Project MAQS – Magnetic-Atom Quantum Simulator – aims at understanding of quantum correlations in many-body systems. Correlations are of fundamental importance for the development of quantum technologies and for their application in physics of condensed matter and quantum information. These quantum technologies should allow to create new states of matter of unusual properties in the future. A supersolid – a crystal being in a superfluid state is one of the most spectacular example of such matter.

Quantum correlations form a basis for quantum cryptography, a method of coding and transmitting information in a way which does not allow for a man-in-the-middle attack such as eavesdropping. They are also at the theoretical foundations of quantum computers, devices which according to theoretical predictions will outclass the present ones.

Quantum correlations are still very cryptic and difficult to imagine. The main idea of the MAQS project is to study quantum correlations not in the typical setting of semiconducting materials used in electronic devices but in significantly larger systems of ultracold atoms placed periodically in space in optical lattices created by laser beams, mimicking this way a real crystal. Point-like electrons of a real crystal are substituted here by much larger atoms which can be directly photographed. Such simulators will allow for a direct observation of quantum processes. Simulating of quantum matter by atoms in optical lattices should be as useful as simulating a plane in an aerodynamic tunnel.

Experimental groups from Paris, Stuttgart, Florence and Innsbruck involved in the MAQS project will use atoms of Chromium, Dysprosium and Erbium. These species are characterized by large magnetic moments, i.e. they behave like small magnets and interact mutually on relatively large distance. These dipole-dipole interactions are responsible for long-range correlations in systems of such magnetic atoms. These correlations are important for the abovementioned applications. Researchers involved in the project plan to build experimental setups allowing for strengthening of the magnetic interaction between atoms. One option is to put them in a very tight lattice of sites separated by a distance comparable to the wavelength of UV light. The other possibility is to make magnetic molecules by combining two magnetic atoms together. Such systems will be monitored using techniques allowing for ultrahigh resolution. Quantum correlations will be measured in real space as well as in momentum space. Experimental results will be analyzed in collaboration with theory groups from Lyon, Innsbruck and Warsaw. Theorists will make predictions about possible results of experiments and will develop efficient and practical methods to characterize quantum correlations in the studied systems, in particular quantum entanglement.

These new techniques, both experimental and theoretical, should allow for investigation of two types of problems: studying new states of matter such as the abovementioned supersolid phase, and exploring quantum dynamics and processes responsible for thermalization of atomic samples. Researchers believe that methods developed by the MAQS consortium which allow for a direct observation of quantum processes as well as for the creation of new states of matter and can help to make quantum technologies available for applications in our everyday life.

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)

Publications:

**Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate**

Safoura S. Mirkhalaf, Emilia Witkowska, and Luca Lepora*Phys. Rev. A* **101**, 043609 (2020)

**Producing and storing spin-squeezed states and Greenberger-Horne-Zeilinger states in a one-dimensional optical lattice**

Marcin Płodzień, Maciej Kościelski, Emilia Witkowska, and Alice Sinatra*Phys. Rev. A* **102**, 013328 (2020)

**Pauli Crystals–Interplay of Symmetries **

Mariusz Gajda, Jan Mostowski, Maciej Pylak, Tomasz Sowiński and Magdalena Załuska-Kotur*Symmetry* *12*(11), 1886 (2020)

**Criticality-enhanced quantum sensing in ferromagnetic Bose-Einstein condensates: Role of readout measurement and detection noise**

Safoura S. Mirkhalaf, Daniel Benedicto Orenes, Morgan W. Mitchell, and Emilia Witkowska*Phys. Rev. A* **103**, 023317 (2021)

**Pauli crystals in harmonic trap and on a sphere**

Filip Gampel, Mariusz Gajda, Magdalena Załuska-Kotur and Jan Mostowski*Physics Letters* **422**, 127799 (2021)

**Spin distillation cooling of ultracold Bose gases**

Tomasz Świsłocki, Mariusz Gajda, Mirosław Brewczyk and Piotr Deuar *Scientific Reports*** 11**, 6441 (2021)

**Atoms in a spin dependent optical potential: ground state topology and magnetization**

Piotr Szulim, Marek Trippenbach, Y B Band, Mariusz Gajda and Mirosław Brewczyk*New J. Phys.*** 24,** 033041 (2022)

**One- and two-axis squeezing via laser coupling in an atomic Fermi-Hubbard mode**

T. Hernández Yanes, M. Płodzień, M. Mackoit Sinkevičienė, G. Žlabys, G. Juzeliūnas, and E. Witkowska*Phys. Rev. Lett.*** 129,** 090403 (2022)

**One-axis twisting as a method of generating many-body Bell correlations**

Marcin Płodzień, Maciej Lewenstein, Emilia Witkowska, and Jan Chwedeńczuk*Phys. Rev. Lett.*** 129,** 250402 (2022)

**Accelerating many-body entanglement generation by dipolar interactions in the Bose-Hubbard model **

Marlena Dziurawiec, Tanausú Hernández Yanes, Marcin Płodzień, Mariusz Gajda, Maciej Lewenstein, and Emilia Witkowska *Phys. Rev. A* **107**, 013311 (2023)

**Manifestation of relative phase in dynamics of two interacting Bose-Bose droplets**

Maciej Pylak, Filip Gampel, Marcin Płodzień, and Mariusz Gajda *Phys. Rev. Research* **4**, 013168 (2022)

**Continouos simultaneous measurement of position and momentum of a particle **

Filip Gampel and Mariusz Gajda *Phys. Rev. A* **107**, 012420 (2023)

**On Repeated Measurements of a Quantum Particle in a Harmonic Potential**

Filip Gampel and Mariusz Gajda *Acta Phys. Pol. A ***143**, S131 (2023)

**Spin squeezing in open Heisenberg spin chains**

T. Hernández Yanes, G. Žlabys, M. Płodzień, D. Burba, M. Mackoit Sinkevičienė, E. Witkowska, and G. Juzeliūnas*Phys. Rev. B ***108**, 104301 (2023)

**Generation of scalable many-body Bell correlations in spin chains with short-range two-body interactions**

Marcin Płodzień, Tomasz Wasak, Emilia Witkowska, Maciej Lewenstein, Jan Chwedeńczuk*Preprint *

This project is supported by the National Science Center (NCN), grant no. UMO-2019/32/Z/ST2/00016.