Converting the signal-recycling cavity into an unstable optomechanical filter to enhance the detection bandwidth of gravitational-wave detectors

Joe Bentley, Philip Jones, Denis Martynov, Andreas Freise, and Haixing Miao

Phys. Rev. D 99, 102001 – Published 14 May 2019

Abstract

Current and future interferometeric gravitational-wave detectors are limited predominantly by shot noise at high frequencies. Shot noise is reduced by introducing arm cavities and signal recycling, however, there exists a trade-off between the peak sensitivity and bandwidth. This comes from the accumulated phase of signal sidebands when propagating inside the arm cavities. One idea is to cancel such a phase by introducing an unstable optomechanical filter. The original design proposed in [Phys. Rev. Lett. 115, 211104 (2015)] requires an additional optomechanical filter coupled externally to the main interferometer. Here we consider a simplified design that converts the signal-recycling cavity itself into the unstable filter by using one mirror as a high-frequency mechanical oscillator and introducing an additional pump laser. However, the enhancement in bandwidth of this new design is less than the original design given the same set of optical parameters. The peak sensitivity improvement factor depends on the arm length, the signal-recycling cavity length, and the final detector bandwidth. For a 4 km interferometer, if the final detector bandwidth is around 2 kHz, with a 20 m signal-recycling cavity, the shot noise can be reduced by 10 decibels, in addition to the improvement introduced by squeezed light injection. We also find that the thermal noise of the mechanical oscillator is amplified at low frequencies relative to the vacuum noise, while having a flat spectrum at high frequencies.

Received 20 March 2019

DOI:https://doi.org/10.1103/PhysRevD.99.102001

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Gravitational wave detection Optomechanics Quantum fluctuations & noise Quantum optics

Gravitation, Cosmology & AstrophysicsAtomic, Molecular & Optical

Authors & Affiliations

Joe Bentley, Philip Jones, Denis Martynov, Andreas Freise, and Haixing Miao

Institute for Gravitational Wave Astronomy, School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom

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Vol. 99, Iss. 10 — 15 May 2019

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Images

Figure 1
Figure (a) shows a reflection-readout design such as in [43]. The unstable filter alone is highlighted by the blue dashed box. Figure (b) shows the new transmission-readout setup proposed in this paper. The signal recycling cavity is pumped with laser light at $ω_{0} + ω_{m}$ , and the mirror above the signal recycling mirror is mechanically suspended with mechanical resonance frequency $ω_{m}$ . ETM: End Test Mass, ITM: Input Test Mass, SRM: Signal Recycling Mirror, iSRM: Internal SRM (to form an impedance-matched cavity with the ITM)
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Figure 2
Figure (a) shows the peak sensitivity improvement ratio of the transmission-readout setup to a tuned signal-recycled Michelson interferometer as a function of broadened detector bandwidth $Γ_{detector}$ as given in Eq. (30). Here advanced LIGO parameters are used (4 km arm length, 40 kg test mass, 800 kW arm power), and additionally an ITM transmissivity of 0.045 and SRM transmissivity of 0.0003 are used. The SRC length solved for the detector bandwidth is also plotted to show how it could be varied to improve the peak sensitivity with these transmissivities. The dotted line is plotted for our chosen SRC length of 20 m, giving a detector bandwidth of around 1790 Hz, and therefore an enhancement factor of 10 dB. The circled value and inset highlights the chosen values used in figure (b), which shows the total quantum noise with the unstable filter mirror at zero temperature. The tuned Michelson bandwidth set to the effective bandwidth of the new transmission readout setup as discussed at the end of Sec. 3. We also assume 10 dB frequency-dependent squeezing over the entire frequency range as outlined in [16].
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Figure 3
Figure showing the setup analyzed in Sec. 3, which is a simplified version of Fig. 1. $\hat{a}$ describes the unstable filter cavity mode, $\hat{A}$ describes the differential arm cavity mode, $\hat{b}$ is the mirror oscillation mode, $h$ is the GW strain signal, and the mirror is coupled to an external heat bath described by the continuum field ${\hat{b}}_{th}$ , shown by the dotted line. The cavity field $\hat{a}$ is coupled to the external continuum fields ${\hat{a}}_{in}$ , ${\hat{a}}_{out}$ .
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Figure 4
Surface plot showing the peak sensitivity improvement power ratio of the transmission-readout setup to a tuned Michelson as a function of both detector bandwidth $Γ_{detector}$ and arm length, showing the (log) inverse cube-root dependence of the enhancement factor on the arm length. The parameters are as in Fig. 2.
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Figure 5
Figure showing the total quantum noise of the transmission-readout setup after including the thermal noise at various environmental temperatures, using the parameters in Fig. 2, including the detector bandwidth marked by the green star. At low frequencies the thermal noise is amplified relative to the vacuum noise, while at high frequencies it has a flat spectrum.
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Figure 6
Figure showing an example of the local sensing control scheme applied to the transmission-readout setup. A control force $f_{c} (t)$ is applied to the mechanically suspended mirror, whose displacement is read out by the local sensing laser. The local sensing readout and main readout are optimally combined by coefficients $k_{1}$ and $k_{2}$ to recover the bandwidth broadened sensitivity.
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