Many-body Rabi oscillations of Rydberg excitation in small mesoscopic samples

We investigate the collective aspects of Rydberg excitation in ultracold mesoscopic systems. Strong interactions between Rydberg atoms influence the excitation process and impose correlations between excited atoms. The manifestations of the collective behavior of Rydberg excitation are the many-body Rabi oscillations, spatial correlations between atoms as well as the fluctuations of the number of excited atoms. We study these phenomena in detail by numerically solving the many-body Schr\"edinger equation.Comment: 8 pages, 5 figure

Sharp quadrature error bounds for the nearest-neighbor discretization of the regularized stokeslet boundary integral equation

The method of regularized stokeslets is a powerful numerical method to solve the Stokes flow equations for problems in biological fluid mechanics. A recent variation of this method incorporates a nearest-neighbor discretization to improve accuracy and efficiency while maintaining the ease-of-implementation of the original meshless method. This method contains three sources of numerical error, the regularization error associated from using the regularized form of the boundary integral equations (with parameter $\varepsilon$), and two sources of discretization error associated with the force and quadrature discretizations (with lengthscales $h_f$ and $h_q$). A key issue to address is the quadrature error: initial work has not fully explained observed numerical convergence phenomena. In the present manuscript we construct sharp quadrature error bounds for the nearest-neighbor discretisation, noting that the error for a single evaluation of the kernel depends on the smallest distance ($\delta$) between these discretization sets. The quadrature error bounds are described for two cases: with disjoint sets ($\delta>0$) being close to linear in $h_q$ and insensitive to $\varepsilon$, and contained sets ($\delta=0$) being quadratic in $h_q$ with inverse dependence on $\varepsilon$. The practical implications of these error bounds are discussed with reference to the condition number of the matrix system for the nearest-neighbor method, with the analysis revealing that the condition number is insensitive to $\varepsilon$ for disjoint sets, and grows linearly with $\varepsilon$ for contained sets. Error bounds for the general case ($\delta\geq 0$) are revealed to be proportional to the sum of the errors for each case.Comment: 12 pages, 6 figure

Fano Lineshapes Revisited: Symmetric Photoionization Peaks from Pure Continuum Excitation

In a photoionization spectrum in which there is no excitation of the discrete states, but only the underlying continuum, we have observed resonances which appear as symmetric peaks, not the commonly expected window resonances. Furthermore, since the excitation to the unperturbed continuum vanishes, the cross section expected from Fano's configuration interaction theory is identically zero. This shortcoming is removed by the explicit introduction of the phase shifted continuum, which demonstrates that the shape of a resonance, by itself, provides no information about the relative excitation amplitudes to the discrete state and the continuum.Comment: 4 pages, 3 figure

Observation of a resonant four-body interaction in cold cesium Rydberg atoms

Cold Rydberg atoms subject to long-range dipole-dipole interactions represent a particularly interesting system for exploring few-body interactions and probing the transition from 2-body physics to the many-body regime. In this work we report the direct observation of a resonant 4-body Rydberg interaction. We exploit the occurrence of an accidental quasi-coincidence of a 2-body and a 4-body resonant Stark-tuned Forster process in cesium to observe a resonant energy transfer requiring the simultaneous interaction of at least four neighboring atoms. These results are relevant for the implementation of quantum gates with Rydberg atoms and for further studies of many-body physics.Comment: 5 pages, 5 figure

Many-body theory of excitation dynamics in an ultracold Rydberg gas

We develop a theoretical approach for the dynamics of Rydberg excitations in ultracold gases, with a realistically large number of atoms. We rely on the reduction of the single-atom Bloch equations to rate equations, which is possible under various experimentally relevant conditions. Here, we explicitly refer to a two-step excitation-scheme. We discuss the conditions under which our approach is valid by comparing the results with the solution of the exact quantum master equation for two interacting atoms. Concerning the emergence of an excitation blockade in a Rydberg gas, our results are in qualitative agreement with experiment. Possible sources of quantitative discrepancy are carefully examined. Based on the two-step excitation scheme, we predict the occurrence of an antiblockade effect and propose possible ways to detect this excitation enhancement experimentally in an optical lattice as well as in the gas phase.Comment: 12 pages, 8 figure

Observation of blue-shifted ultralong-range Cs2_{2} Rydberg molecules

We observe ultralong-range blue-shifted Cs$_{2}$ molecular states near $ns_{1/2}$ Rydberg states in an optical dipole trap, where $31\leq n\leq34$. The accidental near degeneracy of $(n-4)l$ and $ns$ Rydberg states for $l>2$ in Cs, due to the small fractional $ns$ quantum defect, leads to non-adiabatic coupling among these states, producing potential wells above the $ns$ thresholds. Two important consequences of admixing high angular momentum states with $ns$ states are the formation of large permanent dipole moments, $\sim 15-100\,$Debye, and accessibility of these states via two-photon association. The observed states are in excellent agreement with theory. Both projections of the total angular momentum on the internuclear axis are visible in the experiment

Modulation of endothelial cell KCa3.1 Channels during endothelium-derived hyperpolarizing factor signaling in mesenteric resistance arteries

Arterial hyperpolarization to acetylcholine (ACh) reflects coactivation of KCa3.1 (IKCa) channels and KCa2.3 (SKCa) channels in the endothelium that transfers through myoendothelial gap junctions and diffusible factor(s) to affect smooth muscle relaxation (endothelium-derived hyperpolarizing factor [EDHF] response). However, ACh can differentially activate KCa3.1 and KCa2.3 channels, and we investigated the mechanisms responsible in rat mesenteric arteries. KCa3.1 channel input to EDHF hyperpolarization was enhanced by reducing external [Ca2+]o but blocked either with forskolin to activate protein kinase A or by limiting smooth muscle [Ca2+]i increases stimulated by phenylephrine depolarization. Imaging [Ca2+]i within the endothelial cell projections forming myoendothelial gap junctions revealed increases in cytoplasmic [Ca2+]i during endothelial stimulation with ACh that were unaffected by simultaneous increases in muscle [Ca2+]i evoked by phenylephrine. If gap junctions were uncoupled, KCa3.1 channels became the predominant input to EDHF hyperpolarization, and relaxation was inhibited with ouabain, implicating a crucial link through Na+/K+-ATPase. There was no evidence for an equivalent link through KCa2.3 channels nor between these channels and the putative EDHF pathway involving natriuretic peptide receptor-C. Reconstruction of confocal z-stack images from pressurized arteries revealed KCa2.3 immunostain at endothelial cell borders, including endothelial cell projections, whereas KCa3.1 channels and Na+/K+-ATPase {alpha}2/{alpha}3 subunits were highly concentrated in endothelial cell projections and adjacent to myoendothelial gap junctions. Thus, extracellular [Ca2+]o appears to modify KCa3.1 channel activity through a protein kinase A-dependent mechanism independent of changes in endothelial [Ca2+]i. The resulting hyperpolarization links to arterial relaxation largely through Na+/K+-ATPase, possibly reflecting K+ acting as an EDHF. In contrast, KCa2.3 hyperpolarization appears mainly to affect relaxation through myoendothelial gap junctions. Overall, these data suggest that K+ and myoendothelial coupling evoke EDHF-mediated relaxation through distinct, definable pathways

Photoionization Rates of Cs Rydberg Atoms in a 1064 nm Far Off-Resonance Trap

Experimental measurements of photoionization rates of $nD_{5/2}$ Rydberg states of Cs ($50 \leq n \leq 75$) in a 1064 nm far off-resonance dipole trap are presented. The photoionization rates are obtained by measuring the lifetimes of Rydberg atoms produced inside of a 1064 nm far off-resonance trap and comparing the lifetimes to corresponding control experiments in a magneto-optical trap. Experimental results for the control experiments agree with recent theoretical predictions for Rydberg state lifetimes and measured photoionization rates are in agreement with transition rates calculated from a model potential.Comment: 12 pages, 4 figure