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Infinite densities can describe the long-time properties of systems when ergodicity is broken and the equilibrium Boltzmann-Gibbs distribution fails. We here perform semiclassical Monte Carlo simulations of cold atoms in dissipative optical lattices with realistic parameters. We show that the momentum infinite density, as well as its scale invariance, should be observable in shallow potentials. We further evaluate the momentum autocorrelation function in the stationary and aging regime.
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In this Colloquium we discuss the anomalous kinetics of atoms in dissipative optical lattices, focusing on the ``Sisyphus laser cooling mechanism. The cooling scheme induces a friction force that decreases to zero for high atomic momentum, which in turn leads to unusual statistical features. We study, using a Fokker-Planck equation describing the semi-classical limit of the system, the shallow optical lattice regime where the momentum distribution of the particles is heavy-tailed and the spatial diffusion is anomalous. As the depth of the optical lattice is tuned, transitions in the dynamical properties of the system occur, for example a transition from Gaussian diffusion to a Levy walk and the breakdown of the Green-Kubo formula for the diffusion constant. Rare events, in both the momentum and spatial distributions, are described by non-normalized states, with tools adapted from infinite ergodic theory. We present experimental observations and elementary explanations for the physical mechanisms of cooling that lead to these anomalous behaviors, comparing theory with available experimental and numerical data.
Brownian motors, or ratchets, are devices which rectify Brownian motion, i.e. they can generate a current of particles out of unbiased fluctuations. The ratchet effect is a very general phenomenon which applies to a wide range of physical systems, and indeed ratchets have been realized with a variety of solid state devices, with optical trap setups as well as with synthetic molecules and granular gases. The present article reviews recent experimental realizations of ac driven ratchets with cold atoms in driven optical lattices. This is quite an unusual system for a Brownian motor as there is no a real thermal bath, and both the periodic potential for the atoms and the fluctuations are determined by laser fields. Such a system allowed us to realize experimentally rocking and gating ratchets, and to precisely investigate the relationship between symmetry and transport in these ratchets, both for the case of periodic and quasiperiodic driving.
The rectification of noise into directed movement or useful energy is utilized by many different systems. The peculiar nature of the energy source and conceptual differences between such Brownian motor systems makes a characterization of the performance far from straightforward. In this work, where the Brownian motor consists of atoms interacting with dissipative optical lattices, we adopt existing theory and present experimental measurements for both the efficiency and the transport coherence. We achieve up to 0.3% for the efficiency and 0.01 for the Peclet number.
In the study of relaxation processes in coherent non-equilibrium dynamics of quenched quantum systems, ultracold atoms in optical superlattices with periodicity two provide a very fruitful test ground. In this work, we consider the dynamics of a particular, experimentally accessible initial state prepared in a superlattice structure evolving under a Bose-Hubbard Hamiltonian in the entire range of interaction strengths, further investigating the issues raised in Ref. [Phys. Rev. Lett. 101, 063001 (2008)]. We investigate the relaxation dynamics analytically in the non interacting and hard core bosonic limits, deriving explicit expressions for the dynamics of certain correlation functions, and numerically for finite interaction strengths using the time-dependent density-matrix renormalization (t-DMRG) approach. We can identify signatures of local relaxation that can be accessed experimentally with present technology. While the global system preserves the information about the initial condition, locally the system relaxes to the state having maximum entropy respecting the constraints of the initial condition. For finite interaction strengths and finite times, the relaxation dynamics contains signatures of the relaxation dynamics of both the non-interacting and hard core bosonic limits.
Ultra-cold alkali atoms trapped in two distinct hyperfine states in an external magnetic field can mimic magnetic systems of spin 1/2 particles. We describe the spin-dependent effective interaction as a spin-spin interaction. As a consequence of the zero-range, the interaction of spin 1/2 bosons can be described as an Ising or, alternatively, as an XY-coupling. We calculated the spin-spin interaction parameters as a function of the external magnetic field in the Degenerate Internal State (DIS) approximation. We illustrate the advantage of the spin-spin interaction form by mapping the system of N spin 1/2 bosons confined by a tight trapping potential on that of N spin 1/2 spins coupled via an infinite range interaction.
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