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arXiv:1203.1851

Förster interaction induced phase shift in a pair state interferometer

J. Nipper, Jonathan Balewski, Alexander Krupp, Sebastian Hofferberth, R. Löw, Tilman Pfau

Published Mar 8, 2012• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.1203.1851

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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.
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 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.
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.
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.
Cold atoms in highly excited Rydberg states are promising candidates to implement quantum logic gates of a quantum computer via long-range dipole-dipole interaction. Two-qubit gates require a controlled interaction of only two close Rydberg atoms. We report on the first spectroscopic observation of the resonant dipole-dipole interaction between two cold rubidium Rydberg atoms confined in a small laser excitation volume. The interaction strength was controlled by fine-tuning of the Rydberg levels into a Förster resonance using the Stark effect. The observed resonance line shapes are in good agreement with numerical Monte Carlo simulations.
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. In our experiments with a few cold Rb Rydberg atoms we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the Förster resonances, since the population transfer at the resonances occurs on a time scale of $\sim$100 ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted Förster resonances, while non-sharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions 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(nP3/2)+Rb(nP3/2)→Rb(nS1/2)+Rb([n+1]S1/2){\rm Rb}(nP_{3/2} )+{\rm Rb}(nP_{3/2} )\to {\rm Rb}(nS_{1/2} )+{\rm Rb}([n+1]S_{1/2} )Rb(nP3/2​)+Rb(nP3/2​)→Rb(nS1/2​)+Rb([n+1]S1/2​) for two Rb Rydberg atoms interacting in a time-varying electric field.