We show that Rydberg states in an ultra-cold 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 Rydber
g states while the second half returns atoms to the ground state, as in the experiment of Raitzsch et al. [Phys. Rev. Lett. 100 (2008) 013002]. Near to 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 half-way 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. We finally demonstrate the utility of the omega-expansion for the approximate description of correlation dynamics through an echo sequence.
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 collectiv
e 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 Schredinger equation.
We investigate the excitation dynamics of Rydberg atoms in ultracold atomic samples by expanding the excitation probability and the correlation function between excited atoms in powers of the isolated atom Rabi frequency $Omega$. In the Heisenberg pi
cture, we give recurrence relations to calculate any order of the expansions, which ere expected to be well-behaved for arbitrarily strong interactions. For homogeneous large samples, we give the explicit form of the expansions, up to $Omega^4$, averaged over all possible random spatial distributions of atoms, for the most important cases of excitation pulses and interactions.
We have calculated long-range molecular potentials of the $0_g^{+}$, $0_u^{-}$ and $1_u$ symmetries between highly-excited rubidium atoms. Strong $np+np$ potentials characterized by these symmetries are important in describing interaction-induced phe
nomena in the excitation spectra of high $np$ Rydberg states. Long-range molecular resonances are such phenomena and they were first reported in S.M. Farooqi {it et al.}, Phys. Rev. Lett. {bf 91} 183002. One class of these resonances occurs at energies corresponding to excited atom pairs $(n-1)d+ns$. Such resonances are attributed to $ell$-mixing due to Rydberg-Rydberg interactions so that otherwise forbidden molecular transitions become allowed. We calculate molecular potentials in Hunds case (c), use them to find the resonance lineshape and compare to experimental results.
