a hydrogen beam to characterize the asacusa antihydrogen ... · 41 of their magnetic moments...
TRANSCRIPT
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: [email protected] (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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