Enhancement of thermal Casimir-Polder potentials of ground-state polar molecules in a planar cavity

Abstract

We analyze the thermal Casimir-Polder potential experienced by a ground-state molecule in a planar cavity and investigate the prospects for using such a setup for molecular guiding. The resonant atom-field interaction associated with this nonequilibrium situation manifests itself in oscillating standing-wave components of the potential. While the respective potential wells are normally too shallow to be useful, they may be amplified by a highly reflecting cavity whose width equals a half-integer multiple of a particular molecular transition frequency. We find that with an ideal choice of molecule and the use of a cavity bounded by Bragg mirrors of ultrahigh reflectivity, it may be possible to boost the potential by up to two orders of magnitude. We analytically derive the scaling of the potential depth as a function of reflectivity and analyze how it varies with temperature and molecular properties. It is also shown how the potential depth decreases for standing waves with a larger number of nodes. Finally, we investigate the lifetime of the molecular ground state in a thermal environment and find that it is not greatly influenced by the cavity and remains in the order of several seconds.

Casimir-Polder effect with thermally excited surfaces

“…For this reason Re[G zz (z, ω o )] decays much faster than Re[G xx,yy (z, ω o )]. In reality this term will dominate the far field of CP interaction for excited state atoms or molecules [40,41]. At very large temperatures or at very large distances from the surface it will eventually dominate the interaction between a surface and a ground state atom.…”

Repulsive Casimir and Casimir–Polder forces

“…Care must also be taken with the m = 0 term in the cosine series. The result of a straightforward calculation leads to dζ 2π 14) where the term divergent as ξ → 1 may, through a similar calculation, be shown to be that corresponding to the vacuum in absence of the wedge, that is, that obtained from the free Green's dyadic. Therefore, we must subtract this term off, to obtain the static Casimir energy (7.7), which for this situation is…”

“…From this, we can work out the energy of the system from 14) where the factor of 1/2 comes from the fact that this must be the energy required to assemble the system. In computing this energy we must, of course, drop the self-energy of the dipole due to its own field.…”

“…In this respect ultracold molecules [12] or Rydberg atoms [13] would seem more promising out-of-equilibrium systems, since they both take much longer to thermalize, but oscillations only become dominant so far from the wall as to be unobservable. Schemes to amplify the oscillating potential using a planar [14] and cylindrical [15] cavity were explored, of which the latter showed some promise for observing the effect for Rydberg atoms. A related possibility seems to be the use of excited media [16].…”

Casimir-Polder Potential in Thermal Non-Equilibrium

“…It was demonstrated that even ground state particles are subject to an oscillating force component in the presence of macroscopic bodies at nonzero temperature. While utterly unobservable for atoms (which are essentially in their ground state when thermalized at room temperature), there could be some hope of observing and even using this effect for molecules, 11,12 which have excited states of very low energy. A similar investigation was recently made 13 by applying Keldysh theory to the system of two atoms prepared in an arbitrary state, in the presence of an external (thermal) electromagnetic field.…”