Semiclassical relaxation dynamics of cold bosonic atoms in three-site optical lattices using truncated Wigner approximation (TWA)

A formalism is only as reliable as our understanding of its limitations. We show in this thesis the formalism breakdown of Truncated Wigner approximation (TWA) – one of the many semiclassical methods used in numerically studying various quantum systems involving cold atoms and in quantum optics. We apply TWA to the Bose-Hubbard Model and benchmark its results from those obtained in Exact Diagonalization (ED), a fully quantum mechanical method. Superimposing the results of TWA and ED in a plot of the occupation number per lattice site, we find that qualitatively TWA captures the relaxation dynamics of the physical system relatively well when compared with ED in the weakly interacting (WI) regime (U/J ≤ 1). In the strongly interacting (SI) regime (U/J > 1), TWA only succeeds in capturing some general behavior of the system and fails for giving exact values especially at longer times. Therefore, TWA is reliable to qualitatively describe the physics of a quantum system, but caution must be afforded when it will be used to determine a precise quantity, e.g., occupation number per lattice site at an exact point in time.