Sorting mesoscopic objects with periodic potential landscapes: Optical fractionation

Ladavac, Kosta; Kasza, Karen E.; Grier, David G.

doi:10.1103/physreve.70.010901

Cited by 192 publications

(182 citation statements)

References 16 publications

(21 reference statements)

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“…Previous studies.-The dramatic influence of a tilt on the transport in a one-dimensional biased periodic potential has been explored experimentally for a colloidal particle on a corrugated optical vortex [10,11], and has been exploited for optical particle fractionation and separation [12][13][14]. Explicit expressions for v and for D for the case of a tilted cosine potential were first given in [15][16][17][18] and further generalised in [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium version of the Einstein relation

Hurowitz

Cohen

2014

Phys. Rev. E

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The celebrated Einstein relation between the diffusion coefficient D and the drift velocity v is violated in non-equilibrium circumstances. We analyze how this violation emerges for the simplest example of a Brownian motion on a lattice, taking into account the interplay between the periodicity, the randomness and the asymmetry of the transition rates. Based on the non-equilibrium fluctuation theorem the v/D ratio is found to be a non-linear function of the affinity. Hence it depends in a non-trivial way on the microscopics of the sample.

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Section: Introductionmentioning

confidence: 99%

Nonequilibrium version of the Einstein relation

Hurowitz

Cohen

2014

Phys. Rev. E

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“…For ease of modeling we treat the exit also as a step described by the lattice vector to the trap that would have captured the exiting particle had the trap array been extended to infinity in the x direction. In the physical system [5], colloidal particles are driven through an array of optical traps by a steady flow in the surrounding medium oriented at angle θ to the trap array's [10] axis. These particles are also subject to random thermal forces causing them to diffuse.…”

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confidence: 99%

Statistically Locked-In Transport through Periodic Potential Landscapes

Gopinathan

Grier

2004

Phys. Rev. Lett.

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Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a Devil's staircase hierarchy of commensurate trajectories depending on the orientation of the driving force. Recent experiments on colloidal spheres flowing through arrays of optical traps do indeed reveal such a hierarchy, but not with the predicted structure. The microscopic trajectories, moreover, appear to be random, with commensurability emerging only in a statistical sense. We introduce an idealized model for periodically modulated transport in the presence of randomness that captures both the structure and statistics of such statistically locked-in states.Objects driven through periodic potential energy surfaces face a myriad of choices: either they follow the driving force or they become entrained along any of the commensurate directions through the landscape. Variants of this problem appear in areas as diverse as driven charge density waves [1], electronic energy states in twodimensional electron gases [2], atom migration on crystal surfaces [3], chemical kinetics, and flux flow in type-II superconductors [4]. Quite recently, this problem was investigated [5] using a monolayer of colloidal spheres in flowing water as a model system and a square array of holographic optical tweezers [6] to provide the periodic potential energy surface. Depending on the array's orientation with respect to the driving force, the spheres were observed to trace out a Devil's staircase hierarchy of commensurate directions through the array, with particular directions being preferentially selected over certain ranges of orientations [5]. Trajectories deflected by a preference for commensurability are said to be kinetically locked in to the lattice. This anticipated result [7] was accompanied by two surprises. In the first place, not all kinetically lockedin states were centered on simple commensurate directions. Still more surprisingly, particles' microscopic trajectories in high-order locked-in states did not consist of sequences of commensurate jumps, but rather consisted of seemingly random lower-order hops whose combination, nonetheless, were commensurate. The appearance of statistical rather than deterministic commensurability suggests an unexpected role for thermal randomness in structuring transport through periodic potentials, and has been dubbed statistical lock-in [5].This Letter presents a highly simplified model for statistically locked-in transport through mesoscopic potential energy landscapes that nonetheless accounts for the emergence of combination jumps and their statistical commensurability. In particular this model reveals how the potential energy landscape's structure and extent establish the discrete spectrum of travel directions selected by biased random walkers. While our discussion is directed toward the purely classical behavior of flowing colloids, similar results should emerge for biased quantum mechanical hopping through arrays of potential An applied force drives objects through the array...

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“…Powering the hologram with 1.8 W provides each trap with an estimated 1.3 ± 0.3 mW, after accounting for the hologram's diffraction efficiency and other losses in the optical train. Each trap, therefore, has an estimated width of σ = 0.85 µm [38] and a depth of 9 k B T [39].…”

Section: Experimental Demonstrationmentioning

confidence: 99%