Coherent excitation of Rydberg atoms in an ultracold gas

We demonstrate two schemes for the coherent excitation of Rydberg atoms in an ultracold gas of rubidium atoms employing the three-level ladder system 5S_1/2-5P_3/2-n?_j. In the first approach rapid adiabatic passage with pulsed laser fields yields Rydberg excitation probabilities of 90% in the center of the laser focus. In a second experiment two-photon Rydberg excitation with continuous-wave fields is applied which results in Rabi oscillations between the ground and Rydberg state. The experiments represent a prerequisite for the control of interactions in ultracold Rydberg gases and the application of ultracold Rydberg gases for quantum information processing.     

Antiblockade in Rydberg excitation of an ultracold lattice gas

It is shown that the two-step excitation scheme typically used to create an ultracold Rydberg gas can be described with an effective two-level rate equation, greatly reducing the complexity of the optical Bloch equations. This allows us to efficiently solve the many-body problem of interacting cold atoms with a Monte Carlo technique. Our results reproduce the observed excitation blockade effect. However, we demonstrate that an Autler-Townes double peak structure in the two-step excitation scheme, which occurs for moderate pulse lengths as used in the experiment, can give rise to an antiblockade effect. It is most pronounced for atoms arranged on a lattice. Since the effect is robust against a large number of lattice defects it should be experimentally realizable with an optical lattice created by CO2 lasers.     

Local blockade of Rydberg excitation in an ultracold gas

In the laser excitation of ultracold atoms to Rydberg states, we observe a dramatic suppression caused by van der Waals interactions. This behavior is interpreted as a local excitation blockade: Rydberg atoms strongly inhibit excitation of their neighbors. We measure suppression, relative to isolated atom excitation, by up to a factor of 6.4. The dependences of this suppression on both laser irradiance and atomic density are in good agreement with a mean-field model. These results are an important step towards using ultracold Rydberg atoms in quantum information processing.     

Dipole-dipole excitation and ionization in an ultracold gas of Rydberg atoms

In cold dense Rydberg atom samples, the dipole-dipole interaction strength is effectively resonant at the typical interatomic spacing in the sample, and the interaction has a 1/R3 dependence on interatomic spacing R. The dipole-dipole attraction leads to ionizing collisions of initially stationary atoms, which produces hot atoms and ions and initiates the evolution of initially cold samples of neutral Rydberg atoms into plasmas. More generally, the strong dipole-dipole forces lead to motion, which must be considered in proposed applications.     

Echo experiments in a strongly interacting Rydberg gas

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.     

Suppression of excitation and spectral broadening induced by interactions in a cold gas of Rydberg atoms

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 principal quantum numbers n approximately 60 and n approximately 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.     

Long-range molecular resonances in a cold Rydberg gas

We present evidence for molecular resonances in a cold dense gas of rubidium Rydberg atoms. Single UV photon excitation from the 5s ground state to np Rydberg states (n=50-90) reveals resonances at energies corresponding to excited atom pairs (n-1)d+ns. We attribute these normally forbidden transitions to avoided crossings between the long-range molecular potentials of two Rydberg atoms. These strong van der Waals interactions result in avoided crossings at extremely long range, e.g., approximately 58 000 times the Bohr radius (a(0)) for n=70.     

Dynamics of resonant energy transfer in a cold Rydberg gas

We investigate excitation transfer and migration processes in a cold gas of rubidium Rydberg atoms. Density-dependent measurements of the resonant population exchange for atoms initially excited into the 32P_3/2(|m_J|=3/2) state are compared with a Monte Carlo model for coherent energy transfer. The model is based on simulations of small atom subensembles involving up to ten atoms interacting via coherent pair processes. The role of interatomic mechanical forces due to the resonant dipole-dipole interaction is investigated. Good agreement is found between the experimental data and the predictions of the model, from which we infer that atomic motion has negligible influence on the energy transfer up to Rydberg densities of 10⁸ cm^-3, that the system has to be described in terms of many-body dynamics, and that the energy transfer preserves coherence on microsecond timescales.     

Rabi oscillations and excitation trapping in the coherent excitation of a mesoscopic frozen Rydberg gas

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.     

Rydberg excitation of Bose-Einstein condensates

Rydberg atoms provide a wide range of possibilities to tailor interactions in a quantum gas. Here, we report on Rydberg excitation of Bose-Einstein condensed 87Rb atoms. The Rydberg fraction was investigated for various excitation times and temperatures above and below the condensation temperature. The excitation is locally blocked by the van der Waals interaction between Rydberg atoms to a density-dependent limit. Therefore, the abrupt change of the thermal atomic density distribution to the characteristic bimodal distribution upon condensation could be observed in the Rydberg fraction. The observed features are reproduced by a simulation based on local collective Rydberg excitations.     

Two-electron excitation in helium-like ions by electron impact

Calculation of cross-sections for the two-electron excitation in helium-like ions by electron impact employing Coulomb-Born-Oppenheimer (CBO) approximation is presented. Analytical expressions for the differential and total scattering cross-sections without using partial wave expansion of the wavefunction reported earlier have been used. The total and differential scattering cross-sections for each of the excitations 1s ^{2 1} S* → 2s ^{2 1} S ^e , 2s2p ^1.3 P ⁰, 2p ^{2 1} S ^e ,³ P ^e,¹ D ^e in Be²⁺ and B³⁺ are computed. Results for Li⁺ reported earlier are also included for comparison.     

Spectroscopy of the three-photon laser excitation of cold Rubidium Rydberg atoms in a magneto-optical trap

The spectra of the three-photon laser excitation 5S _1/2 → 5P _3/2 → 6S _1/2 nP of cold Rb Rydberg atoms in an operating magneto-optical trap based on continuous single-frequency lasers at each stage are studied. These spectra contain two partly overlapping peaks of different amplitudes, which correspond to coherent three-photon excitation and incoherent three-step excitation due to the presence of two different ways of excitation through the dressed states of intermediate levels. A four-level theoretical model based on optical Bloch equations is developed to analyze these spectra. Good agreement between the experimental and calculated data is achieved by introducing additional decay of optical coherence induced by a finite laser line width and other broadening sources (stray electromagnetic fields, residual Doppler broadening, interatomic interactions) into the model.     

Expansion of an interacting fermi gas

We study the expansion of a dilute ultracold sample of fermions initially trapped in an anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular, the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similar to what happens with Bose-Einstein condensates. Vice versa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.     

Back and forth transfer and coherent coupling in a cold Rydberg dipole gas

Coupling by the resonant dipole-dipole energy transfer between cold cesium Rydberg atoms is investigated using time-resolved narrow-band deexcitation spectroscopy. This technique combines the advantage of efficient Rydberg excitation with high-resolution spectroscopy at variable interaction times. Dipole-dipole interaction is observed spectroscopically as avoided level crossing. The coherent character of the process is linked to back and forth transfer in the np + np <--> ns + (n + 1)s reaction. Decoherence in the ensemble has two different origins: the atom motion induced by dipole-dipole interaction and the migration of the s-Rydberg excitation in the environment of p-Rydberg atoms.     

Excitation picture of an interacting Bose gas

Atomic Bose–Einstein condensates (BECs) can be viewed as macroscopic objects where atoms form correlated atom clusters to all orders. Therefore, the presence of a BEC makes the direct use of the cluster-expansion approach–lucrative e.g. in semiconductor quantum optics–inefficient when solving the many-body kinetics of a strongly interacting Bose. An excitation picture is introduced with a nonunitary transformation that describes the system in terms of atom clusters within the normal component alone. The nontrivial properties of this transformation are systematically studied, which yields a cluster-expansion friendly formalism for a strongly interacting Bose gas. Its connections and corrections to the standard Hartree–Fock–Bogoliubov approach are discussed and the role of the order parameter and the Bogoliubov excitations are identified. The resulting interaction effects are shown to visibly modify number fluctuations of the BEC. Even when the BEC has a nearly perfect second-order coherence, the BEC number fluctuations can still resolve interaction-generated non-Poissonian fluctuations.     

Quantum entanglement in an interacting electron gas

The entanglement between two electrons in a degenerate electron gas is studied as a function of their separation. We have taken into account the screened Coulomb interaction between electrons. It is found that interaction leads to a suppression of the entanglement distance. The interaction leads also to a direct dependence of entanglement distance on density.     

Lorentz gas interacting with an inhomogeneous thermostat

The equilibrium distribution of a Lorentz gas (“electrons”) interacting with an inhomogenous thermostat (“atoms”) is examined with consideration of 1) the concept of volumes available and forbidden for the gas particles and 2) the solution of the kinetic equation. Analytical calculations for “electrons” and “atoms” repelling each other with the force ≈r⁻⁵ (where r is the distance between the particles) have shown that the coordinate- and velocity-dependent variables in the distribution function cannot be separated. In particular, this leads to the dependence of the average kinetic energy per “electron” on the coordinate: it is higher in the region with higher density of the “atoms”. It is assumed that the Gibbs distribution does not describe the properties of the system under consideration, because in this case the interaction between the system and thermostat cannot be considered small. Scientific-Research Physical-Technical Institute at N. I. Lobachevskii Nizhnii Novgorod State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 38–43, June, 1999.