# Status and plans of the Gravitational Behaviour of Antihydrogen at Rest
experiment

PHILIPP BLUMER on behalf of the GBAR collaboration  ETH Zurich, Institute for
Particle Physics and Astrophysics
Otto-Stern-Weg 5, 8093 Zurich, Switzerland

###### Abstract

The GBAR experiment aims to directly test the Weak Equivalence Principle of
ultracold antihydrogen in Earth’s gravitational field. The gravitational
acceleration $\overline{g}$ will be measured to a precision of $1\,\%$ using a
classical free fall of the anti-atoms from a fixed height. Reaching a
precision of $10^{-6}$ is planned by performing a ”quantum free fall”
experiment by detecting quantum interference of $\mathrm{\overline{H}}$ due to
quantum gravitational bound states above a reflecting surface. Additionally, a
$\mathrm{\overline{H}}$ Lamb shift measurement is being prepared in parallel
that will allow to determine the antiproton charge radius at the level of
$10\,\%$.

##  1 The GBAR experiment

Neutral antihydrogen atoms ($\mathrm{\overline{H}}$), consisting of one
antiproton ($\mathrm{\overline{p}}$) and one positron ($\mathrm{e^{+}}$), are
used to test the behaviour of antimatter in the terrestrial gravitational
field at the AD facility at CERN. A first direct approach by releasing
$\mathrm{\overline{H}}$ from a magnetic trap constraints the ratio of the
gravitational to the inertial mass of $\mathrm{\overline{H}}$ between $-65$
and $100$, with the sign of the gravitational acceleration $\overline{g}$
undetermined [1]. The unique approach of the Gravitational Behaviour of
Antihydrogen at Rest (GBAR) experiment is to synthesise positively charged
antihydrogen ions ($\mathrm{\overline{H}^{+}}$) that can be trapped in a Paul
trap and sympathetically cooled to a few $\mathrm{\mu K}$ temperature by
coupling them to laser-cooled $\mathrm{Be^{+}}$ ions, minimizing their initial
velocities [2]. The excess $\mathrm{e^{+}}$ is then photo-detached using a
$1640\,\mathrm{nm}$ laser and the now neutral $\mathrm{\overline{H}}$
experiences a classical free fall from a fixed height. By measuring the time
of flight and annihilation position the acceleration $\overline{g}$ can be
determined in a first phase with a precision of $1\%$. In a second phase
measuring quantum interferences, due to quantum gravitational bound anti-atoms
above a reflecting surface, will allow to reach a $10^{-6}$ precision [3].
GBAR’s unique formation of ultracold $\mathrm{\overline{H}}$ and
$\mathrm{\overline{H}^{+}}$ may open the way for new exciting possibilities,
such as optical trapping of ultracold anti-atoms [4] and the production of
molecular anti-ions [5]. Those experiments will result in an unprecedented
sensitivity to test Lorentz and CPT symmetry, helping to shed light on the
observed baryon asymmetry.

As a byproduct of the free fall experiment, the $\mathrm{\overline{H}}$ Lamb
shift, i.e. the energy difference of the $2\mathrm{S_{1/2}}$ and
$2\mathrm{P_{1/2}}$ states, can be measured. Measuring the Lamb shift with an
uncertainty of $100\,\mathrm{ppm}$ will determine the antiproton charge radius
at the level of $10\%$ and probe CPT by looking for a difference in the energy
levels from ordinary hydrogen atoms [6].

##  2 Production of antihydrogen atoms and ions

The $\mathrm{\overline{H}^{+}}$ is fabricated inside a so-called reaction
chamber via two charge-exchange processes

$\displaystyle\mathrm{\overline{p}}+\mathrm{Ps}$
$\displaystyle\rightarrow\mathrm{\overline{H}}+\mathrm{e^{-}}$ (1)
$\displaystyle\mathrm{\overline{H}}+\mathrm{Ps}$
$\displaystyle\rightarrow\mathrm{\overline{H}^{+}}+\mathrm{e^{-}}.$

The upgrade to the antiproton decelerator at CERN, the Extra Low ENergy
Antiproton (ELENA) storage ring delivers every $110\,\mathrm{s}$ a bunch of
about $5\times 10^{6}$ $\mathrm{\overline{p}}$ at a kinetic energy of
$100\,\mathrm{keV}$. They have to be efficiently decelerated to a few
$\mathrm{keV}$ energies for an optimal $\mathrm{\overline{H}}$ production.
This is done using a drift tube that can switch from $-100\,\mathrm{kV}$ to
$0\,\mathrm{V}$ when the $\mathrm{\overline{p}}$ bunch is inside the tube.
With this technique it was shown that the beam can be decelerated to
$8\,\mathrm{keV}$, though it increases the beam emittance [8].

The GBAR LINAC produces electrons with a kinetic energy of $9\,\mathrm{MeV}$
in a pulse width duration of $2.85\,\mathrm{\mu s}$ and a repetition rate of
up to $300\,\mathrm{Hz}$. Positrons are then generated via pair production of
high-energy $\gamma$’s due to electrons impinging on a tungsten target. At a
LINAC rate of $200\,\mathrm{Hz}$ the positron flux is about $4\times
10^{7}\,\mathrm{e^{+}}/\mathrm{s}$ [9]. The $\mathrm{e^{+}}$ are then
accumulated in a buffer gas trap, and afterwards stacked in a ultra-high
vacuum high field trap. Routinely trapping $1.5\times
10^{8}\,\mathrm{e^{+}}/110\,\mathrm{s}$ has been achieved in the fall of 2021
and a maximum of $1.4\times 10^{9}\,\mathrm{e^{+}}$ within $1100\,\mathrm{s}$
has been demonstrated. The accumulated $\mathrm{e^{+}}$ are then ejected onto
a porous silica film inside a cavity, forming a positronium ($\mathrm{Ps}$)
cloud in vacuum. The conversion probability of $\mathrm{e^{+}}$ to
ortho-$\mathrm{Ps}$ with a lifetime of $142\,\mathrm{ns}$ is about $30\,\%$.
Due to losses in the $\mathrm{e^{+}}$ transport onto the target about $1\times
10^{6}\,\mathrm{Ps}$ were formed during an ELENA cycle inside the cavity of
size $2\,\mathrm{mm}\times 2\,\mathrm{mm}\times 20\,\mathrm{mm}$ in 2021. The
low energy $\mathrm{\overline{p}}$ flying through the $\mathrm{Ps}$ cloud will
first form $\mathrm{\overline{H}}$ and then $\mathrm{\overline{H}^{+}}$ as
described in Eq. 1. It follows that a high density of the order of
$10^{11}\,\mathrm{Ps}/\,\mathrm{cm^{3}}$ is needed to form a single
$\mathrm{\overline{H}^{+}}$ [2]. As a byproduct to the
$\mathrm{\overline{H}^{+}}$ production many neutral $\mathrm{\overline{H}}$
atoms are formed and a parasitical Lamb shift measurement can be undertaken.
Thus, the resulting beam of $\mathrm{\overline{p}}$, $\mathrm{\overline{H}}$
and $\mathrm{\overline{H}^{+}}$ exits the reaction chamber, passes through the
Lamb shift setup and is afterwards split in an electrostatic field to
dedicated detection systems, as is shown in Fig. 1.

Figure 1: General scheme of the $\mathrm{\overline{H}}$ and
$\mathrm{\overline{H}^{+}}$ production and the experimental setup for the
$\mathrm{\overline{H}}$ Lamb shift measurement.

##  3 Lamb Shift measurement as a byproduct of antihydrogen production

A fraction of the produced $\mathrm{\overline{H}}$ will be in the metastable
$2\mathrm{S_{1/2}}$ state. When passing through two microwave field regions
they can be excited to the $2\mathrm{P_{1/2}}$ state depending on the
resonance frequency. Since the transition frequencies of the hyperfine states
are close to each other it is beneficial to remove unwanted states using a
state selector and subsequently scan the isolated
$2\mathrm{S_{1/2}}(F=0,m_{F}=0)\rightarrow 2\mathrm{P_{1/2}}(F=1,m_{F}=0)$
transitions with a MW transmission line, see Fig. 1. Remaining
$\mathrm{\overline{H}}(2\mathrm{S})$ are quenched to the $2\mathrm{P}$ state
in a static electric field where they relax to the ground state with a
$1.6\,\mathrm{ns}$ lifetime emitting a Lyman-$\alpha$ photon with a wavelength
of $122\,\mathrm{nm}$. With the surrounding CsI-coated MCP detectors the
Ly-$\alpha$ photons are counted as a function of the MW frequency thus
determining the $\mathrm{\overline{H}}$ Lamb shift. The setup was commissioned
with Muonium at PSI where the detection efficiency was validated to be
$\epsilon=\epsilon_{LyA}\times\epsilon_{\mathrm{Geo/Qnch}}=16\%$ [11, 12].
This includes the geometrical and quenching efficiency
$\epsilon_{\mathrm{Geo/Qnch}}=40\%$ simulated using SIMION and the MCP
efficiency with a quantum efficiency of $50\%$ to convert a photon to a free
electron $\epsilon_{LyA}=\epsilon_{MCP}\times\epsilon_{QE}=40\%$ [13, 14].

##  4 Capture and cooling of antihydrogen ions

After its production the $\mathrm{\overline{H}^{+}}$ is captured and cooled to
ultracold temperatures in two steps. First, the single
$\mathrm{\overline{H}^{+}}$ is trapped and sympathetically cooled by Coulomb
interaction in a RF Paul trap filled with a laser-cooled $\mathrm{Be^{+}}$ ion
cloud. An efficient sympathetic cooling process is needed to circumvent a
possible photo-detachment of the excess $\mathrm{e^{+}}$ by the
$313\,\mathrm{nm}$ laser used to cool the $\mathrm{Be^{+}}$. It is most
efficient when the mass ratio of the ions is small which is not the case for
$\mathrm{Be^{+}}$ and $\mathrm{\overline{H}^{+}}$ with a ratio of $9/1$.
Simulations show that $\mathrm{HD^{+}}$ ions can be added to reach a
temperature in the range of $5-100\,\mathrm{mK}$ within a cooling time of a
few $\mathrm{ms}$ [15]. To further cool the $\mathrm{\overline{H}^{+}}$ ion,
it is then transported to a precision trap to form a
$\mathrm{Be^{+}}/\mathrm{\overline{H}^{+}}$ ion pair. Applying ground state
Raman sideband cooling to the ion pair will cool the
$\mathrm{\overline{H}^{+}}$ to $10\,\mathrm{\mu K}$ temperature corresponding
to initial velocities of $\sim 1\,\mathrm{m/s}$ [2, 15].

##  5 Classical free fall

Figure 2: GEANT4 rendering of the classical free fall simulation with the
tracks of the $\mathrm{\overline{H}}$ atoms (blue) inside the free fall
chamber (red). The 6 Micromegas triplets and 4 TOF detectors are shown in
grey.

Figure 3: Micromegas detector used for tracking of charged pions from
$\mathrm{\overline{H}}$ annihilations in the GBAR experiment [16].

A laser pulse with a $1640\,\mathrm{nm}$ wavelength ionizes the
$\mathrm{\overline{H}^{+}}$, triggering the start of the free fall $t_{i}$.
The now neutral $\mathrm{\overline{H}}$ is no longer held by the precision
trap and falls from a height of $z_{i}=30\,\mathrm{cm}$ inside a so-called
Free Fall Chamber (FFC), see Fig. 3. The initial velocity of the anti-atom
directly affects its trajectory and recent simulations have shown that a
hexagonal FFC maximizes the vertical flight path while having the best
mechanical stability. The $\mathrm{\overline{H}}$ will inevitably come in
contact with the vacuum vessel and annihilate, producing on average three
charged pions $\pi^{\pm}$. Surrounding position sensitive Micromegas detectors
track the trajectory of the pions, allowing for the reconstruction of the
$\mathrm{\overline{H}}$ annihilation position with a focus on the vertical
$z_{f}$-component. The Micromegas detectors of size $50\,\mathrm{cm}\times
50\,\mathrm{cm}$ are arranged in groups of three, of which at least two must
record a pion hit to reconstruct its flight path [16]. Additionally, TOF
scintillator bars are forming the outer layer of the detection setup, and are
used to measure the precise free fall time $t_{f}$ and help reject cosmic ray
signals [17]. The gravitational acceleration is then extracted from the
classical formula

$z_{f}=z_{i}+v_{z}^{i}(t_{f}-t_{i})+\frac{1}{2}\overline{g}(t_{f}-t_{i})^{2}$
(2)

where the initial vertical velocity $v_{z}^{i}$ is a priori unknown. Detailed
simulations of the initial position and velocity distributions are ongoing and
using a realistic GEANT4 simulation an advanced analysis of the reconstruction
is studied.

##  6 Quantum reflection and the quantum free fall

The phenomenon of quantum reflection of $\mathrm{\overline{H}}$ on a surface
rather than being annihilated, plays an important role for the GBAR experiment
[18]. It has to be taken into consideration in the analysis of the classical
free fall experiment since $\mathrm{\overline{H}}$ can be reflected on the
free fall chamber and thus increase the measured time of flight. But the
effect can also be exploited to reach a $\overline{g}$ precision of $10^{-6}$
by detecting the interference pattern produced by anti-atoms bouncing on a
mirror surface before experiencing a classical free fall [3, 18]. The
experimental idea is based on the concept of the neutron whispering gallery
experiment [19]. A sketch of this simplified scheme considering only two
dimensions (X and Z) is shown in Fig. 5. The $\mathrm{\overline{H}}$ atoms are
dropped from a small height and bounce on a mirror of length $d$ and height
$H$ above the detection plane. The dashed lines represent the
$\mathrm{\overline{H}}$ quantum states due to the gravitational and mirror
potential. The different possible paths through these states create an
interference pattern in momentum space. By letting the atoms free fall from
the end of the mirror results in a detectable interference pattern in
position/time space as shown in Fig. 5.

Figure 4: Two dimensional scheme for the detection (red line) of quantum
interference due to quantum reflection of $\mathrm{\overline{H}}$ on a mirror
surface (blue line) [3].

Figure 5: Probability distribution on the detection plane of the interference
pattern in one dimension [3].

##  7 Summary

The unique approach of the GBAR experiment to measure the free fall of
$\mathrm{\overline{H}}$ in the Earth’s gravitational field, consists of
synthesizing $\mathrm{\overline{H}^{+}}$ and cooling it to a few $\mathrm{\mu
K}$ temperature, before photo-detaching the excess positron and releasing the
neutral anti-atom. It has been shown that the individual
$\mathrm{\overline{p}}$ deceleration works as proposed. However, reliably
producing, trapping and transporting positrons and consecutively forming
$\mathrm{Ps}$ must be improved for the beamtime in $2022$ to get
$\mathrm{\overline{H}}$ and $\mathrm{\overline{H}^{+}}$ in a second step. In
parallel the $\mathrm{\overline{H}}$ Lamb shift setup has been commissioned
with hydrogen and is ready for measurements with the anti-atoms as soon as
those are available in GBAR. Detailed simulations of the classical and quantum
free fall have been undertaken.

## Acknowledgments

This work is supported by the Swiss National Foundation under the grants
197346 and 201465.

## References

## References

  * [1] The ALPHA Collaboration, Nat Commun 4, 1785 (2013).
  * [2] P. Pérez, et. al., Hyperfine Interact 233, 21-27 (2015).
  * [3] P.-P, Crépin, et. al., Phys. Lett. A 99, 042119 (2019).
  * [4] P. Crivelli and N. Kolachevsky, Hyperfine Interact 241, 60 (2020).
  * [5] E. Myers, Phys. Rev. A 98, 010101 (2018).
  * [6] P. Crivelli, et. al., Phys. Rev. D 94, 052008 (2016).
  * [7] J. Walz and T. Hänsch, General Relativity and Gravitation 36, 561-570 (2004).
  * [8] A. Husson et. al., Nucl. Instrum. Methods A 1002, 165245 (2021).
  * [9] M. Charlton et. al., Nucl. Instrum. Methods A 985, 164657 (2021).
  * [10] V. Kostelecký and A. Vargas, Phys. Rev. D 92, 056002 (2015).
  * [11] G. Janka et. al., The European Physical Journal C 80, 804 (2020).
  * [12] B. Ohayon et. al., Phys. Rev. Lett. 128, 011802 (2022).
  * [13] A. Temsin and O. Siegmund, Proc. SPIE 3765, 441-451 (1999).
  * [14] J. Wiza, Nucl. Instrum. Methods 162, 587-601 (1979).
  * [15] L. Hilico et. al., Int. J. Mod. Phys. Conf. Ser. 30, 1460269 (2014).
  * [16] G. Janka, Lamb Shift of Exotic Atoms: Precision Measurement in Muonium and Progress Towards the First Direct Determination in Antihydrogen. Ph.D. thesis, ETHZ (2022).
  * [17] B.H. Kim, et. al., Nucl. Instrum. Methods A 973, 164162 (2020).
  * [18] G. Dufour, et. al., Advances in High Energy Physics 2015, 379642 (2015).
  * [19] V. Nesvizhevsky, et. al., Nature Physics 6, 114-117 (2010).