Surface-induced heating of cold polar molecules

We study the rotational and vibrational heating of diatomic molecules placed near a surface at finite temperature on the basis of macroscopic quantum electrodynamics. The internal molecular evolution is governed by transition rates that depend on both temperature and position. Analytical and numerical methods are used to investigate the heating of several relevant molecules near various surfaces. We determine the critical distances at which the surface itself becomes the dominant source of heating and we investigate the transition between the long-range and short-range behavior of the heating rates. A simple formula is presented that can be used to estimate the surface-induced heating rates of other molecules of interest. We also consider how the heating depends on the thickness and composition of the surface.

Figure 1

Free-space lifetimes of the ground state against rotational heating as a function of environment temperature for LiH (thick solid line), NH (thick dashed line), OH(a) (thick dotted line), OD(a) (thin solid line), and KCs (thin dashed line).

Figure 2

Ground-state vibrational heating lifetimes in free space vs temperature for LiH (thick solid line), CaF (thick dashed line), YbF (thin solid line), and BaF (thick dotted line).

Figure 3

Exact critical distances for surface-induced heating vs frequency of the molecular transition. (a) Rotational heating. (b) Vibrational heating. Surface materials are gold (circles), iron (squares), platinum (diamonds), and ITO (triangles). Frequencies of the plotted data points correspond (left to right) to RbCs, KRb, NaRb, LiCs, BaF, LiRb, YbF, CaF, NaCs, KCs, LiH, NH, OD(a), and OH(a). Solid lines indicate the slope corresponding to the ${\omega }^{-3∕4}$ frequency dependence given by the empirical formula (89).

Figure 4

Heating rates for (a) OH, (b) LiH, (c) CaF, and (d) NaCs vs distance from a gold surface. Solid lines: total heating rate. Dotted lines: vibrational excitation rate. Dashed lines: rotational excitation rate.

Figure 5

Heating rate for ground-state NaCs as a function of the distance from gold (solid line), iron (dashed line), and ITO (dotted line) surfaces.

Figure 6

Heating rate for ground state LiH as a function of distance from fictitious metamaterials with $\epsilon \left({\omega }_{k0}\right)=\mu \left({\omega }_{k0}\right)=\pm 10+i$ (solid line), $\epsilon \left({\omega }_{k0}\right)=10+i$, $\mu \left({\omega }_{k0}\right)=-10+i$ (dashed line), and $\epsilon \left({\omega }_{k0}\right)=-10+i$, $\mu \left({\omega }_{k0}\right)=10+i$ (dotted line).

Figure 7

Heating rate of NaCs as a function of distance from an ITO surface with thickness $10\mu \mathrm{m}$ (thick solid line), $1\mu \mathrm{m}$ (dashed line), $0.1\mu \mathrm{m}$ (dotted line), and $0.01\mu \mathrm{m}$ (dashed-dotted line). The thin solid line shows how the result changes for a $0.01\mu \mathrm{m}$ thick surface when the ITO is coated onto borosilicate glass.