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Current laser-interferometric gravitational wave detectors suffer from a fundamental limit to their precision due to the displacement noise of optical elements contributed by various sources. Several schemes for Displacement-Noise Free Interferometers (DFI) have been proposed to mitigate their effects. The idea behind these schemes is similar to decoherence-free subspaces in quantum sensing i.e. certain modes contain information about the gravitational waves but are insensitive to the displacement noise. In this paper we derive quantum precision limits for general DFI schemes, including optimal measurement basis and optimal squeezing schemes. We introduce a triangular cavity DFI scheme and apply our general bounds to it. Precision analysis of this scheme with different noise models shows that the DFI property leads to interesting sensitivity profiles and improved precision due to noise mitigation and larger gain from squeezing. Further extensions of this scheme are presented.

Several complicated non-linear models exist which simulate the physical processes leading to fluctuations in global climate. Some of these more advanced models use observations to constrain various parameters involved. However, they tend to be very computationally expensive. Also, the exact physical processes that affect the climate variations have not been completely comprehended. Therefore, to obtain an insight into global climate, we have developed a physically motivated reduced climate model. The model utilizes a novel mathematical formulation involving a non-linear delay differential equation to study temperature fluctuations when subjected to imposed radiative forcing. We have further incorporated simplified equations to test the effect of speculated mechanisms of climate forcing and evaluated the extent of their influence. The findings are significant in our efforts to predict climate change and help in policy framing necessary to tackle it.