Probing atom-surface interactions from tunneling-time measurements via rotation-transport on an atom chip

TL;DR

This work introduces a rotation‑transport scheme on an atom chip to measure atom–surface interactions in the Casimir–Polder regime. By adiabatically moving a $^{87}$Rb BEC toward a surface using a reflected optical dipole trap combined with a magnetic trap, the authors show that the tunneling lifetime toward surface‑bonded states encodes the CP coefficient $c_4$ via a distance‑dependent barrier. Numerical modeling maps trap parameters and demonstrates the CP‑dependent modification of the barrier, enabling extraction of $c_4$ with projected relative precision around a few percent to a few tens of percent depending on calibration quality and parameter control. The method provides a versatile, species‑agnostic approach to locally probe atom–surface interactions with potential extensions to verify $1/z^4$ scaling, CP→LJ crossovers, and CP contributions to trap dynamics on atom chips.

Abstract

We propose a novel method to measure the interaction between an ultracold gas of neutral atoms and a surface. This solution combines an optical dipole trap reflected by the surface, a magnetic trap formed by current carrying wires embedded below the surface, and a rotation of the surface itself. It allows to adiabatically transport a $^{87}$Rb BEC from few $μ$m to few hundred nm of the surface. At such distances, atom-surface interaction strongly affects the trapping potential, causing an increase of the tunneling rate towards the surface. In this paper, we show that the measurement of the lifetime of the cloud and its comparison to a tunneling model will allow to extract the Casimir-Polder (CP) force coefficient in the retarded regime ($c_4$). Our model includes noise-induced heating, calibration biases of experimentally controlled parameters and accuracy of the atom lifetime measurement. Using typical trapping parameters and experimental uncertainties, we numerically estimate the relative uncertainty of $c_4$ to be 10%. This method can be implemented with any atomic species that can be magnetically and optically trapped.

Figures (4)

• Figure 1: a) Drawing of the chip's copper substrate: (top) side view, (bottom) top view. A gold mirror (yellow) is glued on top of the substrate. The rotating axis of the chip (dashed black line, along $y = y_L$) aligns with the top surface of the chip above the mirror. A Z-shaped wire (grey dotted line) carrying a current $I_Z(t)$ is embedded in a groove between the mirror and the substrate. A 1064 nm laser (red fading circle) is reflected by the mirror at the center of the chip (origin of both frames of reference). b) Interference fringes (interfringe $i(t)$) are produced at a distance $z_0(t)$ from the chip by reflecting the laser beam (fixed, propagating along $+z_L$) while rotating the chip, resulting in a time-dependent angle of incidence $\theta(t)$. c) 1D cut of the total (plain line) and optical (dashed line) potential in the perpendicular ($z$) direction at $\theta=65^\circ$. The wave-function (green) can tunnel toward the surface at $z=0$ with a time scale $\tau_t$. d) Semi-log plot of the trap center position $z_0$ as a function of $\theta$ in the absence of CP forces. The vertical lines represent the lowest trapping angle one can reach when including CP forces with $c_4=2.1 \cdot 10^{-55}$ J.m$^4$ for different optical powers $P$.
• Figure 2: a) 1D cuts of the potential in the transverse directions. Along $x$ at $(y_0,z_0)$ (left axis, colors, no markers). Along $y$ at $(x_0,z_0)$ (right axis, grey, with markers). 2D maps of trap parameters in the absence of CP forces, as a function of both $P$ and $\theta$ : b) (resp. (c)) Trap frequency in the $x$ (resp. $z$) direction. d) Barrier height ($U_0$). The shaded area below the black line annotated N.T. (no trap), corresponds to a non trapping configuration when including CP forces with $c_4=2.1 \cdot 10^{-55}$ J.m$^4$. These parameters are achievable nevertheless in the second fringe where the CP force induce very little modification and could be neglected.
• Figure 3: 2D maps of the tunnel time, $\text{log}_{10}\left( \tau_t \right)$, limited by the tunneling time toward the surface when including CP forces. Contour lines of annotated values are plotted in black. (a-b) share the same colormap (on top). They are computed at $P=1.2$ W for (a) and $\theta=55 ^\circ$ for (b). The y-axis for (a) (resp. (b)) is $\theta$ (resp. $P$). The right y-axis in (a) shows the equivalent trap center position $z_0$. c) 2D map as a function of $P$ and $\theta$ for $c_4=2.1 \cdot 10^{-55}$ J.m$^4$. The red line corresponds to $\tau_t =\tau_{3b}$
• Figure 4: a) 2D map of the three-body recombination time ($log_{10}\left( \tau_{\rm 3b} \right)$) as a function of $P$ and $\theta$. Contour lines of annotated values are plotted in black. The red line corresponds to $\tau_{\rm 3b}=\tau_{\rm t}$. b) Fluctuation-limited lifetime ($\tau_k$) as a function of the trapping frequency ($\nu_z$). The black curve is for a continuous rotation motor (Teckceleo). The grey curve is for a stepper motor (New Focus), driven at $2$ kHz.