We present a theoretical investigation into the expansion dynamics of Rydberg-dressed ultracold Fermi gases. The effective interaction potential induced by Rydberg dressing significantly modifies the intrinsic properties and dynamical behavior of the quantum gas. The strength and range of these interactions can be precisely tuned by varying the intensity and detuning of the applied laser field. By employing mean-field theory and utilizing the density distribution of the atomic cloud to describe the quantum system dynamics, we theoretically describe the time-dependent evolution of the atomic cloud during the free expansion process, encompassing both non-interacting and unitary Fermi gases. Notably, the specific quantum states of the ground-state atoms play a pivotal role in shaping the effective interaction potential within the Rydberg-dressed quantum system. We elucidate how the interaction potential influences the rate and mode of the atom cloud’s expansion by hydrodynamic expansion arising from Rydberg-dressed atoms in distinct spin hyperfine states. This investigation may deepen our understanding of the behavior and interactions in quantum many-body systems and offer broad potential for future applications like the exploration of novel quantum phase transitions and emergent phenomena.
We present a theoretical investigation into the expansion dynamics of Rydberg-dressed ultracold Fermi gases. The effective interaction potential induced by Rydberg dressing significantly modifies the intrinsic properties and dynamical behavior of the quantum gas. The strength and range of these interactions can be precisely tuned by varying the intensity and detuning of the applied laser field. By employing mean-field theory and utilizing the density distribution of the atomic cloud to describe the quantum system dynamics, we theoretically describe the time-dependent evolution of the atomic cloud during the free expansion process, encompassing both non-interacting and unitary Fermi gases. Notably, the specific quantum states of the ground-state atoms play a pivotal role in shaping the effective interaction potential within the Rydberg-dressed quantum system. We elucidate how the interaction potential influences the rate and mode of the atom cloud’s expansion by hydrodynamic expansion arising from Rydberg-dressed atoms in distinct spin hyperfine states. This investigation may deepen our understanding of the behavior and interactions in quantum many-body systems and offer broad potential for future applications like the exploration of novel quantum phase transitions and emergent phenomena.
Rydberg-dressed ground state atoms are atoms with an electron off-resonantly excited to a very high energy state, i.e., a state of high principal quantum number n ≫ 1. This thesis investigates the quantum dynamics of interacting Rydberg-dressed ground state atoms trapped in several multi-well potential traps. Rydberg atoms are atoms with exaggerated properties. One of their most interesting properties is that they exhibit a strong and long-ranged interaction that can be tuned leading to a variety of different quantum behaviours. My work focuses on studying the effects of these interacting atoms when loaded in multi-well potential traps. Generally, multi-well systems are considered as the simplest example of a finite optical lattice structure. For this reason, this thesis covers three research topics that examine the effects of long-range interaction on Rydberg-dressed atoms trapped in several potential confinements. I begin, in the introduction, by discussing the theoretical background of relevance to this work. It starts with presenting the physics of Bose-Einstein condensate. Then, the fundamentals of the interaction between two-level atom and light are analytically studied. This study has the purpose of understanding both; the dressed interacting atoms and optical lattices. The definition, characteristics, and the nature of the interaction between Rydberg atoms are analysed afterwards. The second chapter examines the dynamics of an ensemble of interacting Rydberg- dressed atoms trapped in static, i.e., time-independent, multi-well potentials using a mean-field theoretical approach. I choose one-dimensional double- and triple-well in addition to a two-dimensional quadruple-well potentials. The time-dependent non-linear Gross-Pitaevskii equation is used to numerically explore the ensemble’s quantum dynamics. Solving the dynamical differential equations along with tuning the strength of the applied long-range interaction shows that the behaviour of non-interacting Rydberg-dressed atoms does not differ conceptually according to the geometry of the trapping potential. However, this changes when the interactions are switched on where the shape of the confinement leads to interesting outcomes especially in the non-linear interacting limit, such as macroscopic quantum self-trapping. After investigating an ensemble of interacting Rydberg-dressed atoms in static multi-well potential traps, the second research topic examines the dynamical evolution of these atoms when loaded in a finite optical lattice using the extended Bose-Hubbard model. In this chapter, the atoms ensemble is assumed to be in a superfluid state where I investigate both, the order parameter when the Rydberg excitation laser is applied and the interference pattern of the condensates in different dimensions. The study shows the emerging long-range interactions lead to a rapid collapse of the superfluid order parameter and in general allow only for partial revivals. In addition, the interference experiments can directly reveal the interaction between Rydberg-dressed atoms. In the fourth chapter, the dynamics of Rydberg-dressed atoms trapped in a dynamical, i.e., time-dependent, potential confinement is presented. The dynamical trap is constructed such that it begins as a harmonic oscillator and ends as a double- well potential. The analysis investigates an ensemble of contact-interacting atoms via the time-dependent non-linear GP equation.
Interacting ultracold atomic quantum gases provide an ideal test bed to study strongly correlated quantum matter. The interactions between atoms in such an ultracold quantum gas are typically short-ranged and well described by an effective contact potential. Introducing longer-range interactions promises the realization of novel quantum phases which are absent in systems with only short-range interactions. Trapped atoms, resonantly laser-coupled to highly excited, strongly interacting Rydberg states have been proposed as a versatile platform to realize such long-range interacting quantum matter. In a first experiment presented in this thesis, we combined the single-atom-sensitive local preparation and detection enabled by a quantum gas microscope to prepare and microscopically characterize an ensemble of rubidium-87 atoms trapped in an optical lattice in the regime of strong Rydberg blockade. There, we observe collectively enhanced optical coupling in an effective two-level system, the so-called “superatom”, and infer the presence of entanglement. Detuned optical coupling to Rydberg states, termed “Rydberg dressing”, has been proposed as an alternative approach to induce long-range interactions. Rather than directly exciting an atom to a Rydberg state, the properties of the latter are admixed to a ground state, which consequently acquires long-range interactions. In the context of this thesis, we have designed a laser system in the ultraviolet spectral range to admix Rydberg P-state character to the ground state of atoms in an optical lattice. In an emerging Ising quantum magnet, the presence of Rydberg-dressed interactions was demonstrated by an interferometric technique combined with spatially resolved spin correlation measurements. The theoretically predicted tunability of the isotropy and range of the interaction were confirmed experimentally. While these initial measurements exhibited unexpected dissipation, in a subsequent experiment in a one-dimensional spin chain this dissipation was overcome. We substantiated the improved coherence times by tracking the time evolution of the magnetization upon suddenly switching on interactions and observing coherent collapse and revival dynamics, one of the hallmarks of coherent quantum evolution. Our results establish Rydberg-dressed interactions in ultracold gases and pave the way to realize and study novel exotic quantum phases.
The strong interaction between Rydberg atoms can be used to control the strength and character of the interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Elaborate theoretical proposals for the realization of various complex phases and applications in quantum simulation exist. Also a simple model has been already developed that describes the basic idea of Rydberg dressing in a two-atom basis. However, an experimental realization has been elusive so far. We present a model describing the ground state of a Bose–Einstein condensate dressed with a Rydberg level based on the Rydberg blockade. This approach provides an intuitive understanding of the transition from pure two-body interaction to a regime of collective interactions. Furthermore it enables us to calculate the deformation of a three-dimensional sample under realistic experimental conditions in mean-field approximation. We compare full three-dimensional numerical calculations of the ground state to an analytic expression obtained within Thomas–Fermi approximation. Finally we discuss limitations and problems arising in an experimental realization of Rydberg dressing based on our experimental results and point out possible solutions for future approaches. Our work enables the reader to straight forwardly estimate the experimental feasibility of Rydberg dressing in realistic three-dimensional atomic samples.
Ultracold atoms are used to study various fundamental physics, including many-body system, nonequilibrium dynamics, and find many applications in quantum computing and quantum sensing. In this thesis, we studied the dynamics of ultracold atom gases with controllable two-body interactions. One of the major concerns is to manipulate the atomic states with electromagnetic fields. Here, we will show four projects associated with this topic. The first project is about the Sagnac interferometer based on trapped Bose-Einstein condensate. We explored the dynamics of the atoms and their relation to the sensitivity. We came up with an optimised driving field, and the performance is examined with interactions taken into consideration. The second project is about the quantum dynamics of bosonic atoms in an optical lattice with long-range interactions by Rydberg-dressing. It has been widely studied due to its controllable strength, length and anisotropy, which paves the new approach to engineering exotic quantum states and improving the performance of quantum devices. We found that phase transitions of Mott-insulator, superfluid supersolid, and density wave during a quench process. The correlation of the atoms is studied which reveals the properties of long-range interactions. The third project shows new designs of the magneto-optical trap for atom cooling. They are proposed to be manufactured by 3D printing technology. We simulated their performance and optimised the geometric parameters. The time-response and impedance have also been analysed. The fourth project studies the ground state of Rydberg-dressed fermions from the perspective of Fermi surface deformation. We calculated the deformation manifested by the aspect ratio and the appearance of Cooper pairs. The power-law scaling relations have been found with respect to the laser field, atom density and the quantum number of Rydberg states.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the s-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
Combining ultracold atomic gases with the peculiar properties of Rydberg excited atoms gained a lot of theoretical and experimental attention in recent years. Embedded in the ultracold gas, an interaction between the Rydberg atom and the surrounding ground state atoms arises through the scattering of the Rydberg electron from an intruding perturber atom. This peculiar interaction gives rise to a plenitude of previously unobserved effects. Within the framework of the present thesis, this interaction is studied in detail for Rydberg P-states in rubidium. Due to their long lifetime, atoms in Rydberg states are subject to scattering with the surrounding ground state atoms in the ultracold cloud. By measuring their lifetime as a function of the ground state atom flux, we are able to obtain the total inelastic scattering cross section as well as the partial cross section for associative ionisation. The fact that the latter is three orders of magnitude larger than the size of the formed molecular ion indicates the presence of an efficient mass transport mechanism that is mediated by the Rydberg–ground state interaction. The immense acceleration of the collisional process shows a close analogy to a catalytic process. The increase of the scattering cross section renders associative ionisation an important process that has to be considered for experiments in dense ultracold systems. The interaction of the Rydberg atom with a ground state perturber gives rise to a highly oscillatory potential that supports molecular bound states. These so-called ultralong-range Rydberg molecules are studied with high resolution time-of-flight spectroscopy, where we are able to determine the binding energies and lifetimes of the molecular states between the two fine structure split 25P-states. Inside an electric field, we observe a broadening of the molecular lines that indicates the presence of a permanent electric dipole moment, induced by the mixing with high angular momentum states. Due to the mixing of the ground state atom’s hyperfine states by the molecular interaction, we are able to observe a spin-flip of the perturber upon creation of a Rydberg molecule. Furthermore, an incidental near-degeneracy in the underlying level scheme of the 25P-state gives rise to highly entangled states between the Rydberg fine structure state and the perturber’s hyperfine structure. These mechanisms can be used to manipulate the quantum state of a remote particle over distances that exceed by far the typical contact interaction range. Apart from the ultralong-range Rydberg molecules that predominantly consist of only one low angular momentum state, a class of Rydberg molecules is predicted to exist that strongly mixes the high angular momentum states of the degenerate hydrogenic manifolds. These states, the so-called trilobite- and butterfly Rydberg molecules, show very peculiar properties that cannot be observed for conventional molecules. Here we present the first experimental observation of butterfly Rydberg molecules. In addition to an extensive spectroscopy that reveals the binding energy, we are also able to observe the rotational structure of these exotic molecules. The arising pendular states inside an electric field allow us, in comparison to the model of a dipolar rotor, to extract the precise bond length and dipole moment of the molecule. With the information obtained in the present study, it is possible to photoassociate butterfly molecules with a selectable bond length, vibrational state, rotational state, and orientation inside an electric field. By shedding light on various previously unrevealed aspects, the experiments presented in this thesis significantly deepen our knowledge on the Rydberg–ground state interaction and the peculiar effects arising from it. The obtained spectroscopic information on Rydberg molecules and the changed reaction dynamics for molecular ion creation will surely provide valuable data for quantum chemical simulations and provide necessary data to plan future experiments. Beyond that, our study reveals that the hyperfine interaction in Rydberg molecules and the peculiar properties of butterfly states provide very promising new ways to alter the short- and long-range interactions in ultracold many-body systems. In this sense the investigated Rydberg–ground state interaction not only lies right at the interface between quantum chemistry, quantum many-body systems, and Rydberg physics, but also creates many new and fascinating possibilities by combining these fields.