**Tan’s two-body contact across the superfluid transition of a planar Bose gas**

We developed a spectroscopic method to measure Tan’s contact for a weakly interacting two-dimensional Bose gas across the Berezinskii-Kosterlitz-Thouless superfluid transition. Our measurements connect well to theoretical predictions both in the low and high temperature regimes. Around the critical region, further theoretical efforts are required to describe our data.

**Reference :**

Y. -Q. Zou, B. Bakkali-Hassani, C. Maury, É. Le Cerf, S. Nascimbene, J. Dalibard, J. Beugnon

arXiv:2007.12385*Tan’s two-body contact across the superfluid transition of a planar Bose gas*

**Magnetic dipolar interaction between hyperfine clock states in a planar alkali Bose gas**

Using high resolution spectroscopy, we show that the two hyperfine clock states of rubidium atoms, despite their zero magnetic moment feature magnetic dipole-dipole interactions in a planar Bose gas. We show that the induced frequency shift is independent of the cloud shape and size but that it can be controlled thanks to the orientation of an external magnetic field.

**Reference :**

Y. -Q. Zou, B. Bakkali-Hassani, C. Maury, É. Le Cerf, S. Nascimbene, J. Dalibard, J. Beugnon

arXiv:2007.12389*Magnetic dipolar interaction between hyperfine clock states in a planar alkali Bose gas*

**Dynamical symmetry and breathers in a two-dimensional Bose gas**

We investigated the far from equilibrium dynamics of a 2D cloud of atoms in an harmonic trap. Starting from a uniform density distribution with various shapes, we use scaling/conformal invariance properties of the weakly-interacting 2D Bose gas to describe the dynamics of the cloud. In particular, we show how to connect the evolutions of clouds of different sizes and atom numbers in 2D harmonic traps with variable frequencies. Finally, we reveal the existence of two specific breather solutions: a triangle evolves periodically with a period *T*/2 (see picture) and a disk with a period 2*T*, where *T* is the period associated to the harmonic confinement. This surprising observation is confirmed by numerical simulations of the Gross-Pitaevskii equation but it remains a challenge to justify it from the basic properties of this equation.

**Reference :**

R. Saint-Jalm, P.C.M. Castilho, E. Le Cerf, B. Bakkali-Hassani, J.L. Ville, S. Nascimbene, J. Beugnon, J. Dalibard

Phys. Rev. X **9**, 021035 (2019) and arXiv:1903.04528*Dynamical symmetry and breathers in a two-dimensional Bose gas*

**Sound propagation in a 2D superfluid Bose gas**

We studied the propagation of sound in a 2D Bose gas confined in a box potential. Below the critical temperature for the superfluid transition, we observed the propagation of a sound wave with a velocity compatible with the hydrodynamic prediction for second sound. Above the critical temperature we observed an unexpected damped sound mode that is attributed to a collisionless sound mode.

**References :**

J.L. Ville, R. Saint-Jalm, E. Le Cerf, M. Aidelsburger, S. Nascimbène, J. Dalibard, J. Beugnon

Phys. Rev. Lett. **121**, 145301 (2018) and arXiv:1804.04037

see also Synopsis in APS Physics*Sound propagation in a uniform superfluid two-dimensional Bose gas*

**Phase relaxation when merging independent BECs**

We investigated the relaxation of the phase profile after merging a set of independent BECs arranged in a ring configuration. During the relaxation process superfluid currents are stochastically formed at long times. We fully characterized the distribution of winding numbers of these superfluid currents and compare it to the geodesic rule prediction. We also studied the short time evolution to gain a microscopic insight into the merging dynamics.

**References :**

M. Aidelsburger, J.L. Ville, R. Saint-Jalm, S. Nascimbène, J. Dalibard, J. Beugnon

Phys. Rev. Lett. **119**, 190403 (2017) and arXiv:1705.02650

*Relaxation Dynamics in the Merging of N Independent Condensates*

* *

**Light diffusion in a cold and dense 2D gas**

Our 2D gas is an interesting system to investigate light diffusion. Our dense clouds allow us to investigate the regime where the typical distance between atoms is smaller the the optical wavelength. In this regime, atoms respond collectivelly to the light excitation. Understanding the response of this many-body system is a challenging issue. We performed two experimental studies in which we studied first the coherent response of the cloud, probing the light transmission through the atomic slab and second the incoherent response looking at in-plane photon propagation after a localized excitation.

**References :**

L. Corman, J.L. Ville, R. Saint-Jalm, M. Aidelsburger, T. Bienaimé, S. Nascimbène, J. Dalibard, J. Beugnon

Phys. Rev. A **96**, 053629 (2017) [Editor’s suggestion] and arXiv:1706.09698

*Transmission of near-resonant light through a dense slab of cold atoms*

R. Saint-Jalm, M. Aidelsburger, J.L. Ville, L. Corman, Z. Hadzibabic, D. Delande, S. Nascimbène, N. Cherroret, J. Dalibard, J. Beugnon

Phys. Rev. A **97**, 061801(R) (2018) and arXiv:1802.04018*Resonant-light diffusion in a dense disordered atomic layer*