Transport and Non-Equilibrium Dynamics in Optical Lattices. From Expanding Atomic Clouds to Negative Absolute Temperatures
Stephan Mandt
Transport properties and nonequilibrium dynamics in strongly correlated materials are \ntypically difficult to calculate. This holds true even for minimalistic model Hamiltonians \nof these systems, such as the fermionic Hubbard model. \nUltracold atoms in optical lattices enable an alternative realization of the Hubbard \nmodel and have the advantage of being free of additional complications such as phonons, \nlattice defects or impurities. This way, cold atoms can be used as quantum simulators of \nstrongly interacting materials. Being thermally isolated systems, however, we show that \ncold atoms in optical lattices can also behave very differently from solids and can show a \nplethora of novel dynamic effects. \nIn this thesis, several out-of equilibrium processes involving interacting fermionic atoms \nin optical lattices are presented. We first analyze the expansion dynamics of an initially \nconfined atomic cloud in the lowest band of an optical lattice. While non-interacting atoms \nexpand ballistically, the cloud expands with a dramatically reduced velocity in the presence \nof interactions. Most prominently, the expansion velocity is independent of the attractive \nor repulsive character of the interactions, highlighting a novel dynamic symmetry of the \nHubbard model. \nIn a second project, we discuss the possibility of realizing negative absolute temperatures in optical lattices. Negative absolute temperatures characterize equilibrium states \nwith an inverted occupation of energy levels. Here, we propose a dynamical process to realize equilibrated Fermions at negative temperatures and analyze the time scales of global \nrelaxation to equilibrium, which are associated with a redistribution of energy and particles \nby slow diffusive processes. \nWe show that energy conservation has a major impact on the dynamics of an interacting \ncloud in an optical lattice, which is exposed to an additional weak linear (gravitational) \npotential. Instead of ‘falling downwards‘, the cloud diffuses symmetrically upwards and \ndownwards in the gravitational potential. Furthermore, we show analytically that the \nradius R grows with the time t according to R ∼ t^1/3, consistent with numerical simulations \nof the Boltzmann equation. \nFinally, we analyze the damping of Bloch oscillations by interactions. For a homogeneous system, we discuss the possibility of mapping the dynamics of the particle current to \na classical damped harmonic oscillator equation, thereby giving an analytic explanation for \nthe transition from weakly damped to over-damped Bloch oscillations. We show that the \ndynamics of a strongly Bloch oscillating and weakly interacting atomic cloud can be discribed in terms of a novel effective “stroboscopic” diffusion equation. In this approximation, \nthe cloud’s radius R grows asymptotically in time t according to R ∼ t^1/5 .
•Jan 1, 2012•2 citations