  Sliding phases have been long sought after in the context of coupled
XY-models, as they are of relevance to various many-body systems such as
layered superconductors, freestanding liquid-crystal films, and cationic
lipid-DNA complexes. Here we report an observation of a dynamical sliding phase
superfluid that emerges in a nonequilibrium setting from the quantum dynamics
of a three-dimensional ultracold atomic gas loaded into the P-band of a
one-dimensional optical lattice. A shortcut loading method is used to transfer
atoms into the P-band at zero quasimomentum within a very short time duration.
The system can be viewed as a series of "pancake"-shaped atomic samples. For
this far-out-of-equilibrium system, we find an intermediate time window with a
lifetime around tens of milliseconds, where the atomic ensemble exhibits robust
superfluid phase coherence in the pancake directions, but no coherence in the
lattice direction, which implies a dynamical sliding phase superfluid. The
emergence of the sliding phase is attributed to a mechanism of
cross-dimensional energy transfer in our proposed phenomenological theory,
which is consistent with experimental measurements. This experiment potentially
opens up a novel venue to search for exotic dynamical phases by creating
high-band excitations in optical lattices.
