**Superfluid fraction of a spatially modulated Bose gas**

We determine both theoretically and experimentally the superfluid fraction of a Bose-Einstein condensate subjected to a sinusoidal lattice. We show that this superfluid fraction can be obtained through the use of the celebrated Leggett’s formula or equivalently by measuring the speed of sound waves in the system.

**Reference:**

G. Chauveau, C. Maury, F. Rabec, C. Heintze, G. Brochier, S. Nascimbene, J. Dalibard, J. Beugnon, S. M. Roccuzzo, and S. Stringari

Phys. Rev. Lett. 130, 226003 (2023) (Editor’s suggestion) and arXiv:2302.01776*Superfluid fraction in an interacting spatially modulated Bose-Einstein condensate*

**Precision measurements of atom-dimer scattering length**

We create Rb_{2} dimers in their electronic ground state in a planar Bose gas via single-photon microwave photoassociation. Using high resolution spectroscopy we determine the scattering length describing low energy collisions between a dimer and the atoms of bath.

**Reference:**

C. Maury, B. Bakkali-Hassani, G. Chauveau, F. Rabec, S. Nascimbene, J. Dalibard, J. Beugnon

Phys. Rev. Research **5**, L012020 (2023) and arXiv:2211.05049*Precision measurements of atom-dimer interactions in a uniform planar Bose gas*

**Townes soliton and Bose mixtures**

Townes soliton is a celebrated example of two-dimensional soliton. It is a particular solution of the non-linear Schrödinger equation which we realize here with matter waves. Townes soliton is expected, for a given interaction strength, at a well-defined atom number and features scale-invariance. In this work, we deterministically prepare this soliton through optical imprinting in a two-component Bose gas and observe its main properties.

**References:**

B. Bakkali-Hassani, C. Maury, Y.-Q. Zou, É. Le Cerf, R. Saint-Jalm, P. C. M. Castilho, S. Nascimbene, J. Dalibard, J. Beugnon

Phys. Rev. Lett. **127**, 023603 (2021) and arXiv:2103.01605*Realization of a Townes soliton in a two-component planar Bose gas*

B. Bakkali-Hassani, C. Maury, S. Stringari, S. Nascimbene, J. Dalibard, J. Beugnon

arXiv:2207.06239*The cross-over from Townes solitons to droplets in a 2D Bose mixture*

B. Bakkali-Hassani and J. Dalibard

arXiv:2210.14045 (2022)*Townes soliton and beyond: Non-miscible Bose mixtures in 2D*

Y.-Q. Zou, É. Le Cerf, B. Bakkali-Hassani, C. Maury, G. Chauveau, P. C. M. Castilho, R. Saint-Jalm, S. Nascimbene, J. Dalibard, J. Beugnon

J. Phys. B: At. Mol. Opt. Phys. **54** 08LT01 and arXiv:2102.05492*Optical control of the density and spin spatial profiles of a planar Bose gas*

**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

Nat. Commun. **12**, 760 (2021) and 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

Phys. Rev. Lett. **125**, 233604 (2020) and 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.

**Reference:**

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.

**Reference:**

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*

**Loading and compression of a single uniform 2D Bose gas in an optical accordion**

We implemented on our new setup an optical accordion creating a lattice potential with a spacing that can be dynamically tuned between 11 and 2 µm. Atoms are loaded into a single node of this optical lattice in the large spacing configuration which is then decreased almost adiabatically to reach a strong harmonic confinement with a frequency larger than 10 kHz. This allows us to tune the effective 2D interaction strength. An additional flat-bottom in-plane potential is shaped with a high resolution thanks to a spatial light modulator (Digital Micromirror Device) combined with a microscope objective.

**Reference:**

J.L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D. Perconte, S. Nascimbène, J. Dalibard, J. Beugnon

Phys. Rev. A **95**, 013632 (2017) and arXiv:1611.07681*Loading and compression of a single 2D Bose gas in an optical accordion*

**Bose gases in box potentials: investigating Kibble-Zurek mechanism**

We studied the formation of topological defects when quench cooling Bose gases. Atoms are trapped either in a square box-like potential or in a ring. In the box potential we observed the stochastic formation of vortices (see picture) and in the ring geometry we observed the creation of superfluid currents along the ring. Using matter-wave interference techniques we were able to measure the charge and direction of these currents. We also studied in the box potential the emergence of coherence due to the transverse condensation phase transition. We compared the rate of formation of these topological defects with Kibble-Zurek mechanism predictions.

**References:**

L. Chomaz, L. Corman, T. Bienaimé, R. Desbuquois, C. Weitenberg, S. Nascimbène, J. Beugnon, J. Dalibard

Nature Commum. **6**, 6162 (2015) and arXiv:1411.3577*Emergence of coherence in a uniform quasi-two-dimensional Bose gas*

L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weitenberg, S. Nascimbène, J. Dalibard, and J. Beugnon

Phys. Rev. Lett. **113**, 135302 (2014) and arXiv: 1406.4073*Quench-Induced Supercurrents in an Annular Bose Gas*

**Superfluid behavior of a 2D Bose gas**

We demonstrated the superfluid behavior of a 2D Bose gas confined in a harmonic trap. By rotating a defect created by a repulsive laser beam we measured a threshold velocity for heating the cloud. We observed that this threshold is only present when we rotate in the superfluid inner region and not in the thermal outer region.

**Reference:**

R. Desbuquois, L. Chomaz, T. Yefsah, J. Léonard, J. Beugnon, C. Weitenberg, J. Dalibard

Nature Physics **8**, 645 (2012) and arXiv:1205.4536*Superfluid behaviour of a two-dimensional Bose gas*

**Equation of state of the weakly-interacting 2D Bose gas**

We measured the equation of state of a 2D Bose gas and compared it with theoretical predictions. The method is based on the measurement of the in situ density profile of the cloud trapped in a harmonic potential and the use of the local density approximation. We first used a method based on fitting the density profile to extract the chemical potential and the temperature. We also demonstrated a fit-free method to determine the equation of state.

**References:**

R. Desbuquois, T. Yefsah, L. Chomaz, C. Weitenberg, L. Corman, S. Nascimbène, J. Dalibard

Phys. Rev. Lett. 113, 020404 (2014) and arXiv:1403.4030*Fit-free determination of scale invariant equations of state: application to the two-dimensional Bose gas*

T. Yefsah, R. Desbuquois, L. Chomaz, K. J. Günter, J. Dalibard

Phys. Rev. Lett. 107, 130401 (2011) and arXiv:1106.0188*Exploring the thermodynamics of a two-dimensional Bose gas*

S.P. Rath, T. Yefsah, K.J. Günter, M. Cheneau, R. Desbuquois, M. Holzmann, W. Krauth, J. Dalibard

Phys. Rev. A 82, 013609 (2010) and arXiv:1003.4545*The equilibrium state of a trapped two-dimensional Bose gas*