# Experimental perspectives on the matter-antimatter asymmetry puzzle:
developments in electron EDM and $\bar{\textrm{H}}$ experiments

D. Comparat  Laboratoire Aimé Cotton, CNRS, Université Paris-Sud, ENS Paris
Saclay, Université Paris-Saclay, Bâtiment 505, 91405 Orsay, France  C.
Malbrunot  TRIUMF, Vancouver, British Columbia V6T 2A3, Canada  McGill
University, Montréal, Québec, H3A 2T8, Canada  S. Malbrunot-Ettenauer  TRIUMF,
Vancouver, British Columbia V6T 2A3, Canada  Department of Physics, University
of Toronto, Toronto M5S 1A7, Canada  E. Widmann  Stefan Meyer Institute for
Subatomic Physics, Austrian Academy of Sciences, 1030 Vienna, Austria  P.
Yzombard  Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL
Université, Collège de France, Paris, 75252, France

###### Abstract

In the search for clues to the matter-antimatter puzzle, experiments with
atoms or molecules play a particular role. These systems allow measurements
with very high precision, as demonstrated by the unprecedented limits down to
$10^{-30}$ e.cm on electron EDM using molecular ions, and relative
measurements at the level of $10^{-12}$ in spectroscopy of antihydrogen atoms.
Building on these impressive measurements, new experimental directions offer
potentials for drastic improvements. We review here some of the new
perspectives in those fields and their associated prospects for new physics
searches.

##  1 Introduction

The asymmetry between the matter and antimatter content of our universe is one
of the most tantalizing puzzle of modern physics. Many experimental endeavours
are focused on searching for manifestations of the mechanisms that would
produce such an asymmetry. The main contender for an asymmetry-generating
mechanism is CP (Charge and Parity) symmetry violation which, together with
the other Sakharov conditions [1], would generate baryon asymmetry. In the
Standard Model CP-violation present in the CKM matrix fall short by about 10
orders of magnitude to be a possible explanation for the observed baryon
asymmetry of the universe (BAU). The observation of BAU is thus one of the
clear indications of the existence of physics beyond the Standard Model (SM).
The possibility of a baryon asymmetry generation through heavy neutron leptons
(HNL) creation in the early universe has triggered a renewed interest in HNL
searches at colliders (see for example [2], references therein and numerous
dedicated work). Direct measurements of CP violation in the lepton sector are
carried out by long-baseline neutrino experiments [3, 4]. In a complementary
approach to searches at high energies, low energy precision experiments are
looking for lepton-number violating processes such as neutrinoless double beta
decay [5] or scrutinize atoms and molecules in the quest for the existence of
electric dipole moments (EDM) of elementary particles that would indicating P
and T (time-reversal) symmetry violations [6] the latter being equivalent to
CP violation within a CPT-conserving theory. Many beyond-the-Standard-Model
theories predict EDMs close to current experimental sensitivities [7].

In this paper we will review some of the new experimental perspectives for EDM
searches using atoms and molecules which have potential for impressive
improvements to the state-of-the-art while facing challenges that are
currently being addressed by a new and active community. Alternatively, BAU
can be addressed through the lens of CPT violation. CPT violation combined
with baryon number violation could lead to baryon asymmetry in thermal
equilibrium and would have the advantage of being otherwise independent of C-
and CP-violating processes [8, 9]. However, since CPT conservation, through
the so-called CPT theorem, is established as a cornerstone of quantum field
theory, theories involving spontaneous breaking of CPT symmetry are much less
common. Nevertheless, CPT violation arises in various string theory models
(e.g. [10, 11]), as well as in models where the assumptions of the CPT
theorem, such as Lorentz invariance or unitarity are not fulfilled. The group
of Kostelecky has constructed an effective field theory, the Standard Model
Extension (SME), a generalization of the Standard Model and General Relativity
that allows for arbitrary Lorentz and CPT violations. Those violations are
quantitatively controlled by a set of coefficients whose values are to be
determined or constrained by experiment [12]. Tests of CPT violation through
the comparison of fundamental properties of matter and antimatter particles
have been pursued in many sectors; from collider experiments to quasi table-
top experiments. In particular, since about 20 years, experiments at the
antiproton decelerator (AD) at CERN have been dedicated to taming antihydrogen
atoms in order to allow extremely precise comparisons of their atomic spectral
transitions with the analog ones measured in hydrogen. A precision of $2\times
10^{-12}$ [13] has been reached on the 1S-2S transition of trapped
antihydrogen atoms which is only 3 orders of magnitude away from the best
precision achieved on the same transition in a beam of hydrogen. Triggered in
part by the successful laser cooling of antihydrogen atoms [14], perspectives
for substantial improvement of precision are being investigated with slow
beams of hydrogen in a fountain setting. Aside from spectroscopy measurements,
experiments at the AD started more recently exploring diverse experimental
techniques to measure the effect of gravity on neutral atoms made - as far as
valence quarks are concerned - of antimatter. As with spectroscopy
measurements, the realization of sources of slow (anti)-hydrogen atoms will be
the path to high precision. In particular an exciting perspective lies in the
first measurement of (anti)-atomic gravitational quantum states.

##  2 Directions in next generation EDM measurements

An EDM is originating from a spatial separation of opposite electrical charge.
If an EDM of elementary particle exists this extra moment should be aligned
with the spin of the particle to avoid creating an extra degree of freedom
that would make two different electrons, for example, discernible in violation
of the Pauli principle. Since the spin changes sign under time reversal while
the spatial charge distribution remain unchanged, an EDM of an elementary
particle would be an indication of T (and thus through CPT theorem of CP)
violation. Such EDMs of elementary particles clearly differ from conventional
EDMs such as the ones present in polar molecules which are not violating time
reversal symmetry. As discussed in many recent review articles [15, 7, 16],
the quest for an EDM of a fundamental particle originated over seventy years
ago with Ramsey and Purcell’s proposal to test discrete symmetries like
parity. EDMs of elementary particles are strongly suppressed in the Standard
Model of particle physics but are predicted with different magnitudes in
various new physics scenarios. As time passed, numerous experimentally viable
systems, including atoms and molecules, have contributed to setting
increasingly stringent constraints on potential EDMs.

Studying both paramagnetic and diamagnetic systems is necessary for probing
different CP violating mechanisms that induce EDMs. Here, we’ll first focus on
paramagnetic systems, particularly electron EDM (eEDM), which use methods
similar to those for diamagnetic systems [6, 7]. In gas phase experiments,
spectroscopy techniques measure the energy shift $\Delta
E=-\bm{d}_{e}.\bm{E}_{\rm eff}-\bm{\mu}.\bm{B}$ due to applied external
electric $\bm{E}_{\rm ext}$ and magnetic $\bm{B}$ fields. The relationship
between $\bm{E}_{\rm ext}$ and the effective field $\bm{E}_{\rm eff}$ seen by
the electron is connected to Schiff’s theorem and relativistic effects
yielding to [17] $E_{\rm
eff}\sim(\qty{200}{GV/cm})(Z/80)^{3}{{\epsilon}}_{s}{{\epsilon}}_{p}$ for a
$|s{\rangle}$ (we use the standard notation for the orbital angular momentum)
valence electron wave-function
$\left|{\Psi}\right\rangle{\approx}{{\epsilon}}_{s}\left|s\right\rangle+{{\epsilon}}_{p}\left|p\right\rangle+{\dots}$
(value typically reduced by an order of magnitude for a $d$ electron or two
orders of magnitude for an $f$ one) with a $\left|p\right\rangle$ character
created by the external Stark Shift. Thus, high-$Z$ atoms with strongly s-p
hybridized electron wavefunctions under an external field are ideal. For
atoms, weak polarization by $\bm{E}_{\rm ext}$ leads to $E_{\rm
eff}\propto\bm{E}_{\rm ext}$ in the range of $\qtyrange{1e4}{1e7}{V/cm}$,
while polar molecules require only a small $E_{\rm ext}$ (few V/cm) for full
polarization (Stark mixing of opposite parity states) of the molecular bond,
giving $\epsilon_{s}\sim\epsilon_{p}\sim 1/\sqrt{2}$ and thus many orders of
magnitude higher effective field, in the $\qtyrange{1e10}{1e11}{V/cm}$ range.

###  2.1 EDM searches with radioactive molecules

Molecules in which one of the constituent atoms contains a radioactive nucleus
represent intriguing systems for EDM searches. As explained above, high-Z
atoms provide a substantial increase in sensitivity for eEDM experiments. The
ACME collaboration, for instance, exploits the naturally occurring thorium
isotope 232Th ($Z=90$ and a half-life of $1.4\cdot 10^{10}$ years)
incorporated in a thorium monoxide (ThO) molecule. Taking advantage of an
internal electric field of $E_{\rm eff}=78$ GV/cm in the used excited
electronic state, ACME currently establishes a limit on the eEDM of
$|d_{e}|<1.1\cdot 10^{-29}$ e cm (90% confidence limit) [18]. This compares
favourably to $E_{\rm eff}=23$ GV/cm found in singly-charged hafnium
monofluoride (HfF+) which builds upon stable Hf atoms with $Z=72$. While its
HfF+ measurement holds since recently the tightest bound on an eEDM, i.e.
$|d_{e}|<4.1\cdot 10^{-30}$ e cm [19, 20], the next generation JILA experiment
will replace HfF+ with ThF+. This is motivated by the higher $Z$ in
(radioactive) Th and, thus, larger $E_{\rm eff}$ as well as a longer coherence
time reflecting that the EDM sensitivity is found in the electronic ground
state of the molecule [21].

Inspired by the successes and prospects for molecules with long-lived
radionuclides, the research with molecules has recently been extended to
molecular systems containing short-lived atomic nuclei [22]. In these cases
the half-lives are as short as weeks, days or even less. Hence, these
radioisotopes do not occur naturally but can be synthesized in specialized
radioactive ion beam (RIB) facilities. Note that the radioactivity itself is
in most cases not of advantage for these EDM studies but rather an unavoidable
feature of specific nuclides of interest, e.g. when extending to higher Z or
selecting specific nuclear shapes all atomic nuclei are eventually found to be
radioactive. Thus, exploiting short-lived radionuclides allows one to tailor
molecular systems ideally suited for next-generation EDM searches. For
instance, atomic nuclei along an isotopic chain of a chemical element possess
different nuclear spins which provides an opportunity to systematically
explore nuclear-spin dependency of EDM-inducing electron-nucleon couplings
within the same molecular system. Such a program would be difficult to pursue
when being limited to stable or long-lived nuclides. In the previously
mentioned molecules, thorium has a single long-lived isotope, 232Th with a
nuclear spin $I=0$ and is in addition to an eEDM sensitive to nuclear spin-
independent electron-nucleon interaction [23]. The same is true for most
stable or long-lived hafnium isotopes. The exceptions, 177Hf ($I=7/2$) and
199Hf ($I=9/2$), exhibit large spins which complicates experimental efforts
given the many states induced by the hyperfine interaction.

As another major advantage, the work with short-lived radioactive globally
opens the region ‘above’ the stable lead isotope 208Pb on the nuclear chart in
which no chemical element has a stable isotope and many also lack long-lived,
naturally occurring ones. For example, the longest-lived francium (Fr) isotope
is 223Fr with a half-life as short as 23 min. However, intriguing physics
phenomena manifests in this region in and around the actinides. In particular,
strong evidence for octupole-deformed (’pear-shaped’) nuclei has been
collected in radon (Rn), Fr, radium (Ra), actinium (Ac), Th, and protactinium
(Pa) isotopes [24, 22] (and references therein). This exquisite shape, rarely
observed in atomic nuclei, facilitates an enhanced sensitivity for time-
reversal violation inside the atomic nucleus which would otherwise - by force
of a ’re-arrangement’ of the electron cloud- be strongly obscured from
experimenters probing atomic or molecular EDMs. This shielding effect [25] is
formulated in Schiff’s theorem in the limit of nonrelativistic quantum
mechanics but is incomplete also due to the finite size and deformation of the
atomic nucleus. This is referred to as the nuclear Schiff moment. As the
nucleus interacts with the surrounding electrons, the Schiff moment causes a
polarisation of the electron cloud which leads to an atomic or molecular EDM.
This gives rise to small energy shifts in atomic/molecular states when the
spin of the atomic nucleus is aligned along, or against, an external electric
field that polarizes the electron cloud.

For octuple-deformed nuclei the Schiff moment can be large such that the
sensitivity of detecting nuclear T-reversal breaking via an atomic or
molecular EDM is significantly enhanced compared to spherical nuclei [26]. At
this time, the tightest experimental bound on a nuclear Schiff moment arises
from measurements in the (stable) mercury isotope 199Hg. Its measured EDM
limit of $|d_{Hg}|<7.4\cdot 10^{-30}$ e cm (95% confidence limit) translates
to a nuclear Schiff moment of $|S_{Hg}|<3.1\cdot 10^{-13}$ e fm3 [27].
Octuple-deformed nuclei are estimated to come along with enhancement factors
for nuclear Schiff moments which can be two to three orders of magnitude
larger than in 199Hg. Experimental efforts to directly benefit from this
increased sensitivity are pursued in Ra, e.g. [28]. Another strategy, newly
adopted for the next generation of experiments, is to complement the
advantages offered by heavy, octupole-deformed nuclei with the additional
enhancement factors when incorporating them into molecules [22]. These can be
as large as 1’000-10’0000 resulting to a combined increase in intrinsic
sensitivity to nuclear Schiff moments by up to seven orders of magnitude
compared to 199Hg. Such an enormous discovery potential has its price; all
experimentally known examples of (static) octupole deformation are found in
radioactive nuclei and are consequently available only in minute sample sizes
at RIB facilities.

Low yields and short half-lives are commonly encountered in the science of
rare isotopes. Thus, a sophisticated tool box of experimental techniques has
been developed to address them. Among those, methods of atomic, molecular and
optical (AMO) physics such as ion and atom trapping as well as laser
spectroscopy have been specifically adapted to the challenges when exploiting
physics opportunities with RIBs [29]. Exemplary highlights under ’extreme
experimental conditions’ include ion-trap based mass measurements of
radionuclides with half-lives below 10 ms [30] or with yields less than 1 ion
per hour delivered to experimenters [31]. Laser spectroscopy of radioactive
atoms has a long history of successful exploitation of high-resolution methods
such as collinear laser spectroscopy as well as highly sensitive approaches
such as resonant ionization spectroscopy. The field is continuously re-
inventing itself by exploring new experimental methods as well as by expanding
its scientific horizon [32].

As a ground-breaking example of this innovative processes, the successful
formation and identification of molecules containing Ra isotopes in an ion
trap [33] as well as the first spectroscopy of radium monofluoride (RaF)
molecules [34, 35] have been the starting whistle for experimental work with
radioactive molecules. While the general perspective of this newly emerging
field is summarized in Ref. [22], molecules which have been proposed in the
context of EDM searches are for instance RaF [36, 37, 34], RaOH [38, 39], RaO
[40], RaH [41], RaOCH${}_{3}^{+}$ [33, 42], AcF [43], or short-lived ThO [44],
as well as ThOH+, ThF+ [44] or AcO+ [45].

Although their intrinsic enhancement factors are enormous, the radioactive
nature of octupole-deformed nuclides will generally translate into lower
statistics compared to stable molecules or atoms. Hence, experimental
initiatives to measure nuclear Schiff moments with radioactive molecules often
consider atom and ion traps as well as embedding them inside cryogenic solids
to extend the coherence and observation time of the available samples.
Moreover, studies have been initiated to optimize the efficient formation of
these molecules [46], to obtain colder samples, e.g. via direct laser cooling,
sympathetic cooling with co-trapped laser-coolable ions [47] (or atoms), or
formation of molecules starting from ultra-cold atoms themselves [48]. Since
present knowledge about the structure of radioactive molecules is in most
cases based on theoretical calculations, one critical experimental effort will
focus on the spectroscopy of these molecules in order to further characterize
their suitability for EDM searches.

The emerging interest in (short-lived) radioactive molecules in general and in
their potential for unprecedented sensitivity in EDM searches in particular
coincides with the completion of next-generation RIB facilities such as FRIB
at MSU, ARIEL at TRIUMF, FAIR at GSI, or SPIRAL2 at GANIL. An increased
variety in RIBs is therefore expected for experiments, in combination with a
significantly larger availability of specific radionuclides of interest. The
latter will be facilitated by new multi-user capabilities either via parasitic
use of radioactive ions downstream of another RIB experiment or by multiple
driver beams at a single RIB facility enabling simultaneous RIB production and
delivery to various experimental stations. Since known octupole deformed
nuclei have with a few exceptions half-lives of days to years, offline
operation of a previously irradiated production target or isotope harvesting
from a facility’s beam dump are attractive resources of radionuclides of
interest. Hence, the worldwide network of RIB facilities provides an excellent
foundation for the research of radioactive molecules and their use as novel
EDM probes [22].

###  2.2 Solid state systems and cryogenic matrices

The measurement of permanent EDM in atomic, molecular, and nuclear systems can
be conducted in both the gas phase and solid phase. While the gas phase
technique is the most used and established, solid samples can offer
advantages. The first key edge being the macroscopic number $N$ of atoms or
molecules present in a given sample during the total integrated interrogation
time directly improving the statistical averaging of the sensitivity
$\sigma_{d}$ of an EDM measurement: $\sigma_{d}\approx\frac{\hbar}{\epsilon
E_{\rm eff}\tau\sqrt{N}}$; where ${\tau}$ is the single-shot (travelling or
coherence time limited) measurement time, and ${\epsilon}$ the visibility or
polarization fraction of atoms/molecules (i.e. dipole alignment or spin state
preparation efficiency). So, by combining the very high atomic density with
the large sample size of solids, many order of magnitude improvement in
sensitivity can theoretically be expected compared to beam or ion trap
experiments. The second advantage, suggested by Shapiro in 1968, is that new
observables, in addition to the pure spectroscopy shift $\Delta E$, can be
used. This is due to the fact that the electric dipole moment $\bm{d}$ of a
particle is aligned to its total angular momentum and thus to its magnetic
moment $\bm{\mu}$. Compared to the gas phase, two additional measurement
schemes can be used: alignment of $\bm{d}$ using $\bm{E}_{ext}$, creating
macroscopic magnetization due to $\bm{\mu}\|\bm{d}$; or alignement of
$\bm{\mu}$ using $\bm{B}$, leading to dielectric polarization (since
$\bm{d}\|\bm{\mu}$). Both effects can be measured in a sample. A typical setup
for such solid state experiment is shown in Figure 1.

Figure 1: Schematics of a solid state EDM experiment. A solid (in blue), often
formed at or cooled to cryogenic temperature, is doped with high density atoms
or molecules (in green), pumped and probed by lasers under external electric
and/or magnetic fields. The alignment of the EDM $\bm{d}$ along the spin is
schematized on the zoomed part on the right: illustrative case for Cs, or BaF,
doped in solid Ar [49, 50] with a trapping site with one dopant surrounded by
4 vacancies (white) in a tetrahedral symmetry of an fcc crystal (in blue).

####  2.2.1 EDM in solid: results to date

year | sample | eEDM limit in e·cm | method |
---|---|---|---|---
1961 |  KCr- & NH4\- (SO4)2 12H2O | $d_{e}<10^{-13}$ | spectroscopy | [51]
1963 |  Al2O3:Cr & MgO:Cr | $d_{e}=(1\pm 4.6)\texttimes 10^{-16}$ | spectroscopy | [52]
1979 | nickel-zink-ferrite | $d_{e}=(8.1\pm 11.6)\texttimes 10^{-23}$ | Magnetometry | [53]
2004 | GdIG | $d_{e}=(2\pm 3)\texttimes 10^{-24}$ | Voltage | [54]
2011 | GGG | $d_{e}=(-5.57\pm 7.98\pm 0.12)\texttimes 10^{-25}$ | Magnetometry | [55]
2012 |  Eu0.5Ba0.5TiO3 | $d_{e}=(-1.07\pm 3.06\pm 1.74)\texttimes 10^{-25}$ | Magnetometry | [56]
Table 1: List of solid state systems used for eEDM searches and their
published bound results. Whenever stated, statistical and systematic
uncertainties are provided in this order.

We have listed in Table 1 all (to our knowledge) eEDM in solid state results.
The first successful eEDM search in a solid system was performed in 1961 on a
mono-crystal at cryogenic temperatures using a modified version of the
electron paramagnetic resonance (EPR) spectroscopy. The measurement employed
an electric field to measure the linear stark splitting due to the eEDM. In
1963, an improved measurement using Cr atoms in alumina or magnesia applied
both electric and magnetic fields, enabling a line shift measurement. However,
after these works, no further eEDM search using EPR in solids was published.
In 1979, a measurement was performed on nickel-zinc ferrite using an
oscillating electric field and a SQUID to measure the magnetization from the
eEDM-induced sample polarization. Later, two new magnetometry measurements
were conducted on paramagnetic Gadolinium-Gallium-Garnet (GGG) and
Eu0.5Ba0.5TiO3. The GGG measurement had improved sensitivity and systematics
control, while the Eu solid experiment faced challenges due to
ferroelectricity and ferroelectric relaxation. Despite the difficulties, the
Eu solid measurement provided the most stringent eEDM limit in a solid-state
experiment to date due to the enhanced polarizability inside the ferroelectric
crystal. Only one attempt was made to measure the eEDM-induced electric
potential after applying a magnetic field. The experiment used ferrimagnetic
GdIG with Yttrium-doped samples to achieve specific compensation temperatures.
However, complications arose from the pinning of magnetic domains,
significantly limiting the measurement’s sensitivity.

####  2.2.2 EDM in solid: new directions

Following previous work in the above-mentioned experiments, a new direction
started to recently gain importance: the use of atoms or molecules embedded in
a frozen gas at cryogenic temperatures. The idea of matrix isolation
spectroscopy to measure the eEDM is not new and was first proposed by C. Pryor
and F. Wilczek in 1987 [57]. The use of molecules was then mentioned in Refs.
[58, 59]. The main idea is to isolate EDM-relevant species in rare gas
crystals, which are chemically inert elements and thus should not affect
strongly their hosts, allowing them to be manipulated using lasers similarly
to molecular beam experiments. One of the first serious experimental
investigations was undertaken by the group of A. Weis (see the review [60])
using laser desorption of Cs atoms in pressurized solid 4He. Results were not
reproducible because of ion and electrons created by the laser shots with the
clear-cut conclusion that ”one cannot expect an experiment using cesium atoms
implanted in helium crystals to be competitive with other existing EDM
experiments.” [61]. However, thanks to the work of J. D. Weinstein’s group, on
alkali atoms in para-hydrogen, Ne, and Ar matrix [62, 63, 64] there has been
renewed interest in using matrix isolation spectroscopy for EDM searches [19].
Indeed, recent achievements regarding high dopant density
$\sim\qty{1e18}{cm^{3}}$, while maintaining long spin coherence time (as long
as 0.1s) and good optical pumping capacity, are all very positive first steps
toward an initial EDM measurement or spin alignment [65, 66, 67, 68]. After
the proposal [69], a series of studies on atoms (Rb, Cs, Tm, Yb, …) and
molecules (BaF, RaF, ..) in rare-gas (Ne,Ar mainly) or parahydrogen matrices
were conducted[70, 71, 72, 49, 73, 50, 74, 75, 76]. Besides the high sample
size and other advantages mentioned above, measurements in solid can also
offer a few potential additional benefits: the crystal field (typically on the
order of tens of MV/cm) can produce high $E_{\rm eff}$ values, molecules could
align themselves along the local crystal axes due to specific trapping site
environment [69, 50, 74]. This phenomenon would mitigate many of the
systematic effects associated with applying an external electric field during
the EDM measurement cycle. Obviously many other specific systematic effects
have to be mastered along the way to an EDM measurement including laser and
fields stability alignment and homogeneity, isotopic purity quality and
reproductibility of the samples, inhomogeneous broadening effects, magneto-
electric coupling, bleaching effect, diffusion of particles, residual
magnetization or polarization, dielectric relaxation, heat formation or
lattice deformation under application of fields or cryostat-induced vibrations
etc.

These will open and feed collateral areas of research such as sensitive
(co-)magnetometers for instance with co-dopants or using polyatomic molecules
[77], single crystals growth [78, 79, 80], individual atomic detection by
optical means or by ionisation and electrons’ extraction [81, 82, 83], quantum
control and sensing [84] that may help in reaching higher sensitivities in the
future.

####  2.2.3 Related experiments

The EDM experimental apparatus can often be used to detect other spin-
dependent interactions or other tiny effects that would affect the atomic
properties [85]. Among them is the search for ultralight bosonic dark matter
[86] such as axion like particles that typically produced time-varying EDMs,
the effect of which being possibly detected using atomic transitions [87, 88].
This opens new perspectives for dark matter searches such as followed by the
Cosmic Axion Spin Precession Experiment (CASPEr) [89] or by the DEMIURGOS
project [82]. The nEXO experiment is another example of the application of
trapping in cryogenic matrices. nEXO is searching for neutrinoless double beta
decay in xenon; the tagging of the 136Ba atom daughter, resulting from the
decay of 136Xe, is a powerful technique to discriminate background. One of the
techniques for Ba-tagging consists of trapping the atom in a solid xenon
matrix and detecting it through fluorescence imaging [81]. Similar EDM type of
solid state experiments can sometimes be realized using liquid, where spin
precession (of NMR type) measurement can be favored compared to solid phase,
but keeping the advantage of the high density [90, 91]. However in solid, the
existence of a preferential axis of symmetry allow for anisotrope couplings
between angular momenta. In such systems new parity violating observable arise
giving sensitivity to nuclear anapole moments for instance [92, 93, 94, 95,
96].

Ultimately, this solid state methodology can be effectively integrated with
radioactive atoms or molecules housed within crystals. A number of experiments
are progressing towards identifying the best conditions using a transparent
crystal, ideal for optical pumping, which is either doped or stoichiometric
for maximum density, and based on radioactive molecules, which provide high
enhancement and co-magnetometry properties, along with a closed, separately
aligned parity doublet [97, 75, 98, 99, 22, 100]. This illustrates the
profusion of new developments in this area and presages exciting results.

##  3 Directions in next generation $\bar{\textrm{H}}$ experiments

###  3.1 Toward fountain experiments

####  3.1.1 State of the art

The ALPHA collaboration at CERN has in recent years performed several
spectroscopy measurements in antihydrogen trapped in a Ioffe-Pritchard trap
(IPT) [101]: the observation [102] and determination of the 1S-2S two-photon
laser transition (cf. Fig.2 (left) for the various transitions) with accuracy
of $2\times 10^{-12}$ [13], and the observation of $n=1$ hyperfine transitions
[103] and their determination to $4\times 10^{-4}$ precision [104].
Measurements were also done on the $n=2$ fine structure [105] and the
Lyman-$\alpha$ transition [106], which allows the extraction of the Lamb shift
in antihydrogen to a moderate precision of 11 % [105]. A first observation of
laser cooling using a Lyman-$\alpha$ laser [14] promises to achieve narrower
line widths and thus higher precision for the 1S-2S transition.

Figure 2: Left: Level diagram of hydrogen and antihydrogen. Right: Breit-Rabi
diagram of antihydrogen. For hydrogen the quantum numbers $(F,M_{F})=(1,-1)$
and $(1,1)$ are exchanged.

For the 1S-2S transition, the precision that can be ultimately reached in a
trap is difficult to estimate. The best measurement of hydrogen using a cold
beam in a field-free region has an accuracy of $4.2\times 10^{-15}$ [107]. The
measurement of [13] with $\overline{\mathrm{H}}$ was done at a background
field of $B\sim 1$T (needed to trap $\overline{\mathrm{p}}$ before forming
$\overline{\mathrm{H}}$), which leads to a shift of $\sim 600$ kHz
($\widehat{=}\,2.5\times 10^{-10}$). This shift has to be corrected using QED
calculations that depend on the actual value of $B$ which needs to be measured
separately. Furthermore, the velocity distribution of $\overline{\mathrm{H}}$
atoms having finite temperature causes the atoms to move in regions of varying
magnetic field inside the trap, leading to a modification of the line shape
that has to be modeled using simulations. Achieving higher precision will
therefore require one to measure H in the same trap, in which case – since the
line shape depends on the velocity distribution of the atoms – also the
temperature has to be controlled. Alternatively, the atoms can be moved into a
field-free region for spectroscopy as described in the next section.

In-trap hyperfine spectroscopy is more difficult as the magnetic fields and
field gradients necessary for trapping lead to large Zeeman shifts. One can
use combinations of electron spin-flip transitions that yield the zero-field
HFS splitting $\nu_{\mathrm{HF}}$ without knowing the magnetic field, as done
in [103, 104] which extracted $\nu_{\mathrm{HF}}$ = $\nu_{\pi_{1}}$ –
$\nu_{\pi_{2}}$ (cf. Fig.2 (right)). A next step in precision could be
achieved by using double resonance methods as proposed by ALPHA [108], driving
one electron spin flip (e.g. $\nu_{\pi_{1}}$) and one proton spin flip
transition (($F,M_{F})=(1,0)\rightarrow(1,-1)$) simultaneously and making use
of the fact that proton spin-flip transitions have a magnetic-field
insensitive point at $B\sim 0.65$ T [109].

ASACUSA has proposed an in-beam method for hyperfine spectroscopy [110, 111,
112], and shown that the method works at the ppb level with hydrogen [113].
Based on this result they estimated that with a few thousand antihydrogen
atoms, an accuracy of ppm could be reached. A straight-forward extension of
the currently used Rabi method would be to employ a Ramsey method of separated
oscillatory fields [114, 115], where a further factor $\sim 20$ could be
gained. The group of T. Hänsch at the MPQ Munich, has pioneered this method
for optical spectroscopy by applying it to a cryocooled hydrogen beam. They
observed Ramsey fringes on the two-photon 1S-2S transition [116], and improved
the resolution of the line to 6 parts in 10-13, which was the world record at
that time for the resolution of a transition for neutral atoms.

####  3.1.2 Fountain experiments

Figure 3: Schematic drawing of a setup to create ultra-cold H through
evaporative cooling in a superconducting trap IPT1. H atoms can either be
trapped in a normal-conducting trap IPT2 and dropped onto a superfluid He
film, or trapped in IPT3 and released to form a fountain. Adopted from [117].

A further substantial increase in precision can be obtained by moving to much
slower atoms in a field free region. The slower the atoms, the longer they
interact with the applied laser or microwave radiation and thus the narrower
the lines become. This is true as long as the resulting line width is larger
than the natural line width of the transition or the line width of the
radiation source. The best way towards slower atoms is to follow the path of
ultra-cold atoms and to create a fountain from trapped (anti)hydrogen atoms,
where (anti)atoms are expelled from the inhomogeneous field region needed for
trapping and cooling to a field-free region where spectroscopy can be
performed. RF spectroscopy has e.g. been demonstrated in a fountain created
from laser-cooled Na atoms [118], and Cs fountain clocks provide currently the
most accurate definition of the SI second (see e.g. [119]). Cs fountain clocks
make use of a Ramsey method, where the same cavity is traversed twice, once
upwards and twice downwards, reducing systematic effects for a situation with
two cavities. The idea of optical Ramsey spectroscopy applied to hydrogen
atoms in a fountain is a long term endeavor. Simulations show [120] that a
resolution of the natural line width of the 1S-2S transition and thus sub-Hz
precision can be obtained.

Indeed, for (anti)hydrogen, the potential energy difference of 1 m in the
Earth gravitational field corresponds to a temperature of a few mK, and
velocities of a few m/s. Such temperatures can be reached for H in cryogenic
traps using evaporative cooling, e.g. as used in the formation of a Bose
Einstein Condensate of hydrogen [121]. As described in sec. 3.2 3.2.4, the
GRASIAN collaboration [122] has built a large octupole IPT and demonstrated
its operation [117]. Based on this, experiments can be foreseen that use
either trapped H at $T\sim 100\,\mu$K and launch a fountain inside a cryostat,
or alternatively let them fall across a cavity onto a superfluid He film where
they will be reflected and, when passing the cavity again, perform a Ramsey
measurement (cf. Fig. 3, more details will be given in sec. 3.2 3.2.4). For
hyperfine measurements a well-defined magnetic field environment needs to be
created by shielding external fields and applying a homogeneous background
field at the position of the atoms. Such experiments can also be applied to
$\overline{\mathrm{H}}$ as proposed by the GBAR collaboration, see sec. 3.2
3.2.4.

HAICU [123] is another recent experiment aiming at creating a fountain
interferometer compatible with both hydrogen and antihydrogen atoms. It
foresees magnetically compressing (anti)-hydrogen atoms into a mm-scale volume
where three-dimensional Doppler-cooling is applied. A next cooling stage is
achieved via adiabatic expansion to another trap to reach micro-Kelvin
energies before a magnetic launch into a fountain volume.

###  3.2 Gravitational quantum states

####  3.2.1 GQS principle and the historical experiment

The framework of Gravitational quantum states (GQS) of particles was first
derived in 1928 [124] with a massive particle inside a triangular potential
well, and soon it became a popular problem for students in many textbooks on
quantum mechanics [125, 126]. Only nearly 75 years later, scientists
demonstrated this phenomenon through the direct observation of the first GQS
on neutron [127]. Confined on the bottom by the quantum reflections (QR) on a
mirror and on top by gravity, Ultra Cold Neutrons (UCNs) were measured to only
exist in discrete quantum states, as theoretically expected [128]. But until
now, the GQS of atoms, predicted to exist following the same physics than for
the neutrons (n), have never been observed. After the observation of GQS of
neutrons, active analysis of the peculiarities of these phenomena was
initiated and their applications to the search for new physics, such as the
searches for extra fundamental short-range interactions [129], verification of
the Weak Equivalence Principle in the quantum regime [130], extensions of
quantum mechanics [131], extensions of gravity and space theories or tests of
Lorentz invariance [132, 133] were studied. Similar impacts on modern physics
is expected to be triggered by the studies of GQS on (anti)-hydrogen, as for
instance for the WEP tests [134]. The aim of this section is to give a glimpse
about some of the possibilities offered by the studies of GQS and QR with
anti-atoms/atoms. Compared to neutrons, H atoms (whose mass is similar to n)
allow for a larger and slower particle flow allowing a better resolution of
these states. They are a good testbench before moving towards the studies of
GQS on anti-atoms. Besides, compared to neutrons, the reflection mechanism is
different for (anti-)H since it occurs without any contact to the surface,
allowing one to probe different interactions [135]. As (anti)-hydrogen is the
simplest atom (only two particles bound together), its properties can be
calculated very precisely [136] ; thus it is an ideal probe to test precisely
new physics [137, 138]. GQS studies could also be applied to various exotic
systems, such as Muonium or Positronium [139], and recent development on
sources of slow Ps ($\sim$ 10 K) atoms could serve the observation of GQS on
these purely leptonic antimatter-matter bound systems [140].

Figure 4: Figure from [141], cover of EPJD, 77 (March 2023): GQS eigenstates
of 1 atomic-mass particle trapped inside the gravity (top) and QR (bottom)
potential well.

GQS principle: The particle (neutron, H, $\overline{\mathrm{H}}$, etc)
wavefunction $\psi(z)$ in the Earth’s gravitational field ($V(z)=mgz$) above
an ideal mirror is governed by the Schrodinger equation
$\frac{\hbar^{2}}{2\,m}\frac{d^{2}\psi(z)}{dz^{2}}(E-mgz)\psi(z)=0$; where
$\hbar$ is the reduced Planck constant, $m$ is the particle’s mass, $z$ is the
height (perfect reflector at $z$=0), $E$ is the energy of the vertical motion
of the particle, and $g$ is the acceleration in the Earth’s gravitational
field. The solutions of such equations are given by the Airy functions and the
eigenstates are plotted in Fig. 4, with typical energy splitting of peV. In
short, in order to form GQS, the particles need to be trapped long enough
between the gravitational potential and the reflecting surface. Indeed,
following the Heisenberg uncertainty principle $\Delta\tau\,\Delta$E
$\geq\frac{\hbar}{2}$, the time of flight $\Delta\tau$ that the atoms spend in
the confinement region should be long enough such that the uncertainty on the
energy of the states $\Delta$E decreases to be much smaller than the typical
energy of the GQS ($\sim$ peV). The typical interaction time is in $\sim$ms.
This theoretical statement leads to some stringent experimental requirements
(slow enough particles) and explains why the direct observation of QGS remains
currently challenging. Let us point out that GQS of n, H and
$\overline{\mathrm{H}}$ are expected to be formed essentially via identical
process. First, the only parameter of the particle which enters to the
Schrodinger equation for a neutral particle above a perfect mirror is its mass
$m$. Details studies have been performed about the effect of heavier mass
particles and how it affects the GQS derivation [142], but for our discussion
the considered particles n, H and $\overline{\mathrm{H}}$ have nearly the same
mass, close to the atomic mass unit. Second, the flat surface is nearly a
perfect mirror for sufficiently slow H and $\overline{\mathrm{H}}$ due to the
high probability of quantum reflection [143, 135] and the fact that the
characteristic range of raising the surface potential, $\approx
10^{-10}-10^{-9}$ m, is much smaller than the particle wavelength in GQS
$\approx 10^{-5}$ m, such that the particles only see an infinite steep
potential when approaching the surface, and bounce back due to quantum
reflection.

####  3.2.2 Realizing the historical ”fly-through” experiment with hydrogen

The GQS of neutrons have been observed for the first time in 2002 at ILL
[127]. A sketch of the experiment is shown in Fig. 5 (left). A flux of
collimated slow neutrons impinging at grazing angles to a bottom surface (flat
silicon mirror), and on top of it, an “absorber” scatters any neutron that
reaches the top surface, such that only the particles with a well-defined
quantum state fitting in the gap between the mirror and absorber are detected
at the exit. The experiment consists in lifting slowly the absorber above the
mirror such that the spacing between the two increases. As shown in Fig. 5
(right), in the classical regime, we expect the detected flux to increase
continuously as the space between mirror and absorber increases. Whereas, in
the quantum regime, the neutrons can only pass through if the gravity quantum
states can exist between the mirror and absorber, meaning that the spacing is
wider than the typical spread of wavefunction of the GQS. Until reaching the
typical spacing of the first QGS, no flux is expected to be detected. Then, as
the spacing is large enough, a first flux of neutrons is detected,
corresponding to the neutrons into the first GQS ; and in the same way for the
next GQS. In case of QGS formation, the flux of particles detected is a step-
wise form, as experimentally measured (Fig. 5 (right)) for neutrons [127].

Figure 5: (left): experimental schematic for the detection of GQS of neutrons.
(right) experimental data [127] compared to the two flux models (classic and
quantum regimes).

A new international collaboration, GRASIAN [122], aims to observe for the
first time the QGS of hydrogen, using a fly-through experiment similar to what
has been realised with neutrons. A test-bench experiment is being developed at
ETH Zürich in the group of P. Crivelli [141]; results of this experiment will
determine the developments of the rest of the program. Mainly, the foreseen
goals are to use the GQS to test new physics such as extra fundamental short-
range interactions [129] or perform CPT tests [138], developing similar
experiments to antihydrogen (See Sec 3.2.3 below). Another long-term project
would be to trap H [117] for enough time in order to form long-living GQS, and
perform precision microwave and optics spectroscopy to resolve the shifts in
energy due to the GQS, probing then short-range forces (see Sec. 3.2.4
below.).

####  3.2.3 Quantum reflection (QR) experiments

Quantum reflection of massive particles is a well-known and theoretically
well-described phenomenon [135]. Decades ago, hydrogen [144, 145, 146, 147]
and other systems [148] have been scattered off liquid helium surfaces while
neon [149] and sodium atoms [150] have been reflected from room temperature
surfaces. In several cases the sticking probability was measured and not
directly the reflectivity, and in direct measurements at best values of 60$\%$
were observed [150]. The development of cryogenic sources of H beam opens the
possibility of directly measure the high QR ratio theoretically predicted for
(anti-) hydrogen, due to rapidly varying Casimir-Polder potential appearing in
the vicinity of the surface and that can lead to specular reflectivities ¿95
$\%$ [151, 152, 135, 153]. This would allow to “store” hydrogen for long times
by multiple bounces on surfaces, which in turn would allow spectroscopy of
hydrogen with unprecedented accuracy, see Sec. 3.2.4. Within the GRASIAN
collaboration, an experiment at the Stefan Meyer Institute (Vienna) in the
group of E. Widmann, is under development. The idea is to use a cryogenic
hydrogen beam ($\sim$ 4 K), collimated and sent at grazing angle onto
different surfaces, to first measure the QR coefficient (comparison between
specularly reflected and scattered atoms).

QR and GQS formations of ultra-cold anti-atoms find an appealing application
for the measurement of the Earth gravitational acceleration, such as for
instance, within the GBAR collaboration [154]. Shortly, the principle of GBAR
is to form an antihydrogen ion ($\overline{\mathrm{H}}$+), in order to co-trap
it with a laser-cooled berrylium atom, in a Paul trap. Once sympathetically
cooled to $\delta E_{Kin}\sim 10\mu eV$ a photodetachment laser shot removes
the exceeding positron, leading to the neutral $\overline{\mathrm{H}}$ atom to
”fall” under gravity. With a time of flight measurement, the initial proposal
aimed for a 1$\%$ resolution on the ”g” measurement. Due to the extremely low
initial temperature of the $\overline{\mathrm{H}}$ for the GBAR measurement,
intensive studies have been performed to understand the QR that will occur on
the vacuum chamber’s walls of the experiment [135, 153]. An interesting
proposal is to make use of these highly probable quantum reflections that will
enable the formation of GQS after several quantum bounces and improve the
direct tests of the Weak Equivalent Principle [155, 134]. Indeed, careful
calculations have been derived and show that an improvement on the expected
sensibility on the measurement on ”g” could reach $10^{-5}$ [156] relative
uncertainty using only $N_{\overline{\mathrm{H}}}=$ 1000 anti-atoms. To put
this number in perspective, as of now, the direct experimental bounds on the
ratio of gravitational mass and inertial mass for antihydrogen are :
$-65<(\frac{M_{g}}{M})_{\bar{\textrm{H}}}<110$ [157]. The principle of the
measurement is sketched in Fig. 6 left, where the initial wavepacket $\zeta$
of one $\overline{\mathrm{H}}$ is shown, that takes into account the photon-
recoil from the photo-detachment process as well as the micro-motion from the
RF trap (using the frequency trap $f$ as a simulation parameter). The anti-
atom falls under the gravitational Earth’s field and undergoes several QR
(red-dashed curve) on the bottom surface of the vacuum chamber, leading to the
formation of gravitational quantum states (depicted in black dashed energy
levels) and to some interferences in the momentum distributions of the anti-
atoms. After a free fall of H $=30$ cm, the interferences can be detected
using a position-sensitive detection (annihilation of the
$\overline{\mathrm{H}}$ can be positioned with 10 $\mu$m resolution), a
typical reconstructed signal is plotted in Fig.6, right. A new design of the
free-fall chamber could enhance even more the resolution of g with fewer
$\overline{\mathrm{H}}$ down to N=10 only [158].

Figure 6: Figure from [156]. Left: schematic representation of the concept of
the experiment. The blue horizontal line represents the quantum mirror of
radius d. The atoms are released at a mean height h above the mirror with a
dispersion $\zeta$ in all space directions. An absorber (orange line) is
placed above the mirror allowing nmax Gravitational Quantum States to pass
through the device. H is the free-fall height, Y and T the positions in space
and time of the detection events on the detector plate in red. Right: the
quantum interferences from the different GQS of the $\overline{\mathrm{H}}$
atoms, lead to the probability current density J(Y; T) on the detection plate,
for Z = - 30cm and X = 0. Parameters: fRFtrap = 20 kHz, $\delta$E = 10
$\mu$eV, $N_{\overline{\mathrm{H}}}=$ 1000.

####  3.2.4 Spectroscopy with ultra-cold trapped (anti)-H

As mentioned in Sec. 3.1, the highly resolved spectroscopy of anti-H/H atoms
is a key method for CPT and direct tests of the QED predictions. We dealt with
the possibility of doing spectroscopic measurement in Ramsey-type fountain
based experiments previously. To continue the overview on possible GQS
experimental applications, let’s discuss here another project that aims to
trap and form 100 µK hydrogen atoms. Trapping and cooling hydrogen atoms at
low temperature and high enough density to form BEC was only performed once by
the group of D. Kleppner at MIT [121] and in the two-dimensional H gas at the
University of Turku [159] in 1998.

A new proposal of trapping H atoms using a magnetic trap for cooling a large
number of H atoms below 1 mK has been recently developed within GRASIAN [160],
in the Turku University in the group of S. Vasiliev. From this preliminary
trap, the cold atoms will be transferred to a secondary trap IPT2 for
selecting only the lowest velocities [117]. Then, the ultra-slow atoms will be
released and fall to bounce onto superfluid helium coated surface, being
trapped by gravity on top and QR on bottom. A vertical magnetic field will
ensure the transverse confinement, forming what has been called a magneto-
gravitional trap [161]. The liquid He surface presents the weakest interaction
potential and provides nearly perfect reflecting conditions for low-energy
atoms [151, 152], allowing for long trapping time ¿ 1s, and enabling the
formation of long-living GQS states (high n). Within this magneto-
gravitational trap, highly resolved spectroscopy of 1S-2S states of H atoms
(natural linewidth of $\sim$ 1.2 Hz or 0.125 s lifetime), will be possible,
with drastically reduced second-order Doppler effect, one of the main
systematic effects limiting the current measurement [107]. The ultimate goal
would be to be able to perform the spectroscopy of the GQS energy splitting
($\sim$ 200 Hz difference between the n=1 and n=2 GQS states on hydrogens),
with various spectroscopic methods, such as Ramsey-type spectroscopy described
in [161]. Building upon ALPHA’s Ioffe Pritchard trap (magnetic bottle type
trap) for antihydrogen atoms, the laser cooling developed in the same
apparatus [14], and the 1S-2S spectroscopy methods that are currently being
improved to eventually match the precision achieved in H atoms [13], could
open a path for performing the GQS spectroscopic measurements on ultra-cold
antihydrogen atoms as well. This would allow an ultimate direct comparison
with $\overline{\mathrm{H}}$/H predictions for the GQS energy shifts, where
one could dream of probing the Casimir-Polder shifts on the quantum levitated
states [155]. Directly measuring the energy shifts induced by the formation of
the GQS for both hydrogen and its anti-atom will enable one to test the theory
on short-distance forces [162, 152].

Hyperfine spectroscopy of H could also be performed from the ultra-cold
hydrogen source described above. Here it will not be possible to use the GMT
trap as the strong magnetic field gradients would lead to large frequency
shifts. HFS measurements need to be performed in a region of small but
extremely homogeneous magnetic field. As indicated in Fig. 3, the cold atoms
held at the bottom of IPT2 can be released, traverse a microwave cavity and be
reflected from a superfluid He film. On the way up they pass the cavity a
second time, creating a Ramsey measurement. The atoms can be retrapped at
IPT2, or let fall again to repeat the process. For a fall distance of 10 cm,
the QR coefficient is $\sim 0.88$ [151] and the round-turn time for one bounce
is 0.2 s. Thus it should be possible to reach interaction times of order 1
second, promising sub-Hz precision. For lateral confinement a tube covered
with superfluid He can be used.

Theory also predicts lifetimes of H/$\overline{\mathrm{H}}$ in GQS above
superfluid He of more than 1 s [151], allowing alternatively to build a maser
with walls coated with superfluid He. Both methods can also be used for
$\overline{\mathrm{H}}$, provided a source of $\sim 100\leavevmode\nobreak\
\mu$K temperature can be prepared using e.g. the method proposed by GBAR [154]
or HAICU [123].

##  4 Conclusion

We have reviewed here some of the new experimental developments addressing the
matter-antimatter asymmetry puzzle using atomic and molecular systems. These
low energy systems have the advantage of offering potentials for unprecedented
precision building upon AMO techniques which are being further developed in
the search for CP and CPT symmetry violations. Some of the endeavours
discussed are table-top like experiments (EDM measurements in cryogenic
matrices, hydrogen spectroscopy). Others require accelerators facilities to
generate exotic species (radioactive molecules and antihydrogen atoms), and
thus represent complementary experimental approaches to address fundamental
particle physics questions. In the case of CP violation searches with electron
EDM two major next-generation endeavours are being pursued to surpass gas-
phase experiments’ sensitivities. The first one consists in using short-lived
radionuclides in tailored molecular systems to benefit from extremely large
enhancement factors. The second one consists in combining very high densities
(as offered by solid samples in previous searches) while retaining key
properties for quantum control such as optical pumping techniques, using
cryogenic matrices. On the CPT tests side, the realm of high precision
spectroscopy with antihydrogen atoms and the successful attempts at laser
cooling have widened the horizons and renewed interest in hydrogen fountains
and slow atomic beams in general in particular in view of the increased
precision and perspective for new physics searches that quantum gravitational
states measurement would offer. These ambitious new efforts highlight the
dynamism of the field and the potentials offered by high-precision small- to
mid-scale experiments in the search for physics beyond the Standard Model.

## Acknowledgement

We acknowledge S. Lahs, V. Nesvizhevsky, F. Nez, and S. Reynaud for fruitful
discussions. This work was in part supported by the Agence Nationale de la
Recherche (ANR) under the project ANR-21-CE30 -0028-01, the Austrian Science
Fund (FWF) [W1252-N27] (Doktoratskolleg Particles and Interactions), and the
Natural Sciences and Engineering Council of Canada (NSERC). TRIUMF receives
federal funding via a contribution agreement with the National Research
Council of Canada.

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