aqora

Theory of Fractional Lévy Kinetics for Cold Atoms Diffusing in Optical Lattices

David A. Kessler, Eli Barkai

Recently, anomalous superdiffusion of ultracold 87Rb atoms in an optical lattice has been observed along with a fat-tailed, Lévy type, spatial distribution. The anomalous exponents were found to depend on the depth of the optical potential. We find, within the framework of the semiclassical theory of Sisyphus cooling, three distinct phases of the dynamics as the optical potential depth is lowered: normal diffusion; Lévy diffusion; and x∼t(3/2) scaling, the latter related to Obukhov's model (1959) of turbulence. The process can be formulated as a Lévy walk, with strong correlations between the length and duration of the excursions. We derive a fractional diffusion equation describing the atomic cloud, and the corresponding anomalous diffusion coefficient.Recently, anomalous superdiffusion of ultracold 87Rb atoms in an optical lattice has been observed along with a fat-tailed, Lévy type, spatial distribution. The anomalous exponents were found to depend on the depth of the optical potential. We find, within the framework of the semiclassical theory of Sisyphus cooling, three distinct phases of the dynamics as the optical potential depth is lowered: normal diffusion; Lévy diffusion; and x∼t(3/2) scaling, the latter related to Obukhov's model (1959) of turbulence. The process can be formulated as a Lévy walk, with strong correlations between the length and duration of the excursions. We derive a fractional diffusion equation describing the atomic cloud, and the corresponding anomalous diffusion coefficient.

arXiv:1202.0701Physical Review LettersJun 8, 2012105 citations

On the Diffusion of Atoms in an Optical Lattice

Todd A. Van Woerkom

Jan 1, 20100 citations

Quantum diffusion in optical lattices

T. L. Bailey, C. A. Bertulani, Eddy Timmermans

Bulletin of the American Physical SocietyOct 22, 20100 citations

Clock-Line-Mediated Sisyphus Cooling

Chun-Chia Chen, Jacob L. Siegel, B. D. Hunt +6 more

We demonstrate subrecoil Sisyphus cooling using the long-lived ^{3}P_{0} clock state in alkaline-earth-like ytterbium. A 1388-nm optical standing wave nearly resonant with the ^{3}P_{0}→^{3}D_{1} transition creates a spatially periodic light shift of the ^{3}P_{0} clock state. Following excitation on the ultranarrow clock transition, we observe Sisyphus cooling in this potential, as the light shift is correlated with excitation to ^{3}D_{1} and subsequent spontaneous decay to the ^{1}S_{0} ground state. We observe that cooling enhances the loading efficiency of atoms into a 759-nm magic-wavelength one-dimensional (1D) optical lattice, as compared to standard Doppler cooling on the ^{1}S_{0}→^{3}P_{1} transition. Sisyphus cooling yields temperatures below 200 nK in the weakly confined, transverse dimensions of the 1D optical lattice. These lower temperatures improve optical lattice clocks by facilitating the use of shallow lattices with reduced light shifts while retaining large atom numbers to reduce the quantum projection noise. This Sisyphus cooling can be pulsed or continuous and is applicable to a range of quantum metrology applications.We demonstrate subrecoil Sisyphus cooling using the long-lived ^{3}P_{0} clock state in alkaline-earth-like ytterbium. A 1388-nm optical standing wave nearly resonant with the ^{3}P_{0}→^{3}D_{1} transition creates a spatially periodic light shift of the ^{3}P_{0} clock state. Following excitation on the ultranarrow clock transition, we observe Sisyphus cooling in this potential, as the light shift is correlated with excitation to ^{3}D_{1} and subsequent spontaneous decay to the ^{1}S_{0} ground state. We observe that cooling enhances the loading efficiency of atoms into a 759-nm magic-wavelength one-dimensional (1D) optical lattice, as compared to standard Doppler cooling on the ^{1}S_{0}→^{3}P_{1} transition. Sisyphus cooling yields temperatures below 200 nK in the weakly confined, transverse dimensions of the 1D optical lattice. These lower temperatures improve optical lattice clocks by facilitating the use of shallow lattices with reduced light shifts while retaining large atom numbers to reduce the quantum projection noise. This Sisyphus cooling can be pulsed or continuous and is applicable to a range of quantum metrology applications.

arXiv:2406.13782Physical Review LettersJul 31, 202412 citations

Cooling and diffusion of atoms in optical lattices

Laurent Sanchez-Palencia, G. Grynberg

Nov 1, 20000 citations

Damping rates of the atomic velocity in Sisyphus cooling

Laurent Sanchez-Palencia, Michele Schiavoni, F.-R. Carminati +2 more

We present a theoretical and experimental study of the damping process of the atomic velocity in Sisyphus cooling. The relaxation rates of the atomic kinetic temperature are determined for a three-dimensional lin⊥lin optical lattice. We find that the damping rates of the atomic temperature depend linearly on the optical pumping rate, for a given depth of the potential wells. This is at variance with the behavior of the friction coefficient as calculated from the spatial diffusion coefficients within a model of Brownian motion. The origin of this different behavior is identified by distinguishing the role of the trapped and traveling atoms.We present a theoretical and experimental study of the damping process of the atomic velocity in Sisyphus cooling. The relaxation rates of the atomic kinetic temperature are determined for a three-dimensional lin⊥lin optical lattice. We find that the damping rates of the atomic temperature depend linearly on the optical pumping rate, for a given depth of the potential wells. This is at variance with the behavior of the friction coefficient as calculated from the spatial diffusion coefficients within a model of Brownian motion. The origin of this different behavior is identified by distinguishing the role of the trapped and traveling atoms.

arXiv:quant-ph/0309209Journal of the Optical Society of America BMay 1, 20035 citations

Spatial diffusion in a periodic optical lattice: revisiting the Sisyphus effect

Related papers

Spatial diffusion in a periodic optical lattice: revisiting the Sisyphus effect

Related papers