## Introduction

Enormous progress in antihydrogen ($$\overline {\rm{H}}$$) synthesis and trapping has been made in recent years1,2,3 and transitions between internal states have been induced and observed4, 5. While the results of measurements conducted to date are consistent with the charge-parity-time invariance theorem, the field is still very much in its infancy. Significant work will be needed to achieve the levels of measurement precision obtained in the study of matter atoms. Ultimately, precision studies of antihydrogen properties complement, and are complemented by, experiments that probe the foundations of the standard model including studies of antiprotons6, antiprotonic Helium7, muonic atoms8 and positronium, the electron-positron-bound state9.

Antihydrogen is synthesised from antiprotons ($$\overline {\rm{p}}$$) and positrons (e+); the most widely employed method starts with cold plasmas of both species, which are brought together in Penning–Malmberg traps, where axial magnetic fields provide radial confinement and electric fields provide axial confinement (see ref. 10 for a review). Antihydrogen atoms in states where the magnetic moment is anti-aligned with the magnetic field are then confined in a magnetic minimum trap, provided their kinetic energy is low enough1,2,3. This is typically <0.5 K in temperature units for Tesla-scale trapping fields (multiplication by the Boltzmann constant k B to obtain energy units is implicit). Trapped antihydrogen is detected by ramping down the currents in the magnetic trap over 1.5 s and detecting the annihilation of the antiproton when the released atoms hit the wall of the trap. We employ a three-layer silicon vertex detector11 to image the annihilation vertex position of each detected atom. Event topology is used to distinguish antiproton annihilations from cosmic rays.

Here we report a breakthrough in the efficiency of antihydrogen trapping and a method for accumulating or stacking anti-atoms trapped during consecutive production cycles. These advances are realised through the development of a number of techniques that yield both more and colder antihydrogen. Improved methods to produce cold antihydrogen are critically important to most experimental initiatives in the field, and hence the results presented here are of broad relevance; see refs. 3, 10, 12 for examples.

## Results

### Antiproton and positron preparation

The ALPHA apparatus comprises three systems that allow antiproton capture, positron accumulation and antihydrogen synthesis. The central apparatus in which antihydrogen is formed is called ALPHA-2. It has been designed to allow the overlap of laser light and microwaves with trapped antihydrogen; a schematic view of the device is shown in Fig. 1. Antiprotons from the CERN antiproton decelerator13 (AD) are captured14 in a high voltage (4 kV) Penning–Malmberg trap that we refer to as the catching trap (CT, not shown). Once captured they are sympathetically cooled by a batch of pre-loaded electrons which self-cool by the emission of cyclotron radiation in the cryogenic (~6 K) environment of the trap. For this purpose we use a large (radius ~9 mm) plasma comprising ~8.5 × 107 electrons, which reduces the kinetic energy of about 73% of the antiprotons to below 100 eV in 20 s (this efficiency is not a fundamental limitation15; it is merely a practical compromise adopted to realise the demonstrations reported here, without excessive fine-tuning of electron plasma and sequence timing parameters). Any uncooled antiprotons are subsequently ejected by reducing the depth of the potential well. To secure an efficient transfer to the ALPHA-2 apparatus, the combined electron–antiproton plasma is then radially compressed using the rotating wall technique15 in the strong drive regime16. In this regime, the rotating wall achieves a plasma density proportional to the applied frequency up to a maximum. Since the radial extent of the plasma is limited by this maximum, fewer electrons allow for a smaller final size. Prior to applying the rotating wall most of the electrons used for cooling are therefore ejected; ~106 are retained. After compression, the antiprotons are allowed to re-cool for ~10 s before the remaining electrons are ejected. This protocol, which takes 100 s to complete, typically yields a plasma of 1.1 × 105 antiprotons with a radius of 0.2 mm at ~400 K. These antiprotons are then ejected from the CT with 25 eV of kinetic energy by momentarily (~2 μs) dropping the confining potential. Antiproton (and positron) temperatures are obtained from destructive measurements of the axial energy distribution17,18,19. Positron temperatures are measured after each mixing cycle, as part of the process in which charged particles are removed from the trap. Radial distributions are determined by ejecting particles to an externally located multichannel plate/phosphor detector18.

Antiprotons ejected from the CT move ballistically to the ALPHA-2 apparatus (Fig. 1), guided only by static axial magnetic fields. Upon arrival, they are manipulated in a manner analogous to the treatment they received in the CT described above. The recapture process is accomplished using an electrostatic potential well pre-loaded with electrons and the compression, cooling, electron ejection and re-cooling sequences employed in the CT are repeated without antiproton loss, resulting in a plasma with a radial extent of 0.4 mm and a temperature of ~100 K. This preparation takes about 100 s. These p̅ are then evaporatively cooled19 to 40 K over 10 s to leave around 9 × 104 of them in a cloud with a radial extent of 1 mm.

In parallel with the antiproton manipulations described above, positrons are prepared in the opposite end of ALPHA-2. The positrons originate from a radioactive 22Na source that feeds a Surko-type buffer-gas accumulator20. Plasmas comprising between 106 and 108 positrons are generated, depending on the details of the experimental sequence, and transferred to ALPHA-221. In order to control the positron number and density, which would otherwise drift (driven by conditions in the accumulator that evolve on a timescale of days), a combination of evaporative cooling and strong drive rotating wall compression is now used22; this protocol reduces variations to <1 %. Subsequently the positrons are left to thermalise with their surroundings in a deep (117 V) well before eventually being transported to a shallow (3.31 V; Fig. 2a) well in the mixing region (see below). The increase in plasma length associated with the transfer to a shallow well causes the positron plasma to cool adiabatically to about 30 K (cf. ~50 K if this step is omitted)23.

The key drivers underlying the positron and antiproton preparation protocols outlined above can be elucidated as follows; first, overlap during mixing is optimised by ensuring that the p̅ and e+ plasma radii are similar. Second, plasma temperatures as low as achievable are targeted, since this results in improvements in both synthesis and trapping. Finally, small plasmas are prepared to avoid deleterious influence of the octupole field of the magnetic minimum trap. Further discussion of this last point will follow when we describe the stacking procedure.

### Antihydrogen synthesis

Before the final preparation and mixing steps, the magnetic minimum trap is energised. The sequence of electrostatic potentials used in these final stages is shown in Fig. 2. Following the adiabatic cooling step (potential not shown), the positrons are evaporatively cooled (Fig. 2a, b) by lowering the potential barrier on the right from 3.31 to 0.91 V over 600 ms (the electrostatic self-potential of the positrons is initially about 1.8 V). At this point, the positrons start to re-thermalise with their surroundings, and so the potentials are quickly (in 10 ms; Fig. 2c) modified to the point where the antiprotons are on the verge of entering the positron plasma. Finally, the antiprotons and positrons are merged by lowering the potential barrier between them over about 1 s; during this process antiprotons are free to enter the positron plasma and positrons are free to drift to the left (Fig. 2d). While it may seem counter-intuitive to intentionally release positrons from the trap when synthesising antihydrogen, this technique offers two advantages. The potential difference between the antiprotons and the positrons is minimised without accelerating the former, while the latter are continuously cooled via evaporation during the merging process. This effect helps check the heating we observe when the positrons are held in a static well after evaporative cooling. A significant reduction in the post-mixing positron temperature is observed relative to the autoresonant (AR) antiproton injection technique employed previously, in agreement with simulations24. As shown in Table 1, typical temperatures after AR injection mixing were 50–70 K, whereas temperatures after the potential merge mixing process are in the range 15–20 K. The AR process resulted in heating of the positron plasma that could only be reduced by decreasing the number of injected antiprotons, which unfortunately lowered the antihydrogen yield. By contrast, the potential merge process exhibits an antihydrogen formation rate that increases with the number of antiprotons injected, with no adverse temperature effects.

Table 1 compares variations in several key attributes of the two mixing procedures as the number of injected antiprotons is increased. Lower positron temperatures are evident when the potential merge mixing protocol is used. Doubling the number of antiprotons used in AR injection mixing increases the number of antihydrogen formed (Table 1), but simultaneously heats the positrons and ultimately reduces the trapping efficiency. Conversely, starting from a significantly larger initial value, and then doubling the number of antiprotons employed in the potential merge process increases antihydrogen trapping and reveals no measurable change in the positron temperature (Table 1). In fact, the positron temperature remains unchanged during potential merge mixing due to evaporative cooling.

The trapping fraction, while much improved for the potential merge process (likely because of the lower positron temperatures) is a factor of ~3 below what one might expect solely on the basis of the fraction of atoms in a Maxwell–Boltzmann distribution that have energies less than the trap depth (0.54 K in temperature units), which for 20 K $$\overline {\rm{H}}$$ is 1.6 × 10−3. This assumes atoms form in trappable and un-trappable states with equal probability, when in fact theoretical work25,26,27 suggests they are more likely to form in un-trappable states. It also assumes that the antiprotons equilibrate with the positrons before antihydrogen is formed10, 28. If instead the initial antiproton temperature (~40 K) carries over to the $$\overline {\rm{H}}$$ , the discrepancy is almost eliminated. We note that the improvement in trapping efficiency is roughly in accord with expectations for lower positron temperatures10, 28. It is likely the positron density also plays a role in determining the trapping rate. However, because of the inter-dependence between temperature and density imposed by the application of evaporative cooling19, detailed studies of trapping rate as a function of either parameter are still pending. For now, we note that the record trapping rates we have achieved using potential merge mixing yielded about an order of magnitude more trapped atoms in a single 6-month experimental run than were accumulated over several years using AR injection mixing.

### Antihydrogen accumulation

A batch of antiprotons is delivered by the antiproton decelerator roughly every 2 min. The typical preparation time for antihydrogen synthesis as described above is 3–4 min, and experiments with trapped antihydrogen can take up to 20 min. This scenario creates an important resource efficiency and productivity challenge, whose goal is to optimise the number of antihydrogen atoms that are employed in scientific experiments. Additionally, having more trapped atoms present during long exposures to laser or microwave radiation improves the signal-to-background ratio for observation of $$\overline {\rm{H}}$$ annihilations. Building on the advances in plasma control and trapping efficiency described above, we have, therefore, implemented a new experimental protocol that increases the availability of trapped antihydrogen for experiment by making use of a larger fraction of the antiproton pulses that are delivered and the number of antihydrogen atoms available in each trial. We do this by stacking anti-atoms produced in consecutive mixing cycles.

In the absence of the transverse trapping fields, charged particles are constrained by the strong, uniform magnetic field of the Penning–Malmberg trap to move on the magnetic field lines near the axis of our apparatus. When the transverse octupole trapping field is superimposed on the uniform field, the field lines are distorted and some will ultimately guide particles to the wall as they drift in the axial direction. This imposes a dynamic aperture, parameterised by a critical radius, which is the radial limit beyond which loss is incurred. The critical radius for particles passing through our ~30 cm long fully energised neutral trap is about 4.5 mm29, 30. Motivated by this, the electron, positron and antiproton plasmas we prepare have radii of <1 mm, well below this limit.

We have implemented a protocol in which we maintain the magnetic minimum trap fields energised during preparation of the charged particle plasmas. This allows us to produce more antihydrogen while the atoms from a previous synthesis cycle remain trapped. No detrimental effects on plasma preparation were observed, consistent with the dynamic aperture considerations above. We were able to repeat the antihydrogen synthesis process about every 4 min with the magnetic minimum trap on. This antihydrogen stacking procedure was repeated for a maximum of 54 min cycles, limited by thermal considerations in the octupole current supply circuit; hence the first batch of antihydrogen was confined in the apparatus for 16 min. Figure 3 shows the resulting average number of trapped and detected anti-atoms as a function of the number of cycles. The five-cycle experiment yielded 54 detected antihydrogen atoms, with the detection efficiency of 73.0 ± 0.4% implying that about 74 atoms were actually trapped. Here we use the analysis procedure described in ref. 5 where an improved signal-to-background ratio for observed antihydrogen was achieved by re-tuning hit thresholds and track fitting in vertex reconstruction. The background is negligible at about 0.063 ± 0.003 false positives per trial. We observe a linear increase in the number of trapped atoms with the number of stacks, consistent with no loss of antihydrogen and an average accumulation rate of 10.5 ± 0.6 detected $$\overline {\rm{H}}$$ per mixing cycle, or a maximum absolute effective accumulation rate of 2.6 ± 0.2 detected $$\overline {\rm{H}}$$ per minute.

## Discussion

We have demonstrated how detailed plasma control, lower positron temperatures and potential merge mixing of cold e+ and $$\overline {\rm{p}}$$ plasmas has enabled a significant increase in the rate and efficiency of antihydrogen trapping. A key feature of the potential merge mixing protocol is that it allows more antiprotons to be used than previously possible. Furthermore, these developments facilitated the implementation of repeated synthesis cycles contributing to the same batch of trapped antihydrogen, to allow several 10s of anti-atoms to be held simultaneously in the trap. These techniques were key for the recent first observation of the 1S-2S transition in antihydrogen5 and they will almost certainly enhance the precision of any experiment limited by the availability of cold trapped antihydrogen. Importantly, nearly all of these methodologies are equally applicable to experiments that require antihydrogen, but not trapping. The observed strong influence of positron temperature on both antihydrogen formation rate and trapping efficiency indicates that further effort to lower positron temperatures will be well rewarded (e.g., ref. 28). As a final note, it is encouraging that the potential merge mixing technique appears, thus far, to have no upper limit as to the number of antiprotons that may be exploited, thus paving the way for efficient use of the new ELENA facility that is being constructed at CERN31. ELENA promises up to a factor 100 increase in the number of trapped antiprotons available to experiments. All of these developments are encouraging for future fundamental tests with antihydrogen.

### Data availability

The data sets generated during and/or analysed during the current study are available from N.M. and J.S.H. (niels.madsen@cern.ch, jeffrey.hangst@cern.ch) on reasonable request.