Abstract
Bosons with nonzero spin exhibit a rich variety of superfluid and insulating phases. Most phases support coherent spin oscillations, which have been the focus of numerous recent experiments. These spin oscillations are Rabi oscillations between discrete levels deep in the insulator, while deep in the superfluid they can be oscillations in the orientation of a spinful condensate. We describe the evolution of spin oscillations across the superfluid-insulator quantum phase transition. For transitions with an order parameter carrying spin, the damping of such oscillations is determined by the scaling dimension of the composite spin operator. For transitions with a spinless order parameter and gapped spin excitations, we demonstrate that the damping is determined by an associated quantum impurity problem of a localized spin excitation interacting with the bulk critical modes. We present a renormalization group analysis of the quantum impurity problem and discuss the relationship of our results to experiments on ultracold atoms in optical lattices.
Highlights
An important frontier opened by the study of ultracold atoms has been the investigation of Bose-Einstein condensates of atoms carrying a nonzero total spin F
The dynamics of the atomic condensate is described by a multi-component Gross-Pitaevski (GP) equation, and this allows for interesting oscillations in the orientation of the condensate in spin space
This paper has described a variety of representative models of spin dynamics across the superfluid insulator transition of spinful bosons
Summary
An important frontier opened by the study of ultracold atoms has been the investigation of Bose-Einstein condensates of atoms carrying a nonzero total spin F. The oscillations in the superfluid condensates[1,2,3,4,5,6] are described by classical GP equations of motion obeyed by the multicomponent order parameter, representing the collective evolution of a macroscopic condensate of atoms It is the purpose of this paper to connect these distinct spin oscillations to each other across the superfluid-insulator quantum phase transition. In this case, it is likely that all excitations with non-zero spin remain gapped across the quantum critical point. The dispersion of the gapped excitation is argued to be an irrelevant perturbation, and so to leading order one need only consider the coupling of a localized spin excitation interacting with the bulk critical modes This gives the problem the character of a quantum impurity problem.
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