Abstract
Proposed near-future upgrades of the current advanced interferometric gravitational wave detectors include the usage of frequency dependent squeezed light to reduce the current sensitivity-limiting quantum noise. We quantify and describe the degradation effects that spatial mode-mismatches between optical resonators have on the squeezed field. These mode-mismatches can to first order be described by scattering of light into second-order Gaussian modes. As a demonstration of principle, we also show that squeezing the second-order Hermite-Gaussian modes $\mathrm{HG}_{02}$ and $\mathrm{HG}_{20}$, in addition to the fundamental mode, has the potential to increase the robustness to spatial mode-mismatches. This scheme, however, requires independently optimized squeeze angles for each squeezed spatial mode, which would be challenging to realise in practise.
Highlights
The current advanced gravitational-wave detectors, e.g., the Advanced LIGO [1] detectors, are dual-recycled Michelson interferometers with arm cavities, as shown in figure 1
We show the quantum noise limited sensitivity for various levels of mode-mismatches between the interferometer and the filter cavity, while keeping the squeezer mode matched to the filter cavity
If a higher-order mode involved in this process picks up a different phase than the fundamental mode when reflected off the filter cavity, this mode-mismatch enables for potentially anti-squeezed states to mix in with the squeezed states—which would be worse than just a loss
Summary
The current advanced gravitational-wave detectors, e.g., the Advanced LIGO [1] detectors, are dual-recycled Michelson interferometers with arm cavities, as shown in figure 1. In this case, there are scattering points (spatial basis changes) before and after the filter cavity, which allows the squeezed states to coherently scatter to higher-order modes and back to the fundamental mode. If a higher-order mode involved in this process picks up a different phase than the fundamental mode when reflected off the filter cavity, this mode-mismatch enables for potentially anti-squeezed states to mix in with the squeezed states—which would be worse than just a loss This coherent scattering effect can be seen in figure 3 at low frequencies where the fundamental mode is near-resonant while the higher-order modes are off resonance, and at the two local peaks where the second and fourth order modes are resonant while the fundamental mode is off resonance. For practical implementation it would require a more detailed study and experimental demonstration
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