Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation

The shot-noise limited peak sensitivity of cavity-enhanced interferometric measurement devices, such as gravitational-wave detectors, can be improved by increasing the cavity finesse, even when comparing fixed intracavity light powers. For a fixed light power inside the detector, this comes at the price of a proportional reduction in the detection bandwidth. High sensitivity over a large span of signal frequencies, however, is essential for astronomical observations. It is possible to overcome this standard sensitivity-bandwidth limit using nonclassical correlations in the light field. Here, we investigate the internal squeezing approach, where the parametric amplification process creates a nonclassical correlation directly inside the interferometer cavity. We theoretically analyze the limits of the approach and measure 36% increase in the sensitivity-bandwidth product compared to the classical case. To our knowledge, this is the first experimental demonstration of an improvement in the sensitivity-bandwidth product using internal squeezing, opening the way for a new class of optomechanical force sensing devices.

Figure 1

The three curves show the quantum measurement noise of a cavity-enhanced interferometer with the same coherent light power in its arms, normalized to a phase signal optical transfer function. The peak sensitivity $\mathcal{S}$ is defined as inverse of the minimum of the curves; the bandwidth $\mathcal{B}$ is the frequency at which the noise rises by 3 dB above its minimal value. The standard sensitivity-bandwidth product remains constant for a given coherent light power inside the cavity: to increase the peak sensitivity by 6 dB, the finesse $\mathcal{F}$ has to be increased by a factor of 4, thus, the bandwidth decreases by the same amount (compare blue dashed and green dashed-dotted curves). The internal squeezing approach is depicted schematically on the subplot: a phase quadrature of the input coherent light field is squeezed inside the cavity, deamplifying the signal at the same time. Signal deamplification is less than the amount of squeezing on the detector, so the sensitivity increases. Increased amplitude quadrature, according to the QCRB, leads to enhancement of the sensitivity-bandwidth product beyond the standard limit. Therefore, when increasing the peak sensitivity by 6 dB of internal squeezing, the resulting bandwidth is broader (red solid curve) than the one achievable classically.

Figure 2

Experimental setup—The ISC is resonant for both the fundamental wavelength 1550 nm and the second harmonic wavelength 775 nm. Through the highly reflective (HR) back mirror, a beam at 1550 nm is injected carrying a phase modulation signal between 5.5 to 151 MHz and a sideband at 54 MHz for PDH cavity length stabilization. The output signal consisting of squeezed light and deamplified signal sideband is detected on a balanced homodyne detector using 2.8 mW local oscillator (LO) power, with an overall detection efficiency of $\sim 85\%$. The phase of the local oscillator is actively stabilized to the phase quadrature, and the phase of the pump is stabilized to produce squeezing in the phase quadrature.

Figure 3

Beating the standard sensitivity-bandwidth limit with internal squeezing. In the main plot, we demonstrate the increase in the signal-to-noise ratio for a total quantum efficiency of 0.82: squeezing data (green rhomb) with fit (green dashed line), from which the squeezing factor is estimated; the signal deamplification is represented by the red dots. It is compared to the results of the theoretical modeling (black solid line) with parameters obtained from the squeezing measurement, where the grey area represents the confidence interval based on the estimation error. The subplot shows four experimentally achieved enhancement factors (26%, 31%, 33%, 36%) representing four different overall quantum efficiencies, together with theoretical curves versus detected squeeze factor. Two effects are demonstrated: the dependence on the detection efficiency $\eta$ (different curves) and the existence of the optimal squeezing for each set of parameters. The maximal enhancement in the sensitivity-bandwidth product obtained in the experiment is 36% (red solid curve). The data on the main plot corresponds to the green (dotted) curve with 82% detection efficiency and 26% enhancement.