An ensemble of two level quantum systems coupled to a fluctuating external environment is a common paradigm in many fields of study. This coupling leads to decoherence that limits the usefulness of these systems, e.g. as qubits in quantum computation systems. Application of external pulses can reduce the decoherence by utilizing symmetry properties of the coupling Hamiltonian to average out its effect, a method commonly referred to as dynamical decoupling. In the case of trapped atoms these techniques can be especially useful since the fluctuations are inherent to the desirable high densities required to achieve a good overall efficiency of quantum operations.

The atomic coherence of a dense trapped atomic ensemble is mostly limited by inhomogeneous broadening induced by the trapping potential and elastic collisions between the atoms. When the collision rate is slow enough, the inhomogeneous broadening can be overcome by a single echo pulse. For high collision rate, on the other hand, the echo technique fails, and the coherence is lost.

In this work we employ an echo pulse train sequence on dense ⁸⁷Rb-atom ensemble trapped in a far-of-resonance optical dipole trap. We demonstrate a coherence time exceeding 3 sec, sec of the superposition state in an ensemble with collision rate higher than 100Hz.

We farther show that the fluctuations in the energy difference of the internal states can be formulated in the framework of system-reservoir theory. Using narrow bandwidth interrogation pulse we measure the spectral function for trapped atomic cloud, and find that it exhibits interesting non-monotonic behavior. As was shown by Kofman and Kurizki (PRA 76, 042310, 2007), the decoherence rate is determined by the overlap integral of the control pulse spectrum and the spectral function, hence a detailed knowledge of the latter can be exploited to design optimal decoupling pulse sequence.