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In every connected component of every stratum of Abelian differentials, weconstruct square-tiled surfaces with one vertical and one horizontal cylinder.We show that for all but the hyperelliptic components this can be achieved inthe minimum number of squares necessary for a square-tiled surface in thatstratum. For the hyperelliptic components, we show that the number of squaresrequired is strictly greater and construct surfaces realising these bounds.Using these surfaces, we demonstrate that pseudo-Anosov homeomorphismsoptimising the ratio of Teichm\"uller to curve graph translation length are, ina reasonable sense, ubiquitous in the connected components of strata of Abeliandifferentials. Finally, we present a further application to filling pairs onpunctured surfaces by constructing filling pairs whose algebraic and geometricintersection numbers are equal.

Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs