We present experiments measuring an interaction-induced phase shift of Rydberg atoms at Stark-tuned Fo ¨rster resonances.The phase shift features a dispersive shape around the resonance, showing that the interaction strength and sign can be tuned coherently.We use a pair-state interferometer to measure the phase shift.Although the coupling between pair states is coherent on the time scale of the experiment, a loss of visibility occurs as a pair-state interferometer involves three simultaneously interfering paths and only one of them is phase shifted by the mutual interaction.Despite additional dephasing mechanisms, a pulsed Fo ¨rster coupling sequence allows for observation of coherent dynamics around the Fo ¨rster resonance.
We present experiments measuring an interaction-induced phase shift of Rydberg atoms at Stark-tuned Fo ¨rster resonances.The phase shift features a dispersive shape around the resonance, showing that the interaction strength and sign can be tuned coherently.We use a pair-state interferometer to measure the phase shift.Although the coupling between pair states is coherent on the time scale of the experiment, a loss of visibility occurs as a pair-state interferometer involves three simultaneously interfering paths and only one of them is phase shifted by the mutual interaction.Despite additional dephasing mechanisms, a pulsed Fo ¨rster coupling sequence allows for observation of coherent dynamics around the Fo ¨rster resonance.
We present experiments measuring an interaction induced phase shift of Rydberg atoms at Stark tuned Förster resonances. The phase shift features a dispersive shape around the resonance, showing that the interaction strength and sign can be tuned coherently. We use a pair state interferometer to measure the phase shift. Although the coupling between pair states is coherent on the time scale of the experiment, a loss of visibility occurs as a pair state interferometer involves three simultaneously interfering paths and only one of them is phase shifted by the mutual interaction. Despite additional dephasing mechanisms a pulsed Förster coupling sequence allows to observe coherent dynamics around the Förster resonance.
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.
The field of coherent control has today been seeing significant progress, in a wide array of physical systems. One such system is the Rydberg atom. The long lifetime, strong dipole interactions, multiple degrees of freedom, and simple atomic structure make Rydberg atoms particularly appealing for experiments involving coherent control. The same properties have led to the exploration of Rydberg atoms as candidates for quantum information storage, processing and retrieval. Quantum information processing is a particular application of coherent control. Rather than being disparate subjects of study, coherent control of Rydberg atoms and processing of information stored as phase in different Rydberg levels are two sides of the same coin. In this dissertation, we experimentally characterize the effect of a half-cycle pulse on the phases of the states of a Rydberg wave packet and their mutual coherence. This has bearing both on our ability to control the states of the atom and on our ability to measure the information stored as quantum phase. We observe delay dependent phase shifts and losses of coherence. Despite a loss of information due to transfer of quantum amplitude to states outside the data register, we demonstrate partial retrieval of that information by the application of a second half cycle pulse. We also present an essential states model of the interaction, and we compare results from the model to experimental features observed. Although the particulars may vary, the concepts involved are quite general and may be applied to multilevel systems other than Rydberg atoms.
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.
We report on experiments exploring Stark-tuned Förster resonances between Rydberg atoms with high resolution in the Förster defect. The individual resonances are expected to exhibit different angular dependencies, opening the possibility to tune not only the interaction strength but also the angular dependence of the pair state potentials by an external electric field. We achieve a high resolution by optical Ramsey interferometry for Rydberg atoms combined with electric field pulses. The resonances are detected by a loss of visibility in the Ramsey fringes due to resonances in the interaction. We present measurements of the density dependence as well as of the coherence time at and close to Förster resonances.
Long-range interactions between cold Rydberg atoms are being investigated for neutral-atom quantum computing, quantum simulations, phase transitions in cold Rydberg gases and other applications. Fine tuning of the interaction strength can be implemented using Förster resonances between Rydberg atoms controlled by an electric field. The observation of the Stark-tuned Förster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the Förster resonance. The application of the radio-frequency field causes additional Förster resonances between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the Förster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned Förster resonances Rb( nP 3/2 ) + Rb( nP 3/2 ) → Rb( nS 1/2 ) + Rb([ n + 1] S 1/2 ) for two Rb Rydberg atoms interacting in a time-varying electric field.