Mapping Out Atom-Wall Interaction with Atomic Clocks

We explore the feasibility of probing atom-wall interaction with atomic clocks based on atoms trapped in engineered optical lattices. Optical lattice is normal to the wall. By monitoring the wall-induced clock shift at individual wells of the lattice, one would measure the dependence of the atom-wall interaction on the atom-wall separation. We find that the induced clock shifts are large and observable at already experimentally demonstrated levels of accuracy. We show that this scheme may uniquely probe the long-range atom-wall interaction in all three qualitatively distinct regimes of the interaction: van der Waals (image-charge interaction), Casimir-Polder (QED vacuum fluctuations), and Lifshitz (thermal-bath fluctuations) regimes.

Figure 1

Inset: Idealized setup for measuring atom-wall interaction with optical lattice clocks. Clouds of ultracold atoms are trapped in an optical lattice operating at a “magic” wavelength. By monitoring the wall-induced clock shift at individual trapping sites, one measures a dependence of the atom-wall interaction on the atom-wall separation. Main figure: Fractional clock shifts for Sr as a function of separation from a gold surface at three temperatures, $T=77\mathrm{K}$ (blue dots), $T=300\mathrm{K}$ (red squares), and $T=600\mathrm{K}$ (brown diamonds). Individual points represent shifts in individual trapping sites of the optical lattice. The first well is placed at ${\lambda }_m/4$ and subsequent points are separated by ${\lambda }_m/2$.

Figure 2

Dynamic polarizabilities of imaginary frequency $\alpha (i\omega )$ of the Sr clock levels, $5s5p{}^{3}P_0$ (dotted line) and $5s^2{}^{1}S_0$ (dashed line) as a function of frequency. Differential polarizability $\Delta \alpha (i\omega )={\alpha }_{{}^{3}P_0}(i\omega )-{\alpha }_{{}^{1}S_0}(i\omega )$ is shown with a solid line. All quantities are in atomic units.

Figure 3

Sr clock shift of Fig. 1 normalized to the Casimir-Polder limit, Eq. (7) at $T=77\mathrm{K}$ (blue dots), $T=300\mathrm{K}$ (red squares), and $T=600\mathrm{K}$ (brown diamonds).