From optical lattice clocks to the measurement of forces in the Casimir regime

We describe an experiment based on atoms trapped close to a macroscopic surface, to study the interactions between the atoms and the surface at very small separations $(0.6–10\mu \mathrm{m})$. In this range the dominant potential is the QED interaction (Casimir-Polder and van der Waals) between the surface and the atom. Additionally, several theoretical models suggest the possibility of Yukawa-type potentials with sub-millimeter range, arising from new physics related to gravity. The proposed setup is very similar to neutral atom optical lattice clocks, but with the atoms trapped in lattice sites close to the reflecting mirror. A sequence of pulses of the probe laser at different frequencies is then used to create an interferometer with a coherent superposition between atomic states at different distances from the mirror (in different lattice sites). Assuming atom interferometry state-of-the-art measurement of the phase difference and a duration of the superposition of about $0.1\mathrm{s}$, we expect to be able to measure the potential difference between separated states with an uncertainty of $\approx {10}^{-4}\mathrm{Hz}$. An analysis of systematic effects for different atoms and surfaces indicates no fundamentally limiting effect at the same level of uncertainty, but does influence the choice of atom and surface material. Based on those estimates, we expect that such an experiment would improve the best existing measurements of the atom-wall QED interaction by ⩾ 2 orders of magnitude, while gaining up to four orders of magnitude on the best present limits on new interactions in the range between $100\mathrm{nm}$ and $100\mu \mathrm{m}$.

Figure 1

Wannier-Stark states in position (left) and momentum (right) representations for $U_0=5E_r$, $10E_r$, and $50E_r$, calculated numerically (see [22] for details).

Figure 2

Wannier-Stark ladder of states and coupling between states by the probe laser.

Figure 3

Relative coupling strength of the transition in the same well ${\mid {\Omega }_0∕\Omega \mid }^2$ and transitions into the first four neighboring wells ${\mid {\Omega }_{\pm 1}∕\Omega \mid }^2$ and ${\mid {\Omega }_{\pm 2}∕\Omega \mid }^2$ as a function of the lattice depth $U_0$. The vertical dashed line corresponds to $U_0=5E_r$.

Figure 4

(Color online) Experimental principle: Vertical standing wave with atoms in the first and third wells (right), and interferometer created by the sequence of pulses described in the text (left).

Figure 5

(Color online) Limits [66] on $U_{\mathit{Yuk}}$ at very short ranges (adapted from [65]). The solid red line indicates estimated limits from the present proposal when using a differential measurement between isotopes.

Figure 6

(Color online) Limits [66] on $U_{\mathit{Yuk}}$ at short ranges (adapted from [65]). The solid red line is as for Fig. 5. The solid green line indicates expected limits from the present proposal with atoms at $\approx 10\mu \mathrm{m}$ from the surface.