Light-Mediated Collective Atomic Motion in an Optical Lattice Coupled to a Membrane

We observe effects of collective atomic motion in a one-dimensional optical lattice coupled to an optomechanical system. In this hybrid atom-optomechanical system, the lattice light generates a coupling between the lattice atoms as well as between atoms and a micromechanical membrane oscillator. For large atom numbers we observe an instability in the coupled system, resulting in large-amplitude atom-membrane oscillations. We show that this behavior can be explained by light-mediated collective atomic motion in the lattice, which arises for large atom numbers, small atom-light detunings, and asymmetric pumping of the lattice, in agreement with previous theoretical work. The model connects the optomechanical instability to a phase delay in the global atomic backaction onto the lattice light, which we observe in a direct measurement.

Figure 1

(a) Optomechanical coupling scheme of atoms in an optical lattice and a micromechanical membrane oscillator in an optical cavity. (b) Modeling the atoms as beam splitters (BSs) allows us to describe light-mediated collective motion of the atoms (see text).

Figure 2

Observation of self-oscillations. (a) Evolution of $⟨x_m^2(t)⟩$ with time for different $N_{\mathrm{lat}}$. Red traces: Lattice is ramped up at $t=50\mathrm{ms}$. Blue trace: Lattice is running at $P_0=3.4\mathrm{mW}$ continuously with $N_{\mathrm{lat}}=0$. Dashed gray: Room temperature level. (b) Total membrane damping rate ${\mathrm{\Gamma }}_{\mathrm{tot}}$ versus $N_{\mathrm{lat}}$. Filled red circles: Data extracted from traces as in (a). Larger red circles: Data points of traces in (a). Empty blue circles: Numerical simulation with exact model with four beam splitters (BS). Empty green diamonds: As blue, but with 2 BS. Empty orange squares: As blue and green, but with only 1 BS. Empty red triangles: Simulation of linearized model with 2 BS fitted to the data. For all four curves, ${\mathrm{\Gamma }}_a=233{\mathrm{s}}^{-1}$ and $\alpha =0.11$. Insets: Simulated displacement $x_i$ of an array of 10 BS as a function of time for $0.3\times {10}^7$ (left) and $8\times {10}^7$ (right) atoms.

Figure 3

Atomic backaction on the lattice light. (a) Amplitude (electrical power) and (b) phase of atomic backaction versus modulation frequency $\mathrm{\Omega }$. Dashed vertical lines: Membrane frequency ${\mathrm{\Omega }}_m/2\pi =276\mathrm{kHz}$ and frequency of the atoms in the center of the trap ${\mathrm{\Omega }}_a(0)/2\pi =450\mathrm{kHz}$. Shaded areas: region in which the coupled system can become unstable if the coupling is strong enough. Inset in (a): Measurement setup. PD: photodiode. Thick dashed (dashed-dotted) lines: Behavior expected from the one-BS model (two-BS model) for $N=3\times {10}^8$, ${\mathrm{\Omega }}_a=2\pi \times 275\mathrm{kHz}$, ${\mathrm{\Gamma }}_a=2\pi \times 150\mathrm{kHz}$, and $R=0.06$. The modeled amplitudes are scaled down by 43 dB to adjust to the data.