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1 This content has been downloaded from IOPscience. Please scroll down to see the full text. Download details: IP Address: This content was downloaded on 06/04/2018 at 00:28 Please note that terms and conditions apply. You may also be interested in: Antimatter Matters: Progress in Cold Antihydrogen Research Yasunori Yamazaki The AEgIS experiment at CERN: measuring antihydrogen free-fall in earth s gravitational field to test WEP with antimatter R S Brusa, C Amsler, T Ariga et al. CERN looks inside anti-atoms Belle Dumé Status report on the GBAR CERN experiment Pascal Debu Trapped antihydrogen: A new frontier in fundamental physics N Madsen and The Alpha Collaboration Exploring the WEP with a pulsed cold beam of antihydrogen M Doser, C Amsler, A Belov et al. Measurement of the ground-state hyperfine splitting of antihydrogen B Juhász, E Widmann and S Federmann Discrete Symmetries CP, T, CPT J Bernabeu Precision experiments with antihydrogen: an outlook Michael Doser

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5 Yasunori Yamazaki RIKEN, 2-1 Hirosawa, Wako, Saitama, , Japan Michael Doser CERN EP, 1211 Geneve 23, Switzerland Patrice Pérez IRFU, CEA, Université Paris-Saclay, F Gif-sur-Yvette, France IOP Publishing

6 ª IOP Publishing Ltd 2018 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher, or as expressly permitted by law or under terms agreed with the appropriate rights organization. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency, the Copyright Clearance Centre and other reproduction rights organisations. Permission to make use of IOP Publishing content other than as set out above may be sought at permissions@iop.org. Yasunori Yamazaki, Michael Doser and Patrice Pérez have asserted their right to be identified as the authors of this work in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act ISBN (ebook) DOI / Version: Physics World Discovery ISSN (online) British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library. Published by IOP Publishing, wholly owned by The Institute of Physics, London IOP Publishing, Temple Circus, Temple Way, Bristol, BS1 6HG, UK US Office: IOP Publishing, Inc., 190 North Independence Mall West, Suite 601, Philadelphia, PA 19106, USA

7 Contents Abstract Acknowledgments Author biographies vi vii viii 1 Introduction 1 2 Background 3 Discovery of the concept of antimatter 3 CPT symmetry 4 Antihydrogen formation processes 5 3 Current directions 7 Antihydrogen beam with a cusp trap via three-body recombination 7 Preparation of cold antiprotons and cold positrons 9 Pulsed antihydrogen beam: the AEgIS experiment 10 Producing antihydrogen ion beams outside traps 13 4 Outlook 16 Additional resources 17 v

8 Abstract Why does our universe consist purely of matter, even though the same amount of antimatter and matter should have been produced at the moment of the Big Bang 13.8 billion years ago? One of the most potentially fruitful approaches to address the mystery is to study the properties of antihydrogen and antiprotons. Because they are both stable, we can in principle make measurement precision as high as we need to see differences between these antimatter systems and their matter counterparts, i.e. hydrogen and protons. This is the goal of cold antihydrogen research. To study a fundamental symmetry charge, parity, and time reversal (CPT) symmetry which should lead to identical spectra in hydrogen and antihydrogen, as well as the weak equivalence principle (WEP), cold antihydrogen research seeks any discrepancies between matter and antimatter, which might also offer clues to the missing antimatter mystery. Precision tests of CPT have already been carried out in other systems, but antihydrogen spectroscopy offers the hope of reaching even higher sensitivity to violations of CPT. Meanwhile, utilizing the Earth and antihydrogen atoms as an experimental system, the WEP predicts a gravitational interaction between matter and antimatter that is identical to that between any two matter objects. The WEP has been tested to very high precision for a range of material compositions, but no such precision test using antimatter has yet been carried out, offering hope of a telltale inconsistency between matter and antimatter. In this Discovery book, we invite you to visit the frontiers of cold antimatter research, focusing on new technologies to form beams of antihydrogen atoms and antihydrogen ions, and new ways of interrogating the properties of antimatter. vi

9 Acknowledgments We would like to thank CERN, specifically the Antiproton Decelerator (AD) team and the Radio Frequency (RF) team, for their great efforts and support. This work was partly supported by a Grant-in-Aid for Specially Promoted Research ( ) of the Japan Society for the Promotion of Science, Special Research Projects for Basic Science of RIKEN. vii

10 Author biographies Yasunori Yamazaki Yasunori Yamazaki was a professor at the University of Tokyo from 1993 to In 1997, he received a joint-appointment as RIKEN Chief Scientist, and then continued his career at RIKEN as Distinguished Senior Scientist from 2011 to He was also appointed as a deputy Executive Research Director of RIKEN from 2014 till today, and was the International Chairperson of the International Conference on Photonic, Electronic and Atomic Collisions (ICPEAC) from 2005 to Yamazaki studies fundamental physics via antimatter and radiation biology via micro-irradiation on living cells. Awards have included a Fellowship of the American Physical Society in 2011, 15th Matsuo Foundation Hiroshi Takuma Memorial Award in 2011 and 52nd Toray Science and Technology Prize in Michael Doser Michael Doser is a research physicist at CERN, the European Organization for Nuclear Research, in Geneva, Switzerland. Since 1983, he has worked with antimatter, using it either as a tool (to study the strong interaction, in the framework of the ASTERIX (Antiproton Stop Experiment with trigger on Initial X-rays) and Crystal Barrel experiments at CERN, and the electron positron colliders at KEK in Japan and SLAC in the US) or as an object of study itself (formation of the first cold antihydrogen atoms in the framework of the ATHENA (AnTiHydrogEN Apparatus) experiment). Since 2009, he has been the spokesperson of the AEgIS (Antihydrogen Experiment: Gravity, Interferometry, Spectroscopy) experiment at CERN whose goals include measurement of the gravitational interaction between matter and antimatter. In addition, he is Editor of Physics Letters B and Review of Particle Properties. Patrice Pérez Patrice Pérez is a particle physicist at CEA-Saclay, France, in the Institute for Research into the Fundamental Laws of the Universe. He participated in experiments at CERN on proton proton collisions then high energy neutrinos, at KEK in Japan on electron positron collisions in 1987 then at the former Large Electron Positron Collider. Since 2002, Pérez has been exploring ways to employ particle physics techniques to study the fourth force, i.e. viii

11 gravitation, at the particle level. For intense antihydrogen formation, he proposed in 2003 with a colleague to use a particle accelerator to produce one of its ingredients, the positron. After several studies in Yamazaki s laboratory at RIKEN, he founded the GBAR (Gravitational Behaviour of Antihydrogen at Rest) collaboration at CERN. ix

12 Physics World Discovery Antihydrogen Beams Yasunori Yamazaki, Michael Doser and Patrice Pérez 1 Introduction Figure 1 schematically shows the history of our Universe, which started approximately 13.8 billion years ago in the extremely high-temperature and high-density event known as the Big Bang. Several key steps are symbolically shown, including the birth of protons and neutrons 10 5 s after the Big Bang, the formation of hydrogen atoms at 0.38 million years, star formation after 300 million years, the birth of the Earth at 9.2 billion years, etc. Only 0.6 billion years after the birth of the Earth, living creatures emerged, i.e. living creatures have witnessed at least one third of the history of the Universe, and now we human beings are seriously considering how the Universe started and why we exist. It is believed that the same amount of matter and antimatter was produced in the Big Bang because particles and antiparticles are always created in pairs according to our present understanding of modern physics. In a similar manner, antimatter and matter annihilate in pairs when they meet. In other words, nothing should remain in the Universe but free-floating energy, or an antimatter Universe should coexist with our matter Universe. However, every effort to find celestial antimatter has been unsuccessful till now, which strongly indicates that the Universe consists solely of matter. What happened to all the antimatter? The gravitational interaction between matter and antimatter could play an important role in elucidating this missing antimatter mystery, which motivates the research described in this book. Fundamental symmetries may hold the key to unlocking this mystery. Symmetries are an essential concept in modern physics, and are categorized into continuous and discrete symmetries, which are related to conservation laws. Charge conjugation (C), parity operation (P) and time reversal (T) are the components of discrete symmetry transformations. And CPT symmetry the simultaneous application of all three transformations is expected to be the most fundamental of them all. It is worth noting that the conservation of CPT symmetry is guaranteed in the framework of the Standard Model (SM) of elementary particle physics. However, P, CP and T symmetry have already been found to be violated. CPT symmetry is the last one still evading our pursuit. Important consequences of CPT symmetry are that the mass, total lifetime, absolute charge and magnetic moment of an antiparticle should be exactly the same as those of the corresponding particle. In addition, the spectroscopic properties of a doi: / ch1 1 ª IOP Publishing Ltd 2018

13 Figure 1. Schematic timeline showing the evolution of the Universe. The whole history of our Universe is only three times longer than the history of the Earth (and accordingly living matter). complex antiparticle system (e.g. antihydrogen) should again be identical to the corresponding complex particle system (e.g. hydrogen). These attributes provide potential avenues to test CPT symmetry. If the particle is stable, observation time can be infinitely long, and accordingly, the mass/energy of the particle conjugates in question can potentially be determined with arbitrarily high precision. In normal high-precision measurements, experimental results are compared with predictions of precise and reliable theories that take into account all known interactions, in an attempt to find some deviations. The residue, if successfully detected, can be attributed to unknown interactions and/or some unexplored dynamics. CPT symmetry tests are conceptually different. Research can be conducted purely experimentally, without contributions from precise and detailed theoretical calculations. And once a tiny difference between matter and antimatter is observed, violation of CPT symmetry is automatically concluded, pointing to new physics beyond the SM, and potentially leading to new understanding of the missing antimatter mystery. A drawback, however, is the fact that there are no clear guidelines suggesting the necessary precision because no theoretical predictions are available. Another approach to elucidating the missing antimatter mystery is to study the effect of gravity on antimatter. We experience gravity every day as an attractive force between matter. But we do not know how gravity acts between matter and antimatter or between antimatter and antimatter. The weak equivalence principle (WEP) states that the trajectory of a test object is independent of its composition and structure. Hence, matter and antimatter should be equal under gravity. However, this has never been tested. Since we can only produce antimatter at the particle or atomic level, we turn to quantum theories for guidance, despite there being no complete theory that connects the quantum world and general relativity. For instance, in superstring theories there is no constraint on the effect of gravity on antimatter with respect to that on matter. Again, just as for CPT violation, in this domain there is as little theoretical guidance. 2

14 Indirect constraints come from precise measurements made on matter itself since matter particles are considered to contain a small fraction of antimatter. Comparison of the cyclotron frequency of an antiproton or a proton in the same magnetic field at the same gravitational potential also gives an indirect constraint. More encouragingly, a direct constraint was obtained when antineutrinos from supernova SN1987a arrived on Earth and one neutrino was also detected with a very small time-difference. This single event is, however, hardly reproducible for cross checking. An antihydrogen atom a positron bound to an antiproton is the simplest and most stable anti-atom. Its mirror image is hydrogen an electron bound to a proton which is one of the most precisely studied and best understood systems in physics research. High-resolution comparisons of both systems constitute one of the best tests of CPT symmetry, and the key ingredient is antihydrogen, which is the target of this article. Syntheses of antihydrogen (H) atoms have been intensively studied in recent decades to formulate stringent tests of CPT symmetry via high-precision spectroscopy either of the 1S 2S transition or ground state hyperfine transitions. In parallel, WEP test studies of the gravitational interaction between antimatter (H) and matter (the Earth) have also been conducted. This ebook explores the frontiers of cold antimatter research, focusing on new technologies to form antihydrogen and antihydrogen ion beams for CPT and WEP experiments. Three different schemes to produce antihydrogen beams are discussed: a three-body recombination process in an anti-helmholtz coil like p + e + e H + e ; a charge transfer reaction between a cold antiproton and positronium like p+ Ps H + e ; and consecutive two positron transfers from two positroniums to form a fast antihydrogen ion like + p + 2Ps H + Ps + e H + 2e. 2 Background Discovery of the concept of antimatter Paul Dirac unintentionally uncovered the antielectron in the 1930s. A twin of the electron with opposite charge, the antielectron emerges naturally from the equations underpinning his relativistic quantum theory of electrons formulated in Initially ignoring the significance of his theoretical finding out of pure cowardice, just four years later Carl Anderson accidentally stumbled on antielectrons (called positrons) in cosmic rays, proving that Dirac s theory describes the real physical world. Dirac s work also predicted the antiproton as the partner of the proton, but the idea was not fully accepted by the community due, for example, to the magnetic moment of the proton being much larger than that predicted by theory. It took about a quarter of a century to solve this problem, with the antiproton finally being observed by Owen Chamberlain, Emilio Segrè, Clyde Wiegand and Thomas Ypsilantis in Since then, various antiparticles have been experimentally produced and identified, including the anti-neutron (n) in 1958, anti-deutron (d) 4 in 1965 and anti-helium-4 ( He) nuclei in

15 The discovery of antimatter caused a paradigm shift not only in physics but also in society at large. Numerous pop culture references like the Starship Enterprise s engines powered by antimatter in Star Trek and the Illuminati s antimatter bomb exploding in the 2009 movie Angels and Demons show how antimatter has captured the public s imagination. Meanwhile, antimatter physics has rapidly progressed. For example, CERN s BASE (Baryon Antibaryon Symmetry Experiment) collaboration has recently succeeded in determining the magnetic moment of the antiproton with higher precision than that of the proton, which is the most abundant matter in our Universe. CPT symmetry As discussed in the Introduction, CPT symmetry the simultaneous application of C, P and T transformations is automatically conserved in the framework of the SM, which is based on a local quantum field theory in a flat space time fulfilling Lorentz invariance and unitarity. If some of the conditions that conserve CPT symmetry are not satisfied, e.g. when space time is curved by the gravitational interaction and/or a non-local interaction plays a role, CPT symmetry might be violated. It should also be noted that the physics origin of the violations of P and CP symmetries in weak interactions is not yet understood in detail. To study how a CPT violating system works and what can be predicted, the so-called Standard Model Extension (SME) has been developed by Alan Kostelecký and his colleagues. SME is constructed by adding possible CPT violating interactions artificially as small perturbations to the standard CPT conserving Lagrangian of the SM. Based on this approach, physical quantities such as hyperfine transitions of antihydrogen and hydrogen atoms are found to be sensitive to CPT violating interactions. Further, SME gives a physical reason as to why the precision in energy scale is conceptually better than relative precision to discuss CPT symmetry. For example, the precision of 1S 2S and ground state hyperfine transitions of hydrogen atoms have often been given as Δv 1S-2S /v 1S-2S = and Δv HF /v HF = , respectively, inferring that the former is higher in precision. If, however, we compare the same quantities in the energy/frequency scale, they are Δv 1S 2S =10 Hz and Δv HF = Hz, respectively, which shows the hyperfine transition is the better quantity to test CPT symmetry if we follow the argument of SME. The research on K 0 and K 0, which discovered CP violation for the first time, confirmed that CPT symmetry is conserved to the best relative precision, m(k ) m(k ) / m(k) < In the energy scale following the discussion of SME, the above value is converted to m(k 0 ) m(k 0 ) < GeV 10 5 Hz. Comparing this precision ( 10 5 Hz) with those of hydrogen spectroscopy ( 10 Hz/ 3 10 Hz), it is highly feasible that antihydrogen spectroscopy is the most stringent test of CPT symmetry. It is also noted that the level of CP violation of the K 0 and K 0 system is 17 Im( m12) GeV, and so the CPT violation level has only been tested to a few percent of the CP violation. It is therefore rather evident that experiments should be conducted with much higher precision. 4

16 Regarding CPT violation related to the gravitational interaction, the Planck mass ħc 1 given by 19 2 mpl = ( ) 2( 10 GeV c ) is the critical quantity to be considered, where G ħ is the Planck constant divided by 2π, and G the gravitational constant. Actually, a point particle with Planck mass seriously distorts space time, and becomes a black hole. This energy range is far too high to be accessible to present accelerators and will probably never be reached, even in the far future. Even now, the Large Hadron Collider (LHC) the biggest accelerator in the world is 10 3 of the Earth s size, and we will shortly hit a conceptual plateau. To get around this limitation when we consider influences of the gravitational interaction on CPT violation, a possible measure could be the ratio of the particle mass (m) involved in the system and the Planck mass, i.e. R = mm / PL, which is for a proton/antiproton. It is noted that the level of CPT conservation tested with K 0 and K 0 described above is comparable to this ratio. It would also be worth reconsidering our strategy in studying the fundamental laws of nature not only by pushing to higher and higher energies, but also by adopting softer and humbler highsensitivity methods. Such high-precision schemes, which can be complementary to high energy physics, are called listening to the whisper of nature. Antihydrogen formation processes Typical atomic processes that yield antihydrogen (H) atoms are: + p + e H + h v (1) + p + e + Nhv H + (N + 1)h v (2) * + p e e H + e (*:high Rydberg states) (3) + p + (e e ) H + e (4) p + A H + e + A (5) These processes can be split into two categories, considering the way in which energy and momentum are conserved before and after the reaction. Processes (1) and (2) manage conservations via photon emission, and are called radiative recombination and laser-induced recombination processes, respectively. The rate of radiative recombination is proportional to ρt 1/2, where ρ and T are density and temperature of the positron cloud, respectively. Process (3) is a three-body recombination process involving one antiproton and two free positrons, the reaction rate of which is proportional to ρ 2 T 9/2. It is the principal mechanism to synthesize antihydrogen when positron density is high and positron temperature is low. Process (4) is also a three-body recombination process, this time involving an antiproton and a positronium, the bound state of a positron and electron, where the 5

17 electron in the positronium takes care of energy and momentum conservation. This can also be regarded as a charge transfer process from a positronium atom. The reaction cross-section is rather large, around cm 2 for ground state positronium, and becomes even larger for positronium in excited states. It is also noted that the electronic states of antihydrogen can be controlled by varying the excited states of positronium. For all the antihydrogen formation processes discussed above, energy transfer to the third particle (E tr ) is 10 ev or lower, and the corresponding momentum transfer is bigger for an electron (positron) emission than a photon emission by a factor of (2m e c 2 /E tr ) 1/2. Because of this factor, the final density of state (p 2 dp) and accordingly the reaction rate are much bigger for the electron (positron) emission processes than for the photon emission processes. In a sense, process (5) is a positron capture process from the positron sea, where A is an atom that plays the role of the third particle that takes care of momentum conservation. Actually, IKP Jülich scientist Walter Oelert and his colleagues successfully used this process in producing energetic antihydrogen atoms for the first time, shooting 1.4 GeV antiprotons on Xe atoms in The study of cold antihydrogen, which started in 1997, celebrated its first milestone in 2002 when CERN s ATHENA (AnTiHydrogEN Apparatus) and ATRAP (Antihydrogen TRAP) experiments successfully synthesized cold H atoms by employing the three-body recombination scheme in a uniform magnetic field. The next step was then to prepare H atoms in a controllable way suitable for physics experiments. Two different approaches have been explored. The most straightforward one is to trap antihydrogen atoms in a magnetic bottle so that they can be observed for a macroscopic time, which in principle allows high-precision measurements at the cost of perturbations due to the non-uniform magnetic field. Another approach is to extract antihydrogen atoms and place them in a field-free region as a focused beam, where the intrinsic nature of antihydrogen can be studied without unnecessary perturbation at the cost of weak beam intensity. After several years of experimental developments, the successor to ATHENA the ALPHA collaboration realized a second milestone in 2010: the successful trapping of 39 Hs, which was realized by ATRAP in One month after ALPHA s successful antihydrogen trapping experiment in 2010, the ASACUSA (Atomic Spectroscopy And Collisions Using Slow Antiprotons) collaboration reported successful synthesis of H atoms using an anti-helmholtz coil magnetic field, a so-called cusp trap. This was a major step in extracting an H beam to a fieldfree region for high-precision microwave spectroscopy, which was followed by antihydrogen beam formation in Figure 2 shows the hyperfine energy levels of H/ H in their ground states as a function of an external magnetic field. Two of the energy levels increase with increasing magnetic field, i.e. they are attracted towards lower magnetic fields, and are named low-field seeking (LFS) states. The other two levels are opposite, and are named high-field seeking (HFS) states. By preparing a particular magnetic field distribution that has a spatial point with a minimum magnetic field strength, atoms in LFS states can be trapped. It is seen that the energy level varies 14 GHz ( 0.7 K) 6

18 Figure 2. Ground state hyperfine levels of a (anti)hydrogen atom as a function of external magnetic field. for a magnetic field strength of 1 T. Considering that construction of a magnet with a magnetic field difference of 1 T or so is feasible, Hs with a kinetic energy of 1 K or less can be trapped. Looking at the level variation from the viewpoint of spectroscopy, the hyperfine states are quite fragile to the external magnetic field, i.e. the intrinsic hyperfine transition frequency of 1.4 GHz is easily modified by a weak magnetic field, which indicates that high-resolution spectroscopy is not easy in the presence of a spatially varying magnetic field. 3 Current directions Antihydrogen beam with a cusp trap via three-body recombination We have two potential transitions of antihydrogen/hydrogen for high-resolution spectroscopy: 1S 2S transition and ground-state hyperfine transitions. The former can be realized by trapping antihydrogen atom(s) in a magnetic bottle to provide a meaningful observation time. The non-relativistic 1S 2S transition energy of hydrogen is given by Δ E = 1S 2S qq e p mc 4 2 4πε ħc 0 = 3 1 m αc 4 2 ( ) 2 (6) where m is the reduced mass of electron (m = m e /(1 + m e /m p )), m e and m p the electron and proton mass, respectively, q e and q p the electron and proton charges, respectively, ε 0 the dielectric constant of vacuum, and α the fine structure constant. It is seen that the transition energy is determined by the electron mass, i.e. the 1S 2S transition primarily probes the electron mass, and other effects show up as a small correction. In the case of ground state hyperfine transitions, transition energy originates from the interaction between proton and electron magnetic moments, and increases when the proton and electron overlap is larger, e.g. in the case of S states, particularly the 7

19 1S state. The transition frequency between the singlet (F = 0) and the triplet (F = 1) states of hydrogen in the 1S state is given by 2 4α m m μ μ e p 2 3m 2 Δ EHF = m( αc) α Δ E1S 2S (7) 3π m m μ μ m e p B N where μ e and μ B (= qeħ/2me) are the magnetic moment of the electron and Bohr magneton, respectively, and μ p and μ N are the magnetic moments of the proton and nucleon, respectively. It is seen that the hyperfine transition energy is directly proportional to the product of proton and electron magnetic moments, which are expected to be sensitive to CPT violation according to SME. As is discussed in the Background section, the hyperfine transition is fragile to magnetic field. It is therefore important to extract antihydrogen atoms out from the antihydrogen synthesizing region where a strong magnetic field is indispensable for the efficient production of antihydrogen atoms. The ACASUSA collaboration invented an axially symmetric superconducting magnet with a minimum magnetic field point (called the cusp magnet ), which can produce, extract and focus antiatoms in LFS states. Figure 3 shows a schematic drawing of the central part of the setup developed by the ASACUSA collaboration, which consists of a double-cusp trap to synthesize antihydrogen atoms and extract those in LFS states, a microwave cavity to induce hyperfine transitions from LFS to HFS when the microwave frequency exactly matches the transition frequency, a superconducting sextupole magnet to refocus antihydrogen atoms in LFS states and an antihydrogen beam detector. When antihydrogen atoms are converted into HFS in the cavity, the antihydrogen atoms are defocused by the sextupole magnet, and the number of antihydrogen atoms reaching the antihydrogen beam detector decreases. By this method, the transition energy/frequency is exactly evaluated. Cold antihydrogen atoms are produced by gently mixing a cold antiproton cloud with a cold positron cloud near the upper coil p Figure 3. Schematic drawing of the central part of the ASACUSA CUSP experiment. From left to right: superconducting double anti-helmholtz magnet of the cusp trap (grey), microwave cavity (green), sextupole magnet (red and grey) and antihydrogen detector (gold). If the microwave frequency matches the HF transition frequency, the antihydrogen atom makes a transition from LFS to HFS, and is defocused by the sextupole magnet. Credit: Stefan Meyer Institute. 8

20 Antihydrogen Beams of the double anti-helmholtz coils via the three-body recombination process. In order to de-excite antihydrogen atoms in highly excited states, a high-density electron plasma is under preparation. Figure 4 shows a photo of the experimental setup. In addition to the central components described in figure 3, an antiproton accumulator and positron accumulator are seen. The antiproton accumulator can provide a monoenergetic 10 ev beam of antiprotons. A Micromegas tracking detector installed in the cusp trap delivers information on the annihilation position of antihydrogen by tracking trajectories of pions emitted during antiproton annihilation as the merging point of tracks. Preparation of cold antiprotons and cold positrons The Antiproton Decelerator (AD) at CERN provides 5.3 MeV pulsed antiprotons of per shot every 100 s or so. In the case of the ASACUSA collaboration, a radio-frequency quadrupole decelerator (RFQD) was developed by the CERN accelerator group, and efficiently decelerates antiprotons down to 100 kev, which Figure 4. The ASACUSA-CUSP setup. 9

21 are trapped by the antiproton accumulator (see figure 4), cooled by preloaded electrons and finally transported to the cusp trap, in which positrons are preloaded to produce antihydrogen atoms. Typically, million cold antiprotons are trapped per one AD shot; a times higher efficiency than achieved by other collaborations. The positron accumulator collects positrons emitted from a sodium-22 ( 22 Na) source. Neon ice deposited around the positron emitting window is used as an efficient degrader. Degraded positrons are further degraded in a Penning trap using nitrogen as buffer gas. A complementary hyperfine transition experiment with a hydrogen beam in LFS states was also recently made with a precision of by Martin Diermaier and colleagues. Pulsed antihydrogen beam: the AEgIS experiment While the formation of a continuous beam of antihydrogen atoms opens up a range of physics measurements, it is beneficial (and in some cases crucial) to develop techniques that allow the formation and launch of a number of atoms simultaneously, and thus fine-tuning or tagging of the velocity of each atom. Such pulsed formation of antihydrogen atoms lies at the heart of the AEgIS (Antihydrogen Experiment: Gravity, Interferometry, Spectroscopy) experiment, whose goal is to measure the gravitational interaction between matter and antimatter, and to carry out background-free measurements of the HFS of antihydrogen atoms. The standard technique to form antihydrogen atoms is via three-body recombination in Penning traps; antiprotons are injected into positron plasmas, where they stochastically and continuously form antihydrogen atoms in Rydberg states that then propagate through the positron plasma, undergoing further collisional excitation or de-excitation processes. The resulting emission is determined by the positron plasma temperature, density and aspect ratio, as well as by the antiproton injection energy. While it is tempting to consider the possibility of injecting sub-ev antiprotons into a dense positron plasma to form an antihydrogen beam, this would result in a beam with a high axial velocity (O(eV)), making it unsuitable for gravity measurements. Indeed, antihydrogen formation in this case is a three-body process, and thus depends on the positron density, as does the rate of energy loss of antiprotons in the same plasma. Forming slow antihydrogen atoms requires thermalization of the injected antiprotons in the positron plasma, and thus either high positron density or multiple passes of the antiprotons through a low-density plasma. In the second case, one does not obtain axially enhanced emission. In the first case, antihydrogen formation occurs rapidly and before significant energy loss has occurred: the resulting antihydrogen is axially emitted, but fast. Striking an optimal balance between positron density and injection energy to maximize the rate for slow axially-emitted antihydrogen prior to complete thermalization is thus complicated by these two competing processes of energy loss (low in a low-density plasma) and antihydrogen formation rate (high in a high-density plasma, and thus occurring before significant deceleration can occur). 10

22 In order to achieve controlled production of slow antihydrogen atoms in specific quantum states, for which the time of formation is well defined, a second antihydrogen formation process is more suitable: resonant charge exchange defined as * + * Ps p H + e (8) In this process, positronium (Ps) is formed in the vicinity of cold antiprotons, with which it subsequently interacts to form antihydrogen atoms whose velocity is dominated by that of the antiprotons. If Ps formation is pulsed, as is the case when bursts of positrons are implanted in a nanostructured material, then antihydrogen atoms will be formed in a single burst, and will be isotropically emitted with a velocity distribution dominated by the initial antiproton velocity. The formation cross-section depends strongly on the relative velocity between positronium and antihydrogen, and very strongly on the internal quantum state of the positronium atom. The antihydrogen formation rate can thus be enhanced by laserexciting the Ps into a Rydberg state, e.g. n = 15 in the case of AEgIS (figure 5). The resulting antihydrogen atoms due to angular momentum conservation will also be in a Rydberg state n n Ps 2 1/2. Beam formation can build upon the concomitant electric dipole, which provides a handle through which the Rydberg (anti)hydrogen atoms can be accelerated (or decelerated) axially, via Stark acceleration, within a few tens of μs. Typical acceleration field gradients of a few thousand V cm 1 applied over several μs should then result in an increase in the axial velocity component of several hundred m s 1. The resulting beam velocity distribution and divergence, however, depend on the initial antiproton temperature distribution, distribution of sub-states (n, k, m) of the Figure 5. Schematic of the AEgIS pulsed antihydrogen formation scheme. Positrons are injected into a converter; backwards-emitted o-ps is excited in a two-step process into a Rydberg state; the resulting Ps* undergoes a charge exchange reaction with cold antiprotons; the resulting Rydberg antihydrogen atoms that expand into 4π at a velocity defined by the initial antiproton temperature are Stark-accelerated into a (enhanced emission direction) beam. 11

23 Rydberg antihydrogen and details of the applied field gradient. In practice, given a statistical distribution of the population of all possible sub-states, application of a time-varying electric field will accelerate the formed antihydrogen atoms in an uncontrollable manner, parallel and antiparallel to the Penning trap s axis, and by internal-state dependent amounts. Thus, the antihydrogen atoms will form a twolobed (upstream and downstream) broadband beam of excited atoms. While half of the atoms are thus accelerated in the wrong direction, the downstream lobe because the moments of formation and acceleration are well defined constitutes a pulsed source. The velocity of the source can then be reconstructed atom-by-atom by the time difference between formation and annihilation at the end of the flight path, thus allowing retroactive classification if needed. While such a velocity-tagged beam is suitable for gravity measurements, in order for the produced pulsed Rydberg antihydrogen beam to be applicable for HFS measurements, de-excitation into the ground state must be ensured. This is also beneficial for gravity measurements, since coupling of the magnetic moment of the antihydrogen atoms to any potential external magnetic field gradients, which could mimic gravitational anomalies, is then minimal. Transitions from Rydberg states to the ground state should occur on a time scale commensurate with the experimental scale of a few metres. For n = 20, cascade times of O(10 μs) ensure that for low velocity beams (v z 500 m s 1, corresponding to an axial antiproton temperature of 10 K) atoms should easily have reached the ground state within a metre of the point at which they were formed; however, only a very small fraction of atoms formed with significantly higher temperatures will have decayed within this useful range. For more highly excited antihydrogen atoms, such as those formed in three-body recombination, with n 40 and corresponding lifetimes of several 100 μs, the situation is even more severe: only a vanishingly small fraction will have decayed to the ground state within the useful range. Furthermore, since at least initially, experiments with antihydrogen beams will likely be statistically limited, any increase in the flux of available antihydrogen atoms is beneficial. For these reasons, alternative beam formation techniques building on pulsed atom formation are being explored (and need to be developed). The flux of antihydrogen atoms into a fixed size aperture is determined both by beam divergence (which is in turn determined by the temperature of the antiprotons relative to the acceleration-supplied additional axial velocity) and the efficiency of the acceleration scheme (a mixed-state initial population is more difficult to accelerate than a singlestate population). While sympathetic cooling of antiprotons via laser-cooled anions addresses the first concern, the second can be addressed by de-exciting the Rydberg atoms to the ground state prior to re-exciting them in a controlled manner into a specific Stark state, and then accelerating them optimally. Other schemes successfully implemented for Rydberg atoms are also envisaged, although these too will require dedicated development before they can be adapted to antihydrogen atoms in a broad distribution of Rydberg states. Of particular interest is a Rydberg mirror, which could allow part of the backward-emitted flux to be salvaged by reflecting it downstream. As an example, a (anti)hydrogen atom in (n = 27, k = 18, m =0,2 Stark states) with a velocity corresponding to a temperature 12

24 of 20 K is reflected by an electric strength of 2000 V cm 1 ; an antihydrogen atom in (n = 34, k = 28, m = 0,2) with the same velocity would be reflected by an electric field strength of 1000 V cm 1. An appropriately shaped (extended) Rydberg mirror could be even more effective, if an appropriate planar equivalent of the (three-dimensional) Rydberg mirror could be implemented. If the (extended) Rydberg mirror forms a parabola, and if the antihydrogen source is sited at its focus, all backward-emitted Rydberg antihydrogen atoms impinging on the mirror will be transformed into a parallel beam directed in the downstream direction. Furthermore, such a mirror should be able to reflect all (n, k, m) states; assuming that their velocity distribution is dominated by the Stark acceleration term, a short distance downstream of the source the axial coordinate of each atom maps to its velocity and thus its internal (n, k, m) state. This opens the possibility of a second Stark manipulation of the cloud of atoms, whereby a position- and time-dependent Stark deceleration (acceleration) akin to bunch rotation for charged particle beams in accelerators or δ-kick cooling in atomic physics could reduce the momentum spread of the atomic beam. Finally, in the longer term, once sufficiently low temperature ( 1 K) Rydberg antihydrogen atoms can be formed in large enough numbers, a similar approach based on magnetic mirroring can be envisaged. Magnetic field gradients of 1 T cm 1 are now achievable and used in the case of antihydrogen magnetic multipole traps with a well depth of 0.5 K for ground state antihydrogen atoms. For Rydberg atoms, even lower gradients would be sufficient to transform a 4π source inside such a trap into a directionally emitted source if one of the axially confining solenoids were to be removed, thus forming a partially open-ended container. Combined with control of the inner state of ultra-cold antihydrogen atoms, these techniques promise to permit the formation of finely tuned antihydrogen atomic beams in the near future. Producing antihydrogen ion beams outside traps The goal of the GBAR (Gravitational Behaviour of Antihydrogen at Rest) experiment is to observe the free fall of antihydrogen atoms and measure their acceleration in the gravity field of the Earth. The principle is to mimic Galileo s Leaning Tower of Pisa experiment but here with simple atoms. The velocity of the anti-atoms must be reduced to a fraction of a metre per second. Then the time it takes them to fall from a height of the order of 20 cm is measured and compared to that of normal matter. Since it is not possible to reach such low velocities directly with anti-atoms, the trick is to first produce anti-ions that can be slowed down to such velocities. Such + anti-ions, named H, are made of one antiproton and two positrons. Once the antiions are quasi at rest, being held by electromagnetic fields, a laser shot kicks out one of the two positrons. What is left is a neutral anti-atom of very low velocity. Being neutral, electromagnetic fields cannot hold it anymore and it falls freely. To conduct the experiment, anti-ions will be produced by twice repeating the reaction used in AEgIS. In the first step, an antiproton collects a positron from a positronium to form a neutral anti-atom: 13

25 p + Ps H + e This anti-atom then interacts with another positronium to collect the second positron and form an anti-ion (see figure 6): + + H Ps H + e The probability that each of these steps occurs is low, and the fact that there are two steps requires a large number of antiparticles to obtain anti-ions in enough quantities for a 1% precision gravity measurement. Typically for 10 million antiprotons launched onto a cloud of 10 billion positroniums, we may expect a few thousand anti-atoms and just one anti-ion. Thus, it is crucial that this kind of experiment focuses on the efficiency of all the processes. The antiprotons from the AD will be transferred in a small decelerator ring called ELENA (Extra Low ENergy Antiproton). Their 5 MeV energy will be reduced in ELENA to 100 kev by using a radio frequency cavity. The antiprotons will be distributed along the 30 m circumference in four bunches of about 5 million antiprotons each. It takes about 25 s to reach this energy. While decelerating, the beam has a tendency to blow up. In order to obtain beam divergence compatible with experiments, the beam undergoes a process called electron cooling. This is achieved by injecting a cloud of electrons into a section of the ring. The antiprotons that traverse this cloud exchange energy with the electrons and ultimately see their energy and angular dispersion reduced. The sum of these processes, including similar ones that take place in the AD to reach 5 MeV energy, takes about 110 s. The four bunches are then ejected towards four experiments. During , all experiments using antiprotons will stay connected to the AD while only GBAR will be connected to ELENA. The reactions that produce anti-atoms and anti-ions are more efficient at low energies. The antiprotons must be further slowed down. This is usually done by inserting a metallic degrader foil in the beam at the expense of losing a very large Figure 6. Two-step reactions that produce an antihydrogen beam and anti-ions. 14

26 fraction of the antiprotons by annihilation in the foil. In the case of GBAR, an electrostatic decelerator was built to reduce the energy to 1 kev. The 100 kev beam goes through a cylindrical electrode placed at a negative (because the antiprotons have a negative electric charge) high voltage of 99 kv so that it only interacts with the resulting electrical field and not with matter. Other electrodes are located along the resulting beam to keep it focused. The target for the antiprotons to produce antihydrogens is a cloud of positroniums. They will be produced by dumping a bunch of positrons onto a specially developed porous silica plate. The positrons diffuse in this material and lose energy until they bind with one of its electrons to form positronium. The pores have a typical diameter of 6 nm. Their density is such that they join together to form nanotubes that can reach the surface of the plate. When a positronium is formed near such a nanotube it is ejected inside it and bounces on its boundaries, losing energy at each bounce, and finally finding its way out to the surface to then exit into vacuum. This process was found to be optimal, with 40% efficiency when the incoming positrons have an energy of about 4 kev, and the positroniums leave the surface with an energy of about 80 mev. We expect to dump 10 billion positrons onto this porous surface to form a cloud of Ps out of it. In order to constrain the Ps to stay grouped and form a high-density target for the antiprotons, this plate will be completed by three other plates that form a small tube of rectangular cross-section (see figure 7). One of those plates is made of a 30 nm thin membrane of silicon nitride to let the positrons enter the tube without loss. Laser light can also be shined into this Figure 7. Schematic of antihydrogen and anti-ion beam production in GBAR. Positrons enter through a very thin membrane made of Si 3 N 4 into a cell where they hit a converter to produce o-ps, itself excited to n = 2or3. Antiprotons enter this cell where they interact with Ps to produce antihydrogen and anti-ions that are detected with microchannel plates. 15

27 tube to bring Ps into its second or third excited state because we expect that the interaction of those excited states with antiprotons is more efficient than when Ps is in its fundamental energy level. The large number of positrons necessary to obtain one anti-ion per ELENA pulse every 110 s requires a powerful source. All experiments already installed at CERN are using a radioactive 22 Na source that produces positrons. However, such sources have a maximum activity of the order of Bq, which results at best in a flux of 10 million slow positrons per second, which is not enough. We have thus chosen another kind of source based on the creation of electron positron pairs when energetic electrons hit a high Z target. A small electron linear accelerator produces electrons of 10 MeV energy that hit a tungsten target, producing positrons of 1 MeV average energy. These are moderated with tungsten meshes that can sustain the 2 kw electron flux and produce slow positrons ( 3 ev) with an expected flux of 100 million per second. These can in turn be accumulated in Penning traps during the time between two antiproton pulses from ELENA to reach 10 billion positrons. The resulting beam of anti-atoms and anti-ions will be used to perform experiments on them. Unfortunately, the anti-atom beam energy being of the order of 1 kev means we cannot use it directly for spectroscopy of its fundamental level, but we could use it for spectroscopy of other levels and possibly to probe the radius of the antiproton. There is also an ongoing project to add a Penning trap in the antiproton line within GBAR. This device will allow the antiproton beam energy, hence that of the anti-atoms, to be reduced. In essence, the anti-ions will be produced one by one. In turn, their energy will be reduced using sympathetic cooling with matter ions such as Be +, themselves cooled with lasers. Hence, anti-ion energy is expected to be reduced to energies of the order of a few nano electronvolts, making this anti-matter readily usable for precision experiments. 4 Outlook From this brief review, we have learned about ongoing antihydrogen research, finding that the approach to experiments with antihydrogen beams is in stark contrast to trap-based research. These two approaches are applied in various studies, including hyperfine transition experiments and gravity experiments. Irrespective of approach though, in all antihydrogen research the most critical issue is the number of available antihydrogen atoms. In parallel to various efforts to increase the production efficiency of antihydrogen atoms, a groundbreaking development is in progress at CERN: the construction of a new decelerator ring called ELENA. ELENA cools and decelerates a 5.3 MeV antiproton beam from the AD down to 100 kev. Thus, the number of available antiprotons for experiments is expected to increase by a factor of This development will effectively herald a new era for antihydrogen physics. At the same time, developing beams of (stable) neutral antimatter systems to probe fundamental symmetries opens the door to contemplating beams made up of neutral mixed matter antimatter systems, such as positronium or protonium, as well as more exotic purely antimatter systems like antihydrogen molecular systems. 16