Wolfgang Alt

Models of dispersal in biological systems

In order to provide a general framework within which the dispersal of cells or organisms can be studied, we introduce two stochastic processes that model the major modes of dispersal that are observed in nature. In the first type of movement, which we call the position jump or kangaroo process, the process comprises a sequence of alternating pauses and jumps. The duration of a pause is governed by a waiting time distribution, and the direction and distance traveled during a jump is fixed by the kernel of an integral operator that governs the spatial redistribution. Under certain assumptions concerning the existence of limits as the mean step size goes to zero and the frequency of stepping goes to infinity the process is governed by a diffusion equation, but other partial differential equations may result under different assumptions. The second major type of movement leads to what we call a velocity jump process. In this case the motion consists of a sequence of “runs” separated by reorientations, during which a new velocity is chosen. We show that under certain assumptions this process leads to a damped wave equation called the telegraphers equation. We derive explicit expressions for the mean squared displacement and other experimentally observable quantities. Several generalizations, including the incorporation of a resting time between movements, are also studied. The available data on the motion of cells and other organisms is reviewed, and it is shown how the analysis of such data within the framework provided here can be carried out.

Quantum Walk in Position Space with Single Optically Trapped Atoms

Strolling Out on a Quantum Walk In a random walk, a walker moves one step to the left or one step to the right depending on the outcome of a coin toss. The distribution between possible locations is well known and forms the basis for algorithms in information processing, describing diffusion processes in physics or biology, and has even been used as a model for stock market prices. Karski et al. (p. 174) use a single caesium atom trapped in a one-dimensional optical lattice to implement the quantum counterpart—a quantum walk. The coherence of a quantum system results in a departure from the classical picture, producing a distribution that is quite different that depends on the internal state of the atom. The results may have implications for search algorithms and quantum information processing protocols. A single cesium atom trapped in an optical lattice is used to illustrate a quantum walk. The quantum walk is the quantum analog of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to extensive applications in quantum information science. In our experiment, we implemented a quantum walk on the line with single neutral atoms by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice. With the use of site-resolved fluorescence imaging, the final wave function is characterized by local quantum state tomography, and its spatial coherence is demonstrated. Our system allows the observation of the quantum-to-classical transition and paves the way for applications, such as quantum cellular automata.

Cold-atom physics using ultrathin optical fibers : Light-induced dipole forces and surface interactions

The strong evanescent field around ultrathin unclad optical fibers bears a high potential for detecting, trapping, and manipulating cold atoms. Introducing such a fiber into a cold-atom cloud, we investigate the interaction of a small number of cold cesium atoms with the guided fiber mode and with the fiber surface. Using high resolution spectroscopy, we observe and analyze light-induced dipole forces, van der Waals interaction, and a significant enhancement of the spontaneous emission rate of the atoms. The latter can be assigned to the modification of the vacuum modes by the fiber.

Single atoms in an optical dipole trap: towards a deterministic source of cold atoms

We describe a simple experimental technique which allows us to store a small and deterministic number of neutral atoms in an optical dipole trap. The desired atom number is prepared in a magneto-optical trap overlapped with a single focused Nd:YAG laser beam. Dipole trap loading efficiency of 100% and storage times of about one minute have been achieved. We have also prepared atoms in a certain hyperfine state and demonstrated the feasibility of a state-selective detection via resonance fluorescence at the level of a few neutral atoms. A spin relaxation time of the polarized sample of 4.2+/-0.7 s has been measured. Possible applications are briefly discussed.

Transient behavior of a chemotaxis system modelling certain types of tissue inflammation

A spatially-distributed mathematical model for the inflammatory response to bacterial invasion of tissue is proposed which includes leukocyte motility and chemotaxis behavior and chemical mediator properties explicitly. This system involves three coupled nonlinear partial differential equations and so is not amenable to analysis. Using scaling arguments and singular perturbation techniques, an approximating system of two coupled nonlinear ordinary differential equations is developed. This system now permits analysis by phase plane methods. Using the approximating model, the dependence of the dynamic behavior of the inflammatory response upon key process parameters, including leukocyte chemotaxis, is studied.

Continuum model of cell adhesion and migration

The motility of cells crawling on a substratum has its origin in a thin cell organ called lamella. We present a 2-dimensional continuum model for the lamella dynamics of a slowly migrating cell, such as a human keratinocyte. The central components of the model are the dynamics of a viscous cytoskeleton capable to produce contractile and swelling stresses, and the formation of adhesive bonds in the plasma cell membrane between the lamella cytoskeleton and adhesion sites at the substratum. We will demonstrate that a simple mechanistic model, neglecting the complicated signaling pathways and regulation processes of a living cell, is able to capture the most prominent aspects of the lamella dynamics, such as quasi-periodic protrusions and retractions of the moving tip, retrograde flow of the cytoskeleton and the related accumulation of focal adhesion complexes in the leading edge of a migrating cell. The developed modeling framework consists of a nonlinearly coupled system of hyperbolic, parabolic and ordinary differential equations for the various molecular concentrations, two elliptic equations for cytoskeleton velocity and hydrodynamic pressure in a highly viscous two-phase flow, with appropriate boundary conditions including equalities and inequalities at the moving boundary. In order to analyse this hybrid continuum model by numerical simulations for different biophysical scenarios, we use suitable finite element and finite volume schemes on a fixed triangulation in combination with an adaptive level set method describing the free boundary dynamics.

Nearest-neighbor detection of atoms in a 1D optical lattice by fluorescence imaging.

We overcome the diffraction limit in fluorescence imaging of neutral atoms in a sparsely filled one-dimensional optical lattice. At a periodicity of 433 nm, we reliably infer the separation of two atoms down to nearest neighbors. We observe light induced losses of atoms occupying the same lattice site, while for atoms in adjacent lattice sites, no losses due to light induced interactions occur. Our method points towards characterization of correlated quantum states in optical lattice systems with filling factors of up to one atom per lattice site.

Quantum engineering: An atom-sorting machine

Laser cooling and trapping techniques allow us to control and manipulate neutral atoms. Here we rearrange, with submicrometre precision, the positions and ordering of laser-trapped atoms within strings by manipulating individual atoms with optical tweezers. Strings of equidistant atoms created in this way could serve as a scalable memory for quantum information.

Optical control of the refractive index of a single atom.

We experimentally demonstrate the elementary case of electromagnetically induced transparency with a single atom inside an optical cavity probed by a weak field. We observe the modification of the dispersive and absorptive properties of the atom by changing the frequency of a control light field. Moreover, a strong cooling effect has been observed at two-photon resonance, increasing the storage time of our atoms twenty-fold to about 16 seconds. Our result points towards all-optical switching with single photons.

Analysis of dephasing mechanisms in a standing-wave dipole trap

We study in detail the mechanisms causing dephasing of hyperfine coherences of cesium atoms confined by a far-off-resonant standing-wave optical dipole trap [S. Kuhr et al., Phys. Rev. Lett. 91, 213002 (2003)]. Using Ramsey-spectroscopy and spin-echo techniques, we measure the reversible and irreversible dephasing times of the ground-state coherences. We present an analytical model to interpret the experimental data and identify the homogeneous and inhomogeneous dephasing mechanisms. Our scheme to prepare and detect the atomic hyperfine state is applied at the level of a single atom as well as for ensembles of up to 50 atoms.