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              <p>The effect of a parallel magnetic field on superconducting two-leg ladders is investigated numerically. The magnetization curve displays an irrational plateau at a magnetization equal to the hole density. Remarkably, its stability is fundamentally connected to the existence of a well-known magnetic resonant mode. Once the zero-field spin gap is suppressed by the field, pairs acquire a finite momentum characteristic of a Fulde-Ferrell-Larkin-Ovchinnikov phase. In addition, above the irrational plateau dominant superconducting correlations change from singlet to S^z=0 triplet. This provides a simple mechanism in which the Pauli limit is exceeded as suggested by recent experiments.</p>
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