**Exploring the topology of a quantum Hall system at the microscopic level **

Quantum Hall systems are characterized by the quantization of the Hall conductance — a bulk property rooted in the topological structure of the underlying quantum states. In condensed matter devices, material imperfections hinder a direct connection to simple topological models, and restrict the existence of fragile topological phases to defect-free samples. Artificial systems, as realized with photonic platforms or cold atomic gases, open novel possibilities by enabling specific probes of topology or flexible manipulation e.g. using synthetic dimensions encoded in internal degrees of freedom. However, the sizes of synthetic dimensions realized so far remain moderate, making the notion of a bulk irrelevant. We realized a disorder-free quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension and one synthetic dimension encoded in the atomic spin *J*=8. We demonstrated that the large number, 2*J*+1=17, of magnetic sublevels leads to distinct behaviors in the bulk, where motion is inhibited due to a flattened energy band, and along the edges, where the particles are free to move in only one direction. We also showed that the low-energy excitations take the form of cyclotron and skipping orbits. Furthermore, we measured the transverse drift induced by a weak force, and found a uniform Hall response in the bulk, reaching 98(5)% of the quantized value expected for a topological system. Our findings pave the way towards the realization of quantum many-body systems with non-trivial topology, such as mean-field Abrikosov vortex lattices or fractional quantum Hall states, as supported by numerical simulations of interacting bosons in our setting.

T. Chalopin, T. Satoor, A. Evrard, V. Makhalov, J. Dalibard, R. Lopes, S. Nascimbene*Exploring the topology of a quantum Hall system at the microscopic level *

arXiv:2001.01664 (2020)

**Probing quantum criticality and symmetry breaking at the microscopic level **

We report on an experimental study of the Lipkin-Meshkov-Glick model of quantum spins interacting at infinite range in a transverse magnetic field, which exhibits a ferromagnetic phase transition in the thermodynamic limit. We used Dysprosium atoms of electronic spin *J*=8, subjected to a quadratic Zeeman light shift, to simulate 2*J*=16 interacting spins 1/2. We probed the system microscopically using single magnetic sublevel resolution, giving access to the spin projection parity, which is the collective observable characterizing the underlying Z2 symmetry. We measured the thermodynamic properties and dynamical response of the system, and studied the quantum critical behavior around the transition point. In the ferromagnetic phase, we achieved coherent tunneling between symmetry-broken states, and tested the link between symmetry breaking and the appearance of a finite order parameter.

V. Makhalov, T. Satoor, A. Evrard, T. Chalopin, R. Lopes, S. Nascimbene*Probing quantum criticality and symmetry breaking at the microscopic level*

Phys. Rev. Lett. **123**, 120601 (2019)

**Sensing magnetic fields with non-gaussian quantum fluctuations **

The precision of a quantum sensor can overcome its classical counterpart when its constituants are entangled. In gaussian squeezed states, quantum correlations lead to a reduction of the quantum projection noise below the shot noise limit. However, the most sensitive states involve complex non-gaussian quantum fluctuations, making the required measurement protocol challenging. Here we measured the sensitivity of non-classical states of the electronic spin J=8 of dysprosium atoms, created using light-induced non-linear spin coupling. Magnetic sublevel resolution enabled us to reach the optimal sensitivity of non-gaussian (oversqueezed) states, well above the capability of squeezed states and about half the Heisenberg limit.

A. Evrard, V. Makhalov, T. Chalopin, L.A. Sidorenkov, J. Dalibard, R. Lopes, S. Nascimbene*Enhanced magnetic sensitivity with non-gaussian quantum fluctuations*

Phys. Rev. Lett. **122**, 173601 (2019)

**Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom**

Coherent superposition states of a mesoscopic quantum object play a major role in our understanding of the quantum to classical boundary, as well as in quantum-enhanced metrology and computing. However, their practical realization and manipulation remains challenging, requiring a high degree of control of the system and its coupling to the environment. We used dysprosium atoms – the most magnetic element in its ground state – to realize coherent superpositions between electronic spin states of opposite orientation, with a mesoscopic spin size J=8. We drove coherent spin states to quantum superpositions using non-linear light-spin interactions, observing a series of collapses and revivals of quantum coherence. These states feature highly non-classical behavior, with a sensitivity to magnetic fields enhanced by a factor 13.9(1.1) compared to coherent spin states – close to the Heisenberg limit 2J=16 – and an intrinsic fragility to environmental noise.

T. Chalopin, C. Bouazza, A. Evrard, V. Makhalov, D. Dreon, J. Dalibard, L.A. Sidorenkov, S. Nascimbene*Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom*

Nat. Commun. **9**, 4955 (2018)

**Anisotropic light-shift and magic-polarization of the intercombination line of Dysprosium atoms in a far-detuned dipole trap**

We characterized the anisotropic differential AC Stark shift for the Dy 626 nm narrow line transition, induced in a far-detuned 1070 nm optical dipole trap, and observed the existence of a “magic polarization” for which the polarizabilities of the ground and excited states are equal. From our measurements we extracted both the scalar and tensorial components of the dynamic dipole polarizability for the excited state, αse=179(5)α0 and αte=35(2)α0, respectively, where α0 is the atomic unit for the electric polarizability. Furthermore, we utilized our findings to optimize the efficiency of Doppler cooling of a trapped gas, by controlling the sign and magnitude of the inhomogeneous broadening of the optical transition.

T. Chalopin, V. Makhalov, C. Bouazza, A. Evrard, A. Barker, M. Lepers, J.-F. Wyart, O. Dulieu, J. Dalibard, R. Lopes, S. Nascimbene*Anisotropic light-shift and magic-polarization of the intercombination line of Dysprosium atoms in a far-detuned dipole trap*

Phys. Rev. A **98**, 040502(R) (2018)

**Magneto-optical trapping of Lanthanide atoms on a narrow optical transition**

We studied the magneto-optical trapping of Dysprosium atoms on a narrow optical transition. The Dysprosium atoms are laser cooled using the optical transition at 626 nm, whose small linewidth of about 100 kHz leads to a Doppler temperature of 3.3 microK. As the radiative forces are relatively weak, gravity plays a crucial role and may lead to a complete polarization of the atomic spin. In this regime, we trap up to several hundred million atoms at a temperature of 10 microK. We also investigated the influence of light-induced molecular dynamics, which leads to atom loss and additional heating.

D. Dreon, L. A. Sidorenkov, C. Bouazza, W. Maineult, J. Dalibard, S. Nascimbene*Optical cooling and trapping of highly magnetic atoms: The benefits of a spontaneous spin polarization*

J. Phys. B: At. Mol. Opt. Phys. **50**, 065005 (2017) .pdf

Previous projects can be found here.