In 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 performed transport measurements on La$_{1.7}$Eu$_{0.2}$Sr$_{0.1}$CuO$_{4}$ and La$_{1.48}$Nd$_{0.4}$Sr$_{0.12}$CuO$_{4}$, cuprates with striped spin and charge orders, in perpendicular magnetic fields ($H_perp$), and also with an additional field applied parallel to CuO$_2$ layers ($H_parallel$). We detected several phenomena predicted to arise from the existence of a PDW, including an enhancement of interlayer SC phase coherence with increasing $H_parallel$. Our findings are consistent with the presence of local, PDW pairing correlations that compete with the uniform SC order at $T_{c}^{0}< T<(2-6) T_{c}^{0}$, where $T_{c}^{0}$ is the $H=0$ SC transition temperature, and become dominant at intermediate $H_perp$ as $Trightarrow 0$. These data also provide much-needed transport signatures of the PDW in the regime where superconductivity is destroyed by quantum phase fluctuations.
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