Optical tweezers use the forces exerted by a strongly focused beam of light to trap and move objects ranging in size from tens of nanometres to tens of micrometres. Since their introduction in 1986, the optical tweezer has become an important tool for research in the fields of biology, physical chemistry and soft condensed matter physics. Recent advances promise to take optical tweezers out of the laboratory and into the mainstream of manufacturing and diagnostics; they may even become consumer products. The next generation of single-beam optical traps offers revolutionary new opportunities for fundamental and applied research.

http://physics.nyu.edu/grierlab/nreview2c/nreview2c.pdf

A revolution in optical manipulation

This review summarizes theoretical progress in the field of active matter, placing it in the context of recent experiments. This approach offers a unified framework for the mechanical and statistical properties of living matter: biofilaments and molecular motors in vitro or in vivo, collections of motile microorganisms, animal flocks, and chemical or mechanical imitations. A major goal of this review is to integrate several approaches proposed in the literature, from semimicroscopic to phenomenological. In particular, first considered are ``dry'' systems, defined as those where momentum is not conserved due to friction with a substrate or an embedding porous medium. The differences and similarities between two types of orientationally ordered states, the nematic and the polar, are clarified. Next, the active hydrodynamics of suspensions or ``wet'' systems is discussed and the relation with and difference from the dry case, as well as various large-scale instabilities of these nonequilibrium states of matter, are highlighted. Further highlighted are various large-scale instabilities of these nonequilibrium states of matter. Various semimicroscopic derivations of the continuum theory are discussed and connected, highlighting the unifying and generic nature of the continuum model. Throughout the review, the experimental relevance of these theories for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular material is discussed. Promising extensions toward greater realism in specific contexts from cell biology to animal behavior are suggested, and remarks are given on some exotic active-matter analogs. Last, the outlook for a quantitative understanding of active matter, through the interplay of detailed theory with controlled experiments on simplified systems, with living or artificial constituents, is summarized.

Hydrodynamics of soft active matter

I. the origin of species by means of natural selection

Entangled quantum states are not separable, regardless of the spatial separation of their components This is a manifestation of an aspect of quantum mechanics known as quantum non-locality An important consequence of this is that the measurement of the state of one particle in a two-particle entangled state defines the state of the second particle instantaneously, whereas neither particle possesses its own well-defined state before the measurement Experimental realizations of entanglement have hitherto been restricted to two-state quantum systems, involving, for example, the two orthogonal polarization states of photons Here we demonstrate entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum As these modes can be used to define an infinitely dimensional discrete Hilbert space, this approach provides a practical route to entanglement that involves many orthogonal quantum states, rather than just two Multi-dimensional entangled states could be of considerable importance in the field of quantum information, enabling, for example, more efficient use of communication channels in quantum cryptography

Entanglement of the orbital angular momentum states of photons

Cell motility in viscous fluids is ubiquitous and affects many biological processes, including reproduction, infection and the marine life ecosystem. Here we review the biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming, tens of micrometers and below. At this scale, inertia is unimportant and the Reynolds number is small. Our emphasis is on the simple physical picture and fundamental flow physics phenomena in this regime. We first give a brief overview of the mechanisms for swimming motility, and of the basic properties of flows at low Reynolds number, paying special attention to aspects most relevant for swimming such as resistance matrices for solid bodies, flow singularities and kinematic requirements for net translation. Then we review classical theoretical work on cell motility, in particular early calculations of swimming kinematics with prescribed stroke and the application of resistive force theory and slender-body theory to flagellar locomotion. After examining the physical means by which flagella are actuated, we outline areas of active research, including hydrodynamic interactions, biological locomotion in complex fluids, the design of small-scale artificial swimmers and the optimization of locomotion strategies. (Some figures in this article are in colour only in the electronic version) This article was invited by Christoph Schmidt.

/pdf/the-hydrodynamics-of-swimming-microorganisms-bonwl3c7w2.pdf

The hydrodynamics of swimming microorganisms

A method is introduced to build microscopic light driven rotors that are created and manipulated in laser tweezers. Laser light-induced two-photon polymerization of light curing resins is applied to generate effective rotating particles several microns in size. The dynamics of rotation are evaluated. Mechanical devices consisting of multiple moving parts driven by these rotors are produced. It is shown that the combination of the techniques of microfabrication by two-photon polymerization by light and the light-induced trapping and rotation offers a powerful tool with which to build complex mechanical machines of micrometer size.

Complex micromachines produced and driven by light

Randomly moving but self-propelled agents, such as Escherichia coli bacteria, are expected to fill a volume homogeneously. However, we show that when a population of bacteria is exposed to a microfabricated wall of funnel-shaped openings, the random motion of bacteria through the openings is rectified by tracking (trapping) of the swimming bacteria along the funnel wall. This leads to a buildup of the concentration of swimming cells on the narrow opening side of the funnel wall but no concentration of nonswimming cells. Similarly, we show that a series of such funnel walls functions as a multistage pump and can increase the concentration of motile bacteria exponentially with the number of walls. The funnel wall can be arranged along arbitrary shapes and cause the bacteria to form well-defined patterns. The funnel effect may also have implications on the transport and distribution of motile microorganisms in irregular confined environments, such as porous media, wet soil, or biological tissue, or act as a selection pressure in evolution experiments.

A Wall of Funnels Concentrates Swimming Bacteria

In many naturally occurring habitats, bacteria live in micrometer-size confined spaces. Although bacterial growth and motility in such constrictions is of great interest to fields as varied as soil microbiology, water purification, and biomedical research, quantitative studies of the effects of confinement on bacteria have been limited. Here, we establish how Gram-negative Escherichia coli and Gram-positive Bacillus subtilis bacteria can grow, move, and penetrate very narrow constrictions with a size comparable to or even smaller than their diameter. We show that peritrichously flagellated E. coli and B. subtilis are still motile in microfabricated channels where the width of the channel exceeds their diameters only marginally (∼30%). For smaller widths, the motility vanishes but bacteria can still pass through these channels by growth and division. We observe E. coli, but not B. subtilis, to penetrate channels with a width that is smaller than their diameter by a factor of approximately 2. Within these channels, bacteria are considerably squeezed but they still grow and divide. After exiting the channels, E. coli bacteria obtain a variety of anomalous cell shapes. Our results reveal that sub-micron size pores and cavities are unexpectedly prolific bacterial habitats where bacteria exhibit morphological adaptations.

/pdf/bacterial-growth-and-motility-in-sub-micron-constrictions-gxtb2epe5m.pdf

Bacterial growth and motility in sub-micron constrictions

We have constructed a linear array of coupled, microscale patches of habitat. When bacteria are inoculated into this habitat landscape, a metapopulation emerges. Local bacterial populations in each patch coexist and weakly couple with neighbor populations in nearby patches. These spatially distributed bacterial populations interact through local extinction and colonization processes. We have further built heterogeneous habitat landscapes to study the adaptive dynamics of the bacterial metapopulations. By patterning habitat differences across the landscape, our device physically implements an adaptive landscape. In landscapes with higher niche diversity, we observe rapid adaptation to large-scale, low-quality (high-stress) areas. Our results illustrate the potential lying at the interface between nanoscale biophysics and landscape evolutionary ecology.

/pdf/bacterial-metapopulations-in-nanofabricated-landscapes-2iufskim6x.pdf

Bacterial metapopulations in nanofabricated landscapes

Swimming bacteria display a remarkable tendency to move along flat surfaces for prolonged times. This behavior may have a biological importance but can also be exploited by using microfabricated structures to manipulate bacteria. The main physical mechanism behind the surface entrapment of swimming bacteria is, however, still an open question. By studying the swimming motion of Escherichia coli cells near microfabricated pillars of variable size, we show that cell entrapment is also present for convex walls of sufficiently low curvature. Entrapment is, however, markedly reduced below a characteristic radius. Using a simple hydrodynamic model, we predict that trapped cells swim at a finite angle with the wall and a precise relation exists between the swimming angle at a flat wall and the critical radius of curvature for entrapment. Both predictions are quantitatively verified by experimental data. Our results demonstrate that the main mechanism for wall entrapment is hydrodynamic in nature and show the possibility of inhibiting cell adhesion, and thus biofilm formation, using convex features of appropriate curvature.

/pdf/hydrodynamic-trapping-of-swimming-bacteria-by-convex-walls-7zjvv0h6e3.pdf

Peter Galajda

Papers

Complex micromachines produced and driven by light

A Wall of Funnels Concentrates Swimming Bacteria

Bacterial growth and motility in sub-micron constrictions

Bacterial metapopulations in nanofabricated landscapes

Hydrodynamic Trapping of Swimming Bacteria by Convex Walls.