Nonadditivity of Optical and Casimir-Polder Potentials

An atom irradiated by an off-resonant laser field near a surface is expected to experience the sum of two fundamental potentials, the optical potential of the laser field and the Casimir-Polder potential of the surface. Here, we report a new nonadditive potential, namely, the laser-induced Casimir-Polder potential, which arises from a correlated coupling of the atom with both the laser and the quantum vacuum. We apply this result to an experimentally realizable scenario of an atomic mirror with an evanescent laser beam leaking out of a surface. We show that the nonadditive term is significant for realistic experimental parameters, transforming potential barriers into potential wells, which can be used to trap atoms near surfaces.

Figure 1

Difference $\mathrm{\Delta }U=U_{\mathrm{CP}}-U_{\mathrm{LCP}}$ for a perfectly conducting mirror with reflective coefficients $r_s=-1$ and $r_p=1$. The laser intensity is $I=5{\mathrm{W}/\mathrm{cm}}^2$ used for Rb atoms with a transition frequency of ${\tilde{\omega }}_{10}=2.37\times {10}^{15}\mathrm{rad}/\mathrm{s}$. The detuning is $\mathrm{\Delta }=2\pi \times {10}^8\mathrm{rad}/\mathrm{s}$. The angle between the z axis and the orientation of the field $\mathbf{E}({\mathbf{r}}_A)$ is $\theta =\pi /2$.

Figure 2

Upper figure: Total potential with (solid lines) and without (dotted lines) the nonadditive term calculated here, for three different values of the potential scale $U_0$. The dashed lines are the total potential using the perturbative result, as opposed to the nonperturbative one. The parameters taken from Refs. [11, 12] are as follows: decay length $z_0=430\mathrm{nm}$, detuning $\mathrm{\Delta }=2\pi \times {10}^8\mathrm{Hz}$, dipole moment $d=2.53\times {10}^{-29}\mathrm{Cm}$, transition frequency ${\tilde{\omega }}_{10}=2.37\times {10}^{15}\mathrm{rad}/\mathrm{s}$ and quality factor $Q=37.5=-\mathrm{Re}(r_p)$. As reported in Ref. [11] the potential scale is given by $U_0\sim P(\mathrm{W})\times {10}^{-23}\mathrm{J}/\mathrm{W}$, meaning the range of values chosen for this quantity are commensurate with milliwatt laser power. The lower figure shows the positions of the minima and maxima of the additive potential $U_A$ (dotted), the perturbative potential $U_{\mathrm{NA}}^P$ (dashed) and exact nonadditive potential $U_{\mathrm{NA}}^E$ (solid) as a function of the potential scale $U_0$ and the distance. This demonstrates that the nonadditive potential undergoes a transition from a traplike to barrierlike as a function of the atom-surface distance, while the additive potential remains barrierlike for all parameters shown here.