Tunable Cavity Optomechanics with Ultracold Atoms

We present an atom-chip-based realization of quantum cavity optomechanics with cold atoms localized within a Fabry-Perot cavity. Effective subwavelength positioning of the atomic ensemble allows for tuning the linear and quadratic optomechanical coupling parameters, varying the sensitivity to the displacement and strain of a compressible gaseous medium. We observe effects of such tuning on cavity optical nonlinearity and optomechanical frequency shifts, providing their first characterization in the quadratic-coupling regime.

Figure 1

An atom chip is used to transport and position atoms within a Fabry-Perot cavity, where they act as a compressible mechanical element for studies of cavity optomechanics. A cutaway cross section shows the profile of the chip, with copper wires shown in gray.

Figure 2

The atom-induced shift of the cavity resonance at low probe power varies sinusoidally (fit shows contrast of 0.77) with the central atomic position $z_0$. Panels show estimated atomic distributions (gray), relative to the lattice trap potential (red line, top) and cavity probe intensity (blue line, bottom), at maximum linear (left) or quadratic (right) coupling. Here $N=3500$, ${\Delta }_{\mathrm{ca}}/2\pi =-6\mathrm{GHz}$, ${\omega }_z/2\pi =70\mathrm{kHz}$.

Figure 3

Intracavity photon number $\overline{n}$ (or ratio of probe-to-trap curvatures $\eta$) for probe light swept with positive (lighter lines) or negative (darker lines) chirps. Single-shot measurements for four probe powers are shown, with ${\varphi }_0=0$ (blue), $\pi /4$ (red), or $\pi /2$ (green). Horizontal scales are adjusted to account for a 2% loss of atoms between sweeps. Gray traces show measurements for an empty cavity. Pronounced cavity nonlinearity is observed at $\overline{n}\simeq 1$ (input power around 5 pW). Here $N=5400$, ${\Delta }_{\mathrm{ca}}/2\pi =-14\mathrm{GHz}$, and ${\omega }_z/2\pi =32\mathrm{kHz}$. Top graph shows self-consistent solutions for $\overline{n}$ calculated from known experimental parameters. Gray bars show regions of bistability in which two stable cavity and cantilever states are accessible at the same probe power and frequency. The expected line shapes at $\varphi =\pi /2$ for probes with positive and negative chirps are indicated.

Figure 4

Probe-induced shift of the cavity resonance versus the probe-to-trap curvature ratio $\eta$, measured for ${\varphi }_0=0$ (blue triangles, dashed line), ${\varphi }_0=\pi /4$ (red squares, solid line), and ${\varphi }_0=\pi /2$ (green diamonds, dot-dashed line). Representative statistical error bars are shown. The behaviors at the node and antinode are interchanged as the probe potential changes from attractive (${\Delta }_{\mathrm{ca}}/2\pi =-8\mathrm{GHz}$) to repulsive (${\Delta }_{\mathrm{ca}}/2\pi =+8\mathrm{GHz}$). The systematic discrepancy between measurements and theory (lines) arises from atom loss during the measurement; such heating and error are minimized at ${\varphi }_0=0$.

Figure 5

Optomechanical frequency shifts. Top: The mechanical oscillation frequency determined via parametric heating reveals the static frequency shift from quadratic optomechanical coupling; here, ${\Delta }_{\mathrm{ca}}/2\pi =-20.1\mathrm{GHz}$, ${\omega }_z/2\pi =58.5\mathrm{kHz}$, and $\overline{n}=0.8$. Bottom: The oscillation frequency for the linearly coupled mode is derived from the cavity transmission intensity spectrum; here, ${\Delta }_{\mathrm{ca}}/2\pi =-40\mathrm{GHz}$, ${\omega }_z/2\pi =58.9\mathrm{kHz}$, $\overline{n}=3.5$, and $N=3750$. Inset shows this frequency at ${\varphi }_0=\pi /4$ for varying detuning $\Delta$ from the cavity resonance. Solid lines show predictions calculated with no free parameters.