Nonlocal spatial correlations in an interacting atomic gas

We report measurements of the nonlocal two-body spatial correlation function <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msup> <a:mi>g</a:mi> <a:mrow> <a:mo>(</a:mo> <a:mn>2</a:mn> <a:mo>)</a:mo> </a:mrow> </a:msup> <a:mrow> <a:mo>(</a:mo> <a:mi>R</a:mi> <a:mo>)</a:mo> </a:mrow> </a:mrow> </a:math> in an ultracold Bose gas with strong interactions using photoassociation of ultra-long-range Rydberg molecules (ULRRMs) as a spatially selective probe. This technique provides access to <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msup> <b:mi>g</b:mi> <b:mrow> <b:mo>(</b:mo> <b:mn>2</b:mn> <b:mo>)</b:mo> </b:mrow> </b:msup> <b:mrow> <b:mo>(</b:mo> <b:mi>R</b:mi> <b:mo>)</b:mo> </b:mrow> </b:mrow> </b:math> on length scales from 60 to 180 nm, bridging the gap between short-range and long-range correlation measurements. The large <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>s</c:mi> </c:math> -wave scattering length of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mmultiscripts> <d:mi>Sr</d:mi> <d:mprescripts/> <d:none/> <d:mn>86</d:mn> </d:mmultiscripts> </d:math> ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>a</e:mi> <e:mo>=</e:mo> <e:mn>811</e:mn> <e:mspace width="0.16em"/> <e:msub> <e:mi>a</e:mi> <e:mn>0</e:mn> </e:msub> </e:mrow> </e:math> ) enables exploration of the universal regime where <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:msup> <g:mi>g</g:mi> <g:mrow> <g:mo>(</g:mo> <g:mn>2</g:mn> <g:mo>)</g:mo> </g:mrow> </g:msup> <g:mrow> <g:mo>(</g:mo> <g:mi>R</g:mi> <g:mo>)</g:mo> </g:mrow> </g:mrow> </g:math> is governed solely by two-body interactions. Comparison with a weakly interacting isotope, <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mmultiscripts> <h:mi>Sr</h:mi> <h:mprescripts/> <h:none/> <h:mn>84</h:mn> </h:mmultiscripts> </h:math> , highlights interaction-induced suppression of pair correlations. The measured correlation functions agree quantitatively with calculations based on the two-body reduced density matrix, without adjustable parameters. Our results establish Rydberg molecular photoassociation as a powerful tool for probing nonlocal correlations in strongly interacting quantum gases.