Resonant Coupling of a Bose-Einstein Condensate to a Micromechanical Oscillator

We report experiments in which the vibrations of a micromechanical oscillator are coupled to the motion of Bose-condensed atoms in a trap. The interaction relies on surface forces experienced by the atoms at about $1\mu \mathrm{m}$ distance from the mechanical structure. We observe resonant coupling to several well-resolved mechanical modes of the condensate. Coupling via surface forces does not require magnets, electrodes, or mirrors on the oscillator and could thus be employed to couple atoms to molecular-scale oscillators such as carbon nanotubes.

Figure 1

(a) Micro-cantilever on a chip with wires for magnetic trapping of atoms. Cantilever vibrations can be independently probed with a readout laser [19]. (b) Photograph of the atom chip showing the magneto-optical trap (MOT) loading region and the cantilever subassembly with a piezo for cantilever excitation. Rectangle: region shown in (a). (c) Potential $U=U_m+U_s$ for trap parameters as in Fig. 3a. Dashed red line: magnetic potential $U_m$. The surface potential $U_s$ reduces the trap depth to $U_0$. Cantilever oscillations modulate the potential, thereby coupling to atomic motion. Gray lines: $U$ during the extremum positions of the cantilever for an oscillation amplitude $a=120\mathrm{nm}$. Blue line: BEC chemical potential ${\mu }_c$ for 600 atoms.

Figure 2

Fraction $\chi$ of atoms remaining in the trap after $t_h=1\mathrm{ms}$ at distance $d$ from the cantilever surface. Blue (red) data points correspond to a trap with ${\omega }_z/2\pi =10.0\mathrm{kHz}$ (5.1 kHz). Solid lines: fit with a simple model [11, 19]. The extracted cantilever position is shown.

Figure 3

(a) Remaining atoms after $t_h=3\mathrm{ms}$ in a trap with ${\omega }_z/2\pi =10.5\mathrm{kHz}$ at $d=1.5\mu \mathrm{m}$ from the driven cantilever, for varying drive frequency ${\omega }_p$. The dark (light) blue circles correspond to a cantilever amplitude $a=120\mathrm{nm}$ (50 nm) on resonance. Solid lines: Lorentzian fits with 6 Hz FWHM, corresponding to the width of the cantilever resonance. (b) and (c) Contrast $C$ and signal to noise ratio SNR of the observed atomic signal as a function of $d$, for constant $a=90\mathrm{nm}$ and ${\omega }_p={\omega }_m$. Blue (red) data points correspond to ${\omega }_z/2\pi =10.5\mathrm{kHz}$ (5.0 kHz) and $t_h=3\mathrm{ms}$ (20 ms).

Figure 4

Top graph: BEC response as a function of ${\omega }_z$ for constant $a=180\mathrm{nm}$ and $t_h=20\mathrm{ms}$ (dark blue). Data points are connected to guide the eye. Light blue: reference measurement without piezo excitation. We observe two major resonances at ${\omega }_m={\omega }_z$ and ${\omega }_m=2{\omega }_z$, up to four smaller ones (green arrows), and reproducible antiresonances (red arrows). Because of cantilever aging, ${\omega }_m/2\pi =9.68\mathrm{kHz}$ in this measurement. Bottom graph: Set values of $d$, chosen such that $N_r({\omega }_z)\approx \mathrm{const}$ ($N_r(10\mathrm{kHz})=700$, $N_r(5\mathrm{kHz})=1100$) and $N_a$ does not saturate.