A hydrogen beam to characterize the ASACUSA antihydrogen hyperfinespectrometer

C. Malbrunota,b,, M. Diermaierb, M.C. Simonb, C. Amslerb, S. Arguedas Cuendisb,1, H. Breukerc, C. Evansd,e, M.Fleckb,2, B. Kolbingerb, A. Lanzb, M. Lealid,e, V. Maeckelc, V. Mascagnad,e,3, O. Massiczekb, Y. Matsudaf, Y.

Nagatag, C. Sauerzopfb, L. Venturellid,e, E. Widmannb, M. Wiesingerb,4, Y. Yamazakic, J. Zmeskalb

aEuropean Organisation for Nuclear Research, 1211 Geneva 23, SwitzerlandbStefan-Meyer Institute for subatomic physics, Boltzmanngasse 3 1090 Vienna, Austria

cUlmer Fundamental Symmetries Laboratory, RIKEN, 2-1 Hirosawa, Wako, 351-0198 Saitama, JapandDipartimento di Ingegneria dell’Informazione, Universita degli Studi di Brescia, Brescia 25133, Italy

eIstituto Nazionale di Fisica Nucleare, Sez. di Pavia, 27100 Pavia, ItalyfInstitute of Physics, University of Tokyo, 3-8-1 Komaba, Meguro-ku, 153-8902 Tokyo, Japan

gDepartment of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, 162-8601 Tokyo, Japan

Abstract

The antihydrogen programme of the ASACUSA collaboration at the antiproton decelerator of CERN focuses onRabi-type measurements of the ground-state hyperfine splitting of antihydrogen for a test of the combined Charge-Parity-Time symmetry. The spectroscopy apparatus consists of a microwave cavity to drive hyperfine transitions anda superconducting sextupole magnet for quantum state analysis via Stern-Gerlach separation. However, the smallproduction rates of antihydrogen forestall comprehensive performance studies on the spectroscopy apparatus. Forthis purpose a hydrogen source and detector have been developed which in conjunction with ASACUSA’s hyperfinespectroscopy equipment form a complete Rabi experiment. We report on the formation of a cooled, polarized, andtime modulated beam of atomic hydrogen and its detection using a quadrupole mass spectrometer and a lock-inamplification scheme. In addition key features of ASACUSA’s hyperfine spectroscopy apparatus are discussed.

Keywords: atomic hydrogen, antihydrogen hyperfine structure, magnetic resonance, atomic beam

1. Introduction1

1.1. Motivations2

The hydrogen atom has motivated a plethora of ex-3

perimental and theoretical investigations. Presently,4

a compelling reason to pursue such studies originates5

from the growing field of low-energy antimatter re-6

search. To date antihydrogen is the only anti-atom7

that can be formed in a well-controlled environment.8

Corresponding authorEmail address: chloe.m@cern.ch (C. Malbrunot)

1present address: Physics Department, CERN, 1211 Geneva 23,Switzerland

2present address: Ulmer Fundamental Symmetries Laboratory,RIKEN, 2-1 Hirosawa, Wako, 351-0198 Saitama, Japan and Insti-tute of Physics, University of Tokyo, 3-8-1 Komaba, Meguro-ku, 153-8902 Tokyo, Japan

3present address: Dipartimento di Scienza e Alta Tecnologia, Uni-versita degli Studi dellInsubria and INFN sez. di Pavia, Italy

4present address: Max-Planck-Institut fur Kernphysik,Saupfercheckweg 1, 69117 Heidelberg, Germany

Atomic spectroscopy methods in magnetic traps already9

yield precise comparisons of the hydrogen and antihy-10

drogen spectra [1, 2, 3]. Further measurements of the11

antihydrogen ground-state hyperfine splitting (GS-HFS)12

are envisioned in a beam using a Rabi-type spectroscopy13

apparatus described in this manuscript. Any deviation14

in antihydrogen from the measured values in hydrogen15

would indicate a violation of the CPT-symmetry (the16

combined symmetry of charge conjugation, parity, and17

time reversal) which would be a clear signal for physics18

beyond the standard model of particle physics, poten-19

tially providing new insights in the matter-antimatter20

asymmetry puzzle. A measurement of the antihydrogen21

GS-HFS has the potential to yield one of the most pre-22

cise CPT-test on an absolute energy scale. A remarkable23

precision of 2 mHz (corresponding to 1.4 ppt) has been24

achieved in hydrogen maser experiments [4, 5, 6, 7, 8, 9]25

owing to long interaction times by mechanical confine-26

ment. Unfortunately, this method is not transferable27

to antihydrogen, which would annihilate on the confin-28

Preprint submitted to Nuclear Instruments and Methods in Physics Research A December 14, 2018

ing enclosure. Therefore, the method adopted within29

the antihydrogen program of ASACUSA (Atomic Spec-30

troscopy And Collisions Using Slow Antiprotons), pur-31

sued by the ASACUSA-CUSP group, at the Antiproton32

Decelerator (AD) of CERN is Rabi-type magnetic reso-33

nance spectroscopy [10, 11]. This technique requires34

the preparation of a polarized atomic (or molecular)35

beam. It is accomplished with magnetic field gradients,36

which result in spatial separation of atoms in di↵erent37

quantum states. Fig.1 shows the Breit-Rabi diagram for38

hydrogen and antihydrogen indicating the behavior of39

the atoms in an external magnetic field as a function40

of their magnetic moments orientations. Atoms that41

align their magnetic moments with the external mag-42

netic field have a lower energy in higher fields and are43

called high field seekers (hfs). Atoms which follow a44

gradient towards lower magnetic fields are called low45

field seekers (lfs). This property allows spin state se-46

lection in so-called Stern-Gerlach type apparatus and is47

at the heart of the measurement technique adopted here.48

Quantum transitions between lfs and hfs states are in-49

duced by means of an oscillating (or rotating) magnetic50

field. A second magnetic field gradient removes those51

atoms, that have changed their magnetic moment and52

the remaining ones are detected. A resonance structure53

can be recorded as a drop in counting rate (signal) by54

scanning the frequency of the oscillating magnetic field.55

Kusch et al. [13, 14] applied Rabi-type spectroscopy to56

determine the ground-state hydrogen hyperfine splitting57

(1.42 GHz) to an absolute precision of 50 Hz. This58

value was improved by more than an order of magnitude59

using the apparatus described in the present manuscript60

[15].61

1.2. ASACUSA’s antihydrogen hyperfine spectrometer62

The ASACUSA-CUSP group employs a set of63

charged particle traps for the production of a polarized64

beam of antihydrogen. Antiproton bunches extracted at65

energies of 5.3 MeV from the AD are further slowed66

down by ASACUSA’s radiofrequency quadrupole de-67

celerator [16] to 100 keV and then accumulated in a68

Penning-Malmberg trap (MUSASHI) [17].69

In parallel, positrons from the +-decay of 22Na are70

accumulated in a second trap. Antiproton and positron71

bunches are transferred to the mixing trap, which uses72

multi-ring electrodes and superconducting double anti-73

Helmholtz coils to provide both the confining electric74

and magnetic fields for charged particles and the mag-75

netic field gradients for polarization of neutral antihy-76

drogen [18, 19, 20]. ASACUSA reported the observa-77

tion of antihydrogen atoms in a field-free environment78

2.7 m downstream of the mixing region [21], a nec-79

essary step before attempting a spectroscopy measure-80

ment. The quantum-state distribution of antihydrogen81

atoms exiting the formation apparatus was published82

[22] and showed a too small fraction of ground-state83

atoms to achieve the spectroscopy goal. The current fo-84

cus of the collaboration is thus to significantly increase85

the number of ground-state atoms produced.86

For the GS-HFS measurement the antihydrogen87

atoms extracted from the mixing trap will pass a mi-88

crowave cavity for state conversion and a superconduct-89

ing sextupole magnet for state analysis before being de-90

tected by an annihilation detector, as in Fig. 2.91

To guarantee a large acceptance for the scarcely pro-92

duced polarized ground-state antihydrogen the spec-93

troscopy beamline has an open diameter of 100 mm,94

which presents a noteworthy di↵erence from conven-95

tional Rabi-type setups. A cavity of the so-called strip-96

line geometry [23, 24, 25] produces the oscillating mag-97

netic field for driving the hyperfine transitions. This98

resonator type was chosen, as it provides a uniform mi-99

crowave field over the large opening diameter. The cav-100

ity is followed by a superconducting sextupole magnet101

able to focus lfs ground-state antihydrogen atoms of ve-102

locities up to 1000 ms1 onto the antihydrogen detec-103

tor, directly downstream of the sextupole. The detector104

concept is based on the combination of calorimetry and105

track reconstruction measurements. It comprises an in-106

ner BGO crystal read out by multi-channel PMTs pro-107

viding 2D-position resolution and charge deposit infor-108

mation [26, 27], surrounded by two layers of 32 scin-109

tillator bars each, assembled in a hodoscope geometry110

for tracking charged annihilation products (i.e. mainly111

pions) [28]. This apparatus was recently completed by112

two additional layers of 2 2 mm2 square scintillating113

fibres perpendicular to the hodoscope bars to improve114

the spatial resolution in the beam direction [29].115

For characterization of the hyperfine spectrometer, the116

cavity and sextupole magnet, developed for the antihy-117

drogen experiment, were coupled to an atomic hydrogen118

source.119

A detailed description and performance assessment120

of each part of the hydrogen apparatus is provided in121

the following sections. The source of ground-state hy-122

drogen and its performance is detailed in §2.1, including123

a description of the polarization and velocity selection124

as well as modulation stages. The spectroscopy appara-125

tus is described in §2.2: §2.2.1 details the cavity design126

and performances, §2.2.2 the Helmholtz coils’ assem-127

bly for the generation of the external static magnetic128

field, and §2.2.3 the magnetic shielding enclosing the129

cavity and Helmholtz coils setup while §2.2.4 provides130

2

Figure 1: Breit-Rabi diagram for hydrogen and antihydrogen in the presence of a small static magnetic field (modified from [12]). The microwavetransition 1 on hydrogen was measured with the apparatus described in this manuscript. The experimental setup to address both and transitionswill be the subject of a future publication.

information on the superconducting sextupole. The fi-131

nal descriptive section, §2.3, deals with the hydrogen132

detection apparatus. Finally, §3 provides the result of133

a set of characterization measurements performed with134

the apparatus.135

2. Hydrogen experimental apparatus136

The hydrogen beamline is shown in Fig. 3. It com-137

prised several vacuum chambers that were separated138

by apertures enabling di↵erential pumping. The first139

chamber enclosed the hydrogen source providing a cold140

( 50 K) beam of atomic hydrogen to the second cham-141

ber housing a set of two permanent sextupole mag-142

nets, which selected a range of velocities and polar-143

ized the beam. The third chamber housed a chopper144

which modulated the beam. The spectroscopy apparatus145

was placed directly downstream of the chopper cham-146

ber. The cavity was surrounded by a pair of Helmholtz147

coils and enclosed in a 2-layers mu-metal box to shield148

the stray and earth magnetic fields. Next, the hydro-149

gen beam reached the bore of the superconducting sex-150

tupole magnet for spin-state analysis. In the final cham-151

ber a quadrupole mass spectrometer (QMS) selectively152

counted protons (mass-1 particle), which emerged from153

the crossed-beam ionization region using electron im-154

pact. The aforementioned modulation of the beam re-155

sulted in a periodical structure of the detected mass-1156

rate and enabled velocity measurements from the time-157

of-flight and discrimination from the background via158

lock-in amplification. A laser shining through the en-159

tire apparatus was used for alignment as well as time-160

of-flight determination (see §3.1). With the hydrogen161

source ignited the pressure was typically 103 Pa in the162

first pumping stage and better than 5 108 Pa in the163

detection chamber.164

2.1. Polarized and modulated atomic hydrogen source165

The design and operation principles of the atomic hy-166

drogen source is similar to the one described in [30].167

In the present setup, ultra pure molecular hydrogen168

gas was provided by a hydrogen generator (Packard169

9100) via electrolysis of deionised water. A H2 flow170

of typically 0.6 SCCM5 was introduced into a cylin-171

drical pyrex glass tube via an electronically control-172

lable flow meter (Brooks SLA5850). A solid state mi-173

crowave generator (Sairem, GMS 200 W ind C) pro-174

duced 2.45 GHz microwaves that were fed with an175

input power of 60 W via two N-type connectors and176

coaxial cables into the pyrex tube. The plasma was177

ignited with an electrostatic discharge gun and main-178

tained by twin slotted Lisitano type radiators [30] sur-179

rounding the pyrex glass discharge tube. A picture of180

5SCCM is a flow unit representing a standard (at T = 273.15 Kand P = 105 Pa) cubic centimeter per minute.

3

Figure 2: Schematic of the ASACUSA-CUSP apparatus for the measurement of the GS-HFS of antihydrogen. The spectroscopy apparatus isindicated by the gray box.

the glass tube and special structure of the radiator is181

shown in Fig. 4. Atomic and molecular hydrogen ex-182

ited through the small orifice of the pyrex tube into the183

vacuum system and were cooled by passing through a184

PTFE (Polytetrafluoroethylene) tubing kept under cryo-185

genic temperatures (20 K) by the cold-finger of a cry-186

ocooler. Two orientations of the source with respect to187

the beam axis were tried. The straight configuration,188

shown in Fig. 3, allowed for atoms with higher velocity189

components traveling through the center of the PTFE190

tubing with minimal interactions with the walls to pass191

through, while a 90 orientation, pictured in Fig. 5, al-192

lowed for more interactions and suppressed the high ve-193

locity part of the beam.194

The cracking eciency of the hydrogen source is de-195

fined as:196

D = (Ho↵2 Hon

2 )/Ho↵2 (1)197

with Hon2 and Ho↵

2 being the amount of molecular hydro-198

gen in the beam when the hydrogen source is in opera-199

tion or not ignited, respectively. Operational cracking200

eciencies were measured in a dedicated setup, where201

the source was directly connected to the detector. At202

a source pressure of 30 Pa (equivalent to an incoming203

molecular flux of 0.6 SCCM), maximum cracking ef-204

ficiencies around 0.8 were found at room temperature205

which is less than what is reported in the literature ([30]206

indicates for example 0.9 at the same pressure). Inves-207

tigation gave no clear reason for this slightly lower e-208

ciency. The hydrogen rate was sucient to perform the209

experiment and therefore no further improvements were210

sought.211

The cooled hydrogen beam exited the PTFE tubing212

towards a skimmer of 1 mm in diameter and reached the213

second vacuum chamber hosting the set of two perma-214

nent sextupole magnets. To our knowledge, the tech-215

nique to form a polarized and velocity-selected beam216

using a sextupole magnet doublet has not been dis-217

cussed in the literature. Some details on the setup and218

working properties will therefore be provided in the fol-219

lowing. The magnets had an open diameter of 10 mm220

and a pole field of 1.36 T, which corresponds to a221

gradient-constant of G0=108,800 Tm2 (a definition of222

this strength and more details on the properties of sex-223

tupole fields are given in subsection 2.2.4, in context224

with the superconducting analysis magnet). With an225

mechanical length of 65 mm, an integrated gradient (fo-226

cusing strength) of 7,072 Tm1 can be estimated, in rea-227

sonable agreement with the design value of 7,435 Tm1228

[32]. The magnets were made of iron-dominated poles229

(permendur) and samarium-cobalt Sm2Co17 permanent230

magnet blocks acting as magnetic flux generator en-231

closed in a non-magnetic titanium frame. The first mag-232

net provided the initial spin-polarization of the beam by233

removing the two hyperfine states which were attracted234

to high fields (hfs). In conjunction with the second235

magnet and an aperture of 3 mm in diameter between236

the two magnets a narrow velocity range was selected.237

The magnet’s support mechanism governed a symmet-238

ric longitudinal motion of the two sextupoles with re-239

4

Figure 3: Top : technical drawing of the atomic hydrogen beamline (dimensions in mm). Bottom : picture of the apparatus in which the shieldingand Helmholtz coils around the cavity were removed. The hydrogen source is mounted directly upstream of the first vacuum chamber (the so-calledstraight-source configuration) and the plasma is ignited. The quadrupole mass spectrometer (QMS) stage is hidden behind the superconductingmagnet.

5

Figure 4: Photograph of the hydrogen source (modified from [31]).Microwaves are introduced via two N-type coaxial connectors (coax-ial feeds). The slotted line antennas radiate into the glass tube andform a TE011 mode. Molecular hydrogen is introduced at the inlet ofthe pyrex tube (on the left side) and atomic hydrogen exits from theright side into the vacuum system of the first chamber.

Figure 5: Photograph of the source mounted with a 90 orientationwith respect to the beam axis. Atomic hydrogen (originating from theleft-side of the photograph) travel through the PTFE tubing which isbent and enclosed in aluminium blocks cooled via the cold-finger ofa cryocooler. The green laser light originating from the front of thepicture can be seen passing the tubing along the beam axis towardsthe skimmer.

spect to the midway aperture, see Fig. 6. Since the fo-240

cusing length depends on the atom velocity, only a given241

velocity component, depending on the distance between242

the sextupole magnets (ds), was focused onto the aper-243

ture and went through, as illustrated in Fig. 7.244

The velocity-selected beam entered the third vacuum245

chamber through an aperture of 5 mm in diameter. In246

this chamber, a tuning fork chopper (Scitec CH-10)247

modulated the beam. It operated with a maximal open-248

ing of 5 mm, a duty cycle of 50 % and a fixed frequency249

of 178 Hz. The modulation enabled a statistical mea-250

surement of the time-of-flight (TOF) of the atoms from251

the chopper to the detector, by comparison of the detec-252

tor signal to a sinusoidal reference signal from the chop-253

per driver. The operation principle and chopper design254

originated from [33] which pioneered the development255

of helium-temperature hydrogen sources.256

Figure 8 shows simulations of the sextupoles’ veloc-257

ity selection compared to experimental results based on258

TOF measurements (see §3.1) for the 90 source ori-259

entation. The measurements were done on a dedicated260

setup where the cavity and the downstream supercon-261

ducting sextupole were removed and the latter replaced262

by a set a permanent sextupoles, installed directly after263

the chopper chamber, to focus the beam. The distances264

between the source and the sextupole doublet and the265

chopper were however identical to the ones in Fig. 3.266

The distance between the chopper and the QMS detec-267

tor in the configuration used for this velocity character-268

ization was 2.2 m (about 0.5 m less than in the presently269

described setup, see Fig. 3). The measured data lie be-270

tween the two assumed initial beam distributions in the271

simulation and the trend is well reproduced.272

The achieved level of polarization of the beam by273

this magnet assembly has been studied in simulations274

which indicated a proportion of low-field seeking states275

( lfslfs+hfs ) of more than 90 %. The experimental deter-276

mination of the polarization is hindered in the herein277

described apparatus because, apart from a possible hfs278

contamination, only one of the two low-field seeking279

states present in the beam can be addressed with the 1280

transition, see Fig.1. An upgraded apparatus able to ad-281

dress the content of both lfs states (through the 1 and282

1 transitions) and therefore determine the polarization283

of the beam will be described in a future publication.284

2.2. Spectroscopy apparatus285

The spectroscopy apparatus, composed of the mi-286

crowave cavity inducing transitions between the inter-287

nal states of ground state hydrogen, and the supercon-288

ducting sextupole magnet analyzing the spin state, was289

6

Beam! magnet 1! magnet 2!

midway!aperture!

(exchangeable)!

toothed!track!

gear!wheel!

10mm! 65mm! ds!

rotary!feedthrough!

hand wheel!

sliding!rails!

hole circle!

retainerknob!

aperture!holder!

Figure 6: Annotated technical drawing of the two permanent magnetsassembly for beam polarization and velocity selection.

separated from the chopper chamber by an additional290

aperture. Two types of apertures were used: the first291

type had a wall thickness of 3 mm and an open diame-292

ter of 4 mm, producing a narrow beam of approximately293

8 mm in diameter at the cavity centre. The second aper-294

ture type, to increase the beam diameter at the cavity295

for systematic studies, while retaining a good di↵eren-296

tial pumping, was made of a 100 mm long pipe with a297

diameter of 15 mm, producing a beam with a diameter298

of approximately 22 mm in the cavity.299

2.2.1. Cavity300

The cavity design has been detailed elsewhere [23,301

24, 25]; in short it is a pillbox shaped strip line resonator302

(i.e composed of two parallel conducting plates) closed303

o↵ by fine metallic meshes in the direction of the beam,304

allowing close to 96 % transparency for the incoming305

atoms while keeping the RF field from leaking out of the306

chamber, see Fig. 10. The meshes were manufactured307

from a 100 µm thick sheet of stainless steel chemically308

etched to obtain the meshed structure of 5 mm grid size,309

which was then gold-plated.310

The cavity design was motivated by the requirement of311

a high RF-field homogeneity in the plane perpendic-312

ular to the beam axis. The length of the conducting313

plates (measured along the beam, i.e. z direction) had314

to be an integer multiple of the desired resonance half-315

wavelength (it was chosen to be Lcav=105.5 mm corre-316

sponding to half the wavelength of the zero-field hy-317

perfine transition at 1.42 GHz). In contrast the distance318

between the plates could be chosen freely and was set319

to 100 mm, matching the pipe diameter for a standard320

CF100 vacuum flange. Such a cavity consisting of a321

strip line inside a pillbox, can support two degenerate322

transverse electromagnetic (TEM) modes with similar323

resonant frequencies. Fig. 9 illustrates the magnetic324

field distribution of the two modes. In order to retain325

only the desired odd mode, the even mode was sup-326

pressed in the frequency region of interest by addition327

of “wing”-structures (see Fig. 10) to selectively de-tune328

it.329

Simulations show that this geometry reached330

a field inhomogeneity in the plane perpen-331

dicular to the beam direction (x-y plane) of332

2(Bmax Bmin)/(Bmax + Bmin) 3% [25]. Along333

the beam (z direction), the field amplitude follows a334

sin(z/Lcav) distribution: the field vanishes in the center335

of the cavity and has two maxima at the front and back336

walls of the resonator. Thus the magnetic field points at337

opposite directions in the two half-volumes. This field338

configuration leads to a “double-dip” structure in the339

resonance spectrum, as seen in Fig. 11.340

7

Figure 7: Conceptional sketch of the velocity selection (modified from [34], z-axis not to scale). Atoms in the correct spin configuration, theso-called low-field seekers (lfs, in red) will be bent onto the aperture with a velocity-dependent focal radius. Atoms in a high-seeking state (hfs, ingreen) will be bent away by the first magnet. The straight, dashed and dotted lines indicate the trajectories of atoms with di↵erent velocities.

0 20 40 60 80 100 120 1401000

1200

1400

1600

1800

2000

ds (mm)

velo

city

(m/s

)

measured velocitiessimulation results with a divergent beamsimulation results with a parallel beam

Figure 8: Velocity selection as a fonction of the distance ds betweenthe sextupoles. The velocities were measured by time-of-flight, see§3.1. The measurements are compared to simulations where a diver-gent beam from the source was assumed (red solid line). In this con-figuration, the outgoing beam from a point-like source was assumedto be distributed within an opening angle ↵ of 2 (200 angles simu-lated with ↵2 homogeneously distributed) and with initial velocitiesbetween 200 and 2000 m/s (181 homogeneously distributed velocitieswere simulated). A parallel beam configuration was also simulatedfor comparison (green dashed line). Here, the source had a radius rof 5 mm and the atoms were originating from a homogeneously dis-tributed r2 with again 181 di↵erent velocities in the range from 200 to2000 m/s. For both simulations the maximum of the velocity distribu-tion recorded after the doublet is indicated.

X

Y

(a) (b)

Figure 9: Magnetic field distribution of the desired odd (a) and theundesired even mode (b) generated inside the cavity (modified from[25]).

8

Mesh

Wings

Contact springs

X

Y

Z

beam direction

Tuningdisks

striplines

Antennas

150 mm

100

mm

Figure 10: Photograph of the cavity used to drive the hyperfine transi-tion in hydrogen/antihydrogen. The central cavity body and the backclosing flange are visible. The front closing flange is removed to re-veal the inner structure of the cavity: the two strip lines resonatorswhich are 150 mm wide, 105.5 mm long (in beam direction) and sep-arated by a distance of 100 mm, the wing structures and the tuningdisks. The openings for the hydrogen/antihydrogen beam are closed-o↵ by fine gold-plated mesh constraining the RF-field inside the cav-ity. The gold-plated contact springs ensure a good electrical contactbetween the closing flanges and the central body, as well as betweenthe resonators and the flanges. The antennas assembled around thecavity for injection and pick-up of the RF-field are connected viafeedthroughs to the external circuit (see Fig. 14). As shown in Fig. 9,the magnetic field vector points in the x-direction.

341

The cavity consists of a stainless-steel central body342

closed o↵ with copper seals by two modified CF400343

flanges to match the high vacuum requirements of the344

setup. The cavity is equipped with four ports onto which345

UHV-compatible feedthroughs (PMB Alcen) are con-346

necting antennas to the external apparatus. The anten-347

nas lengths were adjusted to achieve an overcritical cou-348

pling necessary to reduce the quality factor of the cavity.349

This was required to retain a few MHz excitation range350

to measure the transitions at several external magnetic351

fields of the order of a few gauss (see §2.2.2). In the352

original design two ports for feeding the microwaves353

in-phase and two ports for pick-up and analysis of the354

signal were envisioned. However, the interference pat-355

-30 -20 -10 0 10 20 30

0.5

1

1.5

2

2.5

3

3.5

Bo

sc (

µT

)

0.0

0.2

0.4

0.6

0.8

1.0

Sta

te c

on

vers

ion

pro

ba

bili

ty

0.0

0.5

1.0 -30 -20 -10 0 10 20 30

Pro

ba

bili

ty

Detune (kHz)

Figure 11: Results of numerical solutions of the optical Bloch equa-tions for a two-states system in a strip line cavity design. The state-conversion probability is given as a function of the de-tuning fre-quency and the amplitude of the oscillating magnetic field Bosc. A mo-noenergetic beam of 1000 ms1 and a cavity length of 105.5 mms areassumed. The horizontal line indicates the required driving strengthto reach the first complete state conversion (“-pulse”). The bottomplot is the projection of the state-conversion probabilities at the linerevealing the characteristic “double-dip” lineshape.

9

tern was found to be very sensitive to slightly di↵er-356

ent electrical lengths of the antennas. Therefore in a357

measurement run, one port was connected to a signal358

generator (Rohde & Schwarz SML02), locked to a ru-359

bidium frequency standard (SRS FS725), via a 42 dB360

amplifier (Mini Circuits ZHL-10W-2G(+)) and a stub-361

tuner (see discussion below). The opposing port was362

used to pick-up and monitor the signal using a spectrum363

analyzer (Agilent Technologies N9010A) connected to364

the same rubidium frequency standard and the remain-365

ing two ports were terminated with 50 connectors, as366

indicated in Fig. 12.367

A comparison of the simulated transmission pattern and368

experimental measurements showed a detuning of the369

desired mode by 26 MHz, necessitating the addition of370

tuning disks (see Fig. 10). It was however observed371

that the central frequency was more eciently tuned by372

changing the distance between the meshes (influenced373

also by the pressure in the cavity, atmospheric pressure374

or vacuum) than by the tuning disks. The length of375

the cavity was therefore tuned by adding 2 mm shims376

between the outer flange of the cavity and the closing377

meshes.378

Flexible gold-plated CuBe2 contact springs (Fig. 10)379

ensure a good electrical connection between the two380

halves of the cavity and close the gap formed by the381

vacuum seal which would cause mode distortion. Spot-382

welding of the springs onto the cavity structure was nec-383

essary to ensure a stability of the connections against384

movements and vibrations and a better reproducibility385

of the transmission pattern. Nevertheless, external tun-386

ability and adjustment of the quality factor was required.387

A coaxial double slug tuner (Microlab FXR SF-31N),388

providing a tunable impedance matching was thus in-389

serted between the amplifier and the input port of the390

cavity. The typical microwave power injected into the391

cavity was of the order of 0.3 mW to drive one half of a392

Rabi oscillation (“-pulse”).393

Figure 13 shows the transmission scattering parame-394

ter S 21 (port 2 being the readout port and port 1 the input395

port) after impedance adjustments using the double slug396

tuner, where fR indicates the resonance frequency of the397

cavity and f the width of the resonance at -3 dB. The398

quality factor, Q= fR f 120 matches well the require-399

ment of a 4 MHz operational bandwidth to allow excita-400

tions within the range of 1420-1424 MHz.401

2.2.2. Helmholtz coils402

In the presence of a static magnetic field, the degen-403

eracy of the hydrogen hyperfine triplet states is lifted404

as illustrated by the Breit-Rabi diagram in Fig. 1. Sev-405

eral transitions are possible between the four hyperfine406

Rubidium frequency standard

Spectrum analyser

CAVITY

50 Ω

50 Ω

Signal generator

Amplifier

Stub tuner

Figure 12: Exciting scheme of the cavity. The RF field from a signalgenerator stabilized by a rubidium standard clock is amplified andinjected via a stub tuner to one port of the cavity. The field is picked-up at another port and readout by a spectrum analyser also stabilized infrequency by the same rubidium clock. All other ports are terminatedwith 50 connectors.

1.38 1.4 1.42 1.44 1.46-20

-10

0

10

20

30

Frequency (GHz)

Pow

er (d

B)

∆ f

fR

Figure 13: Measured transmission scattering parameter (S 21) betweenthe readout and the input port revealing an isolated peak at the correctfrequency and of the desired width.

10

states which can be driven, depending on the relative407

orientation of the RF and static magnetic fields. In the408

setup reported here, a set of Helmholtz coils surrounded409

the spin flip cavity, producing a field perpendicular to410

the incoming particle beam and parallel to the oscillat-411

ing RF field, see Fig. 14. This configuration allows to412

drive the 1 transition (see Fig. 1). The external mag-413

netic field enters only in second order for this transi-414

tion6, making its determination less sensitive to field in-415

homogeneities. Therefore Helmholtz coils producing a416

field inhomogeneity (|B|/|B|) better than 1% in the vol-417

ume of interest could be used.418

The coils had radii of 235 mm (at center of wiring,419

the innermost radius was 220 mm) and 90 windings (10420

rows, 9 windings/row). They were wound with a cop-421

per wire of 1.6 mm in diameter onto a support made of422

fiberglass loaded with epoxy. The coils were mounted423

on aluminum profiles fixed on the side of the cavity by424

threaded brass rod (see Fig. 14), which, together with425

aluminum cylinders were used for accurate spacing of426

the coils. The distance between the coils was optimized427

in the presence of a magnetic shielding, described in428

§2.2.3, to produce the most homogeneous field in the429

region of interest. The optimal distance was found to be430

214 mm which is slightly smaller than the design radius431

of the coils due to the presence of the shielding.432

The current to the coils, connected in series, was deliv-433

ered by a stable power supply (Heinzinger PTNhp) and434

monitored with a digital multimeter (Keithley 2001).435

The current was set between ±1 A, corresponding to436

a maximum magnetic field of 459 µT and a change in437

the 1 transition frequency of a few tens of kHz (see438

Fig.19).439

2.2.3. Magnetic shielding440

To minimize the influence of external stray magnetic441

fields, such as the Earth’s or the downstream sextupole442

magnet’s, in the interaction region, a cuboid two-layer443

magnetic shielding made of mu-metal was built and as-444

sembled around the cavity and Helmholtz coils. The445

outer dimensions (width length height) of the in-446

ner and outer layer were 531 531 606 mm3 and447

561 561 636 mm3 with a thickness of 1 mm and448

2 mm, respectively. Two three-axes flux gate magne-449

tometers (Bartington Mag-03IE1000 read out with Bart-450

ington Decaport) were placed on each side of the cav-451

ity to monitor the magnetic field and any field fluctua-452

tions inside the shielding (Fig.14). The shielding factor,453

6 f1 =E0

h (1 + 12 x2) where x = (gJgI )µB

E0H, E0 is the transition

energy in zero-field, µB the Bohr magneton, gJ , gI the electronic andnuclear g-values and H the strength of the external magnetic field.

cavityfeedthrough

3-axes flux-gate assembly

Helmholtz coils spacer

Helmholtz coils

Figure 14: Photograph of the Helmholtz coils assembly mountedaround the microwave cavity. One of the three-axes flux gate mag-netometers (see §2.2.3) is visible on the flange of the cavity. The striplines are aligned horizontally (not visible) leading to a parallel align-ment of the oscillating and the static magnetic fields, as required todrive the -transition.

the ratio of inside- to outside-shielding magnetic field454

strengths measured, of the configuration depends on the455

orientation of the external field, as the layers have open-456

ings larger than 100 mm in diameter in the axial direc-457

tion, where the beam pipe enters and exits. A COM-458

SOL simulation, assuming a mu-metal relative perme-459

ability of µr > 20, 000, gave shielding factors of typi-460

cally 150 for static axial fields and 800 for static radial461

fields. To experimentally determine the shielding fac-462

tor one additional flux gate magnetometer was placed463

outside the shielding to monitor the inside and outside464

fields in parallel. This was done when the apparatus465

was installed at the ASACUSA antihydrogen setup in466

the hall of the AD. However, only the inner shielding467

layer was present for this measurement. The changes of468

the internal and external stray fields related to the cycle469

of the AD (100 s) could be monitored. A radial shield-470

ing factor of 42 was measured. Similar measurements471

were performed at the hydrogen setup during a ramp-up472

of the superconducting sextupole and a radial shielding473

factor of 54 and 1470 was measured for a single layer474

and two layers of shielding respectively. Axial shielding475

factors are highly dependent on the configuration of the476

external field and are thus dicult to compare experi-477

mentally. The higher measured radial shielding factor478

than simulated can be explained by the conservative µr479

chosen for mu-metal in the simulation.480

11

2.2.4. Superconducting Sextupole481

The spin-state analysis after the interaction is per-482

formed through magnetic sextupole fields, similar to the483

initial beam polarizer. In the radial plane this field con-484

figuration can be parametrized by485

~Br =B0

r20·

x2 y2

2xy

!(2)486

where B0 denotes the field strength at radius r0. The487

absolute value of the magnetic field |B| is proportional488

to r2, the force on the magnetic moment of a parti-489

cle is proportional to the gradient ~r|~B|. Therefore sex-490

tupole magnets produce forces which point radially and491

scale linearly with the distance from the beam axis in492

the regime of field-independent moments. As a conse-493

quence the particles follow harmonic trajectories in the494

radial plane (see Fig. 7). Such a field is characterized by495

the constant ratio of the gradient to the radius496

G0 =1r@|~B|@r= 2

B0

r20. (3)497

In contrast to normal Stern-Gerlach magnets with con-498

stant gradients a sextupole configuration enables two-499

dimensional focusing (defocusing) of a beam of lfs500

(hfs), similar to optical lenses.501

The combination of the quadratic radius dependence502

and the requirement of a large acceptance for antihy-503

drogen (aperture of 100 mm) translates into strong mag-504

netic fields at the poles, hence supplied by supercon-505

ducting coils designed and constructed by Tesla Engi-506

neering Ltd. The coils were placed in a vacuum iso-507

lated tank filled with liquid helium. The heat load on508

the inner vessel is absorbed by a cryocooler which pre-509

vents the boil o↵ of the helium and enables contin-510

uous operation. The warm bore ( 90 K) serves di-511

rectly as the vacuum pipe of the beam experiment and512

can be connected to the adjacent components via stan-513

dard CF100 flanges. A power supply (SMS550C from514

Cryogenic Limited) provides currents up to 400 A to515

the multi-layer bent racetrack coil geometry. The de-516

sign magnetic field of B0=2.42 T is produced at a radius517

of r0=50 mm at the maximum current. The gradient-518

constant is G0=1936 Tm2. The focusing strength of a519

sextupole magnet of e↵ective length L is given by the520

axial integral over the gradient constantR

G0(z)dz. With521

L = 220 mm the expected integrated gradient amounts522

to G0dL=436 Tm1 at 400 A. A measurement at room523

temperature and at 0.8 A yielded, after scaling to 400 A,524

G0dL=515 Tm1, which is even higher than the design525

value.526

2.3. Hydrogen Detection527

A quadrupole mass spectrometer (QMS) (MKS528

Microvision 2 100 D in crossed beam configuration)529

was placed at the end of the beamline and tuned to530

identify particles which atomic mass is one to detect531

atomic hydrogen. The overall eciency of the QMS for532

detection of hydrogen was around 108. The QMS was533

mounted onto translational stages which could move the534

detector in a plane perpendicular to the incoming beam535

for investigating beam profiles and signal optimization.536

The typical area scanned was about 112 mm2 ( ±4 mm537

in the horizontal direction and ±7 mm in the vertical538

direction) and the typical step sizes were of the order of539

a millimeter, which is much larger than the minimum540

step sizes the stage could perform. The on-board single541

channel electron multiplier (SCEM), powered with542

an external high voltage, amplified the signal which543

was fed into another external amplifier (LeCroy - LRS544

333). The total signal amplification was of the order of545

20 dB. The signal was then discriminated, converted to546

TTL and read out by a data acquisition card (NI ADC547

module: PCIe-6361). Figure 15 shows a typical pulse548

after amplification as well as the signal readout scheme.549

High molecular hydrogen background decreases550

the atomic beam detection eciency. Both active and551

passive background suppression methods were there-552

fore used. A non-evaporable getter pump (NEG), in553

combination with two-stage turbo molecular pumping,554

enabled a vacuum level better than 5108 Pa in the555

QMS chamber. Additionally, digital data processing556

using lock-in amplification techniques enabled further557

discrimination against background. Information on558

the phase of the tuning fork chopper (see §2.1) was559

obtained by feeding the monitor signal of the chopper560

driver to a sampling voltage input of the NI ADC561

module. A software algorithm separated the modulated562

content of the count rate from the constant background563

rate [35].564

565

3. Characterization measurements566

3.1. Time-of-flight and velocity measurements567

The time-of-flight t of the hydrogen atoms was deter-568

mined by relating the time-dependent beam count rate569

at the QMS detector and the time-dependent signal of570

the alignment laser on a photo-diode (as a proxy for571

the chopper opening) to the phase of the chopper ref-572

erence signal recorded by the software lock-in ampli-573

fier. From those measurements the mean velocity v of574

the beam was extracted in the following way: v is the575

12

QMS$%$single$pulses$

Amplifier$ discriminator$ NIM$to$TTL$DAQ$card$NI$X%series$counter$

Computer$

Figure 15: Top: typical single ion pulse from the SCEM measuredwith an oscilloscope. Bottom: schematic of the readout chain.

time-of-flight of the hydrogen atoms over the distance576

L between the chopper and the QMS detector, which is577

evaluated using the di↵erence between the phase of a578

laser L shining through the entire apparatus (the time-579

of-flight being negligible) and the phase of the beam sig-580

nal , over the chopper reference signal with frequency581

fch:582

v =Lt=

2 L fch

L(4)583

where L and are expressed in radian and fch is ex-584

tracted from the lock-in amplifier software. The phase585

L is determined from the laser signal, read out by a586

photodiode behind the QMS detector, while is eval-587

uated using the beam count rate measured at the QMS588

as a function of the phase of the chopper (Fig.16). The589

count rate has two components: a constant background590

and a sinusoid-shaped modulated beam signal. Several591

fits to extract were attempted. The one giving the592

best results in terms of goodness-of-fit was a truncated593

positive sine half-wave convoluted with a gaussian. The594

truncation comes from the size of the beam with respect595

to the chopper opening, while the convolution with the596

gaussian takes into account the velocity distribution of597

the beam. Figure 16 shows a typical histogram and the598

residuals of such a fit.599

The knowledge of , L, fch and L yielded, using600

(4), the velocities plotted for example in Fig. 8 where601

Figure 16: Top: count rate at the QMS vs phase of the chopper signal.The fit function (red solid line) is a truncated positive half-wave of asine convoluted with a gaussian. Bottom: residuals of fit.

the error bars take into account the errors on the laser602

phase, on the beam phase (being the dominant ones), on603

the length L and on the chopper frequency fch.604

3.2. Focusing by the superconducting sextupole605

The e↵ect of the superconducting sextupole can be606

characterized using the 2D-scanning stages (§2.3) and607

a measurement of the time-of-flight of the atoms arriv-608

ing at the QMS. Figure 17 shows two-dimensional beam609

profiles indicating the position dependence of either the610

count rate or the velocity of the hydrogen beam recorded611

at the QMS for sextupole current o↵ and for 400 A at612

the maximum ds (highest initial velocity selection). It613

clearly illustrates the focusing of the low velocity com-614

ponents when the magnet is energized. Figure 18 also615

illustrates this behavior at di↵erent initial velocities (5616

di↵erent ds spacings). At lower velocities the sextupole617

current needed to focus a high portion of the low veloc-618

ity component is lower.619

13

I = 0 A

-3 -2 -1 0 1 2 3

-6

-4

-2

0

2

4

6

y posi

tion (

mm

)

I = 400 A

-3 -2 -1 0 1 2 3

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

beam

dete

cted (

kHz)

-3 -2 -1 0 1 2 3x position (mm)

-6

-4

-2

0

2

4

6

y posi

tion (

mm

)

-3 -2 -1 0 1 2 3x position (mm)

1.2

1.4

1.6

1.8

2.0

2.2

2.4

velo

city

(km

/s)

Figure 17: Focusing e↵ect of the analyzing superconducting sex-tupole; top (bottom) panels compare the beam count rate (averagebeam velocity) when the superconducting sextupole is turned o↵ (leftpanels) or energized with the maximum current of 400 A (right pan-els). The data were collected in the straight-source configuration.

0.9

1.0

1.1

1.2

1.3

1.4

0.0 0.4 0.8 1.2 1.6 2.0 2.4

velo

city

(km

/s)

nominal magnetic field at r=50mm (T)

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 100 200 300 400

be

am

ra

te (

kHz)

superconducting sextupole current (A)

ds = 16 mmds = 35 mmds = 54 mmds = 72 mmds = 91 mm

Figure 18: Measured count rates (top) and average beam velocities(bottom) while ramping the superconducting sextupole magnet fromzero up to the maximum current of 400 A (the second x-axis givesthe corresponding magnetic field strength at a radius of 50 mm). Thetrends are compared for 5 di↵erent settings of the distance ds betweenthe sextupole doublet, which pre-selects the beam velocity. The solidlines indicate the running average. The data were collected in the 90 source configuration.

3.3. Measurement of the hyperfine transition620

In [15] we reported the measurement, using this ap-621

paratus, of the ground-state hyperfine splitting of hydro-622

gen through the 1 transition with a relative precision623

of 3 109, which constitutes more than an order of624

magnitude improvement over previous determinations625

in a beam [13, 14]. The ground-state value was ob-626

tained by extrapolating several measurements taken at627

di↵erent external magnetic fields (within the few gauss628

range) to zero-field. Figure 19 shows such an extrapo-629

lation. The investigation of systematic shifts included,630

among others, the size of the beam at the cavity entrance631

(see §2.2), the e↵ect of the shielding factor, the temper-632

ature of the source, and the orientation of the PTFE tub-633

ing. The only potential systematic shift that could be634

identified stems from the frequency standard and was635

on the 1 ppb level. All results were in agreement, within636

their uncertainties, with the more precise literature value637

( flit = 1, 420, 405, 751.768(2) Hz [4, 5]). Therefore sys-638

tematic shifts stemming from the spectroscopy method639

or apparatus can be excluded at the few ppb level for640

the planned measurements on antihydrogen with an ini-641

tial precision goal of 1 ppm.642

4. Summary and Conclusions643

We have described ASACUSA’s hydrogen apparatus644

to commission and characterize the spectroscopy setup645

envisioned for the measurement of the ground-state hy-646

perfine splitting of antihydrogen. The setup, designed647

for high acceptance of the scarce antihydrogen atoms,648

is capable of reaching the specified performance to se-649

lectively drive the 1 transition. A measurement of the650

ground-state hyperfine splitting of hydrogen was per-651

formed [15] with an order of magnitude improved pre-652

cision over previous determination in hydrogen beams.653

The prospects for antihydrogen spectroscopy depend on654

the quality of the antihydrogen beam and in particular655

on the average velocity, polarization and quantum states656

of the atoms exiting the formation region toward the ap-657

paratus. An evaluation of the needed amount of antihy-658

drogen atoms given particular values of those parame-659

ters to reach a ppm precision on antihydrogen has been660

provided in [15].661

An upgrade (improved coils configuration and shield-662

ing) of the apparatus described in this manuscript has663

been performed to allow the simultaneous determina-664

tion of the 1 and 1 transitions and will be the subject665

of a future publication. This is of particular interest for666

the antihydrogen measurement since a single measure-667

ment of the two transitions at a given field is sucient668

to determine the ground-state hyperfine splitting.669

14

31

32

33

34

35

IHC = 0.25 A(a)

coun

t rat

e (k

Hz)

31

32

33

34

35

IHC = 0.25 A(a)

coun

t rat

e (k

Hz)

-2-1 0 1 2

-15 -10 -5 0 5 10 15 20

std.

sco

re

f - flit (kHz)

0

5

10

15

20

(b)

f c - f

lit (k

Hz)

0

5

10

15

20

(b)

f c - f

lit (k

Hz)

0

5

10

15

20

(b)

f c - f

lit (k

Hz)

-2-1 0 1 2

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

std.

sco

re

Helmholtz coil’s current IHC (A)

-2-1 0 1 2

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

std.

sco

re

Helmholtz coil’s current IHC (A)

Figure 19: Determination of the ground-state hyperfine splitting ofhydrogen; (a) the lineshape was measured at di↵erent external mag-netic fields/Helmholtz coils currents (here an example at 250 mA) andprovided the frequency of the 1 transition at those fields indicatedby the blue vertical line; (b) the extrapolations of those values to zeromagnetic field yielded the zero-field transition with a relative preci-sion of 3 109.

Acknowledgments670

This work was funded by the European Research671

Council under European Union’s Seventh Framework672

Programme (FP7/2007- 2013)/ERC Grant agreement673

(291242) and the Austrian Ministry of Science and Re-674

search, Austrian Science Fund (FWF) DK PI (W 1252),675

and supported by the CERN fellowship and summer676

student programmes as well as the DAAD RISE pro-677

gramme.678

The authors wish to thank P. Caradonna for his ini-679

tial contributions to the experimental setup, as well as680

B. Juhasz for proposing the idea of velocity selection via681

a sextupole doublet, and B. Wunschek for performing682

the initial simulations. The authors are also indebted to683

S. Federmann, F. Caspers, T. Kroyer and several mem-684

bers of the CERN BE department (previously in the685

AB department) and TE-MPE-EM groups, who heavily686

contributed to the design and manufacturing of the cav-687

ity. We are grateful to P. A. Thonet and D. Tommasini688

from the CERN TE-MSC-MNC group for their help in689

the design and manufacturing of the sextupole doublet690

and the Helmholz coils, respectively. We acknowledge691

technical support by the CERN Cryolab and Instrumen-692

tation group TE-CRG-CI, especially L. Dufay-Chanat,693

T. Koettig, and T. Winkler. The hydrogen source was694

gracefully provided by the group of H. Knudsen. We695

thank H.-P. E. Kristiansen for providing initial support696

for the assembly and operation. We also wish to thank697

C. Jepsen, J. Hansen, M. Wolf, M. Heil, F. Pitters,698

Ch. Klaushofer and S. Friedreich who contributed to the699

characterization of the apparatus.700

Author’s contributions701

C.A, H.B., C.E, M.F., B.K., M.L., V.M., C.M., V.M.,702

O.M., Y.M., Y.N., C.S., M.C.S, L.V., E.W., Y.Y and703

J.Z. are involved in the ASACUSA-CUSP antihydro-704

gen program. S.A.C., M.D., C.M., O.M., M.C.S, E.W,705

M.W. and J.Z. were involved in the hydrogen experi-706

ment of which apparatus is described in this manuscript.707

All authors contributed to critical discussions regarding708

the published content. The spectroscopy apparatus was709

built and operated by M.D, C.M, O.M., M.C.S and J.Z.710

The measurements described in this manuscript were711

taken by M.D, C.M, M.C.S and in parts by M.W.. B.K.712

and C.S. performed simulations. E.W. proposed the ex-713

periment. C.M. wrote the manuscript which was criti-714

cally reviewed by all authors.715

15

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