In the course of this thesis the techniques of coherent state preparation and interrogation introduced by Stern, Rabi, Ramsey and others are extended to large samples of ultracold Rydberg atoms and molecules. The key technique to realize the coherent control is a Ramsey-like excitation scheme. To achieve this, a Rydberg interferometer is set up and successfully applied in the investigation of the recently discovered ultralong-range Rydberg molecules as well as for the exploration of the dynamics of atomic Rydberg states. Therby, the coherent control of Rydberg molecules is proven. This is a major step towards time resolved investigation of the dynamics of the exotic molecule and opens new opportunities for a more sophisticated understanding of the underlying binding mechanisms. The first experimental application of the interferometer has been given for ultralong-range Rydberg molecules. Following the work of Ramsey, an experimental sequence with two excitation pulses split in time was set up. Because the Rydberg molecules are coherently photoassociated in the experiment, an interference pattern known as Ramsey fringes is created. The loss of visibility of the Ramsey fringe pattern could be described in a two-level model and from these calculations, the lifetime of the molecules was determined interferometrically. Thus aside from being an elegant and unambiguous proof for the coherence of the photoassociation, the occurrence of Ramsey fringes also allows one to see the experiment as an atom-molecule interferometer. These experiments have paved the way towards experimental exploration of the dynamics of these exotic molecule. For another open question in the field of ultralong-range Rydberg molecules - their lifetime - the findings in this thesis brought clarity. From the density-dependent investigations it could be found that the lifetime of the vibrationally excited molecular state is systematically shorter than that of the molecular ground state. These findings confirm the theory that the excited molecular states are bound by quantum reflection: The shortened lifetime can be ascribed to the inward penetration of the bound atomic pair due to imperfect quantum reflection leading to the dissociation of the molecule. In the further course of this thesis, the idea of a Ramsey setup for Rydberg molecules has been extend to Rydberg atoms. With the introduction of a control parameter to tune the relative phase shift between the ground-state arm and the Rydberg arm, the so far empty interferometer has been extended to a full working interferometer. The measurements on the 43s-state in electric fields demonstrated the usability of the interferometer in a simple and well controllable system and the interferometric studies on the 46d-state in crossed external fields can be regarded as the first investigative application of the interferometer. The key point of the investigation is the link between the two observables of the Rydberg interferometer, phase shift and visibility, and the complex value describing the Rydberg state of interest. It was found that the phase shift of the Rydberg state mostly follows the adiabatic energy curves in the electric field calculated for these experimental parameters. However, in the region where avoided crossings du to crossed electric and magnetic field occur, the phase shift behaves substantially different. While the phase rises fast by pi near one avoided crossing, a 2pi jump occurs at another avoided crossing. Since the phase can only be determined in the interval between 0 and 2pi experimentally, the jump cannot be observed as function of the electric field. This limitation has been overcome by taking the phase shift as function of time for different electric fields, which allows to reconstruct the phase at the given field-on time independently. From these measurements, the occurrence of the 2pi jump could be validated. To explore the reasons underlying the behavior of the phase in the electric field, the dynamics of the system has been modeled theoretically. The experimental findings for the phase shift as well as for the visibility are thoroughly reproduced by theory. Especially the characteristic behavior of phase shift and visibility near the avoided crossings is also seen in the calculations. With the help of this modeling one can see the fast pi rise in analogy to the phase of a driven harmonic oscillator that changes from in-phase when the driving frequency is below the resonance of the oscillator and out-of-phase above. The 2pi jump, however, emerges from the complex dynamics of the several levels involved and can not be easily broken down to a two-level picture. Altogether, these findings confirm that the Rydberg interferometer can track the dynamics of the selected Rydberg state and enabled the tomography of the Rydberg state. Moreover, these measurements show the potential of the Rydberg interferometer as tool to explore the dynamic of quantum systems.
In the course of this thesis the techniques of coherent state preparation and interrogation introduced by Stern, Rabi, Ramsey and others are extended to large samples of ultracold Rydberg atoms and molecules. The key technique to realize the coherent control is a Ramsey-like excitation scheme. To achieve this, a Rydberg interferometer is set up and successfully applied in the investigation of the recently discovered ultralong-range Rydberg molecules as well as for the exploration of the dynamics of atomic Rydberg states. Therby, the coherent control of Rydberg molecules is proven. This is a major step towards time resolved investigation of the dynamics of the exotic molecule and opens new opportunities for a more sophisticated understanding of the underlying binding mechanisms. The first experimental application of the interferometer has been given for ultralong-range Rydberg molecules. Following the work of Ramsey, an experimental sequence with two excitation pulses split in time was set up. Because the Rydberg molecules are coherently photoassociated in the experiment, an interference pattern known as Ramsey fringes is created. The loss of visibility of the Ramsey fringe pattern could be described in a two-level model and from these calculations, the lifetime of the molecules was determined interferometrically. Thus aside from being an elegant and unambiguous proof for the coherence of the photoassociation, the occurrence of Ramsey fringes also allows one to see the experiment as an atom-molecule interferometer. These experiments have paved the way towards experimental exploration of the dynamics of these exotic molecule. For another open question in the field of ultralong-range Rydberg molecules - their lifetime - the findings in this thesis brought clarity. From the density-dependent investigations it could be found that the lifetime of the vibrationally excited molecular state is systematically shorter than that of the molecular ground state. These findings confirm the theory that the excited molecular states are bound by quantum reflection: The shortened lifetime can be ascribed to the inward penetration of the bound atomic pair due to imperfect quantum reflection leading to the dissociation of the molecule. In the further course of this thesis, the idea of a Ramsey setup for Rydberg molecules has been extend to Rydberg atoms. With the introduction of a control parameter to tune the relative phase shift between the ground-state arm and the Rydberg arm, the so far empty interferometer has been extended to a full working interferometer. The measurements on the 43s-state in electric fields demonstrated the usability of the interferometer in a simple and well controllable system and the interferometric studies on the 46d-state in crossed external fields can be regarded as the first investigative application of the interferometer. The key point of the investigation is the link between the two observables of the Rydberg interferometer, phase shift and visibility, and the complex value describing the Rydberg state of interest. It was found that the phase shift of the Rydberg state mostly follows the adiabatic energy curves in the electric field calculated for these experimental parameters. However, in the region where avoided crossings du to crossed electric and magnetic field occur, the phase shift behaves substantially different. While the phase rises fast by pi near one avoided crossing, a 2pi jump occurs at another avoided crossing. Since the phase can only be determined in the interval between 0 and 2pi experimentally, the jump cannot be observed as function of the electric field. This limitation has been overcome by taking the phase shift as function of time for different electric fields, which allows to reconstruct the phase at the given field-on time independently. From these measurements, the occurrence of the 2pi jump could be validated. To explore the reasons underlying the behavior of the phase in the electric field, the dynamics of the system has been modeled theoretically. The experimental findings for the phase shift as well as for the visibility are thoroughly reproduced by theory. Especially the characteristic behavior of phase shift and visibility near the avoided crossings is also seen in the calculations. With the help of this modeling one can see the fast pi rise in analogy to the phase of a driven harmonic oscillator that changes from in-phase when the driving frequency is below the resonance of the oscillator and out-of-phase above. The 2pi jump, however, emerges from the complex dynamics of the several levels involved and can not be easily broken down to a two-level picture. Altogether, these findings confirm that the Rydberg interferometer can track the dynamics of the selected Rydberg state and enabled the tomography of the Rydberg state. Moreover, these measurements show the potential of the Rydberg interferometer as tool to explore the dynamic of quantum systems.
Interactions between single atoms are fundamental to physics and to control them is an ultimate goal. The exaggerated properties of Rydberg atoms offer to met the technical challenges to isolate and control single interaction channels in ultracold gases. Here, I present experiments on two subjects related to interactions of Rydberg atoms in dense ultracold clouds. One subject concerns coherence in strongly interacting ensembles of atoms, where the interaction between Rydberg atoms is induced via Stark-tuned Förster resonances. Pulsed experiments, following the idea of Ramsey experiments, are used for high resolution spectroscopy of the Förster defect and phase sensitive detection. Coherent oscillations between pair states and an interaction-induced phase shift of Rydberg atoms are measured. These experiments are accompanied by calculations of the interaction strength and by simulations using the concept of a pair state interferometer. The simulations nicely reproduce the experimental findings and support the observation that the ensemble of atoms in the presence of interactions can be described and controlled coherently. The second subject of this thesis is the measurement of a permanent dipole moment in a homonuclear diatomic molecule that arises by the interaction between a Rydberg atom and a ground state atom. Usually parity symmetry prohibits a permanent dipole moment in diatomic molecules, but here the strong asymmetry between the constituents of the ultralong-range Rydberg molecule allows breaking parity symmetry. These molecules consist of one ground state atom bound inside the Rydberg electron wavefunction of a highly excited atom. Calculations predict dipole moments on the order of 1 Debye. Experimental proof is reported on the measurement of a linear Stark effect of these molecules, in excellent agreement with the calculations.
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.
In this work the existence of a novel type of molecule is shown whose binding is based solely on electron-atom scattering. These molecules are composed of a Rydberg atom and a ground state atom - here Rb(ns) and Rb(5s) - where the binding arises from scattering of the Rydberg electron from the ground state atom. The ground state atom is bound to the Rydberg wavefunction, which has radii on the order of 100nm, and thus these molecules are of long-range. Although the theoretical description of this interaction goes back to the famous work of Fermi in the year 1934 which was expanded in the following decades by Omont and Greene, the experimental proof of their existence was still missing. Up to now, experimental evidence for the ultralong-range Rydberg molecules was found only in spectral line broadenings. The present experiments have demonstrated the direct photoassociation of these ultralong-range Rydberg molecules for Rb(ns)-Rb(5s) triplet states from a cold and dense sample of rubidium 87 atoms for a range of principal quantum numbers, n, between 34 and 40. The high-resolution photoassociation spectra allowed for the observation of several vibrational states separated by only a few Megahertz. Based on the model by Greene the vibrational ground states v=0 are assigned and the dependence of their binding energy on the principal quantum number, n, is used to extract the triplet s-wave scattering length for electron-Rb(5s) collisions from the data. The remarkably good agreement between experiment and theory for the vibrational ground state v=0 over a range of principal quantum numbers attests to the accuracy of Fermi's original pseudopotential approach in describing interactions in excited multi-atom systems. Aside from this good agreement for the state v=0, the measurements also show that contributions from p-wave scattering cannot be neglected, as a number of excited vibrational states is observed in the experiment that are not predicted from the theory assuming only s-wave scattering. Calculations of Li, Pohl and coworkers have shown that a full solution of the electron-atom scattering is necessary for the assignment of all vibrational states. This work finds the molecular bound states to be very sensitive to both s-wave as well as p-wave electron-atom scattering and the Rydberg molecules turn out to be an accurate experimental platform to study electron-atom collisions in a previously inaccessible ultralow-energy regime. In general, the ultralong-range Rydberg molecules investigated here for rubidium are expected for all species with negative scattering length for electron-atom interaction, e. g. the other alkali atoms. Rydberg atom and ground state atom do not even have to be of the same chemical element, the only requirement is a negative scattering length of the ground state atom for electron scattering. Moreover, the binding force of the Rydberg electron is not restricted to a single ground state atom and molecules with more than one ground state atom can be created. The fact that these exotic molecules have huge bond lengths but nevertheless a vibrational spectrum with several states make a new type of ultracold Rydberg chemistry feasible. In the future, larger polymers or even heteronuclear molecules can be realized, where the number of atoms, the constituent atomic elements and the addressed Rydberg state allow to precisely select the properties of the long-range molecule.
Collisions involving Rydberg atoms reveal detailed information on the state of a background medium and can be used as diagnostic probes of temperature and density distributions in a neutral or ionized gas. Spectroscopy of Rydberg atoms in highly excited states reveals the interaction of the Rydberg electron with core electrons, including relativistic effects, and can be used for precise determination of fundamental constants. The advent of ultracold trapping and cooling methods in the last three decades has ushered in a new paradigm in Rydberg physics control and manipulation. The concept of the Rydberg blockade, for instance, al- lows for precise control of long-range dipolar interaction between atoms, creation of correlated many-body wave functions, and realization of macroscopic quantum entanglement and quan- tum logic operations. The formation of a new class of Rydberg molecules arising from ground and Rydberg atom collisions can be used to manipulate electron-atom scattering phase shifts, form and manipulate molecules with enormous permanent electric dipole moments, study Ry- dberg chemistry at the ultracold, and realize macroscopic quantum polaronic systems. In this thesis, I will investigate charge transfer from covalent ground-Rydberg collisions to form heavy ion pair states. In another related study, I explore the formation of spin-mixed ultralong range Rydberg molecules, by accounting for spin-dependent relativistic fine and hyperfine interac- tion. Such studies help to not only explain experimental observations, but also point to how molecular reactions can be controlled using small electric or magnetic fields.
This thesis describes studies on a Rydberg-dressed ultracold atom system as a versatile platform for non-equilibrium physics research, atom-light interactions analysis and atomic sensing applications. This work includes a description of the experimental system, an ultracold potassium atom setup where we can prepare a gas of atoms in an optical dipole trap and precisely control their ground state properties. To excite the atoms to strongly-interacting Rydberg states, we set up and characterize a high-power and widely tunable excitation laser system, for driving both single and two-photon Rydberg excitations. Together this establishes a unique system for studying the effects of driving, long-range interactions and dissipation (due to the relatively short lifetime of excited states) on many-body dynamics. Using this setup we study the phase structure of a driven-dissipative system out of equilibrium , where exploiting the atom loss rate as an observable,we discover different power-laws depending on the system parameters (i.e driving,dissipation and interaction). We study further in detail a regime which shows loss rates much larger than those for single particles, and discover that due to the Rydberg population decay the system evolves to a self-organized critical state.Our key observations can be well described by effectively classical models for the many-body dynamics, which we understand as a consequence of rapid dephasing of atomic coherences. To quantify the coherence of the atom-light interactions, we realize a Rydberg dressed interferometer. This technique combines the precision of atomic clock transitions with the exaggerated properties of Rydberg atoms such as their long-range interactions and extreme response to electric fields. Using the interferometer, we are able to characterize the Rydberg-dressed ensemble, including the effects of population decay and dephasing both of which affect the coherence time. This enables us to identify power fluctuations in the excitation laser as the dominant effects limiting the coherence in the system, which will be used in the experiment for future improvements of the coherence time. As an additional application, we demonstrate that the Rydberg dressed interferometer can be used to precisely measure static electric fields down to 17 mV/cm which is comparable to state-of-the-art electrometers. These results together highlight the versatility of the Rydberg platform and pave the way towards a better understanding of long-range interacting systems out-of-equilibrium. This work paves the way to new studies of non-equilibrium phenomena and applications of many-body quantum systems which make use of both quantum coherent and dissipative interactions.
In this dissertation I investigate cold Rydberg atoms and molecules in which the angular-momentum character of the quantum states involved strongly influences their properties and dynamics. In the first part I focus on long-range diatomic Rydberg molecules formed by a rubidium D-state Rydberg atom and a second rubidium atom in its ground state. Spectroscopic measurements of molecular binding energies are presented showing the effect of the Rydberg atom size and fine-structure coupling on the molecular potentials. A theoretical model is introduced that takes into account all relevant angular-momentum couplings between the molecular constituents, successfully reproducing experimental observations. Calculations of adiabatic potentials and binding energies, molecular-state lifetimes, electric and magnetic dipole moments are also presented. In the second part, I describe the production and magnetic trapping of cold circular Rydberg atoms. The circular Rydberg atoms are generated out of a cold gas of rubidium using the crossed-fields method and magnetically trapped. The trapping force is employed to induce center-of-mass oscillations of the trapped atom sample. Trap parameters and observed oscillation frequencies are used to measure the magnetic moments of the circular Rydberg atoms. Trap losses and the atomic internal-state evolution in the 300 Kelvin thermal background are also investigated.