Attractive Optical Forces from Blackbody Radiation

Blackbody radiation around hot objects induces ac Stark shifts of the energy levels of nearby atoms and molecules. These shifts are roughly proportional to the fourth power of the temperature and induce a force decaying with the third power of the distance from the object. We explicitly calculate the resulting attractive blackbody optical dipole force for ground state hydrogen atoms. Surprisingly, this force can surpass the repulsive radiation pressure and actually pull the atoms against the radiation energy flow towards the surface with a force stronger than gravity. We exemplify the dominance of the “blackbody force” over gravity for hydrogen in a cloud of hot dust particles. This overlooked force appears relevant in various astrophysical scenarios, in particular, since analogous results hold for a wide class of other broadband radiation sources.

Figure 1

An artist’s view of the interaction between an atom and a hot sphere of radius $R$. From a distance $r$ it appears as a disk of effective radius $R_d$ at distance $r_d$.

Figure 2

Comparison of the spatial decay of various interaction strengths between an atom and a hot sphere of radius $R$: blackbody ($1-\sqrt{r^2-R^2}/r$, red solid line), gravity ($R/r$, blue dashed line), and electrostatic potential ($R^4/r^4$, green dash-dotted line); cf. also Eq. (10). The orange dashed line extrapolates the asymptotic inverse quadratic long-range radiation potential, $R^2/(2r^2)$.

Figure 3

Comparison of the energy shift of the hydrogen ground state induced by black-body radiation ($a_{\mathrm{BB}}$, red lines), the electrostatic interaction ($a_Q$, green dash-dotted lines), and the gravitational potential energy ($a_G$, blue dashed line) at the sphere surface as function of the radius $R$ for a mass density $\rho =1\mathrm{g}/{\mathrm{cm}}^3$.

Figure 4

Gravitational [light gray (blue) lines] and black-body induced [dark gray (red) lines] potential of randomly distributed spheres of size $R=5\mu \mathrm{m}$ and temperature $T=300\mathrm{K}$ such that $a_{\mathrm{BB}}\approx 1.1\times {10}^9{a}_G$ for $\rho =1\mathrm{g}/{\mathrm{cm}}^3$. The dotted lines show the potentials calculated in Eqs. (11, 12) using a distribution of width $\sigma =300\mathrm{m}$. The solid lines are the result of a random sample of $N=8000$ Gaussian distributed spheres.