We report on the observation of ultralong range interactions in a gas of cold Rubidium Rydberg atoms. The van-der-Waals interaction between a pair of Rydberg atoms separated as far as 100,000 Bohr radii features two important effects: Spectral broadening of the resonance lines and suppression of excitation with increasing density. The density dependence of these effects is investigated in detail for the S-and P-Rydberg states with main quantum numbers n ∼ 60 and n ∼ 80 excited by narrow-band continuous-wave laser light. The density-dependent suppression of excitation can be interpreted as the onset of an interaction-induced local blockade.PACS numbers: 32.80. Rm,32.80.Pj,34.20.Cf,03.67.Lx With the advances in laser cooling and trapping, new perspectives for the investigation of Rydberg atoms [1] have been opening. When cooled to very low temperatures, the core motion can be neglected for the timescales of excitation ("frozen Rydberg gas"). Unexpected effects have been discovered, such as the many-body diffusion of excitation [2,3], the population of high-angularmomentum states through free charges [4], or the spontaneous formation and recombination of ultracold plasmas [5,6]. Other fascinating features of cold, interacting Rydberg atoms have been proposed but not been observed so far, e.g. the creation of ultralong range molecules [7,8], whereas molecular crossover resonances have already been found experimentally [9]. One outstanding property of Rydberg atoms is their high polarizability, caused by the large distance between the outer electron and the core. This leads to strong electric field sensitivity and strong long-range dipole-dipole and vander-Waals (vdW) interactions are expected. First indications of interaction effects between Rydberg gases at high densities have been found in an atomic beam experiment [10] and, more recently, collisional evidence for ultralong range interactions in a cold Rydberg gas has been reported [11]. In a frozen gas these interactions make Rydberg atoms possible candidates for quantum information processing [12,13]. One promising approach is based on the concept of a dipole blockade [13], i.e. the inhibition of multiple Rydberg excitations in a confined volume due to interaction-induced energy shifts.In this Letter we report on experimental evidence for ultralong range interactions in a frozen Rydberg gas and we present high-resolution spectroscopic signatures of these interactions. citation from a cold gas [14]. Different to these findings, our experiment makes use of a tunable narrow-bandwidth continuous-wave (cw) laser for Rydberg excitation and thus allows for high-resolution spectroscopy of the resonance lines. By varying the density of Rydberg atoms in a controlled way, the influence of interactions on the strength and the shape of these lines is investigated in detail. Signatures of ultralong range interactions appear as spectral broadening of the excitation lines and saturation of the resonance peak height, the latter being an indication of the dipole blockade.To re...

In the quest for signatures of coherent transport we consider exciton trapping in the continuous-time quantum walk framework. The survival probability displays different decay domains, related to distinct regions of the spectrum of the Hamiltonian. For linear systems and at intermediate times the decay obeys a power-law, in contrast to the corresponding exponential decay found in incoherent continuous-time random walk situations. To differentiate between the coherent and incoherent mechanisms, we present an experimental protocol based on a frozen Rydberg gas structured by optical dipole traps.PACS numbers: 05.60. Gg, 32.80.Rm, 34.20.Cf Recent years have seen an upsurge of interest in coherent energy transfer, given the experimental advances in manipulating and controlling quantum mechanical systems. From the theoretical side, such investigations are of long standing; see, e.g., [1]. Here, tight-binding models, which model coherent exciton transfer, are closely related to the quantum walks (QW An appropriate means to monitor transport is to follow the decay of the excitation due to trapping. The long time decay of chains with traps is a well studied problem for classical systems [8,9]: for an ensemble of chains of different length with traps at both ends the averaged exciton survival probability has a stretched exponential form exp(−bt λ ), with λ = 1/3 (see, e.g., [9]). In contrast, quantum mechanical tight-binding models lead to λ = 1/4 [10, 11]. However, up to now only little is known about the decay of the quantum mechanical survival probability at experimentally relevant intermediate times.Here we evaluate and compare the intermediate-time decays due to trapping for both RW and QW situations by employing the similarity of the CTRW and the CTQW formalisms. Without traps, the coherent dynamics of excitons on a graph of connected nodes is modeled by the CTQW, which is obtained by identifying the Hamiltonian H 0 of the system with the CTRW transfer matrix T 0 , i.e., H 0 = −T 0 ; see e.g. [3, 12] (we will set ≡ 1 in the following). For undirected graphs, T 0 is related to the connectivity matrix A 0 of the graph by T 0 = −A 0 , where (for simplicity) all transmission rates are taken to be equal. Thus, in the following we take H 0 = A 0 . The matrix A 0 has as non-diagonal elements A the Rydberg gases considered in the following, the coupling strength is roughly H (0) k,j / 1 MHz, i.e., the time unit for transfer between two nodes is of the order of a few hundred nanoseconds.The states |j associated with excitons localized at the nodes j (j = 1, . . . , N ) form a complete, orthonormal basis set (COBS) of the whole accessible Hilbert space, i.e., k|j = δ kj and k |k k| = 1. In general, the time evolution of a state |j starting at time t 0 = 0 is given by |j; t = exp(−iH 0 t)|j ; hence the transition amplitudes and the probabilities read α kj (t) ≡ k| exp(−iH 0 t)|j and π kj (t) ≡ |α kj (t)| 2 , respectively. In the corresponding classical CTRW case the transition probabilities follow from a master equation as ...

We present time-resolved spectroscopic measurements of Rydberg-Rydberg interactions in an ultracold gas, revealing the pair dynamics induced by long-range van der Waals interactions between the atoms. By detuning the excitation laser, a specific pair distribution is prepared. Penning ionization on a microsecond timescale serves as a probe for the pair dynamics under the influence of the attractive long-range forces. Comparison with a Monte Carlo model not only explains all spectroscopic features but also gives quantitative information about the interaction potentials. The results imply that the interaction-induced ionization rate can be influenced by the excitation laser. Surprisingly, interaction-induced ionization is also observed for Rydberg states with purely repulsive interactions.PACS numbers: 32.80. Rm, 34.20.Cf, 34.10.+x, 34.60.+z Long-range dipolar interactions ubiquitously appear in nature as the cause for binding forces ranging from atomic and molecular gases [1] all the way to large biological systems [2]. Rydberg atoms have attracted much interest in this context, as they represent an ideal system to study quantum dynamics under the influence of dipolar interactions. As a prominent example from cavity quantum electrodynamics, attractive forces between Rydberg atoms and conducting surfaces have been observed as level shifts in atomic beam experiments [3]. RydbergRydberg interactions leading to resonant energy transfer have been studied in thermal beam experiments [4] and later in ultracold Rydberg gases [5,6,7]. The longrange dipolar interactions can be used to block multiple Rydberg excitation [8,9] and to create many-particle entangled states, which may be employed for quantum information processing [10,11]. So far, investigations of Rydberg-Rydberg interactions have mainly focused on the electronic degrees of freedom neglecting the center-ofmass motion ("frozen Rydberg gas" [7]). In this Letter, we present real-time measurements of the motion of interacting pairs of Rydberg atoms revealing the character and strength of the long-range interparticle interactions.In most molecular and atomic systems the relevant timescales of interparticle dynamics are in the sub-ns regime calling for very fast probes. Ultracold atoms bridge to the ns regime as the thermal energy (T <1 mK) is negligible which allows one to study systems with much weaker interactions or large interatomic distances. Due to the negligible kinetic energy, the dynamics of the gas is fully determined by the interatomic interactions. Interactions in a cold atomic sample have been studied time-resolved in the case of ground state atoms using a pump-probe scheme [12] allowing for coherent control of the collision process [13]. Evidence for interactioninduced motion in cold Rydberg gases was recently found spectroscopically as the cause for Penning ionization [14]. By combining time-resolved and spectroscopic measure- ments, we quantitatively examine the van der Waals (vdW) interactions between two Rydberg atoms. Our measurements can be dir...

We demonstrate the coherent excitation of a mesoscopic ensemble of about 100 ultracold atoms to Rydberg states by driving Rabi oscillations from the atomic ground state. We employ a dedicated beam shaping and optical pumping scheme to compensate for the small transition matrix element. We study the excitation in a weakly interacting regime and in the regime of strong interactions. When increasing the interaction strength by pair state resonances we observe an increased excitation rate through coupling to high angular momentum states. This effect is in contrast to the proposed and previously observed interaction-induced suppression of excitation, the so-called dipole blockade.PACS numbers: 03.65. Yz, 32.80.Pj, 32.80.Rm, 34.20.Cf, 34.60.+z Rydberg atoms, with their rich internal structure, have been in the focus of atomic physics for more than a century [1]. In the last decade Rydberg physics were extended to laser-cooled atomic gases which allowed the study of a frozen system with controllable, strong interactions and negligible thermal contributions. This has opened a wide field in both experiment and theory covering such diverse areas as resonant energy transfer [2,3], plasma formation [4,5], exotic molecules [6,7], and quantum random walks [8,9]. In addition, these frozen Rydberg systems have been proposed as a possible candidate for quantum information processing [10,11]. However, the coherent excitation of Rydberg atoms, an important prerequisite for quantum information protocols, has proven a challenging task. While Rabi oscillations between different Rydberg states have been demonstrated and thoroughly analyzed before [12], Rabi oscillations between the ground state and Rydberg states of atoms have not been observed directly so far, mainly owing to the small transition matrix element.In this Letter we report on the experimental realization and observation of Rabi oscillations between the ground and Rydberg states of ultracold atoms. We demonstrate how strong interatomic interactions influence the coherent excitation of a mesoscopic cloud of atoms. We show that an interaction-induced coupling to a larger number of internal states can be used to trap the excitation. Employed in a controlled way, this effect offers future applications in the experimental realization of quantum random walks with exciton trapping [9].Our experiments are performed with a magneto-optical trap (MOT) of about 10 7 87 Rb atoms at densities of 10 10 cm −3 and temperatures below 100 µK. Rydberg excitation is achieved with two counterpropagating laser beams at 780 nm and 480 nm (see Fig. 1). The laser at 780 nm is collimated to a waist of 1.1 mm ensuring a constant Rabi frequency of 2π × 55 MHz over the excitation volume as determined from Autler-Townes splittings [13]. The laser at 480 nm is referenced to a temperature stabilized Zerodur-resonator and its beam is shaped with a diffractive optical element that produces a flattop beam profile which is characterized with an adapted CCD camera with a spatial resolution of 5.6 µm. The m...

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