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We present the first detection of a correlation between the Lyman-$\alpha$forest and cosmic microwave background (CMB) lensing. For each Lyman-$\alpha$forest in SDSS-III/BOSS DR12, we correlate the one-dimensional power spectrumwith the CMB lensing convergence on the same line of sight from Planck. Thismeasurement constitutes a position-dependent power spectrum, or a squeezedbispectrum, and quantifies the non-linear response of the Lyman-$\alpha$ forestpower spectrum to a large-scale overdensity. The signal is measured at5~$\sigma$ and is consistent with the $\Lambda$CDM expectation. We measure thelinear bias of the Lyman-$\alpha$ forest with respect to the dark matterdistribution, and constrain a combination of non-linear terms including thenon-linear bias. This new observable provides a consistency check for theLyman-$\alpha$ forest as a large-scale structure probe and tests ourunderstanding of the relation between intergalactic gas and dark matter. In thefuture, it could be used to test hydrodynamical simulations and calibrate therelation between the Lyman-$\alpha$ forest and dark matter.

First Detection of Cosmic Microwave Background Lensing and Lyman-{\alpha} Forest Bispectrum