Pure many-body interactions in colloidal systems by artificial random light fields

Abstract

We propose a method to generate pure many-body interactions in colloidal systems by using optical forces induced by random optical fields with an optimized spectral energy density. To assess the feasibility in general settings, we develop a simple model for Lorentzian electric and magnetic dipole response. An optimization procedure is then introduced to design the spectral energy density of the random field that minimizes pair interactions at constant electromagnetic energy density. We conclude that, under rather general circumstances, it is possible to effectively cancel pair interactions within a range of distance. Hence a colloid can be driven to interact exclusively through many-body interactions

Figures (4)

• Figure 1: a-d: Scattering cross section $\sigma_s$ of particles modeled as electric and magnetic dipoles with Lorentzian polarizabilities, characterized by parameters $Q$ and $\Delta$. The contributions $\sigma_s^{(e)}$ and $\sigma_s^{(m)}$ are computed using only the electric ($\alpha_e$) or magnetic ($\alpha_m$) polarizability, respectively. $\sigma_s^{(\mathrm{tot})}=\sigma_s^{(e)}+\sigma_s^{(m)}$.
• Figure 2: a: Normalized minimal loss function $\tilde{L}\equiv L/\|C_m V_m\|_2$ (see text) as a function of quality factor $Q$ of both electric and magnetic polarizabilities and detuning $\Delta$ between electric and magnetic resonances. b: Higher-resolution zoom on the region $Z \le 10$ indicated by the white dashed-square on panel a. The star and the cross are showing the position of the minimum ($\tilde{L}=0.0098$) and maximum ($\tilde{L}=0.67924$) normalized loss functions, respectively. The triangle corresponds to a set of parameters giving an intermediate value of the normalized loss function ($\tilde{L}=0.06218$).
• Figure 3: Pair potential and energy density spectrum obtained at the point with the lowest found normalized cost function $\tilde{L}=0.0098$ (a,d, resp.), at an intermediate value $\tilde{L}=0.06218$ (b,e), and for the worst case $\tilde{L}=0.67924$ (c,f) in figure \ref{['fig:loss_maps']} . In all cases, the obtained potential $V(r)$ is compared with the contribution with maximum coefficient $C_mV_m$ marked as squares in the corresponding energy density spectrum.
• Figure 4: a: Comparison of the total, electric and magnetic contributions to the scattering cross section $\sigma_s$ (see legends) of a dielectric particle ($\epsilon=12$, radius $a=230nm$) computed with Mie theory (solid lines) and with the best fit to a Lorentzian model (dotted lines). b: Minimized pair interaction $U\left ( D \right )$ (temperature $T=300\text{K}$) compared with the contribution with maximal energy density $C_m V_m$ as a function of the surface-to-surface distance $D$. c: Energy density spectrum required to minimize the pair interaction.