Superfluid fraction as a function of dd. Black dots are experimental results derived from the Josephson frequencies. Vertical error bars result from the error propagation of equation ( 3 ), with K = J 2 /(4 UN 34 ); see Methods. Green dots are results from numerical simulations. Error bars are the uncertainties of the linear fits used to determine K and UN 34. Pink points are derived from the experimental phasecurrent relation, as in c. Error bars are estimated using the propagation of equation ( 3 ), with K and its relative uncertainty extracted from linear fits of experimental data. The open pink point at dd = 1.444 is the dataset without the optical-separation technique ( Methods ). The grey band extends between the upper and lower bounds of equation ( 1 ).
