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

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.

Figure 1

(Color online) Casimir-Polder potential of a ground-state LiH molecule inside a gold cavity of width $a=500\mu \text{m}$ at room temperature $\left(T=300\text{K}\right)$. The nonresonant, propagating, and evanescent contributions to the total potential are shown separately.

Figure 2

(Color online) Cavity-induced enhancement of the thermal Casimir-Polder potential of a ground-state LiH molecule inside gold cavities of various widths close to the second resonance $a={\lambda }_{k0}=673\mu \text{m}$. The potential of a single plate at $z=-{\lambda }_{k0}/2$ is also displayed.

Figure 3

(Color online) Propagating part of the thermal Casimir-Polder potentials of a ground-state LiH molecule inside gold cavities of widths $a=\nu {\lambda }_{k0}/2$ corresponding to resonances of different orders $\left(\nu =1,2,3\right)$.

Figure 4

(Color online) Depth $\Delta U$ of the $\nu =2$ potential minimum for rotational and vibrational transitions of various ground-state polar molecules inside gold cavities at $T=300\text{K}$. The different nondegenerate transitions of OH and OD are labeled as (a)–(d) in order of ascending frequencies, cf. Ref. [21].

Figure 5

(Color online) Frequency dependence of the depth $\Delta U$ of the $\nu =2$ potential minimum for polar molecules inside gold cavities at $T=300\text{K}$.

Figure 6

(Color online) Propagating part of the thermal CP potential for a ground-state LiH molecule inside different cavities with constant reflection coefficients. The rotational transition of LiH is assumed to coincide with the $\nu =2$ resonance of the cavities. For comparison, the exact result for a gold cavity is also shown.

Figure 7

(Color online) Reflection coefficients of Bragg mirrors for normal incidence at the rotational transition frequency of LiH vs the number of double layers $N$. Above: GaAs/AlAs mirror, where the results for reduced and vanishing absorption are also displayed for comparison. Below: Vacuum/sapphire mirror at two different temperatures $T=77$ and 300 K.

Figure 8

(Color online) Resonant part of the thermal CP potential associated with the rotational transitions of a ground-state LiH molecule at $\nu =2$ resonance with a gold cavity and a cavity bounded by vacuum/sapphire Bragg mirrors at two different temperatures: 77 K above, 300 K below. The solid black lines represent calculations at constant reflection coefficients as in Fig. 6; the corresponding values of $1-r$ decrease in powers of 10 from ${10}^{-2}$ (lowest curve) to ${10}^{-7}$ (highest curve). The same permittivity is used for gold for both temperatures.

Figure 9

Ground-state rotational heating rate of a LiH molecule in a gold cavity at $\nu =1$ resonance $a=\pi c/{\omega }_{k0}$ (solid line) and to the right of a gold half-space (dashed line) at room temperature $\left(T=300\text{K}\right)$.

Figure 10

(Color online) Graph of $\phi \left(\nu \right)/\nu$ (solid line) and its asymptote (dashed line) as given by Eq. (A13).