Members of the MAQS consortium include:

* *Coordinator: Bruno Laburthe-Tolra (CNRS, FR)*

* Tommaso Roscilde (ENS of Lyon, FR)

* Francesca Ferlaino (Institut für Quantenoptik und
Quanten-information, AT)

* Tilman Pfau (Universität Stuttgart, DE)

* Giovanni Modugno (Istituto Nazionale di Ottica, IT)

* Maciej Lewenstein (Institute of Photonic Sciences, ES)

* Mariusz Gajda (Instytut Fizyki Polskiej Akademii Nauk,
PL)

We propose a quantum simulator made of magnetic atoms in periodic
potentials, which will enable the investigation of quantum-many
body problems associated with long-range dipole-dipole
interactions. We propose to develop a number of new tools to
increase the strength of dipole-dipole interactions
(shorter-period UV lattices, magneto-association of magnetic atoms
into molecules with a stronger magnetic moment), and to control
and measure their interaction at the nano-scale (using
super-resolution techniques and narrow spectroscopic lines). Most
importantly, we will develop new probes to certify the presence of
quantum correlations, which are expected to be particularly strong
in these many-body long-range interacting systems. Experimentally,
we will either probe correlations in real space (microscope,
double-well lattices), in momentum space (Doppler spectroscopy,
time-of-flight), or in the spin sector. These probes will be
developed in close collaboration with theory, to find the best
ways to define and quantify entanglement.

Working towards these aims, our results so far
include: (i) the construction of two new quantum gas microscope
experiments to probe Er and Dy individually, or in a mixture
combination. (ii) the experimental characterization of
correlations by measuring collective spin fluctuations. (iii) a
number of new proposals to characterize entanglement in large spin
systems, such as: methods relevant for quantum gas microscopes;
data-driven approaches to reconstruct optimal Bell inequalities
and entanglement criteria tailored on the input of experiments,
based on collective measurements; methods to retrieve higher-order
correlations from single-shot images; methods to reveal
entanglement in momentum space. A number of new numerical methods
have been devised (time-dependent variational approach,
time-dependent Schwinger-boson approach) or implemented (DMRG,
Exact Diagonalization, BCS mean-field), which allowed to explore
out-of-equilibrium dynamics, and a variety of models with
long-range interactions such as the extended Bose-Hubbard model,
long-range Kitaev chains, long-range XXZ model, or phonon modes in
polarized magnetic atoms localized in an optical lattice.

These first achievements set us in a good way to
complete our program, which is to show that lattice-trapped
magnetic atoms can be used as quantum simulators, in order to
investigate various families of problems. First, we our aim is to
probe low energy phases, and second, out-of-equilibrium situations
to investigate dynamics and quantum thermalization. Thanks to
these improvements, a number of phases could now be within
experimental reach, such as the supersolid or stripe phases, or
peculiar phases of spin systems with long-range interactions. We
will aim at protocols to certify the nature of the quantum
correlations within these systems. Such correlations can be
explored in four different complementary setups: 1) an Er lattice
gas within a Dy bath (Innsbruck); strongly dipolar lattice gases
made of either 2) Dy atoms in UV lattices (Stuttgart) or 3) Dy2
molecules in standard lattices (Pisa/Florence), and 4) Cr atoms
realizing lattice spin models (Paris).

Chromium atoms in their ground state
have a large spin, and a large permanent magnetic dipole moment. The
long range and anisotropic dipole-dipole interactions between the
atoms confer to ultracold chromium gases unique properties.

# Introduction to the
chromium project:

## A dipolar condensate:

## Studies using a chromium BEC:

### see also
PICTURES of our experimental set-up.

**An experimental platform for quantum systems simulation **

By loading a chromium BEC in optical lattices, we have obtained a Mott insulator state comprising a dipolar species, and for the first time demonstrated intersite interactions between the atoms [1]. The dipolar spin exchange dynamics which takes place in this intrinsically many-body system is in agreement with our plaquette simulations taking into account quantum correlations. Our spin system is an excellent tool for quantum simulation, with an interplay between long-range dipolar and short range Van der Waals interactions. We varied the lattice depth from the superfluid to the Mott insulator regime to investigate the coupling between spin dynamics and transport [2].

Our recent research on this topic includes the study of the relaxation of spins after they are tilted with respect to their initial direction. The spins interact under the effect of dipole-dipole interactions, and the many-body system is thus an isolated system which relaxes due to inner forces. We have explored this scenario of quantum thermalization, where the final steady state corresponds to a thermal-like state whose apparent entropy is due to many-body entanglement. Our experiment is well captured by semiclassical simulations based on a discrete Monte Carlo sampling in phase space, that reveal the growth of entanglement during the thermalization process [3].

**Control and use of the spin degrees of freedom**

In a chromium BEC, inelastic dipolar collisions provide spin-orbit
coupling which allows thermalizing the spin degrees of freedom.
Thanks to this thermalization, we have demonstrated a new cooling
mechanism, based on a purification of the BEC after transfer of
thermal atoms in excited Zeeman states [4]. We also have
investigated the interplay between spin dynamics and Bose
condensation to create a multicomponent BEC when a fast shock
cooling process is performed on a depolarized sample [5].

**Production of a new dipolar Femi Sea**

We have obtained the first chromium Fermi Sea with the 53Cr
isotope, despite low isotopic abundance, and extreme complexity of
the atomic structure due to hyperfine splitting. We have taken
advantage of a favourable interspecies scattering length to
optimize evaporation of a Bose Fermi mixture [6]. Loading of
dipolar fermions in optical lattices offer us new possibilities
for quantum magnetism studies.

Selection of publications: (see complete list here and abstracts here)

- De Paz
A., Sharma A., Chotia A., Maréchal E., Huckans J.H., Pedri P.,
Santos L., Gorceix O., Vernac L., Laburthe-Tolra B.,

*Non-equilibrium quantum magnetism in a dipolar lattice gas,*

Physical review letters,**111**, 185305, (2013) - S. Lepoutre, J.
Schachenmayer, L. Gabardos, B. Zhu, B. Naylor, E. Maréchal,
O. Gorceix, A. M. Rey, L. Vernac & B. Laburthe-Tolra,

*Out-of-equilibrium quantum magnetism and thermalization in a spin-3 many-body dipolar lattice system,*

Nature Communications volume**10**, 1714 (2019)

Our team has constructed an experimental setup to generate Bose-Einstein condensates (BECs) made of Chromium atoms. These atoms bear unusual properties due to their exceptionally high magnetic dipole moment. By transferring the chromium BECs into optical lattices, we create and study artificial systems of perfect purity and valuable tunability. Indeed, we can change almost at will their temperature, density, interactions, confining potential strength and shape, etc. Such systems mimic complex systems at the heart of modern condensed matter physics, in particular those related to quatum magnetism. Furthermore, those systems are promising components for the quantum treatment of information. Ultracold atom physics is growing as a fascinating interdisciplinary domain.

Fig 1 : formation of the chromium BEC by forced
evaporation in an optical trap.

The chromium BEC allow us to performed different sudies, using the specificities of chromium. The field of quantum dipolar gases offers many opportunities for research that we are exploring with a particularly strong interest for the transfer of quantum dipolar gases into optical lattices (1D, 2D and 3D).

Another attractive issue is the realization of a
Fermi sea with the fermionic isotope ^{53}Cr. We have
already shown that our experimental set-up allow to prepare at the
same time a mixture of cold fermions and bosons.