Unforutnately, quiiver and polaraxes don’t work together. The only alternative is to create your own polar axes as Cartessian axes, and then tweak until you get the desired result.
This should get you started —
p = linspace(0, 1, 25); % Function To Be Plotted
r = exp(-1.5*p);
a = p*2*pi;
rg = linspace(0, 2*pi, 13); % Angle Coordinate Definition
zv = zeros(size(rg));
cg = linspace(0, 2*pi, 400); % Radial Coordinate Definition
cx = ((0:0.2:1).'*cos(cg)).';
cy = ((0:0.2:1).'*sin(cg)).';
figure
plot([zv; cos(rg)], [zv; sin(rg)],'-k') % Plot Angle Vectors
hold on
plot(cx,cy,'-k') % Plot Radial Vectors
[x,y] = pol2cart(a,r); % Plot Functioon With 'quiver'
u = gradient(x);
v = gradient(y);
quiver(x, y, u, v, '-b')
hold off
axis('equal')
Ax = gca;
Ax.Visible = 'off';
text(cos(rg(1:end-1))*1.11-0.1, sin(rg(1:end-1))*1.1, compose('%d°',0:30:330))
text(cx(1,:),cy(30,:), compose('%.1g',0:0.2:1), 'Horiz','right', 'Vert','top')
Maybe some day this will be easiier.
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