Omnidirectional Transport in Fully Reconfigurable Two Dimensional Optical Ratchets

A fully reconfigurable two-dimensional (2D) rocking ratchet system created with holographic optical micromanipulation is presented. We can generate optical potentials with the geometry of any Bravais lattice in 2D and introduce a spatial asymmetry with arbitrary orientation. Nontrivial directed transport of Brownian particles along different directions is demonstrated numerically and experimentally, including on axis, perpendicular, and oblique with respect to an unbiased ac driving. The most important aspect to define the current direction is shown to be the asymmetry and not the driving orientation, and yet we show a system in which the asymmetry orientation of each potential well does not coincide with the transport direction, suggesting an additional symmetry breaking as a result of a coupling with the lattice configuration. Our experimental device, due to its versatility, opens up a new range of possibilities in the study of nonequilibrium dynamics at the microscopic level.

Figure 1

Experimental setup: spatial light modulator (SLM), lenses (L), spatial filter (SF), half-wave plate (HWP), polarizing beam splitters (PBS), mirrors (M), dichroic mirrors (DM), microscope objectives (MO), attenuation filters (F), and cameras (CCD). The upper inset shows the primitive vectors of the main lattice $\overrightarrow{a}$ and $\overrightarrow{b}$, and the position of the clone lattice defined by $\overrightarrow{\delta }$. The inset in the middle illustrates the displacement of the piezo-stage $X(t)$.

Figure 2

Experimental images showing the paths of an ensemble of particles for [34]: (a) $\mathrm{\Lambda }=13\mu \mathrm{m}$ and (b) $\mathrm{\Lambda }=23\mu \mathrm{m}$. (c) Numerical simulations for the components of the current, $j_x$ (blue) and $j_y$ (red), as a function of $\mathrm{\Lambda }$, for three values of the relative diffusion coefficient $D/D_0$. The shadows around the curves for $D/D_0=0.41$ represent the standard deviations. The inset illustrates the intensity pattern and the direction of the driving (double arrow). Experimental results correspond to $D/D_0=0.41$ (markers). The parameters are $L_x=14.8\mu \mathrm{m}$, $b_x/L_x=0.5$, $b_y/L_x=0.15$, $v_0=21\mu \mathrm{m}/\mathrm{s}$.

Figure 3

(a) Paths of an ensemble of particles for $\mathrm{\Lambda }=10\mu \mathrm{m}$. (b) Normalized current components ($j_x$ blue curves and $j_y$ red curves) vs $\mathrm{\Lambda }$ for the optical lattice shown in the inset, for three values of $D/D_0$. $L_x=14.8\mu \mathrm{m}$, $v_0=50\mu \mathrm{m}/\mathrm{s}$, $b_x=0.5Lx$, and $b_y=0.2Lx$. (c) Current components for $D/D_0=0.41$ and three values of $b_y/L_x$. The shadows in (b) and (c) correspond to the standard deviations for $D/D_0=0.41$ and $b_y/L_x=0.2$. The markers represent experimental values.

Figure 4

$j_x$ (blue) and $j_y$ (red) vs $\mathrm{\Lambda }$ for the optical lattice shown in the inset, for three values of $D/D_0$. $L_x=18.5\mu \mathrm{m}$, $b_x=Lx/3$, $b_y=Lx/9$, and $v_0=24\mu \mathrm{m}/\mathrm{s}$. Markers denote experimental values for $D/D_0=0.41$. The image on top shows the trajectories of several particles for $\mathrm{\Lambda }=11\mu \mathrm{m}$ [34].