Spin dynamics across the superfluid-insulator transition of spinful bosons

TL;DR

This paper investigates how spin oscillations in spinful bosons evolve across the superfluid-insulator transition, revealing the role of critical modes and impurity effects in damping behaviors, with implications for ultracold atom experiments.

Contribution

It provides a theoretical framework for understanding the damping of spin oscillations across the transition, including a renormalization group analysis of impurity effects.

Findings

Damping of spin oscillations depends on the nature of the order parameter.

Quantum impurity models describe the damping in spinless order parameter transitions.

Results are relevant for interpreting ultracold atom experiments.

Abstract

Bosons with non-zero 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.