The high voltage and energy density has made lithium-ion batteries ubiquitous in portable electronics, such as iPods, laptops and mobile phones. At present, they are typically composed of lithium cobaltate as a cathode, lithium ion-conducting organic polymer as an electrolyte, and lithium metal or graphite as an anode. A major concern is the safety aspect of liquid and common polymeric electrolytes. Liquid-free batteries show some advantages over the currently commercialized ones, including thermal stability, absence of leakage and pollution, resistance to shocks and vibrations, large electrochemical windows of application, and potential to incorporate in microelectronic circuits. Lithium lanthanum titanate is currently the best solid state electrolyte. We propose to test a series of theoretical predictions on the diffusion mechanism via quasi-elastic neutron scattering.