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Investigation of fast light effect for gravitational wave detection and related applications to precision metrology

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Optical interferometers and resonators are commonly used for precision measurement. These devices can accurately measure the phase shifts of light induced by small changes in the optical path in the device. To meet the need for ultra-sensitive measurement, researchers have developed various approaches to build better and more sensitive devices. Here we explore application of the fast light effect, which means that the group velocity of light is faster than the vacuum speed of light, to such devices, considering both active and passive versions of the resonators. The advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) was able to make the first direct detection of gravitational wave in 2016, and made five more observations later. However, these events are the most violent cosmological phenomena. This is just the beginning of the gravitational wave astronomy. There is still interest in building a better detector to detect weaker signals and signals farther away. In this thesis, we investigate schemes for improving the sensitivity of gravitational wave detector using fast light or white light cavity effect. In a white light cavity, a broader range of frequencies are resonant without any increase in the cavity loss compared to an empty cavity. Specifically, we propose and analyze two schemes, coupled-cavity signal-recycling scheme and white-light-cavity signal-recycling scheme, using a cavity that contains a dispersive medium for signal recycling. The additional dispersion compensates the original positive dispersion in the system including the optomechanical effects and therefore generates the white light cavity effect. Following the two photon formalism, we show that the quantum noise limited sensitivity-bandwidth product of the detector can be enhanced by a factor of ~20. Furthermore, we propose two possible ways to implement the negative dispersion medium which is also required to add minimal additional noise to the detector. In the first implementation, we make use of the non-degenerate Zeeman sublevels in cold Rb atoms. However, the aLIGO operates at 1064 nm, and suitable transitions in Rb or other alkali atoms are not available at this wavelength. In the other implementation, we use a microresonator that supports optomechanical interaction at the wavelength of 1064nm. However, with the parameters required for the sensitivity enhancement, the optomechanical system enters an instability region where the control field is depleted. To stabilize the system, we present an observer-based feedback control process. For the noise analysis of atomic systems used as the NDM, we develop a master equation method for rigorously determining the quantum noise of a field interacting with a complex atomic system. We consider different types of atomic systems, which illustrate a wide range of variations in the degree of disagreement between the predictions of the Caves model and the master equation approach. In the rest part of the thesis, we investigate the fast light enhancement in active resonators, in which the cavity itself contains an active gain medium. We first develop the fast-light enhanced Brillouin laser based active fiber optic sensor (AFLIFOS) that can perform simultaneously or separately as a gyroscope and as a sensor for strain and other common mode effects. Two Brillouin lasers are counterpropagating in the primary fiber resonator, and are separated in frequency by 12 times the free spectral range. The superluminal effects are produced by coupling two auxiliary resonators to the primary resonator. We optimize the parameters of the system and show that under the optimized condition, when the effective change in the length of the primary resonator is 0.1pm, corresponding to a rotation rate of 1.410-3 deg/sec, the enhancement factor of the sensitivity is ~8.2103. We also investigate the superluminal laser gravitational wave detector, which makes use of a pair of orthogonally oriented superluminal lasers. Here an active resonator is used instead of the interferometer which is fed by an external laser, and a gain medium whose effective index as a negative dispersion is used to produce the sensitivity enhancement. The beat frequency of the two lasers tracks the amplitude of the GW signal, if the response time of the cavity to a change in the cavity length is shorter than the period of the GW. Using a 10m long superluminal laser with an effective group index of 10-4, the detector can achieve a quantum noise limited sensitivity similar or smaller than the current Advanced LIGO.

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