Squeezed Light Evades Back-Action in 40-Kilogram Oscillator

Continuous position measurements face a quantum trade-off: reducing readout imprecision generally increases radiation-pressure force noise, and vice versa. In gravitational-wave interferometers, both terms shape sensitivity across much of the observing band. This study uses LIGO’s differential arm motion as a macroscopic test mass, then engineers the quantum state entering the dark port so that the two noise channels become correlated rather than merely competing.

The experiment is unusual because the measured object is not a microfabricated resonator. Feedback turns the differential motion of LIGO’s 40-kg mirrors into a narrow, sub-Hz-linewidth optomechanical mode, placing its resonance in a region where radiation-pressure back-action substantially contributes to motion. The authors report that frequency-dependent squeezing reduces observed displacement near that resonance by about 47% through correlation-driven cancellation.

Core Contribution

The central contribution is an experimental separation of three terms that are often combined in a measured noise spectrum: effective imprecision, effective back-action, and their cross-correlation. Frequency-independent squeezing improves high-frequency imprecision, but it does not supply the frequency-shaped correlation needed to counter radiation pressure at the trapped-mode resonance. Frequency-dependent squeezing does.

That distinction matters for interferometric sensing. Squeezing is already used to lower quantum noise in gravitational-wave detectors, but a broadband reduction in one quadrature does not automatically evade back-action. The paper’s claim is narrower and more useful: by rotating the injected squeezed state with frequency, the measurement can produce a negative correlation term precisely where back-action is most consequential.

Technical Approach

The apparatus combines the arm cavities, signal-recycling cavity, antisymmetric-port readout, and digital feedback acting on the test-mass suspensions. The control loop modifies the nominal differential-arm susceptibility $\chi_0$ into an effective susceptibility $\chi_{\mathrm{eff}}$, creating a trap resonance at 151 Hz while leaving the broadband loop behavior comparatively unchanged away from that narrow feature.

Figure 1 lays out both the optical chain and its equivalent feedback model. Thermal, technical, and radiation-pressure forces drive the mechanical response; interferometric sensing adds measurement imprecision; and the calibrated error signal is digitally filtered and returned as a feedback force. This representation makes clear that the reported cancellation is assessed at the observed-displacement level, after the sensing and feedback dynamics are included.

The authors compare three input states: unmodified vacuum, frequency-independent squeezing, and frequency-dependent squeezing. Their quantum-noise model decomposes the frequency-dependent case into $S_{xx}^{\mathrm{imp}}$, $S_{xx}^{\mathrm{ba}}$, and $S_{xx}^{\mathrm{imp,ba}}$. Cancellation requires the last term to be negative, so that it offsets part of the positive back-action contribution rather than simply redistributing noise between frequencies.

Results and Analysis

The measured spectra cover the trapped-mode region as well as the 40–145 Hz band used to examine the noise model against coating thermal noise. Figure 2 shows that the frequency-dependent configuration falls below both vacuum and frequency-independent squeezing near the resonance. The reported approximately 47% reduction is therefore not just a high-frequency shot-noise improvement: it is localized to the regime where the feedback-defined oscillator has its strongest response.

Figure 3 provides the more diagnostic evidence. Frequency-independent and frequency-dependent squeezing offer similar imprecision reduction at higher frequencies, whereas only the frequency-dependent configuration develops a negative imprecision–back-action correlation over the trapped-mode band. Its cross term cancels part of the inferred back-action term, and the back-action-evasion metric rises over the same range. That alignment between the decomposition, sign of the correlation, and observed resonance suppression supports the mechanism claimed in the paper.

The result is experimentally persuasive because it compares three quantum-state configurations in the same interferometer and tests a model against spectra, not just a single integrated noise number. But its practical scope is narrow. The reported effect is centered on a feedback-created 151 Hz mode rather than demonstrated as a broadband sensitivity improvement for astrophysical searches. It nevertheless establishes a route for using frequency-dependent quantum correlations as an active measurement resource in kilogram-scale optomechanics and future interferometric detectors.