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.
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.
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.
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.
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.
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.
This thesis includes both experimental and theoretical investigations of fluctuation-induced transport phenomena, presented in a series of nine papers, by studies of the dynamics of cold atoms in dissipative optical lattices. With standard laser cooling techniques about 108 cesium atoms are accumulated, cooled to a few μK, and transferred into a dissipative optical lattice. An optical lattice is a periodic light-shift potential, and in dissipative optical lattice the light field is sufficiently close to resonance for incoherent light scattering to be of importance. This provides the system with a diffusive force, but also with a friction through laser cooling mechanisms. In the dissipative optical lattices the friction and the diffusive force will eventually reach a steady state. At steady state, the thermal energy is low enough, compared to the potential depth, for the atoms to be localized close to the potential minima, but high enough for the atoms to occasionally make inter-well flights. This leads to a Brownian motion of the atoms in the optical lattices. In the normal case these random walks average to zero, leading to a symmetric, isotropic diffusion of the atoms. If the optical lattices are tilted, the symmetry is broken and the diffusion will be biased. This leads to a fluctuation-induced drift of the atoms. In this thesis an investigation of such drifts, for an optical lattice tilted by the gravitational force, is presented. We show that even though the tilt over a potential period is small compared to the potential depth, it clearly affect the dynamics of the atoms, and despite the complex details of the system it can, to a good approximation, be described by the Langevin equation formalism for a particle in a periodic potential. The linear drifts give evidence of stop-and-go dynamics where the atoms escape the potential wells and travel over one or more wells before being recaptured. Brownian motors open the possibility of creating fluctuation-induced drifts in the absence of bias forces, if two requirements are fulfilled: the symmetry has to be broken and the system has to be brought out of thermal equilibrium. By utilizing two distinguishable optical lattices, with a relative spatial phase and unequal transfer rates between them, these requirements can be fulfilled. In this thesis, such a Brownian motor is realized, and drifts in arbitrary directions in 3D are demonstrated. We also demonstrate a real-time steering of the transport as well as drifts along pre-designed paths. Moreover, we present measurements and discussions of performance characteristics of the motor, and we show that the required asymmetry can be obtained in multiple ways.
We show theoretically that the dynamics of cold atoms in the lowest-energy band of a stationary optical lattice can be transformed and controlled by a second, weaker, periodic potential moving at a constant speed along the axis of the stationary lattice. The atom trajectories exhibit complex behavior, which depends sensitively on the amplitude and speed of the propagating lattice. When the speed and amplitude of the moving potential are low, the atoms are dragged through the static lattice and perform drifting orbits with frequencies an order of magnitude higher than that corresponding to the moving potential. Increasing either the speed or amplitude of the moving lattice induces Bloch-like oscillations within the energy band of the static lattice, which exhibit complex resonances at critical values of the system parameters. In some cases, a very small change in these parameters can reverse the atom's direction of motion. In order to understand these dynamics we present an analytical model, which describes the key features of the atom transport and also accurately predicts the positions of the resonant features in the atom's phase space. The abrupt controllable transitions between dynamical regimes, as well as the associated set of resonances, provide a mechanism for transporting atoms between precise locations in a lattice, as required for using cold atoms to simulate condensed matter or as a stepping stone to quantum information processing. The system also provides a direct quantum simulator of acoustic waves propagating through semiconductor nanostructures in sound analogs of the optical laser (saser).