

z

z

el. p

oten

tial

el. p

oten

tial

el.

p


t = 200 ns

t = 500 ns

few s

el. potential

el. potential

z

z

z

99.9% lost

0.1%

B = 5T

e‐

p







cooled by electrons



e-

degrader

t = 200 ns

t = 500 ns

t = few s

99.9% lost0.1%

E < 5 keV


z

z

z

el. p

oten

tial

el. p

oten

tial

el.

p


t = 200 ns

t = 500 ns

few s

el. potential

el. potential

z

z

z

99.9% lost

0.1%

B = 5T

e‐

p







cooled by electrons



e-

degrader

t = 200 ns

t = 500 ns

t = few s

99.9% lost0.1%

E < 5 keV


z

z

zel

. pot

entia

lel

. pot

entia

lel

.

p


t = 200 ns

t = 500 ns

few s

el. potential

el. potential

z

z

z

99.9% lost

0.1%

B = 5T

e‐

p

1

2

3

4

• Electrons (~108) loaded in the trap

• Thin Al foil (degrader) used to select low energy antiprotons

e

e

e

p

p

p

9 kV

120 V

• p caught and cooled (electron cooling)• ~7 K reached currently

• some 105 p catch per spill

12Positronium formation

• Positronium (Ps) is an exotic atom composed by an e- and a e+

• Ps produced via electron capture of e+ within a nanoporous silica target

• e+ source: 440 MBq (current 15mCi)

Transport efficiency 90%

• Accumulation

AEgIS status: Positrons

Lifetime ~ 100s

e+ source

accumulator

transfer line

• 22Na source• Solid neon moderator

up to 8x108 e+

SiO2

Si

e+

e+

e+

e+

• para-Ps(125 ps) and ortho-Ps(142 ns)

bunches of ~107 e+

transfer ε > 0.8

13Positronium excitation

6.2 AEGIS apparatus 97

6.2.2 Antiprotons catching and cooling

The catching of antiprotons use a techniques identical to that used in the ATHENAapparatus and described in chapter 2.2.

Figure 6.6: Here the trap system of AEGIS is showed. For all the trap an axialmagnetic field is superimposed. The magnetic field is along z and two region withdifferent intensity of field are present: B = 3T int the catching region (on the left),and B = 1T in the antihydrogen production region (right).

Figure 6.7: Catching trap for antipro-tons (bottom) and trap for positronsprovided by positron accumulator(top).

Figure 6.8: Magnification of theproduction region. Antiprotons arecooled in the bottom area, while inthe upper part it is possible to see thetarget for positronium production.

Once antiprotons are captured (see figure 6.6 and 6.7), they are moved from thecatching region to the antihydrogen production region (figure 6.8, lower trap) wherea cooling process cool the antiprotons down below 1 kelvin. Some ideas to coolantiprotons have been briefly described before.

Like in ATHENA, initial cooling will be performed trough electron cooling. elec-trons in the trap forms a plasma. Electrons cool themselves by emission of cyclotronradiation in the magnetic field of the catching trap (B = 3T ). After electron cool-ing, antiprotons have to be moved into the antihydrogen production region (with alower value of magnetic field B = 1T ). If antiprotons and electrons are superim-posed in the same region, the two species reach an equilibrium temperature that,in principle, is the same of the ambient temperature. In the 1T region, this is true

e+

p

double laser pulse

Two stages excitation: • UV (205 nm): n = 1 → 3 • IR (1650-1700 nm): n = 3 → 25 - 35

(1650 nm) (205 nm

)

0.75 eV

6.05 eV

n = 1

n = 2

n = 3

n = 35

continuum

S. Mariazzi et al., Phys. Rev. A 78 (2008) 052512

S. Mariazzi et al., NIM B 269 (2011) 1527

Ps

14Gravity module

x

which must be smaller than the diffraction angle / ¼ kdB=d,where kdB is the de Broglie wavelength of the matter wave.All of these limitations can be alleviated by increasing thegrating period relative to the de Broglie wavelength. Atthe point where d2=L " kdB, diffraction no longer occurs.

The resulting device is the so-called Moire deflectometer,in which diffraction on the gratings is replaced by a (classi-cal) shadow pattern of those particles that converge ontothe third grating. Interestingly, the gross characteristics ofthe interferometer are retained [33], in particular, the verti-cal displacement of the interference pattern according toEq. (2). A three-grating Moire deflectometer has been usedto measure the local gravitational acceleration to a relativeprecision of 2 # 10$4 with a beam of argon atoms travelingat an average velocity of 750 m s$1 [33]. In departing fromthe three-grating deflectometer, we intend to replace thethird grating by a position-sensitive silicon strip detector(see Fig. 4). Thereby the overall transmission of the appa-ratus is increased by the inverse of the grid’s open fraction(roughly a factor of three).

The value of g is extracted from the primary observables(time of flight T and vertical displacement of the fringe pat-tern dx) in the following way, as illustrated by Monte-Car-lo simulations performed by us: First, the ensemble of all Hannihilation events on the detector is plotted as a functionof T, as shown in Fig. 5(a). These events are binned in sym-metric classes of T2, one of which is shown shaded in darkblue in the figure. Secondly, the vertical displacement dx ofthe fringe pattern is extracted for each of the count classes,as illustrated in Fig. 5(b). Thirdly, the vertical displacementfor all count classes is plotted against the mean time offlight in the class. A quadratic fit to that graph, as shownin Fig. 5(c), will then yield g. In these simulations, a gratingperiod of 80 lm was used, and a finite detector resolutionof 10 lm was taken into account.

Our simulations have shown that in order to perform ameasurement of !g to 1% relative precision, about 105 H

atoms at a temperature of 100 mK will be required. Thiscould be achieved within about 2–3 weeks of data taking,assuming the AD beam is shared among four experiments.The grids and detector must be kept precisely aligned forthe entire data taking period, which can be achieved byan auxiliary laser beam. The zero position of the vertical

Fig. 4. Principle sketch of the Moire deflectometry technique with twoidentical gratings and a position-sensitive detector.

a

b

c

Fig. 5. Analysis of deflectometer data (Monte Carlo simulation): (a)detector events are binned according to time-of-flight count classes, (b) thevertical displacement of the fringe pattern is determined for each countclass, and (c) a quadratic fit to the plot of vertical displacement versusmean time of flight yields the local gravitational acceleration g.

A. Kellerbauer et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 351–356 355

frin

ge p

atte

rn

James Storey

How much flux(*) do we need?Δg/g dependancy on vertex position resolution

69

Particles0 1000 2000 3000 4000 5000 6000 7000

g/g

6

-310

-210

-110

mµ1 mµ3 mµ5

mµ7

mµ10

mµ13

mµ15

number of fully reconstructed and time tagged hbar atoms

Δg/g

Higher resolution → fewer Hbar atoms required for the measurement.

Measurement accuracy depends on : • number of detected vertices • detector resolution • alignment, etc… (systematic unc.)







Dy ¼ Fkm

t2 ¼ at2; ð1Þ


ffiffiffiffiNp


ffiffiffiffiNp" #



Light interference

Matter moiréa b

c

40 µm

25 mm

25 mm

Moiré Contact





emulsions

12 μm

15Results: (mini) Moiré test with antiprotons







Dy ¼ Fkm

t2 ¼ at2; ð1Þ


ffiffiffiffiNp


ffiffiffiffiNp" #



Light interference

Matter moiréa b

c

40 µm

25 mm

25 mm

Moiré Contact











Dy ¼ Fkm

t2 ¼ at2; ð1Þ


ffiffiffiffiNp


ffiffiffiffiNp" #



Light interference

Matter moiréa b

c

40 µm

25 mm

25 mm

Moiré Contact





lightantiprotons

ARTICLEReceived 5 Nov 2013 | Accepted 27 Jun 2014 | Published 28 Jul 2014

A moire deflectometer for antimatterS. Aghion1,2, O. Ahlen3, C. Amsler4, A. Ariga4, T. Ariga4, A.S. Belov5, K. Berggren3, G. Bonomi6,7, P. Braunig8,

J. Bremer3, R.S. Brusa9, L. Cabaret10, C. Canali11, R. Caravita2,12, F. Castelli2,12, G. Cerchiari13, S. Cialdi2,12,

D. Comparat10, G. Consolati1,2, H. Derking3, S. Di Domizio14, L. Di Noto9, M. Doser3, A. Dudarev3, A. Ereditato4,

R. Ferragut1,2, A. Fontana7, P. Genova7, M. Giammarchi2, A. Gligorova15, S.N. Gninenko5, S. Haider3, T. Huse16,

E. Jordan13, L.V. Jørgensen3, T. Kaltenbacher3, J. Kawada4, A. Kellerbauer13, M. Kimura4, A. Knecht3,

D. Krasnicky1,14, V. Lagomarsino14,17, S. Lehner18, A. Magnani7,19, C. Malbrunot3,18, S. Mariazzi9,18,

V.A. Matveev5,20, F. Moia1,2, G. Nebbia21, P. Nedelec22, M.K. Oberthaler8, N. Pacifico15, V. Petracek23,

C. Pistillo4, F. Prelz2, M. Prevedelli24, C. Regenfus11, C. Riccardi7,19, O. Røhne16, A. Rotondi7,19, H. Sandaker15,

P. Scampoli4,25, J. Storey4, M.A. Subieta Vasquez6,7, M. Spacek23, G. Testera14, R. Vaccarone14, E. Widmann18,

S. Zavatarelli14 & J. Zmeskal18

The precise measurement of forces is one way to obtain deep insight into the fundamental

interactions present in nature. In the context of neutral antimatter, the gravitational inter-

action is of high interest, potentially revealing new forces that violate the weak equivalence

principle. Here we report on a successful extension of a tool from atom optics—the moire

deflectometer—for a measurement of the acceleration of slow antiprotons. The setup con-

sists of two identical transmission gratings and a spatially resolving emulsion detector for

antiproton annihilations. Absolute referencing of the observed antimatter pattern with a

photon pattern experiencing no deflection allows the direct inference of forces present. The

concept is also straightforwardly applicable to antihydrogen measurements as pursued by the

AEgIS collaboration. The combination of these very different techniques from high energy and

atomic physics opens a very promising route to the direct detection of the gravitational

acceleration of neutral antimatter.

DOI: 10.1038/ncomms5538 OPEN

1 Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy. 2 Istituto Nazionale di Fisica Nucleare, Sez. di Milano, Via Celoria 16, 20133 Milan,Italy. 3 Physics Department, European Organisation for Nuclear Research, 1211 Geneva 23, Switzerland. 4 Laboratory for High Energy Physics, Albert EinsteinCenter for Fundamental Physics, University of Bern, 3012 Bern, Switzerland. 5 Institute for Nuclear Research of the Russian Academy of Sciences, Moscow117312, Russia. 6 Department of Mechanical and Industrial Engineering, University of Brescia, Via Branze 38, 25133 Brescia, Italy. 7 Istituto Nazionale di FisicaNucleare, Sez. di Pavia, Via Agostino Bassi 6, 27100 Pavia, Italy. 8 Kirchhoff Institute for Physics, Heidelberg University, Im Neuenheimer Feld 227, 69120Heidelberg, Germany. 9 Department of Physics, University of Trento and TIFPA-INFN, Via Sommarive 14, 38123 Povo, Trento, Italy. 10 Laboratoire AimeCotton, CNRS, University of Paris-Sud, ENS Cachan, Batiment 505, Campus d’Orsay, 91405 Orsay, France. 11 Physics Institute, University of Zurich,Winterthurerstrasse 190, 8057 Zurich, Switzerland. 12 Department of Physics, University of Milan, Via Celoria 16, 20133 Milan, Italy. 13 Max Planck Institutefor Nuclear Physics, Saupfercheckweg 1, 69117 Heidelberg, Germany. 14 Istituto Nazionale di Fisica Nucleare, Sez. di Genova, Via Dodecaneso 33, 16146Genoa, Italy. 15 Institute of Physics and Technology, University of Bergen, Allegaten 55, 5007 Bergen, Norway. 16 Department of Physics, University of Oslo,Sem Sælandsvei 24, 0371 Oslo, Norway. 17 Department of Physics, University of Genoa, Via Dodecaneso 33, 16146 Genoa, Italy. 18 Stefan Meyer Institute forSubatomic Physics, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria. 19 Department of Physics, University of Pavia, Via Bassi 6, 27100Pavia, Italy. 20 Joint Institute for Nuclear Research, Dubna 141980, Russia. 21 Istituto Nazionale di Fisica Nucleare, Sez. di Padova, Via Marzolo 8, 35131 Padua,Italy. 22 Institute of Nuclear Physics of Lyon, CNRS/IN2P3, University Lyon 1, 69622 Villeurbanne, France. 23 Czech Technical University in Prague, FNSPE,Brehova 7, 11519 Prague 1, Czech Republic. 24 Department of Physics and INFN Bologna, University of Bologna, Via Irnerio 46, 40126 Bologna, Italy.25 Department of Physics, University of Napoli Federico II, Via Cinthia, 80126 Naples, Italy. Correspondence and requests for materials should be addressed toP.B. (email: [email protected]).

NATURE COMMUNICATIONS | 5:4538 | DOI: 10.1038/ncomms5538 | www.nature.com/naturecommunications 1


• AEgIS experiment is taking data (H production expected in 2016)

• Small-scale test of the Moiré deflectometer with p was performed

16

• 146 antiprotons recorded

The pattern of 146 antiprotons detected for the grating indirect contact with the emulsion is depicted in Fig. 2c. The highvisibility implies that the periodicity is well-defined in an area aslarge as 15! 6 mm2 since the data collapses onto one fringe bytaking the detected position modulo the extracted periodicity d ofthe pattern. To extract the periodicity, we employ the Rayleightest23 that is also widely used in astronomy24. The periodicity dand the relative rotation a of the pattern is found by maximizing

Z2 ¼ 2n

Xn

i¼1

sin2pd# yi

! " !2

þXn

i¼1

cos2pd# yi

! " !2" #

; ð2Þ

where n is the total number of antiprotons and yi¼ y0 # cos aþ x0 # sin a depicts the antiproton’s projected coordinate. Thisleads to an inferred periodicity of 40.22±0.02 mm, which isconsistent with the expected emulsion expansion of B1% and thenominal periodicity of 40mm. It is interesting to note that theanalysed area corresponds to 368 slits and, on average, only inevery second slit an antiproton is detected.

In Fig. 2b, the observed moire pattern for antiprotons is shown.The 241 events associated with antiproton annihilations wereaccumulated during the 6.5-h run of the experiment. TheRayleigh tests on sub-segments of the detected patterns reveallocal distortion due to the expansion/shear of the emulsion andallow the identification of regions with negligible distortion.We have restricted the areas to two-thirds of their initial size,which ensures a position uncertainty due to shear to be smallerthan ±1.2 mm.

Absolute deflection measurement. To determine the absoluteposition of the antiproton fringe pattern (parameter a in Fig. 2b),we conduct a comparison with the measurement with light.The results are represented in Fig. 3a,b where the detectedintensity is indicated by the red shading. The alignment isachieved by overlaying the contact patterns as depicted on theright of Fig. 3b. The moire pattern can now be directly comparedwith the Talbot–Lau pattern (left of Fig. 3b) to extract a possibledeflection.

For the quantitative analysis, we extract the orientation of theantimatter (Rayleigh test) and light patterns (Fourier transforma-tion as the data is discrete in space). We find that the relativeangle of the two antiproton patterns, which are 15 mm apart,deviates from the angle measured between the two correspondinglight patterns by Dy¼ 0.92±0.27 mrad.

This observation is consistent with independent systematicstudies of the distortion of emulsions on this large scale25. It isimportant to realize that this angle implies an intrinsic systematic

Hits

0 d/2y position

d0

10

20

30

40

50

Moiré Contact

0 0.2 0.4 0.6 0.8 1x position (mm)

0

0.2

0.4

a b

c0.6

0.8

1

y po

sitio

n (m

m)

0 40 80 1200

40

80

120

y po

sitio

n (µ

m)

x position (µm)0 40 80 120

0

40

80

120

y po

sitio

n (µ

m)

x position (µm)

9.8 µm

Antip

roto

ns

Ligh

t

Figure 3 | Comparison between photon and antiproton patterns. (a) The spatial positions of the detected antiprotons (blue dots) are compared with thesubsequently recorded light pattern (measured intensity indicated by the red shading). The Talbot–Lau fringe pattern provides the zero-force reference,presented here for the same exemplary detector area with ten annihilations as in Fig. 2a. (b) The antiproton and light measurements are aligned byoverlaying the two patterns obtained with the contact grating. The result of this procedure is visualized on the right, where the annihilation positionsof all antiprotons are folded into an area of 80! 80mm2. The moire and Talbot–Lau pattern depicted on the left, without any further alignment, can becompared to determine a shift. (c) The data is projected onto the y axis for quantitative analysis. A relative shift between moire and Talbot–Laupattern indicates that a force is present. The observed mean shift of 9.8 mm is consistent with a mean force of 530 aN.

Vis

ibili

ty

0

0.2

0.4

0.6

0.8

1

y position

100 aN

464 aN

2154 aN

MeasurementSimulation

Force (aN)101 102 103 104 0 d/2 d

Figure 4 | Monte Carlo simulation. A detailed simulation study based onthe expected energy distribution of the antiprotons (see Methods) showsthe visibility for increasingly large forces. As the observed pattern in thepresence of a force is an ensemble of differently shifted patternscorresponding to different transit times t the visibility consequentlydecreases. The measured fringe pattern exhibits a visibility of (71±10) %and is consistent with the result of this simulation. The error bar on themeasured visibility is determined via resampling; the error bar on themeasured force includes the systematic error bound and the one sigmastatistical error bound. The observed high visibility excludes that the fringepattern is shifted by more than one period and sets an upper limit for aforce present without the necessity of referencing.




Mini moiré results

68mm

Aghion S. et al., Nature Communications, 5, 4538 (2014)

Light / antiprotons comparison

- contact pattern as a reference for the alignement (grating shadow)- moiré pattern: shift detected! 'y = 9.8 ± 0.9(stat) ± 6.4(syst) µm(compatible with the measured magnetic field of ~10 G at the position of the deflectometer)

18

Results: (mini) Moiré test with antiprotons

The pattern of 146 antiprotons detected for the grating indirect contact with the emulsion is depicted in Fig. 2c. The highvisibility implies that the periodicity is well-defined in an area aslarge as 15! 6 mm2 since the data collapses onto one fringe bytaking the detected position modulo the extracted periodicity d ofthe pattern. To extract the periodicity, we employ the Rayleightest23 that is also widely used in astronomy24. The periodicity dand the relative rotation a of the pattern is found by maximizing

Z2 ¼ 2n

Xn

i¼1

sin2pd# yi

! " !2

þXn

i¼1

cos2pd# yi

! " !2" #

; ð2Þ

where n is the total number of antiprotons and yi¼ y0 # cos aþ x0 # sin a depicts the antiproton’s projected coordinate. Thisleads to an inferred periodicity of 40.22±0.02 mm, which isconsistent with the expected emulsion expansion of B1% and thenominal periodicity of 40mm. It is interesting to note that theanalysed area corresponds to 368 slits and, on average, only inevery second slit an antiproton is detected.

In Fig. 2b, the observed moire pattern for antiprotons is shown.The 241 events associated with antiproton annihilations wereaccumulated during the 6.5-h run of the experiment. TheRayleigh tests on sub-segments of the detected patterns reveallocal distortion due to the expansion/shear of the emulsion andallow the identification of regions with negligible distortion.We have restricted the areas to two-thirds of their initial size,which ensures a position uncertainty due to shear to be smallerthan ±1.2 mm.

Absolute deflection measurement. To determine the absoluteposition of the antiproton fringe pattern (parameter a in Fig. 2b),we conduct a comparison with the measurement with light.The results are represented in Fig. 3a,b where the detectedintensity is indicated by the red shading. The alignment isachieved by overlaying the contact patterns as depicted on theright of Fig. 3b. The moire pattern can now be directly comparedwith the Talbot–Lau pattern (left of Fig. 3b) to extract a possibledeflection.

For the quantitative analysis, we extract the orientation of theantimatter (Rayleigh test) and light patterns (Fourier transforma-tion as the data is discrete in space). We find that the relativeangle of the two antiproton patterns, which are 15 mm apart,deviates from the angle measured between the two correspondinglight patterns by Dy¼ 0.92±0.27 mrad.

This observation is consistent with independent systematicstudies of the distortion of emulsions on this large scale25. It isimportant to realize that this angle implies an intrinsic systematic

Hits

0 d/2y position

d0

10

20

30

40

50

Moiré Contact

0 0.2 0.4 0.6 0.8 1x position (mm)

0

0.2

0.4

a b

c0.6

0.8

1

y po

sitio

n (m

m)

0 40 80 1200

40

80

120

y po

sitio

n (µ

m)

x position (µm)0 40 80 120

0

40

80

120

y po

sitio

n (µ

m)

x position (µm)

9.8 µm

Antip

roto

ns

Ligh

t

Figure 3 | Comparison between photon and antiproton patterns. (a) The spatial positions of the detected antiprotons (blue dots) are compared with thesubsequently recorded light pattern (measured intensity indicated by the red shading). The Talbot–Lau fringe pattern provides the zero-force reference,presented here for the same exemplary detector area with ten annihilations as in Fig. 2a. (b) The antiproton and light measurements are aligned byoverlaying the two patterns obtained with the contact grating. The result of this procedure is visualized on the right, where the annihilation positionsof all antiprotons are folded into an area of 80! 80mm2. The moire and Talbot–Lau pattern depicted on the left, without any further alignment, can becompared to determine a shift. (c) The data is projected onto the y axis for quantitative analysis. A relative shift between moire and Talbot–Laupattern indicates that a force is present. The observed mean shift of 9.8 mm is consistent with a mean force of 530 aN.

Vis

ibili

ty

0

0.2

0.4

0.6

0.8

1

y position

100 aN

464 aN

2154 aN

MeasurementSimulation

Force (aN)101 102 103 104 0 d/2 d

Figure 4 | Monte Carlo simulation. A detailed simulation study based onthe expected energy distribution of the antiprotons (see Methods) showsthe visibility for increasingly large forces. As the observed pattern in thepresence of a force is an ensemble of differently shifted patternscorresponding to different transit times t the visibility consequentlydecreases. The measured fringe pattern exhibits a visibility of (71±10) %and is consistent with the result of this simulation. The error bar on themeasured visibility is determined via resampling; the error bar on themeasured force includes the systematic error bound and the one sigmastatistical error bound. The observed high visibility excludes that the fringepattern is shifted by more than one period and sets an upper limit for aforce present without the necessity of referencing.




uncertainty in the determination of the relative shift between thelight and antimatter patterns since one cannot know which parthas undergone the deformation. Assuming that both areas of theemulsion corresponding to contact and moire have changed thesame way on the centimetre scale, that is, half of the angulardeviation for each pattern, we can compare the relative positionsof the antiprotons with that of the light pattern as shown inFig. 3b. The contact patterns on the right overlay as these aredirect shadows of the grating (no force dependence), while anupward shift of the antiprotons in the force sensitive moirepattern is noticeable. For quantitative analysis, we collapse thedata onto one fringe (see Fig. 3c) and deduce the relative shift ofDymean¼ 9.8±0.9 mm (stat.) where the error is due to theuncertainties (one sigma) of the involved fits. Estimating abound on the systematic uncertainties, we repeat our analysisassuming that either the contact or the moire pattern has beenchanged due to the distortion. With that we find a minimal shiftof Dymin¼ 3.7±0.9 mm (stat.) and maximal shift of Dymax¼ 16.4±0.9 mm (stat.) leading to a shift of Dymean¼ 9.8±0.9 mm(stat.)±6.4 mm (syst.).

DiscussionThe observed shift of the moire pattern is consistent with a forceacting on the antiprotons. With the assumption of a mean velocityof v¼ 4.5" 106 ms# 1 implying a transit time of t¼ 5.6 ns, we finda mean force of F¼ 530±50 aN (stat.)±350 aN (syst.).

It is important to note that the mere observation of a patternsets an upper bound for the force being present. The impingingantiproton beam has a very broad velocity distribution due to thedegrading process in the foils. Thus, in the case that a force ispresent, the experimentally observed moire pattern is anensemble of differently shifted patterns corresponding to thetransit times t for different velocities. The results of a simulationof the performance of the moire deflectometer are depicted inFig. 4 and clearly reveal how the visibility vanishes forincreasingly large forces (a force of 10 fN reduces the visibilitybelow u¼ 10%). The observed visibility of 71% is consistent witha mean force of B500 aN. The visibility of the antiproton moirepattern on its own (not relying on additional referencing) is anindependent consistency check that the observed pattern isindeed shifted due to a force. Additionally with the observed highvisibility of the moire pattern, we exclude the possibility that theforce has shifted the pattern by more than one period (see Fig. 4).

The measured force could arise from a Lorentz force eithercaused by an electric field of B33 V cm# 1 in direction of thegrating period or a magnetic field component of B7.4 Gperpendicular to the grating period and antiproton direction.The latter is compatible with the measured magnetic field of

B10 G at the position of the deflectometer due to the fringefield of the trapping region and stray fields of neighbouringexperiments in the AD zone.

The results presented are a crucial step towards the directdetection of gravitational acceleration of antihydrogen with theAEgIS experiment. Its concept is based on the formation ofexcited antihydrogen through the charge exchange reaction ofelectromagnetically trapped antiprotons with bunched Rydbergpositronium. The resulting dipole moments of the antihydrogenatoms in a weak electric field allow their subsequent accelerationwith electric field gradients, thus forming a beam towards themoire deflectometer. The measurement of the antihydrogen’sarrival position is realized by detection of the annihilation of itsantiproton—thus using techniques presented here.

It is important to note that the expected absolute shift of theantihydrogen pattern due to gravity is comparable to the oneobserved in the current experiment. Although the gravitationalforce acting on antihydrogen is 10 orders of magnitude smallerthan the sensitivity level reached with the presented smallprototype deflectometer, the resolution of the setup can be simplyimproved by scaling up the deflectometer and the detector.A detailed discussion of the expected performance can be found inrefs 10,19. The main improvement is achieved by increasing thetransit time t (see equation (1)). Using a beam of antihydrogenatoms with a significantly lower velocity of B500 ms# 1 and adistance of 1 m between the gratings (this experiment v¼ 4.5" 106 ms# 1 and L¼ 25 mm) will improve the sensitivity by 11orders of magnitude (eight orders of magnitude due to slowervelocity and three orders of magnitude due to increased length of

38 39 40 41 42

Ang

le (m

rad)

–20

–10

0

10

20

Moiré Z2

Periodicity (µm)

20

40

60

0

Z2Contact

38 39 40 41 42Periodicity (µm)

Ang

le (m

rad)

–20

–10

0

10

20

40

80

120

160

0

Figure 5 | Rayleigh test. The results of the Rayleigh test applied on the antiproton data of the moire deflectometer and the contact grating showunambiguous maxima from which orientation and periodicity of the patterns are extracted.

0

0.1

0.2

0.3

0.4

0100 200 300 400 500 600

Energy of antiprotons (keV)

Pro

babi

lity

Figure 6 | Simulated energy distribution. A Monte Carlo simulationbased on the Geant4 toolkit provides an estimate of the kinetic energydistribution of the antiprotons reaching the moire deflectometer. Thiscalculation takes into account the degrading foil system, the magneticfield and the geometry of the AEgIS apparatus.

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5538 ARTICLE

NATURE COMMUNICATIONS | 5:4538 | DOI: 10.1038/ncomms5538 | www.nature.com/naturecommunications 5


•

• consistent with a B ~ 7.4 G

B ~ 10 G measured at the Moiré position

17Conclusions and future plans

• AEgIS aims at probing the WEP on antimatter• No direct measurement so far G

oal

Res

ults

• The working principle tested using antiprotons• Stray B field → no gravity measurement possible on p

• AEgIS is taking data

• First gravity measurements planned for the next years

• H production expected to be achieved later this year

Futu

re p

lans

• Longer term plans also include H-H spectroscopy

the weak equivalence principle with antimatter: the aegis...

Documents