C. Ates

Nonlocal nonlinear optics in cold Rydberg gases.

We present an analytical theory for the nonlinear optical response of a strongly interacting Rydberg gas under conditions of electromagnetically induced transparency. Simple formulas for the third-order optical susceptibility are derived and shown to be in excellent agreement with recent experiments. The obtained expressions reveal strong nonlinearities, which in addition are of highly nonlocal character. This property together with the enormous strength of the Rydberg-induced nonlinearities is shown to yield a unique laboratory platform for nonlinear wave phenomena, such as collapse-arrested modulational instabilities in a self-defocusing medium.

Coherent population trapping with controlled interparticle interactions

Coherent population trapping (CPT) and the related phenomenon of Electromagnetically Induced Transparency (EIT) are paradigms for quantuminterference effects and have been studied intensely over the last decade [1]. Only recently, EIT involving Rydberg states has attracted much interest, with regard to nonlinear optics [2] as well as in the context of quantum information processing [3]. Whereas CPT and EIT are generally described within a singleatom framework, the situation becomes more involved when interparticle interactions have to be considered. To address the effect of interactions, we investigate CPT in a strongly interacting ultracold Rydberg gas [4]. In our experiment we tune the interaction strength by choosing different Rydberg states and control interactions effects by varying the ground state atom density. Even in the blockade regime we observe a resonance with sub-natural linewidth at the single-particle resonance frequency despite the strong van der Waals interactions among Rydberg atoms. Due to the correlations among the atoms the experimental observations cannot be explained within a meanfield model. A theoretical model that includes interparticle correlations is presented and nicely reproduces the observed features.

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.

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.

Newton's cradle and entanglement transport in a flexible Rydberg chain.

In a regular, flexible chain of Rydberg atoms, a single electronic excitation localizes on two atoms that are in closer mutual proximity than all others. We show how the interplay between excitonic and atomic motion causes electronic excitation and diatomic proximity to propagate through the Rydberg chain as a combined pulse. In this manner entanglement is transferred adiabatically along the chain, reminiscent of momentum transfer in Newtons cradle.

Dynamical phases and intermittency of the dissipative quantum Ising model

We employ the concept of a dynamical, activity order parameter to study the Ising model in a transverse magnetic field coupled to a Markovian bath. For a certain range of values of the spin-spin coupling, magnetic field and dissipation rate, we identify a first order dynamical phase transition between active and inactive {\em dynamical phases}. We demonstrate that dynamical phase-coexistence becomes manifest in an intermittent behavior of the bath quanta emission. Moreover, we establish the connection between the dynamical order parameter that quantifies the activity, and the longitudinal magnetization that serves as static order parameter. The system we consider can be implemented in current experiments with Rydberg atoms and trapped ions.

Thermalization of a strongly interacting closed spin system: from coherent many-body dynamics to a Fokker-Planck equation.

Thermalization has been shown to occur in a number of closed quantum many-body systems, but the description of the actual thermalization dynamics is prohibitively complex. Here, we present a model-in one and two dimensions-for which we can analytically show that the evolution into thermal equilibrium is governed by a Fokker-Planck equation derived from the underlying quantum dynamics. Our approach does not rely on a formal distinction of weakly coupled bath and system degrees of freedom. The results show that transitions within narrow energy shells lead to a dynamics which is dominated by entropy and establishes detailed balance conditions that determine both the eventual equilibrium state and the nonequilibrium relaxation to it.

Motion of Rydberg atoms induced by resonant dipole-dipole interactions

We show that nuclear motion of Rydberg atoms can be induced by resonant dipole–dipole interactions that trigger the energy transfer between two energetically close Rydberg states. How and if the atoms move depends on their initial arrangement as well as on the initial electronic excitation. Using a mixed quantum/classical propagation scheme, we obtain the trajectories and kinetic energies of atoms, initially arranged in a regular chain and prepared in excitonic eigenstates. The influence of the off-diagonal disorder on the motion of the atoms is examined and it is shown that irregularity in the arrangement of the atoms can lead to an acceleration of the nuclear dynamics.

Strong interaction effects on the atom counting statistics of ultracold Rydberg gases

Based on simple rate equations for the Rydberg excitation process, we are able to model microscopically the dynamics of Rydberg excitation in ensembles of a large number of ultracold atoms, which is beyond the capabilities of fully ab initio approaches. Our results for the distribution of Rydberg atom numbers are in good agreement with recent experimental data, confirming the quenching of the distribution caused by Rydberg–Rydberg interactions.

Electromagnetically Induced Transparency in strongly interacting Rydberg Gases

Max Planck Institute for the Physics of Complex Systems,No¨thnitzer Strasse 38, 01187 Dresden, Germany(Dated: January 24, 2011)We develop an efficient Monte-Carlo approach to describe the optical response of cold three-level atoms in the presence of EIT and strong atomic interactions. In particular, we consider a”Rydberg-EIT medium” where one involved level is subject to large shifts due to strong van derWaals interactions with surrounding Rydberg atoms. We find excellent agreement with much moreinvolved quantum calculations and demonstrate its applicability over a wide range of densities andinteraction strengths. The calculations show that the nonlinear absorption due to Rydberg-Rydbergatom interactions exhibits universal behavior.