Optical excitation of stripe-ordered La$_{2-x}$Ba$_x$CuO$_4$ has been shown to transiently enhance superconducting tunneling between the CuO$_2$ planes. This effect was revealed by a blue-shift, or by the appearance of a Josephson Plasma Resonance in the terahertz-frequency optical properties. Here, we show that this photo-induced state can be strengthened by the application of high external magnetic fields oriented along the c-axis. For a 7-Tesla field, we observe up to a ten-fold enhancement in the transient interlayer phase correlation length, accompanied by a two-fold increase in the relaxation time of the photo-induced state. These observations are highly surprising, since static magnetic fields suppress interlayer Josephson tunneling and stabilize stripe order at equilibrium. We interpret our data as an indication that optically-enhanced interlayer coupling in La$_{2-x}$Ba$_x$CuO$_4$ does not originate from a simple optical melting of stripes, as previously hypothesized. Rather, we speculate that the photo-induced state may emerge from activated tunneling between optically-excited stripes in adjacent planes.
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