This paper presents a novel optomechanical system that achieves strong dispersive coupling between a high-finesse optical cavity and a micromechanical membrane. The system uses a 50 nm thick dielectric membrane placed between two rigid, high-finesse mirrors, allowing for direct measurement of the membrane's displacement and enabling quantum state readout. The cavity detuning is proportional to the membrane's displacement, and the system avoids compromising either the optical or mechanical properties of the components. This approach allows for the measurement of the membrane's energy eigenstate and enables the observation of quantum jumps in mechanical systems. The system is designed to overcome two major challenges in optomechanics: integrating sensitive micromechanical elements into high-finesse cavities and reading out the mechanical element's quantum state. The membrane's displacement is measured through the cavity's frequency shift, which is a periodic function of the membrane's position. This allows for a direct measurement of the square of the membrane's displacement, enabling the determination of its energy eigenstate. The system demonstrates strong optomechanical coupling, achieving laser cooling of the membrane's Brownian motion by a factor of 400. The effective temperature of the membrane is measured using the power spectral density of its motion, and the results show a temperature of 6.82 mK, a factor of 4.4 × 10⁴ below the initial temperature of 294 K. The system's performance is limited by thermal excitations, with small corrections due to the rotating wave approximation and imperfect positioning of the membrane. The paper also discusses the feasibility of observing quantum jumps in the membrane using the system. The signal-to-noise ratio for observing a quantum jump is calculated based on the cavity frequency shift per phonon, the sensitivity of the cavity frequency measurement, and the lifetime of a phonon-number state. The results show that the system can achieve a signal-to-noise ratio of approximately 1, making it feasible to observe quantum jumps. The system's design allows for the measurement of the membrane's phonon number eigenstate using a quantum nondemolition (QND) readout. This is achieved by monitoring the optical cavity's detuning, which is proportional to the square of the membrane's displacement. The system's parameters, including the membrane's reflectivity and position, are optimized to ensure high sensitivity and low noise. In conclusion, the paper presents a novel optomechanical system that resolves key technical challenges in optomechanics and enables the observation of quantum effects in mechanical systems. The system's design allows for the measurement of the membrane's energy eigenstate and the observation of quantum jumps, making it a significant advancement in the field of quantum optomechanics.This paper presents a novel optomechanical system that achieves strong dispersive coupling between a high-finesse optical cavity and a micromechanical membrane. The system uses a 50 nm thick dielectric membrane placed between two rigid, high-finesse mirrors, allowing for direct measurement of the membrane's displacement and enabling quantum state readout. The cavity detuning is proportional to the membrane's displacement, and the system avoids compromising either the optical or mechanical properties of the components. This approach allows for the measurement of the membrane's energy eigenstate and enables the observation of quantum jumps in mechanical systems. The system is designed to overcome two major challenges in optomechanics: integrating sensitive micromechanical elements into high-finesse cavities and reading out the mechanical element's quantum state. The membrane's displacement is measured through the cavity's frequency shift, which is a periodic function of the membrane's position. This allows for a direct measurement of the square of the membrane's displacement, enabling the determination of its energy eigenstate. The system demonstrates strong optomechanical coupling, achieving laser cooling of the membrane's Brownian motion by a factor of 400. The effective temperature of the membrane is measured using the power spectral density of its motion, and the results show a temperature of 6.82 mK, a factor of 4.4 × 10⁴ below the initial temperature of 294 K. The system's performance is limited by thermal excitations, with small corrections due to the rotating wave approximation and imperfect positioning of the membrane. The paper also discusses the feasibility of observing quantum jumps in the membrane using the system. The signal-to-noise ratio for observing a quantum jump is calculated based on the cavity frequency shift per phonon, the sensitivity of the cavity frequency measurement, and the lifetime of a phonon-number state. The results show that the system can achieve a signal-to-noise ratio of approximately 1, making it feasible to observe quantum jumps. The system's design allows for the measurement of the membrane's phonon number eigenstate using a quantum nondemolition (QND) readout. This is achieved by monitoring the optical cavity's detuning, which is proportional to the square of the membrane's displacement. The system's parameters, including the membrane's reflectivity and position, are optimized to ensure high sensitivity and low noise. In conclusion, the paper presents a novel optomechanical system that resolves key technical challenges in optomechanics and enables the observation of quantum effects in mechanical systems. The system's design allows for the measurement of the membrane's energy eigenstate and the observation of quantum jumps, making it a significant advancement in the field of quantum optomechanics.