This issue is due to the way the arrowheads are scaled in relation to the range of the axes.
As a workaround, the Quiver plot can be created on a set of axes with equal ranges. Then the axes can be re-labeled appropriately. For example,
x = 15:24;
y = 0.5:0.01:0.59;
u = ones(10);
v = 0.01*ones(10);
scale_factor = range(x)/range(y);
figure;
ah = axes;
quiver(x,y*scale_factor,u,v*scale_factor)
xlim([min(x) max(x)])
ylim([min(y) max(y)]*scale_factor)
set(ah,'YTick',y*scale_factor)
% properly re-label to y-axis
set(ah,'YTickLabel',y)
