The emergence of many-body physical phenomena from the quantum mechanical properties of atoms can be studied using ultracold alkali gases. The ability to manipulate both Bose-Einstein condensates (BECs) and degenerate Fermi gases (DFGs) with designer potential energy landscapes, variable interaction strengths and out-of-equilibrium initial conditions provides the opportunity to investigate collective behaviour under diverse conditions. With an appropriately chosen wavelength, optical standing waves provide a lattice potential for one target species while ignoring another spectator species. A “tune-in” scheme provides an especially strong potential for the target and works best for Li-Na, Li-K, and K-Na mixtures, while a “tune-out” scheme zeros the potential for the spectator, and is pre- ferred for Li-Cs, K-Rb, Rb-Cs, K-Cs, and 39K-40K mixtures. Species-selective lattices provide unique environments for studying many-body behaviour by allowing for a phonon-like background, providing for effective mass tuning, and presenting opportunities for increasing the phase-space density of one species. Ferromagnetism is manifest in a two-component DFG when the energetically preferred many-body configuration segregates components. Within the local density approximation (LDA), the characteristic energies and the three-body loss rate of the system all give an observable signature of the crossover to this ferromagnetic state in a trapped DFG when interactions are increased beyond kF a(0) = 1.84. Numerical simulations of an extension to the LDA that account for magnetization gradients show that a hedgehog spin texture emerges as the lowest energy configuration in the ferromagnetic regime. Explorations of strong interactions in 40K constitute the first steps towards the realization of ferromagnetism in a trapped 40K gas. The many-body dynamics of a 87Rb BEC in a double well potential are driven by spatial phase gradients and depend on the character of the junction. The amplitude and frequency characteristics of the transport across a tunable barrier show a crossover between two paradigms of superfluidity: Josephson plasma oscillations emerge for high barriers, where transport is via tunnelling, while hydrodynamic behaviour dominates for lower barriers. The phase dependence of the many-body dynamics is also evident in the observation of macroscopic quantum self trapping. Gross-Pitaevskii calculations facilitate the interpretation of system dynamics, but do not describe the observed damping.

The emergence of many-body physical phenomena from the quantum mechanical properties of atoms can be studied using ultracold alkali gases. The ability to manipulate both Bose-Einstein condensates (BECs) and degenerate Fermi gases (DFGs) with designer potential energy landscapes, variable interaction strengths and out-of-equilibrium initial conditions provides the opportunity to investigate collective behaviour under diverse conditions. With an appropriately chosen wavelength, optical standing waves provide a lattice potential for one target species while ignoring another spectator species. A “tune-in” scheme provides an especially strong potential for the target and works best for Li-Na, Li-K, and K-Na mixtures, while a “tune-out” scheme zeros the potential for the spectator, and is pre- ferred for Li-Cs, K-Rb, Rb-Cs, K-Cs, and 39K-40K mixtures. Species-selective lattices provide unique environments for studying many-body behaviour by allowing for a phonon-like background, providing for effective mass tuning, and presenting opportunities for increasing the phase-space density of one species. Ferromagnetism is manifest in a two-component DFG when the energetically preferred many-body configuration segregates components. Within the local density approximation (LDA), the characteristic energies and the three-body loss rate of the system all give an observable signature of the crossover to this ferromagnetic state in a trapped DFG when interactions are increased beyond kF a(0) = 1.84. Numerical simulations of an extension to the LDA that account for magnetization gradients show that a hedgehog spin texture emerges as the lowest energy configuration in the ferromagnetic regime. Explorations of strong interactions in 40K constitute the first steps towards the realization of ferromagnetism in a trapped 40K gas. The many-body dynamics of a 87Rb BEC in a double well potential are driven by spatial phase gradients and depend on the character of the junction. The amplitude and frequency characteristics of the transport across a tunable barrier show a crossover between two paradigms of superfluidity: Josephson plasma oscillations emerge for high barriers, where transport is via tunnelling, while hydrodynamic behaviour dominates for lower barriers. The phase dependence of the many-body dynamics is also evident in the observation of macroscopic quantum self trapping. Gross-Pitaevskii calculations facilitate the interpretation of system dynamics, but do not describe the observed damping.

Esta tesis es un trabajo teórico, en el que estudiamos la física de los átomos dipolares bosónicos ultrafríos en retículos ópticos. Éstos gases consisten de átomos o moléculas bosónicas, enfriados bajo la temperatura de degeneración cuántica, típicamente del orden de nK. En éstas condiciones, en una trampa armónica tridimensional (3D), los bosones que interaccionan débilmente condensan y forman un Condensado de Bose Einstein (BEC). Cuando se carga un BEC en un retículo óptico producido por ondas estacionarias de luz láser, se producen nuevos fenómenos físicos. Estos sistemas entonces realizan modelos de tipo Hubbard y pueden ser llevados a regimenes fuertemente correlacionados.En 1989, M. Fisher et. al. predecían que el modelo de Bose-Hubbard homogéneo (BH) presenta la transición de fase cuántica Superfluid-Mott insulator (SF-MI). En 2002, la transición entre éstas dos fases fue observada experimentalmente por primera vez en el grupo de T. Esslinger e I. Bloch. La realización experimental de un BEC dipolar de cromo en el grupo de T. Pfau, y los progresos recientes en las técnicas de enfriamiento y atrapamiento de moléculas dipolares en los grupos de D. Jin e J. Ye, han abierto el camino hacia los gases cuánticos ultra-fríos dominados por la interacción dipolar. La evolución natural, y el reto de hoy en día por parte experimental, es de cargar BEC dipolares en retículos ópticos y estudiar los gases dipolares fuertemente correlacionados.Antes de éste trabajo de doctorado, estudios sobre modelos de BH con interacciones extendidas a los primeros vecinos mostraron la evidencia de nuevas fases cuánticas, como el supersólido (SS) y la fase checkerboard (CB). Debido al carácter de largo alcance de la interacción dipolo-dipolo, que decae con la potencia cúbica inversa de la distancia, es necesario incluir más de un primer vecino para obtener una descripción fiel y cuantitativa de los sistemas dipolares. De hecho, al incluir más vecinos se permiten y se estabilizan aún más nuevas fases.En esta tesis estudiamos modelos de BH con interacciones dipolares, investigando más allá del estado fundamental. Estudiamos un retículo bidimensional (2D) donde los dipolos están polarizados en dirección perpendicular al plano 2D, dando lugar a una interacción dipolar repulsiva e isotrópica. Utilizamos aproximaciones de campo-medio y un ansatz Gutzwiller, que son suficientemente correctos y adecuados para describir este sistema. Encontramos que los gases dipolares en 2D presentan una multitud de estados metaestables de tipo MI, que compiten con el estado fundamental, de modo parecido a sistemas desordenados. Estudiamos en detalle el destino de estos estados metaestables: como pueden ser preparados de manera controlada, como pueden ser detectados, cual es su tiempo de vida debido al tunnelling, y cual es su rol en los procesos de enfriamiento. Además, encontramos que el estado fundamental está caracterizado por estados MI de tipo checkerboard con coeficiente de ocupación n fraccionario (numero medio de partículas por sitio) que depende del cut-off utilizado en el radio de alcance de la interacción. Confirmamos esta predicción estudiando el mismo sistema con métodos Quantum Monte Carlo (worm algorithm). En este caso no utilizamos ningún cut-off en el radio de alcance de la interacción, y encontramos pruebas de una "Devil's staircase" en el estado fundamental, i.e. donde las fases MI aparecen en todos los n racionales del retículo subyacente. Encontramos además, regiones de los parámetros donde el estado fundamental es supersólido, obtenido drogando los sólidos con partículas o con agujeros.En este trabajo, investigamos también como cambia la estructura precedente en 3D. Nos focalizamos en el retículo 3D más sencillo compuesto de dos planos 2D, en el cual los dipolos están polarizados perpendicularmente a los planos; la interacción dipolar es entonces repulsiva por partículas del mismo plano, mientras es atractiva por partículas en el mismo sitio de dos planos diferentes. En cambio suprimimos el tunnelling entre los planos, lo cual hace el sistema equivalente a una mezcla bosónica en un retículo 2D. Nuestros cálculos muestran que las partículas se juntan en parejas, y demostramos la existencia de la nueva fase cuántica Pair Super Solid (PSS).Actualmente estamos estudiando un retículo 2D donde los dipolos están libres de apuntar en ambas direcciones perpendicularmente al plano, lo cual resulta en una interacción a primeros vecinos repulsiva (atractiva) por dipolos alineados (anti-alineados). Encontramos regiones de parámetros donde el estado fundamental es ferromagnético u anti-ferromagnético, y encontramos pruebas de la existencia de la fase cuántica Counterflow Super Solid (CSS).Las nuestras predicciones tienen directas consecuencias experimentales, y esperamos que vengan pronto controladas en experimentos con gases dipolares atómicos y moleculares ultra-fríos. / This thesis is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules, cooled below the quantum degeneracy temperature, typically in the nK range. In such conditions, in a three-dimensional (3D) harmonic trap, weakly interacting bosons condense and form a Bose-Einstein Condensate (BEC). When a BEC is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur.These systems realize then Hubbard-type models and can be brought to a strongly correlated regime. In 1989, M. Fisher et. al. predicted that the homogeneous Bose-Hubbard model (BH) exhibits the Superfluid-Mott insulator (SF-MI) quantum phase transition. In 2002 the transition between these two phases were observed experimentally for the first time in the group of T. Esslinger and I. Bloch. The experimental realisation of a dipolar BEC of Chromium by the group of T. Pfau, and the recent progresses in trapping and cooling of dipolar molecules by the groups of D. Jin and J. Ye, have opened the path towards ultra-cold quantum gases with dominant dipole interactions. A natural evolution and present challenge, on the experimental side is then to load dipolar BECs into optical lattices and study strongly correlated ultracold dipolar lattice gases.Before this PhD work, studies of BH models with interactions extended to nearest neighbours had pointed out that novel quantum phases, like supersolid (SS) and checkerboard phases (CB) are expected. Due to the long-range character of the dipole-dipole interaction, which decays as the inverse cubic power of the distance, it is necessary to include more than one nearest neighbour to have a faithful quantitative description of dipolar systems. In fact, longer-range interactions tend to allow for and stabilize more novel phases.In this thesis we study BH models with dipolar interactions, going beyond the ground state search. We consider a two-dimensional (2D) lattice where the dipoles are polarized perpendicularly to the 2D plane, resulting in an isotropic repulsive interaction. We use the mean-field approximations and a Gutzwiller ansatz which are quite accurate and suitable to describe this system. We find that dipolar bosonic gas in 2D exhibits a multitude of insulating metastable states, often competing with the ground state, similarly as in a disordered system. We study in detail the fate of these metastable states: how can they be prepared on demand, how they can be detected, what is their lifetime due to tunnelling, and what is their role in various cooling schemes. Moreover, we find that the ground state is characterized by insulating checkerboard-like states with fractional filling factors v(average number of particles per site) that depend on the cut-off used for the interaction range. We confirm this prediction by studying the same system with Quantum Monte Carlo methods (the worm algorithm). In this case no cut-off is used, and we find evidence for a Devil's staircase in the ground state, i.e. where insulating phases appear at all rational of the underlying lattice. We also find regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies.In this work, we also investigate how the previous scenario changes in 3D. We focus on the simplest 3D lattice composed of two 2D layers in which the dipoles are polarized perpendicularly to the planes; the dipolar interaction is then repulsive for particles laying on the same plane, while it is attractive for particles at the same lattice site on different layers. Instead we consider inter-layer tunnelling to be suppressed, which makes the system analogous to a bosonic mixture in a 2D lattice. Our calculations show that particles pair into composites, and demonstrate the existence of the novel Pair Super Solid (PSS) quantum phase.Currently we are studying a 2D lattice where the dipoles are free to point in both directions perpendicularly to the plane, which results in a nearest neighbour repulsive (attractive) interaction for aligned (antialigned) dipoles. We find regions of parameters where the ground state is ferromagnetic or antiferromagnetic, and find evidences for the existence of a Counterflow Super Solid (CSS) quantum phase.Our predictions have direct experimental consequences, and we hope that they will be soon checked in experiments with ultracold dipolar atomic and molecular gases.

A system suitable for studying interactions between ⁸⁷Rb Rydberg atoms and metal surfaces has been constructed. This thesis describes the design and construction of the apparatus, and some test results. Atoms in a vapor cell magneto-optical trap are transferred to a macroscopic Ioffe-Pritchard trap, where they will be RF evaporatively cooled and loaded into a magnetic microtrap (atom chip). Confinement of cold clouds at controllable distances (5–200 μm)} from a metal surface is possible. The effects of atom-surface interactions can be studied with Rydberg atom spectroscopy. Some functionality of the apparatus has been demonstrated. Approximately 1.5×10⁷ atoms were loaded into a mirror MOT, and about 6×10⁶ atoms were optically pumped to the |F=2, m_F=2> hyperfine ground state and confined in a macroscopic Ioffe-Pritchard trap. The temperature of the cloud in the trap was 42 ± 5 μK, and the 1/e lifetime is 1–1.5 s. Forced RF evaporation has been used to measure the magnetic field at the trap minimum, but RF evaporative cooling has not yet been demonstrated.

A system suitable for studying interactions between ⁸⁷Rb Rydberg atoms and metal surfaces has been constructed. This thesis describes the design and construction of the apparatus, and some test results. Atoms in a vapor cell magneto-optical trap are transferred to a macroscopic Ioffe-Pritchard trap, where they will be RF evaporatively cooled and loaded into a magnetic microtrap (atom chip). Confinement of cold clouds at controllable distances (5–200 μm)} from a metal surface is possible. The effects of atom-surface interactions can be studied with Rydberg atom spectroscopy. Some functionality of the apparatus has been demonstrated. Approximately 1.5×10⁷ atoms were loaded into a mirror MOT, and about 6×10⁶ atoms were optically pumped to the |F=2, m_F=2> hyperfine ground state and confined in a macroscopic Ioffe-Pritchard trap. The temperature of the cloud in the trap was 42 ± 5 μK, and the 1/e lifetime is 1–1.5 s. Forced RF evaporation has been used to measure the magnetic field at the trap minimum, but RF evaporative cooling has not yet been demonstrated.

This thesis focuses on the analysis of Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) evolution in ultracold superfluid Fermi gases when the interaction between atoms is varied. The tuning of attractive interactions permits the ground state of the system to evolve from a weak fermion attraction BCS limit of loosely bound and largely overlapping Cooper pairs to a strong fermion attraction limit of tightly bound small bosonic molecules which undergo BEC. This evolution is accompanied by anomalous behavior of many superfluid properties, and reveals several quantum phase transitions. This thesis has two parts: In the first part, I analyze zero and nonzero orbital angular momentum pairing effects, and show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the $s$-wave case where the BCS to BEC evolution is just a crossover. In the second part, I analyze two-species fermion mixtures with mass and population imbalance in continuum, trap and lattice models. In contrast with the crossover physics found in the mass and population balanced mixtures, I demonstrate the existence of phase transitions between normal and superfluid phases, as well as phase separation between superfluid (paired) and normal (excess) fermions in imbalanced mixtures as a function of scattering parameter and mass and population imbalance.

Die Arbeit beschäftigt sich mit der Dynamik von Gasen aus hoch angeregten Atomen. Es wird sowohl die Erzeugung von Rydberggasen, als auch ihre Dynamik nach der Laser-Anregung betrachtet. Zur Beschreibung des Anregungsprozesses wird ein quasi-klassischer Zugang verwendet. Er basiert auf der adiabatischen Eliminierung von Kohärenzen aus der vollen Quanten-Beschreibung und führt auf eine klassische Mastergleichung. Diese Näherung ist gerade für typische experimentelle Situationen durchführbar. Die klassische Mastergleichung kann durch ein simples Monte-Carlo-Verfahren für Systeme aus zehntausenden von Teilchen unter voller Berücksichtigung der Rydberg-Rydberg-Wechselwirkung gelöst werden. Mit Hilfe des Monte-Carlo-Verfahrens wird die Anregung von Rydbergatomen in einem ultrakalten Gas untersucht. Die in Experimenten gefundene Anregungsblockade wird durch die Methode gut beschrieben. Bei der Anregung von Rydbergatomen aus einem optischen Gitter wird sogar eine Anregungsverstärkung - eine Antiblockade - vorhergesagt. Die Antiblockade in einem Gitter erlaubt eine Charakterisierung räumlicher Korrelationen der Rydbergatome allein durch die Messung ihrer Dichte. Sie ist robust gegenüber Gitterfehlstellen und sollte mit heutigen experimentellen Techniken nachweisbar sein. Für die Anregung im ungeordneten Gas wird gezeigt, dass sich die räumlichen Korrelationen der Rydbergatome indirekt in den Momenten der Häufigkeitsverteilung angeregter Atome widerspiegeln. Durch die Untersuchung der Fluktuationen in der Zahl angeregter Atome lassen sich die Unterschiede in den Paarkorrelationsfunktionen bei Blockade und Antiblockade im Gas messen. Ein Vergleich mit experimentellen Daten zeigt eine qualitativ gute Übereinstimmung. Für die Dynamik des Rydberggases nach dem Abschalten der Anregungslaser ist der Fall besonders interessant, dass Atome in unterschiedlichen Rydbergzuständen resonant ihre Anregungsenergie austauschen können. In der Arbeit wird argumentiert, dass sich der räumliche Transfer von Anregungsenergie in Rydbergsystemen ohne störende Umgebungseinflüsse gezielt untersuchen lässt. Mit Hilfe der Frenkelschen Exziton-Theorie wird der Energietransfer entlang einer eindimensionalen Anordnung von Rydbergatomen untersucht. Zusätzlich wird dargelegt, dass die exzitonische Anregung auch mechanische Kräfte auf die Rydbergatome induziert. Diese werden mit Hilfe einer quanten-klassischen Methode analysiert. Der Zusammenhang der auftretenden Kräfte mit den Symmetrien der exzitonischen Eigenfunktionen wird aufgezeigt. In einer eindimensionalen Anordnung von Rydbergatomen wird ein adiabatischer Energietransfer vorhergesagt, der an die Bewegung der Atome gebunden ist. Er läuft vollständig auf einer einzigen adiabatischen Potentialfläche ab. Dieser Transport ist langsam genug, um mit heutigen experimentellen Methoden im Prinzip orts- und zeitaufgelöst abgebildet zu werden.

In this thesis, I present experiments on making and probing strongly correlated gases of ultracold atoms in an optical lattice with engineered potentials and dynamics. The quantum gas microscope first developed in our lab enables single-site resolution imaging and manipulation of atoms in a two-dimensional lattice, offering an ideal platform for quantum simulation of condensed matter systems. Here we demonstrate our abilities to generate optical potential with high precision and high resolution, and engineer coherent dynamics using photon assisted tunneling. We also create a system of bilayer quantum gases that brings new imaging capabilities and extends the possible range of our quantum simulation. / Physics

The recent development of quantum gas microscopy for bosonic rubidium atoms trapped in optical lattices has made it possible to study local structure and correlations in quantum many-body systems. / Physics

In the present thesis, “Hydrodynamics of Binary Bose-Einstein Condensates and Hydro-elasticity of the Inner Crust of Neutron Stars”, the hydrodynamic effects, instabilities and superfluid turbulence in binary immiscible ultracold gases, and hydro-elastic macroscopic coupled modes and microscopic structure of the inner layers of the crust of neutron stars, are studied. The ultracold gas dynamics can be realized in the laboratory. The excitation modes of the inner crust determine a number of observable properties such as elasticity, thermal properties and mass transport properties. Here we focus on expanding the details, rather than repeating the results presented in the published articles. In the part of the thesis related to atomic ultracold gases, we utilize the physical parameters in the experimentally realizable parameter region. We numerically simulate the coupled non-linear Schrödinger equations, and calculate observable quantities, such as phase and modulus of the order parameter, conditions needed for observation of the Rayleigh-Taylor instability and for turbulence generation. The numerical calculations are accompanied by analytical description of the processes. The dispersion relation for capillary-gravitational waves at the interface between two ultracold gases, is derived straightforwardly from the superfluid Lagrangian. The equations of motion for centre-of-mass of the superfluids are derived, and then used in our model of the quantum swapping of immiscible superfluids pressed by a strong external force. By numerical simulation, we find that the Kelvin-Helmholtz instability which occurs at the non-linear stage of the Rayleigh-Taylor instability, can generate quantum turbulence with peculiar properties. We find that two-dimensional superfluid systems with weak inter-component repulsion are different from previously studied strongly repulsive binary superfluids, because the quantum Kelvin-Helmholtz instability in weakly repulsive superfluids rolls up the whole interface forming a vortex bundle, similarly to dynamics of the shear fluid layers in the classical hydrodynamics. Production of vortex bundles favours the Kolmogorov spectrum of turbulence, and we find that the Kolmogorov scaling indeed is present in a freely decaying turbulence. In the part of the thesis related to neutron stars, we study the inner crust of neutron stars, where the fully ionized atomic nuclei coexist with a superfluid of neutrons. The interaction between superfluid neutrons and the crystallized Coulomb plasma is due to the interaction between density perturbations (interaction of the scalar type), and between the current - the non-dissipative entrainment effect (interaction of the vector type). We calculate velocities of the collective modes of the crystal coupled to superfluid neutrons. As an input we use the results of microscopic nuclear calculations in the framework of the compressible liquid drop model (the Lattimer and Swesty equation of state), and more recent effective Thomas-Fermi calculations with shell corrections (N. Chamel, and the Brussels theoretical nuclear physics group). Knowledge of velocities as functions of the matter density in the inner crust is important for calculation of a number of dynamic and transport properties. The heat transport properties of the inner crust are directly observable in accreting binary systems (low-mass x-ray binaries). The mass transport properties of the inner crust are directly linked to the rotational evolution, being a key physical ingredient of the pulsar glitch phenomenon. The elastic properties are related to the vibrational modes of the star, and to the breaking stress of the crust. In the second part of our work on neutron stars we investigate the microscopic structure of the inner crust treating the structure as an anisotropic crystal coupled to s-wave superfluid neutron liquid. As we analyse dynamics of the elementary excitations at higher wavenumbers (smaller scales), we reach the edge of the first Brillouin zone. The Lattimer-Swesty data is applicable for wavenumbers much smaller than the edge of the first Brillouin zone. We extrapolate the data through the whole first Brillouin zone to calculate the fastest growth rate of the unstable modes. The crucial step is to calculate the mode velocities in anisotropic crystal incorporating both the induced neutron-proton interactions, and the electron screening properties. We find that the combined influence of these two effects leads to softening of the longitudinal phonon of the lattice above about the Thomas-Fermi screening wavenumber of the electrons. The critical wavenumber when the frequency becomes purely imaginary is about  1/5 - 2/3  of the reciprocal lattice vector, thus validating our assumption. The imaginary mode frequency implies instability at finite wavenumbers. Our calculations suggest that the mode at the first Brillouin zone edge is the most unstable, and thus the structure experiences a displacive phase transition when the central ion of a unit cell of the body-cubic-centred lattice, is displaced to the cube face. Thus, the electronic structure of matter at densities above the neutron drip [1], is richer than previously appreciated, and new microscopic calculations of nuclear structure are necessary which take into account the high-wavenumber physics. Such calculations will provide crucial input to models interpreting the quasi-periodic oscillations in Soft Gamma Repeaters as magnetar x-ray flares, and to the theory of glitches of neutron stars. [1] The neutron drip density is ~3×1011 g cm-3.