# Disordered Quantum Gases with Tunable Interactions

## Disordered Quantum Gases with Tunable Interactions

Permanent staffThomas Bourdel (contact), Alain Aspect,

PhDs: Lucas Lavoine, Alfred Hammond

##### If you are interested in our research, do not hesitate contact us. We offer positions at all levels.

In particular, we offer an internship at M1 or M2 level this year on the development of arbitrary potentials using a digital micro-mirror device.

stage_2021

## Our Research

We especially study gases in reduce dimensions (1D, 2D), where quantum and thermal fluctuations are most important. Importantly, we work with potassium 39, a bosonic element having nice magnetically tunable Feshbach resonances, thus permitting the control of the interatomic interaction. We can add a controllable amount of disorder thought a speckle light field. Disorder competes with the interaction induced superfluidity. For example a superfluid to insulator transition is observed in 2D Bose gases. We can also study non-interacting phenomena such as Anderson localization, i.e. the absence of diffusion due to multiple quantum interference. Recently, we have studied the superfluid propagation in a 1D disordered trap of bright solitons; condensed clouds of atoms which remain together because of attractive interaction.

In April 2017, we have changed the experimental setup, replacing the stainless steel science chamber with a small glass cell (click to see a video). The new setup permits the production of condensates every 6-7 seconds and it allows for high numerical aperture imaging, fast change of the magnetic field and easy RF transfers between spin states, thus allowing quenches of the interaction parameters. This new setup is especially suitable for the study of quantum droplets.

## Some results

#### Observation of the algebraic localization delocalization transition in a 1D disordered potential with a bias force

 Schematic of the experimental sequence. A non-interactiing BEC is launched in a 1D speckle potential. At intermediate disorder strength, both localized and propagating atoms are observed. One-dimensional (1D) Anderson localization phenomena are strongly affected by a bias force, or equivalently a voltage in electronic systems. We experimentally study this case, launching a non-interacting $^{39}$K Bose-Einstein condensate in a 1D disordered potential induced by a far-off-resonance laser speckle, while controlling a bias force. In agreement with theoretical predictions, we observe a transition between algebraic localization and delocalization as a function of our control parameter that is the relative strength of the disorder against the bias force. We also demonstrate that the transition is intrinsically energy independent and that the initial velocity of the wave-packet only plays a role through an effective disorder strength due to the correlation of the disorder.

#### Non-linear scattering of atomic bright solitons

 Histograms of the reflected fraction of slow moving atoms in a disorder potential. a) atoms in a soliton. c) non-interacting atoms. We observe nonlinear scattering of 39K atomic bright solitons launched in a one-dimensional (1D) speckle disorder. We directly compare it with the scattering of non-interacting particles in the same disorder. The atoms in the soliton tend to be collectively either reflected or transmitted, in contrast with the behavior of independent particles, thus demonstrating a clear nonlinear effect in scattering. The observed strong fluctuations in the reflected fraction, between zero and 100%, are interpreted as a consequence of the strong sensitivity of the system to the experimental conditions and in particular to the soliton velocity. This behavior is reproduced in a mean-field framework by Gross-Pitaevskii simulations.

#### Production of strongly bound 39K bright solitons

 Propagation of 39K bright solitons. We report on the production of 39K matter-wave bright solitons, i.e., 1D matter-waves that propagate without dispersion thanks to attractive interactions. Our solitons, close to the collapse threshold, are strongly bound and will find applications in fundamental physics and atom interferometry.

#### All-optical production of Bose-Einstein condensates with tunable interaction

 Size of the condensate after expansion for a variable interaction parameter. We have achieved Bose-Einstein condensation of potassium 39 in an all-optical cooling scheme. It permits to reduce the duration of the experimental cycles to a few seconds. The interactions between atoms are controlled in order to optimize the collision rate during the evaporation and can then be tuned to any desirable value. As an example, we have studied the radial expansion of the gas from an elongated trap exploring the 1D to 3D crossover.

#### Gray molasses cooling of 39K to a high phase-space density

 Temperature of the D1 gray molasses as a function of the D1 cooling intensity per beam. We have developed new techniques in cooling 39K atoms using laser light close to the D1 transition. First, a new compressed-MOT configuration is taking advantage of gray molasses type cooling induced by blue-detuned D1 light. It yields an optimized density of atoms. Then, we use pure D1 gray molasses to further cool the atoms to an ultra-low temperature of 6 µK. The resulting phase-space density is 2x10-4 and will ease future experiments with ultracold potassium. As an example, we use it to directly load up to 3x107 atoms in a far detuned optical trap, a result that opens the way to the all-optical production of potassium degenerate gases.

#### Effect of disorder close to the superfluid phase transition in a two-dimensional Bose gas

 Typical example of a speckle disorder. The superfluid phase transition can be studied as a function of the disorder strength. We experimentally study the effect of disorder on trapped quasi two-dimensional (2D) 87Rb clouds in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. The disorder correlation length is of the order of the Bose gas characteristic length scales (thermal de Broglie wavelength, healing length) and disorder thus modifies the physics at a microscopic level. We analyze the coherence properties of the cloud through measurements of the momentum distributions, for two disorder strengths, as a function of its degeneracy. For moderate disorder, the emergence of coherence remains steep but is shifted to a lower entropy. In contrast, for strong disorder, the growth of coherence is hindered. Our study is an experimental realization of the dirty boson problem in a well controlled atomic system suitable for quantitative analysis.

#### Coherence properties of a 2D trapped Bose gas around the superfluid transition

 2D Momentum distribution for different atom number. The left image corresponds to a normal gas, the middle one to a gas at the superfluid transition and the right one to a gas deep in the superfluid phase. The shrinking of the momentum distribution is related to the increasing coherence in the 2D gas when crossing the BKT superfluid transition. We measure the momentum distribution of a 2D trapped Bose gas and observe the increase of the range of coherence around the Berezinskii-Kosterlitz-Thouless (BKT) transition. We quantitatively compare our observed profiles to both a Hartree-Fock mean-field theory and to quantum Monte-Carlo simulations. In the normal phase, the momentum distribution is observed to sharpen well before the phase transition. This behavior is partially captured in a mean-field approach, in contrast to the physics of the BKT transition.

## Publications

• L. Lavoine, T. Bourdel, 1D to 3D beyond-mean-field dimensional crossover in mixture quantum droplets, arXiv:2011.12394 (2020).
• G. Berthet, L. Lavoine, M. Parit, A. Brolis, A. Boissé, T. Bourdel, Observation of the algebraic localization-delocalization transition in a 1D disordered potential with a bias forcearXiv:1908.01511Phys. Rev. Research 2, 013386 (2020).
• A. Tenart, C. Carcy, H. Cayla, T. Bourdel, M. Mancini, D. Clément, Two-body collisions in the time-of-flight dynamics of lattice Bose superfluidsarXiv:1909.13648Phys. Rev. Research 2, 013017 (2020).
• L. Fouché, A. Boissé, G. Berthet, S. Lepoutre, A. Simoni, and T. Bourdel, Quantitative analysis of losses close to a d-wave open-channel Feshbach resonance in 39K, Phys. Rev. A 99, 022701 (2019).
• A. Boissé, G. Berthet, L. Fouché, G. Salomon, A. Aspect, S. Lepoutre, T. Bourdel, Non-linear scattering of atomic bright solitons in disorderEPL, 117 10007 (2017).
• S. Lepoutre, L. Fouché, A. Boissé, G. Berthet, G. Salomon, A. Aspect, and T. Bourdel, Production of strongly bound 39K bright solitons, PRA 94, 053626 (2016).
• G. Salomon, L. Fouché, S. Lepoutre, A. Aspect, and T. Bourdel, All-optical cooling of 39K to Bose-Einstein condensationPRA 90, 033405 (2014).
• G. Salomon, L. Fouché, P. Wang, A. Aspect, P. Bouyer, T. Bourdel, Gray-molasses cooling of 39K to a high phase space densityEPL 104, 63002 (2014).
• T. Bourdel, Phase diagrams of 2D and 3D disordered Boses gases in the local density approxiamtion, Phys. Rev. A, 86, 063626 (2012).
• T. Plisson, T. Bourdel, C.A. Müller, Momentum isotropisation in random potential,Eur. Phys. J. Special Topics 217, 79 (2013).
• B. Allard, T. Plisson, M. Holzmann, G. Salomon, A. Aspect, P. Bouyer, T. Bourdel, Effect of disorder close to the superfluid phase transition in a two-dimensional Bose gas. Phys. Rev. A 85, 033602 (2012).
• T. Plisson, B. Allard, M. Holzmann, G. Salomon, A. Aspect, P. Bouyer, T. Bourdel, Coherence properties of a 2D trapped Bose gas around the superfluid transitionPhys. Rev. A 84, 061606(R) (2011).
• T. Bourdel, M. Robert-de-Saint-Vincent, J.-P. Brantut, Ch. J. Borde, A. Aspect, P. Bouyer,
Classical and quantum trampoline for ultra-cold atoms, in Quantum phenomena in gravitational field,
Comptes Rendus Physique 12, 779 ( 2011).
• L. Pezze, M. Robert-de-Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, L. Sanchez-Palencia,
Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,
New Journal of Physics 13, 095015 (2011).
• M. Robert-de-Saint-Vincent, J.-P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, P. Bouyer
Anisotropic 2D diffusive expansion of ultra-cold atoms in a disordered potential
Phys. Rev. Lett. 104, 220602 (2010).
• G. Stern, B. Allard, M. Robert-de-Saint-Vincent, J.-P. Brantut, B. Battelier, T. Bourdel, P. Bouyer
A frequency doubled 1534 nm laser system for potassium laser cooling
applied optics 49, 1 (2010).
• M. Robert-de-Saint-Vincent, J.-P. Brantut, Ch.J. Bordé, A. Aspect, T. Bourdel and P. Bouyer
A quantum trampoline for ultra-cold atoms
EPL 89, 10002 (2010).
• J.-F. Clément, J.-P. Brantut, M. Robert-de-Saint-Vincent, R. A. Nyman, A. Aspect, T. Bourdel, and P. Bouyer
All-optical runaway evaporation to Bose-Einstein condensation
Phys. Rev. A 79, 061406 (R) (2009)
• J. P. Brantut, J. F. Clément, M. Robert de Saint Vincent, G. Varoquaux, R.A. Nyman, A. Aspect, T. Bourdel, and P. Bouyer
Light-shift tomography in an optical-dipole trap for neutral atoms
Phys. Rev. A 78, 031401(R) (2008)
• G. Varoquaux, N. Zahzam, W. Chaibi, J.-F. Clément, O. Carraz, J.-P. Brantut, R.A. Nyman, F. Pereira Dos Santos, L. Mondin, M. Rouzé, Y. Bidel, A. Bresson, A. Landragin, P. Bouyer,
I.C.E.: An Ultra-Cold Atom Source for Long-Baseline Interferometric Inertial Sensors in Reduced Gravity,
eprint arXiv: 0705.2922, (2007) ; Rencontres de Moriond Gravitational Waves and Experimental Gravity
• R.A. Nyman, G. Varoquaux, F. Lienhart, D. Chambon, S. Boussen, J.F. Clément, T. Müller, G. Santarelli, F. Pereira Dos Santos, A. Clairon, A. Bresson, A. Landragin, P. Bouyer,
I.C.E.: a transportable atomic inertial sensor for test in microgravity
Applied physics B 84, 673 (2006)
• R. A. Nyman, G. Varoquaux, B. Villier, D. Sacchet, F. Moron, Y. Le Coq, A. Aspect, and P. Bouyer, Tapered-amplified AR-coated laser diodes for Potassium and Rubidium atomic-physics experiments
Review of Scientific Instruments 77, 033105 (2006)

## Offers of Projects for Undergraduates, PhDs and Post-docs

If you are interested in our research, please do not hesitate to contact Thomas Bourdel. We have open positions for PhD or post-docs. We also offer to some motivated undergraduate students at various levels to work with us every year. See the link to a more detail thesis/intership proposition above.

## Former members

• Guillaume Berthet (PhD 2019), now high school and bachelor professor, France
• Amaudric Boissé (PhD 2018), now high school professor, France
• Alessandro Brolis (Post-doc, 2018), now Engineer in Italy.
• Steven Lepoutre (post-doc 2015), now maître de conférence in LAC (Orsay), France
• Lauriane Fouché (PhD 2015), now engineer in CEA, Bordeaux, France
• Guillaume Salomon (PhD 2014), now post-doc in Munich (I. Bloch), Deutschland
• Philippe Bouyer, now director of LP2N, Bordeaux, France
• Pengjun Wang (post-doc 2013), now researcher at Shanxi university, Taiyuan, China
• Baptiste Allard (PhD 2012), now maitre de conférence in Toulouse, France
• Thomas Plisson (PhD 2012), now researcher in CEA, Saclay, France
• Martin Robert-de-saint-Vincent (2011); now CNRS researcher in LPL, Villetaneuse, France
• Jean-Philippe Brantut (PhD 2009), now assistant professor in Lausanne (EPFL), Switzerland
• Jean-Francois clément (PhD 2008), now maitre de conférence in Phlam, Lille, France
• Robert Nyman (post-doc 2008), now research assistant in Imperial College, London, Great Britain
• Gael Varoquaux (PhD 2007) , now researcher in Neurospin, Saclay, France

## Supports

• CNRS
• Université Paris 11
• ANR
• nano-K (IFRAF)
• DIM Sirteq
• IQUPS
• DGA
• European Union through the QUIC project
• Labex PALM