One-Dimensional Optically Bound Arrays of Microscopic Particles

A one-dimensional optically coupled array of colloidal particles is created in a potential well formed by two counterpropagating Gaussian light beams. This array has analogies to linear chains of trapped atomic ions. Breathing modes and oscillations of the center of mass are observed. The stability of the array is in accordance with the Kramers model.

Figure 1

Axial forces for the counterpropagating beam geometry. The peak point for each curve corresponds to the beam waist position. Forces from both beams ($F_1$ and $F_2$) are drawn as positive. The resultant axial force $\Delta F$ is the difference of two forces drawn. The inset shows how particles reside in the resulting potential well.

Figure 2

Experimental data for arrays of (a) two, (b) three, and (c) seven spheres (each $3\mu \mathrm{m}$ in size). The diagrams on the right elucidate how we fill up the approximately harmonic potential well created by the two counterpropagating beams.

Figure 3

Equilibrium positions for particles in the array. The parabolic fit shows the harmonic form (as expected) of the light beam potential. Notably, this allows us to extract important quantitative data about the trap (frequency, light potential).

Figure 4

Observation of a breathing mode. In (a) and (c) we see the displacement of the chain as a whole from the center with the interparticle spacing increasing as one goes farther from the center of the array.

Figure 5

Kramers transition time for the array. The main features of the observed residence times are supported by a general statistical theory showing exponential decay. The fit is appropriately described by an exponential function of the form $\langle {\tau }_K\rangle ={\tau }_0\exp \left[\frac{U}{(n+c)k_{B}T}\right]$ and has the magnitude of the potential barrier $U/k_{B}T$ varied from 4.1 to 5.8 and ${\tau }_0=1$, $c=16$ for particle number $n=1,2,\dots 7$.