  The superfluid density rho_s(T) = 1/lambda^2(T) has been measured at 2.64 GHz
in highly underdoped YBCO, at 37 dopings with T_c between 3 K and 17 K. Within
limits set by the transition width Delta T_c ~ 0.4 K, rho_s(T) shows no
evidence of critical fluctuations as T goes to T_c, with a mean-field-like
transition and no indication of vortex unbinding. Instead, we propose that
rho_s displays the behaviour expected for a quantum phase transition in the (3
+ 1)-dimensional XY universality class, with rho_s0 ~ (p - p_c), T_c ~ (p -
p_c)^1/2 and rho_s(T) ~ (T_c - T)^1 as T goes to T_c.
