We experimentally study anomalous diffusion of ultracold atoms in a one dimensional polarization optical lattice. The atomic spatial distribution is recorded at different times and its dynamics and shape are analyzed. We find that the width of the cloud exhibits a power-law time dependence with an exponent that depends on the lattice depth. Moreover, the distribution exhibits fractional self-similarity with the same characteristic exponent. The self-similar shape of the distribution is found to be well fitted by a Lévy distribution, but with a characteristic exponent that differs from the temporal one. Numerical simulations suggest that this is due to long trapping times in the lattice and correlations between the atom's velocity and flight duration.

Decoherence is a major obstacle to any practical implementation of quantum information processing. One of the leading strategies to reduce decoherence is dynamical decoupling -the use of an external field to average out the effect of the environment. The decoherence rate under any control field can be calculated if the spectrum of the coupling to the environment is known. We present a direct measurement of the bath coupling spectrum in an ensemble of optically trapped ultracold atoms, by applying a spectrally narrow-band control field. The measured spectrum follows a Lorentzian shape at low frequencies, but exhibits non-monotonic features at higher frequencies due to the oscillatory motion of the atoms in the trap. These features agree with our analytical models and numerical Monte-Carlo simulations of the collisional bath. From the inferred bath-coupling spectrum, we predict the performance of well-known dynamical decoupling sequences: CPMG, UDD and CDD. We then apply these sequences in experiment and compare the results to predictions, finding good agreement in the weak-coupling limit. Thus, our work establishes experimentally the validity of the overlap integral formalism, and is an important step towards the implementation of an optimal dynamical decoupling sequence for a given measured bath spectrum.

We study the spectral narrowing induced by collisions in a dense cold atomic ensemble. We report on experiments showing a prolongation of the coherence time of optically trapped 87Rb atoms as the density increases, a phenomenon we call collisional narrowing in analogy to the motional narrowing effect in NMR. We derive an expression for the new dephasing time scale in terms of the collision rate and the inhomogeneous decay time. Remarkably, this time scale universally depends only on the atomic phase space density.

Atomic ensembles have many potential applications in quantum information science. Owing to collective enhancement, working with ensembles at high densities increases the efficiency of quantum operations, but at the same time also increases the collision rate and leads to decoherence. Here we report on experiments with optically trapped 87Rb atoms demonstrating a 20-fold increase of the coherence time when a dynamical decoupling sequence with more than 200 pi pulses is applied. Using quantum process tomography we demonstrate that a dense ensemble with an optical depth of 230 can be used as an atomic memory with coherence times exceeding 3 seconds.

We study, theoretically and experimentally, an ensemble of two-level systems coupled to an environment which induces random jumps in their resonant frequency. We present a closed-form formula for the spectrum in terms of the resonant frequency distribution and the Poisson rate constant. For a normal distribution the spectrum deviates from a generalized Gumbel function, a well-known result for continuous stochastic Gaussian processes. We perform experiments with optically trapped cold 87Rb atoms and show that the predictions of our theory for a 3D harmonic trap match the measured spectra without fitting parameters.