AbstractIn underdoped cuprates, the interplay of the pseudogap, superconductivity, and charge and spin ordering can give rise to exotic quantum states, including the pair density wave (PDW), in which the superconducting (SC) order parameter is oscillatory in space. However, the evidence for a PDW state remains inconclusive and its broader relevance to cuprate physics is an open question. To test the interlayer frustration, the crucial component of the PDW picture, we perform transport measurements on charge- and spin-stripe-ordered La_1.7Eu_0.2Sr_0.1CuO₄ and La_1.48Nd_0.4Sr_0.12CuO₄ in perpendicular magnetic fields (H_⊥), and also with an additional field applied parallel to CuO₂ layers (H_∥). We detect several phenomena predicted to arise from the existence of a PDW, including an enhancement of interlayer SC phase coherence with increasing H_∥. These data also provide much-needed transport signatures of the PDW in the regime where superconductivity is destroyed by quantum phase fluctuations.