Advanced gravitational wave interferometers typically take the form of resonant Michelson interferometers operated on a dark fringe. These arrangements are specifically configured to reject quantum and technical noise from the driving ports and be maximally sensitive in their di↵erential mode of operation. The corollary of this is that detectors are maximally sensitive to disturbances from the ‘dark’ readout port. Vacuum fluctuations entering through the readout port drive the quantum noise of the interferometer. Likewise, detectors are maximally sensitive to stray scattered light entering through this port. Injections of vacuum squeezed states to pre correlate quadratures have demonstrated improvements to sensitivity by 2 -3 dB [66, 123, 124]. Importantly for applications to advanced detectors such squeezed light sources must minimise environmental disturbances from sources such as scattered light in the key audio band (10 Hz -10 kHz). For this reason travelling wave optical parametric oscillators are a strong candidate for squeezing sources as they o↵er up to 41 dB of scattered light suppression [85]. However, schemes for squeezing injection require further isolation, usually met by the inclusion of Faraday type isolators to provide isolation at the cost of degradation of squeezing purity through the introduction of forward propagating loss.
An active path length dither strategy o↵ers one potential route to shifting sources of backscatter within a squeezing generation path out of the detection band of interest. Such a scheme would, as introduced in section 8.3, modulate the entire path length of the light squeezing apparatus in such a way that squeezing quadratures remain fixed. Scattering sources from within the squeezing apparatus that interact with only one of the dithering mirrors will be frequency shifted. If scattered light components can be e↵ectively removed with an active upshifting technique, stringent power isolation requirements (with Faraday isolators) may be relaxed. This will reduce the need for lossy isolation optics, improving the purity of squeezed state delivered to the interferometer. Such a scheme must deliver squeezing such that the modulation implementation does not introduce additional phase noise to the injected squeezing. A possible improvement would utilises a common modulation element for the pump and output squeezed light (such as bouncing o↵ opposite sides of a modulation mirror) or the implementation a control scheme to match modulation depths to reduce phase dither residuals between two modulation depths.
8.5
Chapter summary
We have shown a proof of principle experiment for recovering audio band frequency squeez- ing with a technique for actively shifting sources of scatter noise. The peak scattering noise contribution at low frequency is reduced by 20 dB, giving a significant improvement in the
Conclusions and Further Work
The theme of this thesis has been quantum noise reduction in interferometric gravitational wave detectors. There have been two principle focuses: the first, on instrument designs for speed meter broadband quantum non-demolition measurement; and the second, on the engineering of prepared squeezed states of light suitable for injection into existing power and signal recycled Michelson interferometers. This chapter provides a brief summary of results of theoretical and experimental investigations and proposes a number of future goals and investigations.
9.1
Summary of polarisation speed meter modelling
A theoretical investigation of a polarisation folded speed meter was carried out, inspired by the external sloshing cavity speed meter proposed by Purdue and Chen [22]. There an external long-baseline (⇠4 km) Fabry-P´erot cavity (the ‘sloshing’ cavity’) was installed at the output of a power- and signal-recycled Michelson interferometer. Signals below the sloshing cavity’s pole were cancelled in such a way as to make the instrument’s radiation pressure coupling response constant in frequency. Radiation pressure back-action could then be cancelled over a broad frequency band by judicious choice of readout quadrature. In this work, we proposed to fold this long-baseline Fabry-P´erot into the existing arm cavities of the interferometer on an unused orthogonal polarisation. By recycling signals into an orthogonal storage mode (that is not driven by a coherent field), an additional piece of infrastructure may be avoided also obviating the need to also control its length and alignment.
Two polarisation speed meter schemes were proposed:
• The first was a fixed polarisation coupling regime. In this setup a quarter-wave plate element was installed within the signal recycling cavity of an arm-cavity signal- recycled Michelson. The angle of the wave plate was fixed at a 45 orientation to the carrier light. With optimisation of the arm cavity input test mass transmissivity (relative to the signal recycling mirror) for optimal signal extraction rate, it was shown that the standard quantum limit of the instrument could be matched or beaten by a factor of four.
• The second was a variable coupling scheme, in which the quarter-wave plate could be smoothly rotated from a 45 orientation to 0 from the carrier polarisation. The e↵ective coupling between the polarisations could therefore be dynamically tuned. This allowed for a smooth tuning from quantum non-demolition speed-meter mode to that of a signal recycled Michelson. For modelling of the strain referenced quantum
noise parameters were selected to be close to the Advanced LIGO design. With 850 kW of circulating power and parameters close to the Advanced LIGO mirror mass (40 kg) and baseline length (⇠4km), the strain referenced quantum noise matched the standard quantum limit when at full coupling 45 giving optimal broadband operation. For weaker polarisation coupling, the high frequency sensitivity could be sacrificed for up to an 8 dB factor of improvement below 10 Hz. As Newtonian and seismic noise is strongly dominant below this frequency for ground based detectors, the principle benefits for speed meter operation would be expected to be in the 10-100 Hz range where interferometer sensitivity could be optimised for targeted measurements.
9.1.1 Further work on polarisation speed meter schemes
The theoretical investigation of the polarisation folded speed meter operating at Advanced LIGO design circulating powers shows promise, as a potential future detector concept, for addressing radiation pressure noise. These complement well the parallel work of Danil- ishinet al. who present a realisation of a Sagnac speed-meter based on polarisation optics in a Michelson-like design [140]. However, the results presented here represent an ideal lossless case and do not address issues of polarisation for real experimental optics. As discussed in §5.5, birefringence at the the Michelson beam splitter is a matter of practical concern. Polarisation purity and the goodness of wave plate retarding optics would all be the subject of any survey of the efficacy of building an experimentally realisable polari- sation folded speed meter. Thus, further work in developing this design concept should involve a feasibility survey outlining necessary polarisation specifications, the viability of polarisation optics operating at high power and an analysis of the impact of loss. This would better ascertain whether this design is a realistic implementation for a generation III iteration of the LIGO interferometer.