An exact series expansion of the average velocity of cold atoms in dissipative optical lattices under probe driving, based on the amplitudes of the excited atomic density waves, is derived from the semiclassical equations for the phase space densities of the Zeeman ground-state sublevels. This expansion permits the identification of the precise contribution to the current of a propagating atomic wave for the specific driving, as well as providing the general threshold for the transition into the regime of infinite density.
An exact series expansion of the average velocity of cold atoms in dissipative optical lattices under probe driving, based on the amplitudes of the excited atomic density waves, is derived from the semiclassical equations for the phase space densities of the Zeeman ground-state sublevels. This expansion permits the identification of the precise contribution to the current of a propagating atomic wave for the specific driving, as well as providing the general threshold for the transition into the regime of infinite density.
An exact expression for the average velocity of cold atoms in a driven, dissipative optical lattice in terms of the amplitudes of atomic density waves is derived from semiclassical equations for the phase space densities of the Zeeman ground-state sublevels. The calculations are for a J_{g}=1/2→J_{e}=3/2 transition, as it is customary in theoretical studies of Sisyphus cooling. While the driver, an additional beam of small amplitude, sets the atoms into directed motion, the new expression permits the quantification of the contribution to the atomic motion of a specific atomic wave, revealing unexpected counterpropagating contributions from many modes. Additionally, the method is shown to provide the generic threshold for the transition into the regime of infinite density, regardless of the details, or even the presence, of driving.
Atoms confined in a three-dimensional dissipative optical lattice oscillate inside potential wells, occasionally hopping to adjacent wells, thereby diffusing in all directions. Illumination by a weak probe beam modulates the lattice, yielding propagating atomic density waves, referred to as Brillouin modes, which travel perpendicular to the direction of travel of the probe. The probe is made incident at a small angle relative to a lattice symmetry axis, yielding a driving potential perturbation whose spatial period is not a multiple of the period of the underlying optical potential, thus enabling exploration of the regime of space quasiperiodic drive. A theory, based on the Fourier decomposition of the current into its atomic density wave contributions, reveals that, unlike the previously studied time quasiperiodic case, wherein a lattice driven by two incommensurate frequencies may exhibit abrupt suppression in directed current as the driving transitions from quasiperiodic to periodic, a spatial-quasiperiodically driven lattice exhibits no such abrupt response. Further, detailed modeling of spatial-quasiperiodically driven lattices reveals that directed propagation occurs not only as a consequence of velocity matching between the propagating modulation and the average velocity of the atom oscillating inside a well, as was previously reported in the literature, but also as a distinct consequence of another mechanism, namely, frequency matching between the modulation frequency and the oscillation frequencies. A systematic measurement of the transmitted probe spectra as a function of off-axis probe angle is presented, which is consistent with the velocity- and frequency-matching predictions from the detailed model.
Atoms confined in a three-dimensional dissipative optical lattice oscillate inside potential wells, occasionally hopping to adjacent wells, thereby diffusing in all directions. Illumination by a weak probe beam modulates the lattice, yielding propagating atomic density waves, referred to as Brillouin modes which travel perpendicular to the direction of travel of the probe. The probe is made incident at a small angle relative to a lattice symmetry axis, yielding a driving potential perturbation whose spatial period is not a multiple of the period of the underlying optical potential, thus enabling exploration of the regime of space quasiperiodic drive. A theory, based on the Fourier decomposition of the current into its atomic density wave contributions, reveals that unlike the previously studied time quasiperiodic case, wherein a lattice driven by two incommensurate frequencies may exhibit abrupt suppression in directed current as the driving transitions from quasiperiodic to periodic, a spatial-quasiperiodically driven lattice exhibits no such abrupt response. Further, detailed modeling of spatial-quasiperiodically driven lattices reveals that directed propagation occurs not only as a consequence of velocity-matching between the propagating modulation and the average velocity of the atom oscillating inside a well as was previously reported in the literature, but also as a distinct consequence of a new mechanism, namely, frequency-matching between the modulation frequency and the oscillation frequencies. A systematic measurement of the transmitted probe spectra as a function of off-axis probe angle is presented, which is consistent with the velocity- and frequency-matching predictions from the detailed model.
Abstract We investigated the transport properties of cold atoms in a one-dimensional optical lattice under distance selective dissipation and external driving. We analyze how tunneling, on-site interaction, dissipation and external driving affect the transport of cold atoms. We used mean-field theory and the classical phase space method to explain the dynamics of the system. In order to analyze the transport effect of cold atoms, we calculate the relative density of atoms on each site and the standard deviation of relative density. The manipulation transport of cold atoms can be achieved through a step function like interaction in theory. In particular, we study the transport of cold atoms in the double-well with external driving. The steady states of the system are analytically derived.
Randomly diffusing atoms confined in a dissipative optical lattice are illuminated by a weak probe of light. The probe transmission spectrum reveals directed atomic propagation that occurs perpendicular to the direction of probe beam propagation. Resonant enhancement of this directed propagation is observed as we vary the random photon scattering rate. We experimentally characterize this stochastic resonance as a function of probe intensity and lattice well depth. A simple model reveals how the probe-excited atomic density waves and optical pumping rates conspire to create directed atomic propagation within a randomly diffusing sample.
We theoretically study the influence of the noise strength on the excitation of the Brillouin propagation modes in a dissipative optical lattice. We show that the excitation has a resonant behavior for a specific amount of noise corresponding to the precise synchronization of the Hamiltonian motion on the optical potential surfaces and the dissipative effects associated to optical pumping in the lattice. This corresponds to the phenomenon of stochastic resonance. Our results are obtained by numerical simulations and correspond to the analysis of microscopic quantities (atomic spatial distributions) as well as macroscopic quantities (enhancement of spatial diffusion and pump-probe spectra). We also present a simple analytical model in excellent agreement with the simulations.