Dimensionality plays an important role in physical systems. A gas of ultracold atoms confined in a two-dimensional geometry has very different thermodynamic properties from those observed in a three-dimensional gas. In this thesis, we present experiments performed on a gas of ultracold bosons trapped in two dimensions and interacting weakly with each other. First, we describe this system with a mean-field approach and present the experimental setup that allows us to study it. Then, we describe two experiments dealing with two distinct topics, both conducted in the superfluid regime at near zero temperature. We first describe the creation of dimers by microwave-induced photoassociation of atoms trapped in a flat-bottom potential. This experiment allows us to characterise the interaction potential of our atomic species, rubidium 87. We also characterise the interactions between the dimers created and the bath of free atoms. In a third part, we impose a breaking of translational invariance on our zero-temperature gas of bosons by creating a spatially modulated potential in one of the two directions of the atomic cloud. We show with two distinct measurements that the superfluid density, equal to the total density for a homogeneous gas, decreases when the translational invariance is broken. We measure the sound velocity in the direction parallel and perpendicular to the spatial modulation on the one hand, and estimate the superfluid fraction according to a definition introduced by Leggett in 1970 on the other hand. We then observe a superfluid fraction which decreases as the modulation amplitude increases.
Dimensionality plays an important role in physical systems. A gas of ultracold atoms confined in a two-dimensional geometry has very different thermodynamic properties from those observed in a three-dimensional gas. In this thesis, we present experiments performed on a gas of ultracold bosons trapped in two dimensions and interacting weakly with each other. First, we describe this system with a mean-field approach and present the experimental setup that allows us to study it. Then, we describe two experiments dealing with two distinct topics, both conducted in the superfluid regime at near zero temperature. We first describe the creation of dimers by microwave-induced photoassociation of atoms trapped in a flat-bottom potential. This experiment allows us to characterise the interaction potential of our atomic species, rubidium 87. We also characterise the interactions between the dimers created and the bath of free atoms. In a third part, we impose a breaking of translational invariance on our zero-temperature gas of bosons by creating a spatially modulated potential in one of the two directions of the atomic cloud. We show with two distinct measurements that the superfluid density, equal to the total density for a homogeneous gas, decreases when the translational invariance is broken. We measure the sound velocity in the direction parallel and perpendicular to the spatial modulation on the one hand, and estimate the superfluid fraction according to a definition introduced by Leggett in 1970 on the other hand. We then observe a superfluid fraction which decreases as the modulation amplitude increases.
At sufficiently high phase space densities, the many-body state of a degenerate Bose gas can be described by a single macroscopic wavefunction that undergoes nonlinear dynamics. Ultracold Bose gases are a prominent platform in the field of nonlinear physics, enabling the study of stable stationary wavepackets, known as solitons. In these platforms, atom interactions are often weak and treated within a mean-field approach. However, interactions play a crucial role in the physics of these Bose gases and explain for example the formation mechanism of solitons or the emergence of a remarkable phase of matter: superfluidity. This thesis describes investigations on peculiar dynamics of ultracold Bose gases, which are approximated by zero-temperature physics. After introducing our experimental setup and its theoretical characterization, we discuss the survival of the superfluid property in spatially modulated systems, in connection with Leggett's seminal work in 1970 and the spectacular supersolid phase of matter. We then explore the physics of a specific type of 1D soliton that emerges in a weakly-immiscible two-component mixture, known as the magnetic soliton. Its name originates from its appearance in 1D ferromagnetic spin chains. Magnetic solitons exhibit a captivating periodic motion under a uniform force field, similar to the Bloch oscillations of electrons in solids. Finally, we introduce a new experimental setup for studying Rydberg excitations and the realization of an all-optical Bose-Einstein-Condensate.
Exploration de la physique à N corps dans un gaz de Bose bidimensionnel : interactions atome-dimère et fraction superfluide à température nulle La dimensionnalité joue un rôle important dans les systèmes physiques. Un gaz d’atomes froids confiné dans une géométrie à deux dimensions a des propriétés thermodynamiques très différentes de celles observées dans un gaz à trois dimensions. Dans cette thèse, nous présentons des expériences réalisées sur un gaz de bosons ultra-froids confinés à deux dimensions et interagissant faiblement entre eux. Dans un premier temps, nous décrivons ce système avec une approche de champ moyen et nous présentons le dispositif expérimental qui nous permet de l’étudier. Ensuite, nous décrivons deux expériences traitant deux sujets distincts, toutes deux menées dans le régime superfluide à température quasi-nulle. Nous commençons par décrire des expériences de création de dimères par photoassociation induite par la radiation d’un champ micro-ondes sur des atomes piégés dans un potentiel à fond plat. Cette expérience nous permet de caractériser le potentiel d’interaction de notre espèce atomique, le rubidium 87. Nous caractérisons aussi l’interaction entre les dimères créés et le bain d’atomes libres. Dans une troisième partie, nous imposons une brisure d’invariance par translation à notre gaz de bosons à température nulle en créant un potentiel spatialement modulé dans une des deux directions du nuage atomique. Nous montrons par deux mesures distinctes que la densité superfluide, égale à la densité totale pour un gaz homogène, décroît lorsque l’invariance par translation est brisée. Nous mesurons la vitesse de son dans la direction parallèle et perpendiculaire à la modulation spatiale d’une part, et nous estimons la fraction superfluide d’après une définition introduite par Leggett en 1970 d’autre part. Nous observons alors une fraction superfluide qui décroît lorsque l’amplitude de modulation augmente.
The dimensionality of a system strongly affects its physical properties; the phase transitions that take place and the type of order that arises depend on the dimension. In low dimensional systems phase coherence proves more difficult to achieve as both thermal and quantum fluctuations play a stronger role. The two-dimensional Bose fluid is of particular interest as even if full order is precluded, a residual "quasi-long" range order arises at low temperatures. Then two ingredients have a significant effect on the state of the system: (i) the finite size of a real system enables one to recover of a macroscopic occupation of a single-particle state; (ii) the interactions between particles lead to the emergence of a non-conventional type of phase transition toward a superfluid state.In this thesis, we present an experimental study of the two-dimensional (2D) Bose gas using two different energy landscapes to trap our atoms. In the first part, we use the spatial dependence of some local properties of an inhomogeneous gas to characterize the state of the equivalent homogeneous system. We extract its equation of state with a high accuracy from the gas density profiles and test its superfluid behavior by measuring the heating induced by a moving local perturbation. In the second part, we observe and characterize the emergence of an extended phase coherence in a 2D homogeneous gas in particular via a 3D-to-2D dimensional crossover. We investigate the dynamical establishment of the coherence via a rapid crossing of the dimensional crossover and observe topological defects in the final superfluid state. We compare our findings with the predictions for the Kibble–Zurek mechanism.
Strongly correlated two-dimensional (2D) systems are a fascinating field of study. The reduced dimensionality should in principle impede phenomena such as Bose-Einstein condensation or superfluidity. Yet, evidence suggests that superfluidity and superconductivity are especially robust in 2D: In almost all known high Tc-supercondcutors, strongly correlated 2D structures and higher-partial-wave coupling seem to play a crucial role. In this thesis, we use ultracold homogeneous gases of lithium 6 with tunable interactions to perform analog quantum simulation of these captivating systems.As the main result of this thesis, I present the first measurements of the speed and attenuation of sound waves in ultracold 2D Fermi gases, which we use to probe the thermodynamic and transport properties of the gas. From the speed of sound, we extract the compressibility equation of state and compare it both to an independent static measurement and to quantum Monte Carlo calculations and find reasonable agreement between the three. The damping of the sound waves, which is determined by the shear and bulk viscosities as well as the thermal conductivity of the gas, exhibits a minimumin the strongly correlated regime. Here, the sound diffusivity approaches a universal quantum bound \hbar/m and the strongly correlated 2D Fermi gas thus realizes a nearly perfect fluid.In addition, I report on further related measurements performed in the course of this thesis, which were led by my coworkers N. Luick and L. Sobirey. We show that the 2D Fermi gas is phase coherent by realizing a Josephson junction in the homogeneous gas and observing Josephson oscillationsbetween two reservoirs separated by a thin barrier. When the barrier height is reduced to zero, these oscillations transform smoothly into sound waves. By dragging a lattice though the homogeneous system at variable velocities, we observe a critical velocity for the creation of excitations, proving thatthe system is superfluid. Here, the sound velocity determines the critical velocity for a large range of interaction strengths.Finally, I present the characterization of a novel d-wave Feshbach resonance in ultracold potassium 40 via measurements of the inelastic loss rate L(2) and via the dynamics of spin populations, led by my coworker T. Reimann. The experimental results are compared to theoretical predictions and we observe good agreement between the theoretical and experimental loss rates. The evolution of the spin populations is found to be consistent with the expected behavior for the theoretically predicted exit channel.
Ultracold atoms are exceptional tools to explore the physics of quantum matter. In fact, the high degree of tunability of ultracold Bose and Fermi gases makes them ideal systems for quantum simulation and for investigating macroscopic manifestations of quantum effects, such as superfluidity. In ultracold gas research, a central role is played by collective oscillations. They can be used to study different dynamical regimes, such as superfluid, collisional, or collisionless limits or to test the equation of state of the system. In this thesis, we present a unified description of collective oscillations in low dimensions covering both Bose and Fermi statistics, different trap geometries and zero as well as finite temperature, based on the formalism of hydrodynamics and sum rules. We discuss the different behaviour exhibited by the second excited breathing mode in the collisional regime at low temperature and in the collisionless limit at high temperature in a 1D trapped Bose gas with repulsive contact interaction. We show how this mode exhibits a single-valued excitation spectrum in the collisional regime and two different frequencies in the collisionless limit. Our predictions could be important for future research related to the thermalization and damping phenomena in this low-dimensional system. We show that 1D uniform Bose gases exhibit a non-monotonic temperature dependence of the chemical potential characterized by an increasing-with-temperature behaviour at low temperature. This is due to the thermal excitation of phonons and reveals an interesting analogy with the behaviour of superfluids. Finally, we investigate a gas with a finite number N of atoms in a ring geometry at T = 0. We discuss explicitly the deviations of the thermodynamic behaviour in the ring from the one in the large N limit.
Dynamics play an important role in physics. From classical mechanics, astrophysics, hydrodynamics to quantum physics, the dynamics of physical systems have crucial impact on our understanding of nature. For simple configurations such as in the two-body problem the dynamics can be calculated analytically. However, things get more complicated once the number of contributors in a system increases such as in few- or many-body systems. One way to study such an ensemble is to use a model system where decisive parameters can be controlled. In this thesis I make use of an ultracold cloud of fermionic Lithium-6 atoms close to zero temperature to study dynamics of few- and many-body systems. Two experimental studies to this topic are presented. In the first study, I produced a gas of di-atomic molecules (dimers), consisting of two Lithium-6 atoms in different states, to study the reaction kinetics of the four-body process of a dimer-dimer collision. At temperatures close to absolute zero the internal and external degrees of freedom of the dimers can be well controlled. This allowed us to investigate the kinetics of a single-channel reaction. To resolve the dynamics of the process we heated a gas of molecules and tracked the state of the system as a function of time. We determined the reaction-rate constant of the process for various thermal energies which allowed us to verify the Arrhenius law for molecule-molecule reactions in the ultracold regime. Additionally, we provided first insight into the dependence of this four-body process on the particle interaction. In the second experimental work, I focused on the thermodynamical properties of the ultracold gas. Cooling the gas of Lithium-6 atoms close to zero temperature the gas undergoes a phase transition and superfluidity is established. To study the dynamics in such a gas, we used a local perturbation to produce sound waves. Depending on the excitation scheme we either excited first sound, i.e. a pressure wave, known from classical mechanics, or second sound, i.e. an entropy wave. In the study we focused on second sound and determined the second sound speed as a function of the particle interaction. We found agreement of our results with both - a numerical and an analytical description of the interaction strength dependence of the second sound speed. Besides the experimental work, a theoretical proposal for a novel imaging technique for a 2D ultracold gas in an optical lattice is presented. The scheme is based on a holographic approach and enables the detection of individual particles with only a few hundred scattered photons per atom.