Ultracold quantum matter

Abstract:

For many years, 4 He typified Bose-Einstein superfluids, but recent advances in dilute ultracold alkali-metal gases have provided new neutral superfluids that are particularly tractable because the system is dilute. This chapter starts with a brief review of the physics of superfluid 4 He, followed by the basic ideas of Bose-Einstein condensation (BEC), first for an ideal Bose gas and then considering the effect of interparticle interactions, including time-dependent phenomena. Extensions to more exotic condensates include magnetic dipolar gases, mixtures of two components, and spinor condensates that require a focused infrared laser for trapping of all the various hyperfine magnetic states in a particular hyperfine F manifold of m F states. With an applied rotation, the trapped BECs nucleate quantized vortices. Recent theory and experiment have shown that laser coupling fields can mimic the effect of rotation. The resulting synthetic gauge fields have produced vortices in a nonrotating condensate. © 2012 Elsevier B.V.

Abstract:

We study the suitability of correlator product states for describing ground-state properties of two-dimensional spin models. Our ansatz for the many-body wave function takes the form of either plaquette or bond correlator product states, and the energy is optimized by varying the correlators using Monte Carlo minimization. For the Ising model, we find that plaquette correlators are best for estimating the energy, while bond correlators capture the expected long range correlations and critical behavior of the system more faithfully. For the antiferromagnetic Heisenberg model, however, plaquettes outperform bond correlators at describing both local and long range correlations because of the substantially larger number of local parameters they contain. These observations have quantitative implications for the application of correlator product states to other more complex systems, and they give important heuristic insights, in particular, the necessity of carefully tailoring the choice of correlators to the system considered, and its interactions and symmetries. © 2011 American Physical Society.