Experimental observation of Zitterbewegung is considered a holy grail of the modern physics since its debut in 1930 by Schrödinger. In this thesis we describe the first experimental observation of this effect in a two-dimensional ultracold atomic wave packet. In addition to that, we have also revealed the anisotropic of nature of Zitterbewegung, in the presence of non-Abelian Gauge field.To all my teachers who have prepared me for this adventurous journey of a lifelong student List of Figures2.1 A typical way to realize the Abelian gauge field via Raman scheme. Here L 1 and L 2 each addresses the transition |↑ → |e and |↓ → |e , respectively. The two-photon detuning is δ while both lasers L 1,2 are far off-detuned from the excited-state |e . . . . . . . . . . . . . . . . 2.2 Dispersion relation of a one-dimensional spin-orbit coupled system given by the Hamiltonian in Eq. 2.4. The left panel describes two shifted parabolas when the Raman coupling Ω and two-photondetuning δ are zero. In the middle panel, a non zero Raman coupling opens the gap at zero momentum since this term behaves like a Zeeman term in the Hamiltonian given by Eq. 2.4. The right panel shows the effect of non-zero two-photon detuning δ. The dispersion relation becomes tilted as δ acts as a constant shift in momentum in Eq.