Sub-hertz optomechanically induced transparency with a kilogram-scale mechanical oscillator

Optical interferometers with suspended mirrors are the archetype of all current audio-frequency gravitational-wave detectors. The radiation pressure interaction between the motion of the mirrors and the circulating optical field in such interferometers represents a pristine form of light-matter coupling, largely due to 30 years of effort in developing high-quality optical materials with low mechanical dissipation. However, in all current suspended interferometers, the radiation pressure interaction is too weak to be useful as a resource, and too strong to be neglected. Here, we demonstrate a meter-long interferometer with suspended mirrors, of effective mass $125\mathrm{g}$, where the radiation pressure interaction is enhanced by strong optical pumping to realize a cooperativity of 50. In conjunction with modest resolved-sideband operation, this regime is efficiently probed via optomechanically induced transparency of a weak on-resonant probe. The low resonant frequency and high-Q of the mechanical oscillator allows us to demonstrate transparency windows barely 100 mHz wide at room temperature. Together with a near-unity ($\approx 99.9\%$) out-coupling efficiency, our system saturates the theoretical delay-bandwidth product, rendering it an optical buffer capable of seconds-long storage times.

Figure 1

Experimental system and schematic. (a) Laser light for the experiment is derived from a master-oscillator power amplifier (MOPA) that was developed for Initial LIGO. The 10 W output, at 1064 nm, is spatially filtered by a pre-mode cleaner (PMC); subsequently, its intensity (ISS) and frequency (FSS) are stabilized using respective servos. The light then enters the experimental cavity, whose reflection and transmission are monitored and used for stabilizing the laser-cavity detuning. (b) Left: Picture of the end mirror (EM), consisting of a 1.27 cm diameter mirror, weighing 1 g, suspended as a double pendulum. Right: Picture of the input mirror (IM), consisting of a 7.3 cm diameter mirror, weighing 250 g, suspended as a single pendulum. Inset shows finite-element model of the mirror's fundamental drumhead mode, which is the mechanical oscillator relevant to this work. (c) Simple scheme of optomechanically induced transparency (OMIT). Left shows the bare cavity response (blue), pumped by laser light red-detuned by a mechanical linewidth ($\mathrm{\Delta }=-{\mathrm{\Omega }}_m$), and its two sidebands filtered by the cavity; the radiation-pressure-induced displacement is transduced as additional sidebands (green), which interferes with the injected sidebands. Right shows the resulting effective cavity response.

Figure 2

Sub-hertz optomechanically induced transparency: main figure shows zoom-in of the magnitude (top) and phase response (bottom) of the cavity transmission in a 1 Hz span around resonance at several values of the incident power (legend). Solid lines show model curves. Inset shows the optomechanical cooperativity inferred from the model.

Figure 3

Plot shows delay-bandwidth product in transmission (red) and reflection (blue); dashed lines show models based on Eq. (4). Inset shows the delay in transmission (red) and reflection (blue), with dashed lines showing models based on Eq. (3).

Figure 4

Loop diagram of the OMIT measurement. Red shows optical path, black shows electronic path.

Figure 5

Measured responses of the various elements in the measurement loop.

Figure 6

Example of a wide-band response measurement of the cavity taken at $60\mathrm{mW}$ incident power. The dashed line shows fits. Note that due to the sparse sampling of frequency, the OMIT dip is not visible in such measurements.