Daniel Comparat

We review here the studies performed about interactions in an assembly of cold Rydberg atoms. We focus especially on the review of the dipole–dipole interactions and on the effect of the dipole blockade in the laser Rydberg excitation, which offers attractive possibilities for quantum engineering. We present first the various interactions between Rydberg atoms. The laser Rydberg excitation of such an assembly is then described with the introduction of the dipole blockade phenomenon. We report recent experiments performed in this subject by starting with the case of a pair of atoms allowing the entanglement of the wave-functions of the atoms and opening a fascinating way for the realization of quantum bits and quantum gates. We consider then several works on the blockade effect in a large assembly of atoms for three different configurations: blockade through electric-field induced dipole, through Förster resonance, and in van der Waals interaction. The properties of coherence and cooperativity are analyzed. Finally, we treat the role of dipole–dipole interactions between Rydberg atoms responsible for Penning ionization. The perturbation of the dipole blockade by ions and the evolution of the Rydberg towards an ultracold plasma are discussed.

Some of us have recently reported in Science 321 232 (2008) vibrational cooling of translationally cold Cs_2 molecules into the lowest vibrational level v=0 of the singlet X 1Sigma_g ground electronic state. Starting from a sample of cold molecules produced in a collection of vibrational levels of the ground state, our method was based on repeated optical pumping by laser light with a spectrum broad enough to excite all populated vibrational levels but frequency-limited in such a way to eliminate transitions from v=0 level, in which molecules accumulate. In this paper this method is generalized to accumulate molecules into an arbitrary selected "target" vibrational level. It is implemented by using ultrashort pulse shaping techniques based on Liquid Crystal spatial light modulator. In particular a large fraction of the initially present molecule is transferred into a selected vibrational level such as v=1, 2 and 7. Limitations of the method as well as the possible extension to rotational cooling are also discussed.

We present a method to model the interaction and the dynamics of atoms excited to Rydberg states. We show a way to solve the optical Bloch equations for laser excitation of the frozen gas in good agreement with the experiment. A second method, the Kinetic Monte Carlo method gives an exact solution of rate equations. Using a simple N-body integrator (Verlet), we are able to describe dynamical processes in space and time. Unlike more sophisticated methods, the Kinetic Monte Carlo simulation offers the possibility of numerically following the evolution of tens of thousands of atoms within a reasonable computation time. The Kinetic Monte Carlo simulation gives good agreement with dipole-blockade type of experiment. The role of ions and the individual particle effects are investigated.

We have studied the loading of a single-beam or a crossed dipole trap made by a Nd:YAG laser. The loading was performed from a magnetic trap or after a molasses phase with cesium atoms. Looking for high atomic density to perform a fast evaporation to reach the Bose-Einstein Condensation, we found that a crossed dipole trap with a waist of 30 &mgr;m and a laser power P=10 W, loaded from a molasses, gives a good starting point to begin evaporation with 5 &|m~; 10⁶ atoms loaded in 50 ms.

The smallness of the variation rate of the hamiltonian matrix elements compared to the (square of the) energy spectrum gap is usually believed to be the key parameter for a quantum adiabatic evolution. However it is only perturbatively valid for scaled timed hamiltonian and resonance processes as well as off resonance possible constructive St\"{u}ckelberg interference effects violate this usual condition for general hamiltionian. More general adiabatic condition and exact bounds for adiabatic quantum evolution are derived and studied in the framework of a two-level system. The usual criterion is restored for real two level hamiltonian with small number of monotonicity changes of the hamiltonian matrix elements and its derivative.