Atomic ensembles have many potential applications in quantum information science. Owing to collective enhancement, working with ensembles at high densities increases the overall efficiency of quantum operations, but at the same time also increases the collision rate and markedly changes the time dynamics of a stored coherence. We study theoretically and experimentally the coherent dynamics of cold atoms under these conditions [1]. A closed form expression for the spectral lineshape is derived for discrete fluctuations, written in terms of the bare spectrum and the collision rate. For Gaussian fluctuations the spectrum show deviations from the canonical stochastic theory of Kubo. We measure the spectrum with optically trapped cold ⁸⁷Rb atoms, and find a very good agreement to the theory without fitting parameters. Our measurements also reveal a prolongation of the coherence times as the atomic density increases, a phenomenon we call collisional narrowing in analog to the well known motional narrowing effect in NMR [2]. We explain under what conditions collisional narrowing can be transformed into collisional broadening. We also show that by applying a train of population inverting pulses, the coherence time can be substantially extended [3]. We perform quantum process tomography and demonstrate that using this dynamical decoupling scheme a dense ensemble with a peak optical depth of 230 can be used as a memory with coherence times exceeding 3 sec.

[1]. Sagi, Y., Pugatch, R., Almog, I., and Davidson, N., Phys. Rev. Lett. 104, 253003 (2010).

[2]. Sagi, Y., Almog, I., and Davidson, N., Phys. Rev. Lett. 105, 093001 (2010).

[3]. Sagi, Y., Almog, I., and Davidson, N., Phys. Rev. Lett. 105, 053201 (2010).