A gallery with photos of our experimental setup is available here

Nathan Dupont, Gabriel Chatelain, Maxime Arnal, Juliette Billy, David Guéry-Odelin (septembre 2019)

**Chaos-assisted tunneling resonances in a synthetic Floquet superlattice**

The field of quantum simulation, which aims at using a tunable quantum system to simulate another, has been developing fast in the past years as an alternative to
the all-purpose quantum computer. In particular, the use of temporal driving has attracted a huge interest recently as it was shown that certain fast drivings can create new topological effects,
while a strong driving leads to *e.g.* Anderson localization physics. In this work, we focus on the intermediate regime to observe a quantum chaos transport mechanism called chaos-assisted
tunneling which provides new possibilities of control for quantum simulation. Indeed, this regime generates a rich classical phase space where stable trajectories form islands surrounded by a
large sea of unstable chaotic orbits. This mimics an effective superlattice for the quantum states localized in the regular islands, with new controllable tunneling properties. Besides the
standard textbook tunneling through a potential barrier, chaos-assisted tunneling corresponds to a much richer tunneling process where the coupling between quantum states located in neighboring
regular islands is mediated by other states spread over the chaotic sea. This process induces sharp resonances where the tunneling rate varies by orders of
magnitude over a short range of parameters. We experimentally demonstrate and characterize these resonances for the first time in a quantum system. This opens the way to new kinds of quantum
simulations with long-range transport and new types of control of quantum systems through complexity.

Article: M. Arnal, et al. arXiv: 2003.10387 [cond-mat.quant-gas]

**Beyond effective Hamiltonians: micro motion of Bose-Einstein condensates in periodically driven optical lattices**

We investigate by statistical means a Bose-Einstein condensate held in a one-dimensional optical lattice whose phase undergoes a fast oscillation. The averaged potential experienced by the atoms yields a periodic potential having the same spatial period but with a renormalized depth. However, the atomic dynamics also contains a micromotion whose main features are revealed by a Kolmorogov-Smirnov analysis of the experimental momentum distributions. Furthermore, we discuss the impact of the micromotion on a quench process corresponding to a proper sudden change of the driving amplitude which reverses the curvature of the averaged potential.

Article: M. Arnal, et al. Phys. Rev. A **101**, 013619 (2020).

**Direct cooling in an optical lattice by amplitude modulation**

We report on a generic cooling technique for atoms trapped in optical lattices. It consists in modulating the lattice depth with a proper frequency sweeping. This filtering technique removes the most energetic atoms, and provides with the onset of thermalization a cooling mechanism reminiscent of evaporative cooling. However, the selection is here performed in quasi-momentum space rather than in position space. Interband selection rules are used to protect the population with a zero quasi-momentum, namely the Bose Einstein condensate. Direct condensation of thermal atoms in an optical lattice is also achieved with this technique. It offers an interesting complementary cooling mechanism for quantum simulations performed with quantum gases trapped in optical lattices.

Article: M. Arnal, et al. Phys. Rev. A, **100**, 013416 (2019).

**Resonant excitations of a Bose Einstein condensate in an optical lattice**

We investigate experimentally a Bose Einstein condensate placed in a 1D optical lattice whose phase or amplitude is modulated in a frequency range resonant with the first bands of the band structure. We study the combined effect of the strength of interactions and external confinement on the 1 and 2-phonon transitions. We identify lines immune or sensitive to atom-atom interactions. Experimental results are in good agreement with numerical simulations. Using the band mapping technique, we get a direct access to the populations that have undergone n-phonon transitions for each modulation frequency.

Article: C. Cabrera-Gutiérrez, et al. Eur. Phys. J. D 73, 170 (2019).

**Robust calibration of an optical-lattice depth based on a phase shift**

We report on a new method to calibrate the depth of an optical lattice. It consists in triggering the intrasite dipole mode of the cloud by a sudden phase shift. The corresponding oscillatory motion is directly related to the intraband frequencies on a large range of lattice depths. Remarkably, for a moderate displacement, a single frequency dominates this oscillation for the zeroth and first order interference pattern observed after a sufficiently long time-of-flight. The method is robust against atom-atom interactions and the exact value of the extra external confinement of the initial trapping potential.

Article: C. Cabrera-Gutiérrez, et al. Phys. Rev. A **97**, 043617 (2018)

**Out-of-equilibrium dynamics of a Bose Einstein condensate in a periodically driven band system**

We report on the out-of-equilibrium dynamics of a Bose-Einstein condensate (BEC) placed in an optical lattice whose phase is suddenly modulated. The frequency and the amplitude of modulation are chosen to ensure a negative renormalized tunneling rate. Under these conditions, staggered states are nucleated by a spontaneous four wave mixing mechanism. The nucleation time is experimentally studied as a function the renormalized tunnel rate, the atomic density and the modulation frequency. Our results are quantitatively well accounted for by a Truncated Wigner approach and reveals the nucleation of gap solitons after the quench. The role of quantum versus thermal fluctuations in the nucleation process is discussed. The limit of the effective Hamiltonian approach is also addressed experimentally.

Article: E. Michon, et
al. New Journal of Physics **20**, 053035 (2018).

**Tunneling traversal time**

We report on the measurement of the time required for a wave packet to tunnel through the potential barriers of an optical lattice. The experiment is carried out by loading adiabatically a Bose-Einstein condensate into a 1D optical lattice. A sudden displacement of the lattice by a few tens of nm excites the micromotion of the dipole mode. We then directly observe in momentum space the splitting of the wave packet at the turning points and measure the delay between the reflected and the tunneled packets for various initial displacements. Using this atomic beam splitter twice, we realize a chain of coherent micron-size Mach-Zehnder interferometers at the exit of which we get essentially a wave packet with a negative momentum, a result opposite to the prediction of classical physics.

Article : Phys. Rev. Lett.
**117**, 010401 (2016)

**Our new rubidium BEC**

Bose-Einstein condentensate of rubidium atoms in the F=1, m=-1 state are obtained using an hybrid trap that combines a quadrupole with a maximum gradient of 300 G/cm and a crossed dipole trap generated by a 5W monomode fiber laser. The evaporation in the magnetic trap is performed using microwaves (at 6.8 GHz). Pure BEC with more than 100 000 atoms are obtained every 30 seconds.

**New BEC machine**

The new setup is based on a 2D MOT separated from the science chamber by two successive stages of differential vacuum chambers. It has been optimized for a good optical access, a high optical resolution and a very high stability and reproductibility. The BEC is produced using an hybrid-trap. The laser system involves only one locking system made by phase modulation, all other frequencies are generated using Acousto-Optic Modulator or Electro-Optic Modulator.

**Realization of tunnel barriers for matter waves using spatial gaps**

We experimentally demonstrate the trapping of a propagating Bose-Einstein Condensate in a Bragg cavity produced by an attractive optical lattice with a smooth envelope. As a consequence of the envelope, the band gaps become position-dependent and act as mirrors of finite and velocity-dependent reflectivity. We directly observe both the oscillations of the wave packet bouncing in the cavity provided by these spatial gaps and the tunneling out for narrow classes of velocity. Synchronization of different classes of velocity can be achieved by proper shaping of the envelope. This technique can generate single or multiple tunnel barriers for matter waves with a tunable transmission probability, equivalent to a standard barrier of submicron size.

Article : P. Cheiney et al. EPL **103**, 50006
(2013).

**Matter-wave scattering on an amplitude-modulated optical lattice**

We experimentally study the scattering of guided matter waves on an amplitude-modulated optical lattice. We observe different types of frequency-dependent dips in the asymptotic output density distribution. Their positions are compared quantitatively with numerical simulations. A semiclassical model that combines local Floquet-Bloch bands analysis and Landau-Zener transitions provides a simple picture of the observed phenomena in terms of elementary Floquet photon absorption-emission processes and envelope induced reflections. Finally, we propose and demonstrate the use of this technique with a bichromatic modulation to design a tunable sub-recoil velocity filter.

Article: P. Cheiney et al.Phys. Rev. A **87**, 013623 (2013)

**Optically guided beam splitter for propagating matter waves**

We study experimentally and theoretically a beam splitter setup for guided atomic matter waves. The matter wave is a guided atom laser that can be tuned from quasi-monomode to a regime where many transverse modes are populated, and propagates in a horizontal dipole beam until it crosses another horizontal beam at 45$^{\rm o}$. We show that depending on the parameters of this $X$ configuration, the atoms can all end up in one of the two beams (the system behaves as a perfect guide switch), or be split between the four available channels (the system behaves as a beam splitter). The splitting regime results from a chaotic scattering dynamics. The existence of these different regimes turns out to be robust against small variations of the parameters of the system. From numerical studies, we also propose a scheme that provides a robust and controlled beam splitter in two channels only.

Article: G.L. Gattobigio et al. Phys. Rev. Lett. **109**, 030403 (2012).

**Matter wave probe of classically chaotic potential**

We study an experimental setup in which a quantum probe, provided by a quasi-monomode guided atom laser, interacts with a static
localized attractive potential whose characteristic parameters are tunable. In this system, classical mechanics predicts a transition from regular to chaotic behavior as a result of the coupling
between the different degrees of freedom. Our experimental results display a clear signature of this transition. On the basis of extensive numerical simulations, we discuss the quantum versus
classical physics predictions in this context. This system opens new possibilities for investigating quantum scattering, provides a new testing ground for classical and quantum chaos and enables
to revisit the quantum-classical correspondence.

Article : G. L. Gattobigio et al. Phys. Rev. Lett. **107**, 254104 (2011)

**Distributed Bragg reflector for matter waves**

We report on the experimental study of a Bragg reflector for guided, propagating Bose-Einstein condensates. A one-dimensional attractive optical lattice of finite length created by red-detuned laser beams selectively reflects some velocity components of the incident matter wave packet. We find quantitative agreement between the experimental data and one-dimensional numerical simulations and show that the Gaussian envelope of the optical lattice has a major influence on the properties of the reflector. In particular, it gives rise to multiple reflections of the wave packet between two symmetric locations where Bragg reflection occurs. Our results are a further step towards integrated atom-optics setups for quasi-cw matter waves.

Article: C. M. Fabre et al., Phys. Rev. Lett. **107**, 230401 (2011)

**Zeeman slowers with permanent magnets in a Halbach conﬁguration**

We describe a simple Zeeman slower design using permanent magnets. Contrary to common wire- wound setups, no electric power and water cooling are required. In addition, the whole system can be assembled and disassembled at will. The magnetic field is however transverse to the atomic motion and an extra repumper laser is necessary. A Halbach configuration of the magnets produces a high quality magnetic field and no further adjustment is needed. After optimization of the laser parameters, the apparatus produces an intense beam of slow and cold 87Rb atoms. With typical fluxes of (1–5) ×10^10 atoms/s at 30 m/ s , our apparatus efficiently loads a large magneto-optical trap with more than 10^10 atoms in 1 s, which is an ideal starting point for degenerate quantum gas experiments.

Article: P. Cheiney et al., Rev. Sci. Instrument. **82**, 063115 (2011).

**Guided atom lasers (entropy analysis)**

We have experimentally demonstrated a high level of control of the mode populations of guided-atom lasers (GALs) by showing that the entropies per particle of an optically GAL and the one of the trapped Bose- Einstein condensate (BEC) from which it has been produced are the same. The BEC is prepared in a crossed beam optical dipole trap. We have achieved isentropic outcoupling for both magnetic and optical schemes. We can prepare GAL in a nearly pure monomode regime (85% in the ground state). Furthermore, optical outcoupling enables the production of spinor guided-atom lasers and opens the possibility to tailor their polarization.

Article: G. L. Gattogigio et al., Phys. Rev. A **80**, 041605(R) (2009)

**Guided atom lasers (single transverse mode)**

We report the achievement of an optically guided and quasi-monomode atom laser, in all spin projection states (mF = −1, 0 and +1) of F = 1 in rubidium 87. The atom laser source is a Bose-Einstein condensate (BEC) in a crossed dipole trap, purified to any one spin projection state by a spin-distillation process applied during the evaporation to BEC. The atom laser is outcoupled by an inhomogenous magnetic field, applied along the waveguide axis. The mean excitation number in the transverse modes is ⟨n⟩ = 0.65 ± 0.05 for mF = 0 and ⟨n⟩ = 0.8 ± 0.3 for the low-field seeker mF = −1. Using a simple thermodynamical model, we infer from our data the population in each excited mode.

Article: A. Couvert et al., Europhys. Lett. **83**, 50001 (2008).

**Optimal transport - shortcuts to adiabaticity**

We report the transport of ultracold atoms with optical tweezers in the non-adiabatic regime, i.e. on a time scale on the order of the oscillation period. We have found a set of discrete transport durations for which the transport is not accompanied by any excitation of the centre of mass of the cloud after the transport. We show that the residual amplitude of oscillation of the dipole mode is given by the Fourier transform of the velocity profile imposed to the trap for the transport. This formalism leads to a simple interpretation of our data and simple methods for optimizing trapped particles displacement in the non-adiabatic regime.

Article: A. Couvert et al., Europhys. Lett. **83**, 13001 (2008).

**Strong saturation absorption imaging of dense clouds**

We report on a far above saturation absorption imaging technique to investigate the characteristics of dense packets of ultracold atoms. The transparency of the cloud is controlled by the incident light intensity as a result of the non-linear response of the atoms to the probe beam. We detail our experimental procedure to calibrate the imaging system for reliable quantitative measurements, and demonstrate the use of this technique to extract the profile and its spatial extent of an optically thick atomic cloud.

Article: G. Reinaudi et al., Opt. Lett. **32**, 3143 (2007).

**Previous contribution (performed at ENS Paris)**

**Evaporation of an atomic beam on a material surface**

We report on the implementation of evaporative cooling of a magnetically guided beam by adsorption on a ceramic surface. We use a
transverse magnetic field to shift locally the beam towards the surface, where atoms are selectively evaporated. With a 5-mm-long ceramic piece, we gain a factor of 1.5±0.2 on the phase-space
density. Our results are consistent with a 100% efficiency of this evaporation process. The flexible implemen- tation that we have demonstrated, combined with the very local action of the
evaporation zone, makes this method particularly suited for the evaporative cooling of a beam.

Article: G. Reinaudi et al. Phys. Rev. A. **73**, 035402 (2006).

**A moving magnetic mirror to slow down a bunch of atoms**

A fast packet of cold atoms is coupled into a magnetic guide and subsequently slowed down by reflection on a magnetic potential barrier (‘mirror’) moving along the guide. A detailed characterization of the resulting decelerated packet is performed. We show also how this technique can be used to generate a continuous and intense flux of slow, magnetically guided atoms.

Article: G. Reinaudi et al., Eur. Phys. J. D **40**, 405 (2006).

**Transport of Atom Packets in a Train of Ioffe-Pritchard Traps**

We demonstrate transport and evaporative cooling of several atomic clouds in a chain of magnetic Ioffe- Pritchard traps moving at
a low speed (1 m/s). The trapping scheme relies on the use of a magnetic guide for transverse confinement and of magnets fixed on a conveyor belt for longitudinal trapping. This experiment
introduces a different approach for parallelizing the production of Bose-Einstein condensates as well as for the realization of a continuous atom laser.

Article: T. Lahaye et al. Phys. Rev. A. **74**, 033622 (2006).

**Evaporative cooling of a guided atomic beam**

We report on our recent progress in the manipulation and cooling of a magnetically guided, high-flux beam of 87Rb atoms.
Typically, 7 x 10^9 atoms per second propagate in a magnetic guide providing a transverse gradient of 800 G/cm, with a temperature (550 microK, at an initial velocity of 90 cm/s. The atoms are
subsequently slowed down to 60 cm/s using an upward slope. The relatively high collision rate (5 s^−1) allows us to start forced evaporative cooling of the beam, leading to a reduction of the
beam temperature by a factor of 4, and a tenfold increase of the on-axis phase-space density.

Article: T. Lahaye et al. Phys. Rev. A. **72**, 033411 (2005).

**A magnetically guided atomic beam in the collisional regime**

We describe the realization of a magnetically guided beam of cold rubidium atoms, with a flux of 7 10^9 atoms/s, a
temperature of 400 microK, and a mean velocity of 1 m/s. The rate of elastic collisions within the beam is sufficient to ensure thermalization. We show that the evaporation induced by a
radio-frequency wave leads to appreciable cooling and an increase in the phase space density. We discuss the perspectives to reach the quantum degenerate regime using evaporative
cooling.

Article: T. Lahaye et al. Phys. Rev. Lett. **93**, 093003 (2004).

**Loading of a cold atomic beam into a magnetic guide**

We demonstrate experimentally the continuous and pulsed loading of a slow and cold atomic beam into a magnetic guide. The slow
beam is produced using a vapor loaded laser trap, which ensures two- dimensional magneto-optical trapping, as well as cooling by a moving molasses along the third direction. It provides a
continuous flux larger than 109 atoms/s with an adjustable mean velocity ranging from 0.3 to 3 m/s, and with longitudinal and transverse temperatures smaller than 100 μK. Up to 3 × 108 atoms/s
are injected into the magnetic guide and subsequently guided over a distance of 40 cm.

Article: P. Cren et al., Eur. Phys. J. D. **20**, 107 (2002).

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