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New Journal of Physics

Rotary echo tests of coherence in Rydberg-atom excitation

Kelly Cooper Younge, Georg A. Raithel

Published Apr 3, 2009• 19 citations
Publisher

Abstract

Rotary echoes are employed to study excitation dynamics in many-body Rydberg systems. In this method, a phase reversal of a narrow-band excitation field is applied at a variable time during the excitation pulse. The visibility of the resulting echo signal reveals the degree of coherence of the excitation process. Rotary echoes are measured for several nD5/2 Rydberg levels of rubidium with principal quantum numbers near n=43, where the strength of electrostatic Rydberg-atom interactions is modulated by a Forster resonance. The Rydberg-atom interactions are shown to diminish the echo visibility, in agreement with recent theoretical work. The equivalence of echo signals with spectroscopic data is demonstrated.

DOI
10.1088/1367-2630/11/4/043006

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Rotary echo tests of coherence in Rydberg-atom excitation

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Rotary echoes are employed to study excitation dynamics in many-body Rydberg systems. In this method, a phase reversal of a narrow-band excitation field is applied at a variable time during the excitation pulse. The visibility of the resulting echo signal reveals the degree of coherence of the excitation process. Rotary echoes are measured for several nD5/2 Rydberg levels of rubidium with principal quantum numbers near n=43, where the strength of electrostatic Rydberg-atom interactions is modulated by a Forster resonance. The Rydberg-atom interactions are shown to diminish the echo visibility, in agreement with recent theoretical work. The equivalence of echo signals with spectroscopic data is demonstrated.
Rotary echoes are employed to study excitation dynamics in many-body Rydberg systems. In this method, a phase reversal of a narrow-band excitation field is applied at a variable time during the excitation pulse. The visibility of the resulting echo signal reveals the degree of coherence of the excitation process. Rotary echoes are measured for several n D 5/2 Rydberg levels of rubidium with principal quantum numbers near n =43, where the strength of electrostatic Rydberg-atom interactions is modulated by a Forster resonance. The Rydberg-atom interactions are shown to diminish the echo visibility, in agreement with recent theoretical work. The equivalence of echo signals with spectroscopic data is demonstrated.
We manipulate correlations between Rydberg excitations in cold atom samples using a rotary-echo technique in which the phase of the excitation pulse is flipped at a selected time during the pulse. The correlations are due to interactions between the Rydberg atoms. We measure the resulting change in the spatial pair correlation function of the excitations via direct position-sensitive atom imaging. For zero detuning of the lasers from the interaction-free Rydberg-excitation resonance, the pair-correlation value at the most likely nearest-neighbor Rydberg-atom distance is substantially enhanced when the phase is flipped at the middle of the excitation pulse. In this case, the rotary echo eliminates most uncorrelated (unpaired) atoms, leaving an abundance of correlated atom pairs at the end of the sequence. In off-resonant cases, a complementary behavior is observed. We further characterize the effect of the rotary-echo excitation sequence on the excitation-number statistics.
We simulate the effect of special excitation pulses on a cold gas of atoms. First, a rotary echo sequence is used to examine the coherent nature of a frozen Rydberg gas. If collective excitation and de-excitation is present with little or no source of dephasing, after these pulses the system should be returned to a state with few excitations, and a strong echo signal should occur. We investigate systems that should display a perfect echo and systems where the interaction between atoms reduces the echo signal. A spin echo sequence is also used on a system of coherent hopping excitations, and we simulate how the strength of a spin echo signal is affected by thermal motion.
When ground state atoms are excited to a Rydberg state, van der Waals interactions among them can lead to a strong suppression of the excitation. Despite the strong interactions the evolution can still be reversed by a simple phase shift in the excitation laser field. We experimentally prove the coherence of the excitation in the strong blockade regime by applying an "optical rotary echo" technique to a sample of magnetically trapped ultracold atoms, analogous to a method known from nuclear magnetic resonance. We additionally measured the dephasing time due to the interaction between the Rydberg atoms.
The strong interactions between Rydberg excitations can result in spatial correlations between the excitations. The ability to control the interaction strength and the correlations between Rydberg atoms is applicable in future technological implementations of quantum computation. In this thesis, I investigates how both the character of the Rydberg-Rydberg interactions and the details of the excitation process affect the nature of the spatial correlations and the evolution of those correlations in time. I first describes the experimental apparatus and methods used to perform high-magnification Rydberg-atom imaging, as well as three experiments in which these methods play an important role. The obtained Rydberg-atom positions reveal the correlations in the many-body Rydberg-atom system and their time dependence with sub-micron spatial resolution. In the first experiment, atoms are excited to a Rydberg state that experiences a repulsive van der Waals interaction. The Rydberg excitations are prepared with a well-defined initial separation, and the effect of van der Waals forces is observed by tracking the interatomic distance between the Rydberg atoms. The atom trajectories and thereby the interaction coefficient C6 are extracted from the pair correlation functions of the Rydberg atom positions. In the second experiment, the Rydberg atoms are prepared in a highly dipolar state by using adiabatic state transformation. The atom-pair kinetics that follow from the strong dipole-dipole interactions are observed. The pair correlation results provide the first direct visualization of the electric-dipole interaction and clearly exhibit its anisotropic nature. In both the first and the second experiment, results of semi-classical simulations of the atom-pair trajectories agree well with the experimental data. In the analysis, I use energy conservation and measurements of the initial positions and the terminal velocities of the atom pairs to extract the C6 and C3 interaction coefficients. The final experiment demonstrates the ability to enhance or suppress the degree of spatial correlation in a system of Rydberg excitations, using a rotary-echo excitation process in concert with particular excitation laser detunings. The work in this thesis demonstrates an ability to control long-range interactions between Rydberg atoms, which paves the way towards preparing and studying increasingly complex many-body systems.
The energy level spectrum of a many-body system containing two shared, collective Rydberg excitations is measured using cold atoms in an optical dipole trap. Two pairs of independently tunable laser pulses are employed to spectroscopically probe the spectrum in a double-resonance excitation scheme. Depending on the magnitude of an applied electric field, the Rydberg-atom interactions can vary from resonant dipole-dipole to attractive or repulsive van der Waals, leading to characteristic signatures in the measured spectra. Our results agree with theoretical estimates of the magnitude and sign of the interactions.