Realization of an Optomechanical Interface Between Ultracold Atoms and a Membrane

We have realized a hybrid optomechanical system by coupling ultracold atoms to a micromechanical membrane. The atoms are trapped in an optical lattice, which is formed by retroreflection of a laser beam from the membrane surface. In this setup, the lattice laser light mediates an optomechanical coupling between membrane vibrations and atomic center-of-mass motion. We observe both the effect of the membrane vibrations onto the atoms as well as the backaction of the atomic motion onto the membrane. By coupling the membrane to laser-cooled atoms, we engineer the dissipation rate of the membrane. Our observations agree quantitatively with a simple model.

Figure 1

Optomechanical coupling of atoms and membrane. A laser beam of power $P$ is partially reflected at a SiN membrane of reflectivity $\mathfrak{r}$ and forms a 1D optical lattice for an ultracold atomic ensemble. Motion of the membrane displaces the lattice and thus couples to atomic motion. Conversely, atomic motion is imprinted as a power modulation $\Delta P$ onto the laser, thus modulating the radiation pressure force on the membrane. $\mathfrak{t}$ is the transmittivity of the optics between atoms and membrane. Arrows illustrate the direction of forces and displacements at a specific point in time. In the main text, all forces and displacements are positive if pointing to the right.

Figure 2

Experimental setup. The lattice laser is fiber coupled, power stabilized with a proportional and integral (PI) regulator and an acousto-optic modulator (AOM), and focused into the MOT vacuum chamber. The membrane in a second room-temperature vacuum chamber serves as a partially reflective end mirror for the 1D optical lattice. The membrane motion is read out with a Michelson interferometer. The two lasers are separated with a half-wave plate (WP), a polarizing beam splitter (PBS), and a dichroic mirror (DM). The interferometer signal from the photodetector (PD) is frequency split: the low-frequency part (LP) is used for interferometer stabilization; the high-frequency part (HP) including the membrane signal is used for readout and a piezo transducer (PZT) feedback drive of the membrane. The membrane amplitude is measured with a lock-in amplifier and an oscilloscope. When driven, it is stabilized with a PI regulator and a voltage controlled amplifier (VCA) in the feedback loop ($\Delta \phi$: phase shift).

Figure 3

Backaction of laser-cooled atoms onto the membrane. Top: Measured additional membrane dissipation rate $\Delta \gamma =\Gamma -{\gamma }_m$ due to coupling to atoms as a function of $P$. The rates $\Gamma$ and ${\gamma }_m$ are extracted from exponential fits to averaged decay curves ($2\times 455$ experimental runs per data point). Solid line: Theory for a thermal ensemble in the lattice (see text). Bottom: Lattice atom number in the experiment.

Figure 4

Measured additional membrane dissipation $\Delta \gamma$ as a function of the atom number for resonant coupling ($P=76\mathrm{mW}$). The line is a linear fit. The observed dependence agrees well with theory. Inset: Histogram of measurements of $\Gamma$ for $N=2.3\times {10}^6$ (right) and $N=0$ (left).

Figure 5

Effect of membrane vibrations on the atoms when laser cooling is off. Top: Temperature increase of the atoms along the lattice $\Delta T_{\mathrm{ax}}$ and in the radial direction $\Delta T_{\mathrm{rad}}$ for a driven membrane with respect to reference measurements for an undriven membrane. Bottom: Dependence of the lattice atom number on $P$, for driven ($N$) or undriven ($N_{ref}$) membranes, respectively.