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We analyze theoretically both the fundamental and the technical quantum limitations of the sensitivity of a passive resonant optical gyroscope based on a high finesse monolithic optical microcavity. We show that the quantum back action associated with the resonantly enhanced optical cross- and self-phase modulation results in the standard quantum limit of the angle random walk of the gyroscope, which reaches approximately 0.2 deg/hr 1/2 for a millimeter scale CaF 2 whispering gallery mode resonator based device. [ABSTRACT FROM AUTHOR]

• Quantum measurements. • Back action and Standard Quantum Limit. • Back action evading. • Variational measurement: narrow band back action evading. • Dichromatic variational measurement: broad band back action evading. Quantum back action imposes fundamental sensitivity limits to the majority of quantum measurements. The effect results from the unavoidable contamination of the measured parameter with the quantum noise of a meter. Back action evading measurements take advantage of the quantum correlations introduced by the system under study to the meter and allow overcoming the fundamental limitations. The measurements are frequently restricted in their bandwidth due to a finite response time of the system components. Here we show that probing a mechanical oscillator with a dichromatic field with frequencies separated by the oscillator frequency enables independent detection in two outputs and complete subtraction of the measurement noise associated with the quantum back action. [ABSTRACT FROM AUTHOR]

• A trapped diamagnetic particle in an inhomogeneous magnetic field is studied analytically. • Compact expressions for the frequency and eddy-current-related Q-factor are derived. • The Q-factor grows with reduction of the particle size and the magnetic susceptibility. • Usefulness of the pendulum for the gravity constant measurements is highlighted. We discuss eddy-current-induced limitations of the attenuation of mechanical motion of a diamagnetic particle trapped by an inhomogeneous magnetic field in the Earth's gravitational potential. We show that the mechanical frequency of the particle oscillation is independent on the particle properties and is proportional to the free fall acceleration constant, similarly to the classical mechanical pendulum. The frequency can be used to measure the gravity field. The eddy-current induced attenuation constant does not depend on the mass of the particle and reduces with the particle volume. The quality factor of the mechanical motion can be as high as 109 and is comparable with the attenuation due to interaction of the particle with incompletely evacuated air. A possibility of usage of the particle as a quantum mechanical system is discussed. [ABSTRACT FROM AUTHOR]