Echo pulses and temporal decay of motional coherence in optical lattices

We study the quantized centre-of-mass motion of $^{85}$Rb atoms trapped in an optical lattice.~We have measured the coherence between the quantum vibrational states of the atoms in the lattice wells, and observe a decay of coherence. Here we present studies optimizing echo pulses and using the resulting echoes to study the properties of the sources of decoherence. To generate echo pulses, we use a combination of lattice displacements and delays in order to couple the vibrational states. Experimental results, in agreement with simulations, demonstrate that square pulses are preferable to both single-step and gaussian pulses.~We also study the coupling efficiency as a function of lattice depth, finding that this process is more efficient in shallow lattices. We will discuss a number of other avenues for further improving state coupling, including coherent control via interfering pathways, and adiabatic passage.~ We study the decay of echo amplitude over time in both 1D and 3D lattices.~ In both cases, we observe an initial exponential decay of echo amplitude followed by a plateau before a final decay.~We will discuss the relationship of these features to the time-correlation function of the well-depth fluctuations~experienced by the atoms.