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Atoms confined in a three-dimensional dissipative optical lattice oscillateinside potential wells, occasionally hopping to adjacent wells, therebydiffusing in all directions. Illumination by a weak probe beam modulates thelattice, yielding propagating atomic density waves, referred to as Brillouinmodes which travel perpendicular to the direction of travel of the probe. Theprobe is made incident at a small angle relative to a lattice symmetry axis,yielding a driving potential perturbation whose spatial period is not amultiple of the period of the underlying optical potential, thus enablingexploration of the regime of space quasiperiodic drive. A theory, based on theFourier decomposition of the current into its atomic density wavecontributions, reveals that unlike the previously studied time quasiperiodiccase, wherein a lattice driven by two incommensurate frequencies may exhibitabrupt suppression in directed current as the driving transitions fromquasiperiodic to periodic, a spatial-quasiperiodically driven lattice exhibitsno such abrupt response. Further, detailed modeling ofspatial-quasiperiodically driven lattices reveals that directed propagationoccurs not only as a consequence of velocity-matching between the propagatingmodulation and the average velocity of the atom oscillating inside a well aswas previously reported in the literature, but also as a distinct consequenceof a new mechanism, namely, frequency-matching between the modulation frequencyand the oscillation frequencies. A systematic measurement of the transmittedprobe spectra as a function of off-axis probe angle is presented, which isconsistent with the velocity- and frequency-matching predictions from thedetailed model.

Spatial quasiperiodic driving of a dissipative optical lattice and origin of directed Brillouin modes in a randomly diffusing cold atom cloud