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.
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.
Strongly interacting two-dimensional Fermi systems are one of the great remaining challenges in many-body physics due to the interplay of strong local correlations and enhanced long-range fluctuations. Here, we probe the thermodynamic and transport properties of a 2D Fermi gas across the BEC-BCS crossover by studying the propagation and damping of sound modes. We excite particle currents by imprinting a phase step onto homogeneous Fermi gases trapped in a box potential and extract the speed of sound from the frequency of the resulting density oscillations. We measure the speed of sound across the BEC-BCS crossover and compare the resulting dynamic measurement of the equation of state both to a static measurement based on recording density profiles and to quantum Monte Carlo calculations and find reasonable agreement between all three. We also measure the damping of the sound mode, which is determined by the shear and bulk viscosities as well as the thermal conductivity of the gas. We find that the damping is minimal in the strongly interacting regime and the diffusivity approaches the universal quantum bound ℏ/m of a perfect fluid.
Propagation du son et atténuation à limite quantique dans un gaz de Fermi deux-dimensionnel ultrafroid Les systèmes bi-dimensionnels fortement corrélés sont captivants. À cause de la dimensionnalité réduite, des fluctuations thermiques empêchent un vrai ordre à longue portée et devraient donc entraver des phénomènes comme la condensation Bose-Einstein ou la superfluidité. Malgré cela, la superfluditié et la supraconductivité semblent particulièrement robustes en 2D : Dans presque tous les supraconducteurs à haute température critique les structures 2D ainsi que le couplage en onde d semblent jouer un rôle central. Dans cette thèse, nous utilisons des gaz de lithium 6 ultrafroids et homogènes avec des interactions ajustables pour effectuer des simulations quantiques explorant certaines propriétés de ces systèmes fascinants. Comme résultat principal, je présente les premières mesures de la vitesse et de l’atténuation du son dans un gaz de Fermi 2D ultrafroid, que nous utilisons pour étudier des propriétés thermodynamiques et les coefficients de transport du gaz. La vitesse du son nous permet d’extraire la compressibilité du gaz et nous obtenons un accord raisonnable avec la valeur mesurée indépendamment dans un système statique ou calculée à partir de simulations Monte-Carlo quantiques. L’atténuation des ondes sonores est déterminée par la viscosité et la conductivité thermique du gaz, et approche un minimum dans le régime fortement corrélé. Ce minimum correspond à une limite quantique universelle ~/m pour la diffusivité du son. Le gaz de Fermi 2D fortement corrélé représente donc un fluide quasi-parfait. En outre, je rends compte de deux autres expériences qui ont été réalisées dans le cadre de cette thèse, menées principalement par mes collègues N. Luick et L. Sobirey. Premièrement, nous réalisons une jonction de Josephson en séparant le gaz en deux réservoirs à l’aide d’un laser induisant une fine barrière de potentiel répulsive. Nous observons des oscillations de Josephson entre les deux réservoirs démontrant la cohérence de phase du gaz de Fermi 2D. En réduisant la hauteur de la barrière, ces oscillations sont progressivement transformées en ondes sonores. Dans la deuxième expérience, nous déplaçons un réseau optique à travers le gaz à des vitesses ajustables. Nous observons une vitesse critique pour la création d’excitations, prouvant que le gaz de Fermi 2D est superfluide. La vitesse critique est déterminée par la vitesse du son sur un grand domaine d’interactions. Finalement, je présente la caractérisation d’une nouvelle résonance Feshbach en onde d dans du potassium 40 ultrafroid, un projet qui a été mené principalement par mon collègue T. Reimann. Nous mesurons le taux de pertes inélastiques L⁽²⁾ et l’évolution des populations de spins et nous les comparons à des prédictions théoriques. Nous trouvons un bon accord entre théorie et expérience pour le taux de pertes. L’évolution des populations des spins est compatible avec le comportement prédit par la théorie.
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.
Water flowing down a pipe experiences viscous drag that causes it to lose energy and slow down. A superfluid, such as liquid helium (3He and 4He) or electrons in a superconductor, can flow without friction when in contact with a wall. This fascinating phenomenon, or superfluidity, was discovered by Kapitza [1], Allen and Misener [2] in 1937. The formation of a superfluid is related to the formation of a Bose--Einstein condensate (BEC). 4He is a boson as its total spin is zero, an integer. Condensation in fermionic 3He liquid occurs through composite bosons of paired atoms in a process similar to electron pairing in a superconductor. To explain the peculiar properties of superfluid helium, Landau considered a superfluid to be comprised of two parts: a ‘pure’ superfluid component with zero entropy and viscosity, and a normal component that behaves like ordinary fluid. An interesting manifestation of this two-fluid model is the existence of two types of oscillations, the ‘first and second sounds’ as named by Landau. The ‘first sound’ is a wave that propagates at constant entropy per particle, just like sounds in ordinary fluids. It propagates with pressure and density oscillations. ‘Second sound’, unlike what its name suggests, is not audible as it propagates at nearly constant pressure (isobaric oscillation). Here, entropy density takes the role of pressure/density in normal sound waves. Historically, the observation of the second sound in superfluid helium, and the measurement of its speed, played a crucial role in understanding the nature of superfluid helium. The speed of the second sound can be used to determine the superfluid fraction, i.e. the ratio of the superfluid density to the total fluid density [3,4]. In the past decades, the field of ultracold atomic gases has developed into a fertile ground for studying superfluid physics, as the inter-particle interactions between two atoms can be tuned using the so-called Fano–Feshbach resonances. Systematic studies on Fermi gases can be preformed in the limit of strong interactions, whose properties are difficult to predict but important to the understanding of strongly correlated quantum systems of many particles, such as high-temperature superconductors, quark–gluon plasmas and neutron stars. Quantitative determination of the superfluid fraction in strongly interacting Fermi gases has been an elusive goal of scientists for many years, as the methods that allow the determination of the superfluid fraction in liquid helium cannot be directly applied to ultracold gases. For example, to excite the second sound in liquid helium, a local heat pulse can be created by passing a current through a heating wire submersed in the liquid. The heat pulse can then be detected at the other end of the liquid using a temperature sensitive sensor as illustrated in Fig. 1(a). Such methods cannot be implemented with ultracold atomic gas ensembles that typically contain only about hundreds of thousand atoms at μK (1 millionth of a kelvin) temperatures. Further adding to the difficulties, the propagation of the second sound in liquid helium usually involves no density variation/oscillation. This means that the second sound could not be detected easily with the absorption imaging technique typically used for probing cold atoms, assuming that the strongly interacting Fermi gases behave very much like strongly interacting bosonic liquid helium (4He). (a) Excitation and detection of the second sound in superfluid helium; (b) local heating through the power modulation of an excitation laser beam; (c) the detection of the second sound in a strongly interacting Fermi gas with direct absorption imaging. Recently, the group of Professor Rudolf Grimm from the University of Innsbruck (Austria), in collaboration with a theoretical team from the Trento University (Italy) led by Professors Sandro Stringari and Lev Pitaevskii, successfully measured the speed of second sound in a resonantly interacting Fermi gas using a simple and elegant method. Their results were published in [5]. To observe the second sound, the authors created a local heat pulse at the center of an elongated trapped gas by creating a short burst of modulation to the power of a light beam intercepting this gas (see Fig. 1b). They then measured the speed of the second sound by observing the movement of a thermal-induced density dip along the elongated gas (Fig. 1c). Taking advantage of the inhomogeneous density distributions of the superfluid atoms in the trap, they ingeniously determined the temperature dependence of the superfluid fraction without needing to vary the temperature of the samples. The observation of the second sound in the strongly interacting Fermi gases opens up a new horizon for studying the superfluid properties with tunable interactions. Knowing the speed of second sound can provide a lot of valuable information, allowing physicists working on many-body theories to falsify their models and theories. It demonstrates the importance of using experimentally measured quantities, such as the equation of state employed here, to calibrate and to supplement theoretical investigations. Significant new advances will follow in the understanding of superfluidity of many strongly interacting particles, where faithful theoretical modeling and calculations are impossible at the microscopic level.
We numerically study the transport properties of a two-dimensional Fermi gas in a weakly and strongly interacting regimes, in the range of temperatures close to the transition to a superfluid phase. For that we excite sound waves in a fermionic mixture by using the phase imprinting technique, follow their evolution, and finally determine both their speed and attenuation. Our formalism, originated from a density-functional theory, incorporates thermal fluctuations via the grand canonical ensemble description and with the help of Metropolis algoritm. From numerical simulations we extract temperature dependence of the sound velocity and diffusivity as well as the dependence on the interaction strength. We emphasize the role of virtual vortex-antivortex pairs creation in the process of sound dissipation.
The role of reduced dimensionality in high-temperature superconductors is still under debate. Recently, ultracold atoms have emerged as an ideal model system to study such strongly correlated two-dimensional (2D) systems. Here, we report on the realization of a Josephson junction in an ultracold 2D Fermi gas. We measure the frequency of Josephson oscillations as a function of the phase difference across the junction and find excellent agreement with the sinusoidal current phase relation of an ideal Josephson junction. Furthermore, we determine the critical current of our junction in the crossover from tightly bound molecules to weakly bound Cooper pairs. Our measurements clearly demonstrate phase coherence and provide strong evidence for superfluidity in a strongly interacting 2D Fermi gas.