Geometrically representing spin correlations
Abstract
We develop a general method to visualize spin correlations, and we demonstrate its usefulness in ultracold matter from fermions in lattices to trapped ions and ultracold molecules. Correlations are of fundamental interest in manybody physics: they characterize phases in condensed matter and AMO, and are required for quantum sensing and computing. However, it is often difficult to understand even the simplest correlations  for example between two spin1/2's  directly from the components C^{ab} = <S_{1}^{a}S_{2}^{b} >  <S_{1}^{a} > <S_{2}^{b} > for { a , b } ∈ { x , y , z } . Not only are the nine independent C^{ab} unwieldy, but considering the components also obscures the natural geometric structure. For example, simple spin rotations lead to complex transformations among the nine C^{ab}. We provide a onetoone map between the spin correlations and certain threedimensional objects, analogous to the map between single spins and Bloch vectors. This object makes the geometric structure of the correlations manifest. Moreover, much as one can reason geometrically about dynamics using a Bloch vector  e.g. a magnetic field causes it to precess and dephasing causes it to shrink  we show that analogous reasoning holds for our visualization method.
 Publication:

APS Division of Atomic, Molecular and Optical Physics Meeting Abstracts
 Pub Date:
 May 2016
 Bibcode:
 2016APS..DMP.Q1134W