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arXiv:1607.01398 · Physical Review Letters

Control of Spatial Correlations between Rydberg Excitations using Rotary Echo

Nithiwadee Thaicharoen, Andrew Schwarzkopf, Georg A. Raithel

Published Mar 31, 2017• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.118.133401

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Journal of Physics B Atomic Molecular and Optical Physics•Sep 10, 2008•17 citations
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.
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.
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.
When cold atoms are laser-excited to Rydberg states, the strong interactions between Rydberg excitations can lead to complex many-body entanglement in the system. The excitation process results in spatial correlations between excitations in the system. In most cases, Rydberg excitation positions are anticorrelated such that no two excitations are within a "blockade radius" of each other. Such systems are well-suited for studying basic many-body physics, as well as for future technological applications such as quantum computation. This thesis describes an experimental apparatus we constructed to perform spatially-sensitive detection of Rydberg atoms. We use the apparatus to perform measurements of the Rydberg-Rydberg pair-correlation function. This results in the first direct spatial images of the Rydberg blockade effect. We measure the blockade radius for a variety of S and D Rydberg states in rubidium. We investigate the dependence of the blockade radius on laser detunings and energy level shifts induced by optical potentials due to trapping lasers. Our results have some implications for atom traps used for neutral atom quantum computation. We also present simulations results used to characterize the performance of the imaging system.
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 show that Rydberg states in an ultracold gas can be excited with strongly preferred nearest-neighbor distance if densities are well below saturation. The scheme makes use of an echo sequence in which the first half of a laser pulse excites Rydberg states while the second half returns atoms to the ground state, as in the experiment of Raitzsch et al. [Phys. Rev. Lett. 100, 013002 (2008)]. Near the end of the echo sequence, almost any remaining Rydberg atom is separated from its next-neighbor Rydberg atom by a distance slightly larger than the instantaneous blockade radius halfway through the pulse. These correlations lead to large deviations of the atom-counting statistics from a Poissonian distribution. Our results are based on the exact quantum evolution of samples with small numbers of atoms. Finally, we demonstrate the utility of the $\ensuremath{\omega}$ expansion for the approximate description of correlation dynamics through an echo sequence.
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.