Performance of multiple filter-cavity schemes for frequency-dependent squeezing in gravitational-wave detectors

Abstract

Gravitational-wave detectors use state-of-the-art quantum technologies to reduce the noise induced by vacuum fluctuations, via injection of squeezed states of light. Future detectors, such as Einstein Telescope, may require the use of two filter cavities or a 3-mirror coupled filter cavity to achieve a complex rotation of the squeezing ellipse, in order to reduce the quantum noise over the whole detector bandwidth. In this work, we compare the theoretical feasibility and performances of these two optical layouts and their resilience with respect to different degradation sources (optical losses, mismatching, locking precision), analytically and numerically. We extend previous analysis on squeezing degradation and find that the coupled cavity scheme provides similar or better performances than the two-cavity option, in terms of resilience with respect to imperfections and optical losses. We further highlight the role of mode-mismatch phases in limiting squeezing. Finally, we propose a possible two-step implementation scheme for Einstein Telescope using a single filter cavity that can be possibly upgraded into a coupled filter cavity.

Figures (16)

• Figure 1: Simplified optical scheme for dual-recycled GW interferometer with Frequency-Dependent Squeezing injected through the output port via Faraday cirulator/isolator. Current and future generations of GW detectors use the same simplified scheme, but ET-LF operates in a detuned configuration. Here, for clarity, we represent the arms at a right angle.
• Figure 2: Optical schemes of the two-filter cavity (2FC, top) and coupled filter cavity (CFC, bottom) configurations. Note that, aside from the different cavity configuration, the 2FC differs from the CFC insofar at is requires mode matching lenses between the first filter cavity (FC1) and the second one (FC2), as well as an additional Faraday Isolator (FI).
• Figure 3: Squeezing degradation for the CFC caused by 10% (dashed green) or 20% (dashed red) deviations of the middle mirror's transmission $T_{\text{a}}$, compared to the CFC model with the optimal $T_{\text{a}}$ (solid red) and the two FC case (blue). The sensitivity without squeezing (solid black) is plotted for reference. The 10% and 20% $T_{\text{a}}$ deviations are being partly compensated by adjusting the detunings of the CFC sub-cavities and the injected squeezing angle. Losses are detailed in \ref{['table:params_general']} and \ref{['sec:full_degradation']}. Top: Noise spectral density comparison for a single L-shaped interferometer. Bottom: Quantum enhancement in dB.
• Figure 4: Squeezing degradation for Round Trip Loss per cavity $\Lambda$ for 2FC (solid lines) and CFC (dashed lines), for a total length $L_1 + L_2 = L_a + L_c = 5 \text{km} + 5 \text{km} = 10$ km. From top to bottom: Quantum noise reduction (for 10 dB of input squeezing); Relative quantum noise reduction between CFC and 2FC (a positive value means that CFC performs better than 2FC); the squeezing efficiency $\eta$, the dephasing $\sqrt{\Xi}$ and the misphasing $\Delta \theta_D$.
• Figure 5: Squeezing degradation from quadratic mode mismatch in 2FC (blue, solid envelope) and CFC (red, dashed envelope), for a total length $L_1 + L_2 = L_a + L_c = 5 \text{km} + 5 \text{km} = 10$ km. The blue and orange regions are determined by calculating squeezing curves for the values of $\Upsilon_I$, $\Upsilon_O$, $\Upsilon_{12}$ and $\Upsilon_a$ from \ref{['table:params_general']}, and sweeping the mode mismatch phases ($\psi_{mmO} - \psi_{mmI}$) and ($\psi_{mm12} - \psi_{mmI}$). The inter-cavity mode mismatch 2FC is $\Upsilon_{12} = 0.01$. Some examples of CFC squeezing curves are plotted in orange. From top to bottom: quantum noise reduction with mismatch; ratio of the lower envelopes of CFC to 2FC; efficiency; dephasing; misphasing.