Rotranslational cavity cooling of dielectric rods and disks

We study the interaction of dielectric rods and disks with the laser field of a high-finesse cavity. The quantum master equation for the coupled particle-cavity dynamics, including Rayleigh scattering, is derived for particle sizes comparable to the laser wavelength. We demonstrate that such anisotropic nanoparticles can be captured from free flight at velocities higher than those required to capture dielectric spheres of the same volume and that efficient rotranslational cavity cooling into the deep quantum regime is achievable.

Figure 1

A thin dielectric rod or disk traverses the laser field of a high-finesse cavity with resonance frequency ${\omega }_{\mathrm{c}}$, driven with pump rate $\eta$ and pump frequency ${\omega }_{\mathrm{p}}$. The cavity detuning is $\mathrm{\Delta }={\omega }_{\mathrm{p}}-{\omega }_{\mathrm{c}}$ and $\kappa$ and ${\gamma }_0$ are the cavity linewidth and the Rayleigh scattering rate, respectively. The orientation vector of the dielectric's symmetry axis is denoted by $\mathbf{m}\left(\mathrm{\Omega }\right)$.

Figure 2

(a) Trapping probability as function of the forward velocity for a silicon rod (blue; $\ell =800$ nm, $a=25$ nm) and a sphere (red; $R\simeq 72$ nm) of the same volume. The nanoparticle is launched towards the cavity with forward velocity $v_x$. In order to obtain the trapping probability we solve the classical equations of motion (7) for several thousand initial conditions for each $v_x$. The transverse velocity $v_z$ is uniformly distributed within 5% of the forward velocity $v_x$, assuming a collimated beam. We neglect the weak $y$ dependence, setting $v_y=0$ and $y=0$, and assume the orientational degrees of freedom to be microcanonically distributed with a total rotation frequency of 1 MHz. For the cavity, we chose the following realizable parameters: $\lambda =1.56\mu \mathrm{m}, \kappa =0.78$ MHz, $P_{\mathrm{in}}=10$ mW, $\mathrm{\Delta }=-1.2\kappa , F=330000$. In panel (b) we show the total energy for a sample trajectory with $v_x=0.5$ m/s and $v_z=-0.3$ m/s. The dielectric rod (blue) is captured and cooled while a sphere (red dashed) of the same volume traverses the cavity almost unaffected. Negative energies indicate that the particle is captured.