Sympathetic laser cooling of graphene with Casimir-Polder forces

We propose a scheme to actively cool the fundamental flexural (out-of-plane) mode of a graphene sheet via vacuum forces. Our setup consists of a cold-atom cloud placed close to a graphene sheet at distances of a few micrometers. The atoms couple to the graphene membrane via Casimir-Polder forces. By deriving a self-consistent set of equations governing the dynamics of the atomic gas and the flexural modes of the graphene, we show it is possible to cool graphene from room temperatures by actively (laser) cooling an atomic gas. By choosing the right set of experimental parameters we are able to cool a graphene sheet down to $\sim 60 \mu \mathrm{K}$.

Figure 1

Scheme of the experimental setup of a quantum gas at a distance $z_A$ from a graphene sheet. The motion of the particles is coupled to the flexural modes of graphene via Casimir-Polder interactions. The cooling of the vibrational modes of the gas can be done with the help of the cooling laser with Rabi frequency $\mathrm{\Omega }$. For our calculations, we have chosen an atomic cloud of rubidium $\left({}^{87}\mathrm{Rb}\right)$.

Figure 2

Density plot of the stationary-state flexural mode number (a) and (b) $m_{\text{SS}}$ and (c) $n_{\text{SS}}$ for the parameters $\eta =0.25,\mathrm{\Gamma }=6.07$ MHz, $\nu =2.7$ MHz, ${\omega }_{\text{ph}}=477$ Hz, where in (a) and (c) $\mathrm{\Omega }=10$ MHz and in (b) $g=-47.7$ kHz. The red point in (b) marks the coordinate $g=-47.7$ kHz and $\mathrm{\Delta }=36$ MHz, where $m_{\text{SS}}\sim 0.15$, for which the time evolution in Fig. 3 is calculated and corresponds to $n_{\text{SS}}\approx {\left[exp\left[\hslash {\omega }_{\text{ph}}/\left(k_B{T}_{\text{atoms}}\right)\right]-1\right]}^{-1}\sim 24$, for which the temperature is $T_{\text{atoms}}=560$ nK.

Figure 3

Logarithmic plot of the time evolution of the mean flexural mode number $m$ for the same parameters as in Fig. 2, but with $g=-47.7$ kHz and $\mathrm{\Delta }=36$ MHz. The different lines represent different starting temperatures, from bottom to top, $T=0.01,1,70,300$ K. For these parameter the $m_{\text{SS}}=0.15$, which corresponds to a final temperature of $T_{\text{graph}}=60 \mu \mathrm{K}$. The inset shows a contour plot of ${\gamma }_{\text{eff}}$ as a function of $g$ and $\mathrm{\Delta }$ for the same parameters as in Fig. 2.