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Mitigating nonlinear transduction noise in high-cooperativity cavity optomechanics

Daniel Allepuz-Requena, Zohran Ali, Dennis Høj, Yingxuan Chen, Luiz Couto Correa Pinto Filho, Alexander Huck, Ulrik L. Andersen

Abstract

Coupling mechanical motion to an optical resonator enables displacement measurements approaching the standard quantum limit (SQL). However, increasing the optomechanical coupling strength will inevitably lead to probing of the nonlinear response of the optical resonator. Thermal intermodulation noise (TIN) arising from the nonlinear mixing of thermomechanical motion can further increase the imprecision well above the SQL and has hitherto been canceled up to second order of nonlinearity via operation at the "magic detuning". In this work, we record the output of a membrane-in-the-middle microcavity system operating at room temperature and achieving high cooperativity, $C>n_\text{th}$, and apply a nonlinear transform that removes all orders of TIN, improving the mechanical signal-to-noise ratio by nearly 10 dB. Our results can be applied to experiments affected by third-order TIN, which we expect to be the dominating intrinsic source of noise in high-cooperativity room-temperature cavity optomechanical systems.

Mitigating nonlinear transduction noise in high-cooperativity cavity optomechanics

Abstract

Coupling mechanical motion to an optical resonator enables displacement measurements approaching the standard quantum limit (SQL). However, increasing the optomechanical coupling strength will inevitably lead to probing of the nonlinear response of the optical resonator. Thermal intermodulation noise (TIN) arising from the nonlinear mixing of thermomechanical motion can further increase the imprecision well above the SQL and has hitherto been canceled up to second order of nonlinearity via operation at the "magic detuning". In this work, we record the output of a membrane-in-the-middle microcavity system operating at room temperature and achieving high cooperativity, , and apply a nonlinear transform that removes all orders of TIN, improving the mechanical signal-to-noise ratio by nearly 10 dB. Our results can be applied to experiments affected by third-order TIN, which we expect to be the dominating intrinsic source of noise in high-cooperativity room-temperature cavity optomechanical systems.
Paper Structure (6 sections, 17 equations, 7 figures)

This paper contains 6 sections, 17 equations, 7 figures.

Table of Contents

  1. Introduction
  2. The nonlinear transduction regime
  3. Membrane-in-the-middle of a microcavity
  4. Observation of third order thermal intermodulation noise
  5. Position readout in the nonlinear regime
  6. Conclusions

Figures (7)

  • Figure 1: Dispersive transduction of mechanical motion in a membrane-in-the-middle cavity. (a) In the fast-cavity limit, the intracavity field $a$ adiabatically follows relative detuning fluctuations $\delta\nu$ around the equilibrium $\nu_0$. $\delta\nu$ is caused by linear optomechanical coupling of the membrane's displacement $x$ according to Eq. \ref{['eq:dispersive_coupling']}. The reflected $a_\text{refl.}$ or transmitted $a_\text{tran.}$ field are used to infer $a$ and therefore $\delta \nu$. (b) Depending on the magnitude of the detuning fluctuations, their transduction into cavity occupation $n_\mathrm{c}=\abs{a}^2$ can be approximately linear, nonlinear but unambiguous or, deeply nonlinear and ambiguous.
  • Figure 2: (a) Photograph of the microcavity membrane-in-the-middle (MIM) system. (b) Vertical optical microscope picture, orange dashed line: bottom mirror phononic cell, blue solid line: top mirror phononic cell, red circle: concave micromirror in top substrate, green hexagon: defect in the density phononic membrane. (c) Schematic profile view of the stack forming the MIM system. The membrane's substrate (label 2) and the bottom mirror (label 3) are etched along the same crystalline planes (100) and (101).
  • Figure 3: (a) Experimental setup. ECDL: external cavity diode laser, UHV: ultra high vacuum chamber, PD: photodetector, PID: proportional-integral-derivative controller that adjusts the laser's cavity, ADC: analog-to-digital converter used to record time traces. (b) Left: photocurrent power spectral density (PSD). Right: In situ ringdown measurement of the quality factor of the mechanical resonator. Measured energy (blue) is fit with a model with linear and nonlinear damping (orange). (c) Scan of the laser frequency across the optical resonance at $1572\nm$. The model consists of a Lorentzian resonance with central frequency modulated by two sinusoidal signals of $1.13MHz$ (mode of interest) and $110kHz$ (out-of-bandgap mode). (d) Cavity linewidth (blue, left-hand axis) and single-photon optomechanical rate (orange, right-hand axis) at the accessible HG$_{00}$ optical resonances. (e) Photocurrent PSD measured at increasing detuning with constant intracavity power (1571nm optical resonance). The change in oscillation frequency is fit with a model of optical spring effect.
  • Figure 4: (a) Relative intensity noise (RIN) spectrum of the detected transmission with $C\simeq n_\mathrm{th}$. Orange dashed line: fit with extraneous amplitude noise model. (b) Transmission RIN spectra at the magic detuning at different cooperativities. Dashed white line: spectrum displayed in (a). (c) Relative root mean square (RMS) noise in the frequency range of the membrane mechanical bandgap. Green solid line represents the expected behavior in the absence of technical noise.
  • Figure 5: Nonlinearity measures computed from a direct detection spectrum (top plot, dashed region in Fig. \ref{['fig:PSDs']}(b)). The nonlinearity measures of second-order (second to third plot) and third-order (fourth to bottom plot) have been normalized to their maximum value in the frequency span displayed.
  • ...and 2 more figures