High-performance gyroscopes for rotation sensing are of pivotal significance for navigation in many types of air, ground, marine, and space applications. Based on the Sagnac effect, i.e., two counter-propagating waves in a rotating loop accumulate a rotation-dependent phase difference, gyroscopes have been realized in optical and matter-wave systems. The precision of a purely Sagnac gyroscope, which is proportional to the surface area enclosed by the optical path, is theoretically limited by the classical shot-noise limit.
Pursuing more precise measurement to physical quantities than the classical shot-noise limit by using quantum resources, such as squeezing and entanglement, quantum metrology supplies a way toward achieving gyroscopes with ultimate sensitivity limits. Based on this idea, many schemes of quantum gyroscopes have been proposed.
However, quantum gyroscopes are still at the stage of the proof-of-principle study and their superiority over the conventional ones in the absolute value of sensitivity still has not been exhibited. A key obstacle is that the stability of quantum gyroscopes is challenged by the inevitable noise-induced decoherence, which typically degrades quantum resources of the quantum probe, forces the quantum enhanced precision back to the classical limit, and thus washes out the quantum superiority. This is called the no-go theorem of noisy quantum metrology, and is one of the main bottlenecks to realize quantum gyroscopes. Therefore, how to break through the constraint of the no-go theorem is a main challenge for achieving high-precision quantum gyroscopes.
To address the problems, Ms. Lin Jiao and Prof. Jun-Hong An from Lanzhou University have demonstrated an entanglement-assisted high-precision rotation sensing beyond the classical shot-noise limit in a realistic noisy environment.
The report is based on a scheme of quantum optical gyroscope (QOG) that generalizes the modern fibre-optic gyroscope to quantum level. In the ideal non-decoherent case, its accuracy reaches the super-Heisenberg limit. In the decoherence case, a mechanism is found that allows the ideal accuracy to be recovered asymptotically. The relevant research results were published in Photonics Research, Volume 11, No. 2, 2023 (Lin Jiao, Jun-Hong An. Noisy quantum gyroscope[J]. Photonics Research, 2023, 11(2): 150).
In this scheme, the two-mode squeezed vacuum state is employed as the input state and the parity operator of photon number at the output port is measured. Its schematic diagram is shown in Fig. 1(a). It is remarkable to find that the best sensing error achieved in the scheme is even better than the Heisenberg limit, which reflects the quantum superiority of the used entanglement and measured observable. However, the photon dissipation under the Born-Markovian approximation makes the quantum advantages of this scheme completely vanish [see Figs. 1(b) and 1(c)]. It is called the no-go theorem of noisy quantum metrology and is a main obstacle to achieve the high-precision quantum sensing in practice.
Fig.1 (a) Schematic diagram of the quantum optical gyroscope. (b) Evolution of the sensing error δΩBA (cyan solid line) in the presence of photon loss under the Born-Markovian approximation. (c) Numerical fitting of the scale relation between the global minimum of δΩ and the photon number.
Fig.2 (a) Energy spectrum of the total system consisting of the two optical fields and their environments. Non-Markovian dynamical evolution of δΩ(t) multiplied by a magnification factor P when (ωc∕ω0, P)=(2, 10−1) in (b), (20, 10−2) in (c), and (25, 10−3) in (d).
In order to break through the no-go theorem, the authors make an exact analysis on the non-Markovian decoherence of the QOG. It is found that the exact decoherence sensitively depends on the features of the energy-spectrum features of the total system consisting of the QOG and its environment. As long as one bound state is formed by each optical field of the QOG and its local environment [see Fig. 2(a)], both the evolution time as a resource in enhancing the sensitivity [see Figs. 2(d) and 3(a)] and the ideal super-Heisenberg limit are asymptotically recoverable [see Fig. 3(b)]. This means the no-go theorem is efficiently overcome. It offers us a guideline to achieve a noise-tolerant rotation sensing by manipulating the formation of the bound states, which can be realized by the quantum reservoir-engineering technique.
Fig. 3 (a) Local minima of δΩ(t) as a function of time (a) and N when t = 2.5 × 104 ω0-1 (b) in different ωc.
First, surpassing not only the classical shot-noise limit, but also the Heisenberg limit, the proposed scheme enriches the family of quantum metrology. Second, supplying an efficient way to overcome the long-standing problem of the no-go theorem of noisy quantum metrology, the results expand one's general belief of the decoherence effect on quantum metrology. Finally, the results provide a guideline in realizing high-precision rotation sensing in realistic noisy environments. The recent advances in quantum optical experiments support the realizability of the scheme.
