Numerous quantum mechanical schemes have been proposed that are intended to improve the sensitivity to rotation provided by the classical Sagnac effect in gyroscopes. A general metric is needed that can compare the performance of the new quantum systems with the classical systems. The fidelity (Shannon mutual information between the measurement and the rotation rate) is proposed as a metric that is capable of this comparison. A theoretical upper bound is derived for the fidelity of an ideal classical Sagnac gyroscope. This upper bound for the classical Sagnac gyroscope should be used as a benchmark to compare the performance of proposed enhanced classical and quantum rotation sensors. In fact, the fidelity is general enough to compare the quality of two different apparatuses (two different experiments) that attempt to measure the same quantity.
Numerous quantum mechanical schemes have been proposed that are intended to improve the sensitivity to rotation provided by the classical Sagnac effect in gyroscopes. A general metric is needed that can compare the performance of the new quantum systems with the classical systems. The fidelity (Shannon mutual information between the measurement and the rotation rate) is proposed as a metric that is capable of this comparison. A theoretical upper bound is derived for the fidelity of an ideal classical Sagnac gyroscope. This upper bound for the classical Sagnac gyroscope should be used as a benchmark to compare the performance of proposed enhanced classical and quantum rotation sensors. In fact, the fidelity is general enough to compare the quality of two different apparatuses (two different experiments) that attempt to measure the same quantity.
The fidelity (Shannon mutual information between measurements and physical quantities) is proposed as a quantitative measure of the quality of physical measurements. The fidelity does not depend on the true value of unknown physical quantities (as does the Fisher information) and it allows for the role of prior information in the measurement process. The fidelity is general enough to allow a natural comparison of the quality of classical and quantum measurements. As an example, the fidelity is used to compare the quality of measurements made by a classical and a quantum Mach-Zehnder interferometer.
Abstract We model a gyroscope that exploits quantum effects in an atomic Bose–Einstein condensate to gain a tunable enhancement in precision. Current inertial navigation systems rely on the Sagnac effect using unentangled photons in fibre-optic systems and there are proposals for improving how the precision scales with the number of particles by using entanglement. Here we exploit a different route based on sharp resonances associated with quantum phase transitions. By adjusting the interaction between the particles and/or the shape of their trapping potential we are able to tune the width of the resonance and hence the precision of the measurement. Here we show how we can use this method to increase the overall sensitivity of a gyroscope by adjusting the system parameters as the measurement proceeds and our knowledge of the rotation improves. We illustrate this with an example where the precision is enhanced by a factor of more than 20 over the case without tuning, after 100 repetitions. Metrology schemes with tunable precision based on quantum phase transitions could offer an important complementary method to other quantum-enhanced measurement and sensing schemes.
The Sagnac effect, manifest in the phase shift of a rotating interferometer proportional to its physical area and to the rotation rate of the frame, plays a crucial role in modern physics being generalized to any kind of interferometer. However, as compared to light, the accurate experimental validation of the Sagnac effect for matter-waves remains challenging. We report the accurate measurement of the Sagnac phase shift, induced by the Earth’s rotation, using a large-area cold atom interferometer. We probe the atomic Sagnac phase shift along the two orthogonal horizontal axes in various orientation of the sensor with respect to geographic north and obtain an agreement with the theoretical prediction at the 20 ppm level, improving by twenty five-fold over the previous achievements for matter waves. Our results underline the universality of the Sagnac effect and open new horizons for testing other fundamental theories, as well as for a number of technological applications in seismology, geodesy and inertial navigation systems.
Hong-Ou-Mandel (HOM) interferometry with quantum states has emerged a crucial tool for precision measurement system. Here, a novel scheme for angular velocity measurement in a fiber-optic quantum gyroscope is proposed and demonstrated, based on Sagnac effect of frequency-entangled biphotons and incorporating a HOM interferometer. The time delay resulting from the rotation-induced Sagnac effect between the signal and idler photons generates a shift of HOM dip, which is proportional to the angular velocity. Consequently, a highly sensitivity and stability angular velocity measurement is achieved by monitoring the HOM dip. The sensitivity scale is measured to be 3 . 54 ± 0 . 08 fs / rad / s which is equivalent to a minimally detectable angular velocity of 28.25 ± 0.06 × 10 - 5 r a d / s 58.27 ± 0.12 ° / h with a time delay of 1 a s . The measurement stability of the continuous rotating system, in terms of time Allan deviation (TDEV), reaches 1.93 × 10 - 3 fs at an averaging time of 10,240 s. The corresponding angular velocity measurement stability reaches 55 × 10 - 5 r a d / s . This scheme holds potential for advancing the development of high-performance optical quantum gyroscopes.
Precise positioning and motion tracking are enabling development of key technologies in numerous fields of research and applications such as control, navigation, stabilization, and positioning systems for robotics, medical-imaging applications, virtual reality, computer games, and many more. While rotation sensing can be based on both mechanical and optical effects, optical gyroscopes provide the highest sensitivity and accuracy. Although the details may vary depending on the specific implementation, all optical rotation sensors exploit the Sagnac effect,1 i.e., the interference pattern resulting from the different phase shifts of waves propagating in a circular path along and opposite the direction of rotation. The classical Sagnac phase shift is determined solely by the angular velocity, the optical frequency, and the area enclosed by the closed-loop optical path, and completely independent of the medium’s other properties such as the index of refraction and its dispersion properties.2 This century-old result has been the subject of ongoing debate for several decades, both because of its fundamental nature and because it inherently limits the feasibility of attaining highly sensitive miniaturized rotation sensors. Specifically, it implies that the only ways to enhance the sensitivity and accuracy of optical gyroscopes are to either increase the optical frequency or enlarge the gyro’s area. In practice, both approaches are limited. Recent studies have pointed out the advantages of exploiting the Sagnac effect, generated by electronic resonances, in slow-3 and fast-light4 media (i.e., in which the group velocity is substantially smaller or larger than the speed of light) for fabrication of ultrasensitive optical gyroscopes. However, material properties based on slow/fast-light media suffer from inherent limitations and drawbacks. In particular, such systems are bulky, lossy, require very low temperatures, and are limited to specific wavelengths according to the material’s electronic andoptical properties. Instead, we have been focusing on photonic-resonance-based structures,5, 6 taking advantage of their flexibility, compact dimensions, and excellent optical Figure 1. Schematic of a coupled-resonator optical waveguide (CROW).
Gyroscope for rotation sensing plays a key role in inertial navigation systems. Developing more precise gyroscopes than the conventional ones bounded by the classical shot-noise limit by using quantum resources has attracted much attention. However, existing quantum gyroscope schemes suffer severe deterioration under the influence of decoherence, which is called the no-go theorem of noisy metrology. Here, by using two quantized optical fields as the quantum probe, we propose a quantum gyroscope scheme breaking through the constraint of the no-go theorem. Our exact analysis of the non-Markovian noise reveals that both the evolution time as a resource in enhancing the sensitivity and the achieved super-Heisenberg limit in the noiseless case are asymptotically recoverable when each optical field forms a bound state with its environment. The result provides a guideline for realizing high-precision rotation sensing in realistic noisy environments.