Nonreciprocity enhanced Quantum Gyroscopes based on Surface Acoustic Waves

TL;DR

The paper introduces a quantum gyroscope built from a double-mode surface acoustic wave cavity with multiple-point couplings to a shared waveguide. The resulting time-delayed, non-Markovian dynamics produce topology-dependent nonreciprocity, enabling directionally enhanced signal transfer and improved SNR and angular-velocity sensitivity compared with conventional single-point designs. By analyzing separated, nested, and braided topologies, the work demonstrates that nonreciprocity can be tuned via phase and coupling-point number, yielding measurable gains (up to ~70%) in sensitivity under realistic weak-coupling conditions and shot-noise-limited readout. The proposal is experimentally feasible with current SAW technology and offers a route to on-chip quantum sensing that leverages nonreciprocal transfer as a resource, with prospects for further enhancements as SAW quality factors improve.

Abstract

Surface acoustic waves (SAWs), as Rayleigh waves generated by elastic media, have been used in gyroscopes for over 40 years due to their unique propagation characteristics. However, their working principle, based on Coriolis effects, has become increasingly ineffective for addressing modern sensing challenges in complex scenarios. Fortunately, recent advancements in quantized SAWs offer a promising solution: SAWs operating at extremely low pump powers (approximately at the single-phonon level) can exhibit substantial quantum coherence, enabling investigations into the fundamental limits of SAW gyroscopes as constrained by the Heisenberg uncertainty relation. In particular, when multiple SAWs couple to a common waveguide at distinct locations, the nonlocality arising from the spatial separation among coupling points induces directional coupling between the SAWs. To elucidate this directionality, we propose a quantum gyroscope characterized by multiplepoint couplings. Unlike traditional single-point coupling designs, our gyroscope exhibits distinctive time-delayed dynamics that depend on the system's topologies. We emphasize that these dynamics invalidate the Markovian approximation, even when the time delay is relatively small. Through a comprehensive analysis of all possible topologies, we observe that the directional coupling implies an inherent nonreciprocal transfer. This nonreciprocity confers signiffcant advantages to our gyroscope compared to traditional designs, notably enhancing both the signal-to-noise ratio and sensitivity. Speciffcally, it enables the extraction of output signals that would otherwise be obscured by noise. Consequently, our ffndings suggest that systems with multiple-point couplings and the associated nonreciprocity can serve as valuable resources for advancing quantum sensing technologies.

Figures (13)

• Figure 1: (Color online) Schematic of the quantum gyroscope. (a) Toy model. The SAW cavity supports two orthogonal modes $x$ and $y$, and they couple together when the plate rotates at an unknown angular velocity $\Omega$. Consequently, the SAW cavity serves as a fundamental gyroscope configuration in the $x-y$ plane. By coupling the $x$ mode and the auxiliary cavity to the same waveguide at distant points, we establish a coupled quantum giant-cavity system. To analyze the underlying directional coupling, two detection ports, D1 and D2, are employed for readout. Port D1 connects to the auxiliary cavity, while port D2 couples to the $x$ mode. (b) An accessible realization in experiments (without detectors). The whole setup is fabricated by multiple-layer lithograph technology. The layer 1 consists of a sapphire substrate whose surface is covered with an aluminum membrane. The aluminum membrane is used for etching the LC resonator (auxiliary cavity) and the waveguide, where the multiple-point couplings between them is realized by multiple capcitors (not given). The layers 2 and 3 consist of elastic media exhibiting the piezoelectric effect, used to generate SAWs in the $x$ and $y$ directions, respectively. Additionally, one can etch interdigital transducers (IDTs) in layers 2 and 3 to form Bragg gratings, which truncate the traveling SAWs into standing waves, thereby constructing a double-mode SAW cavity. Besides, one can also use multiple IDTs to construct the muliplt-point coupling between $x$ mode and the waveguide (not given).
• Figure 2: (Color online) Schematic of the topologies between modes $a$ and $b_x$. For the double-body system examined in this paper, there are three types of topologies: (a) separated, (b) nested, and (c) braided. The topologies labeled (ii) are mirror images of those labeled (i).
• Figure 3: The effective patterns of topologies: (a) Separated, (b) Nested, and (c) Braided. In (a), the separated topology is the most fundamental for the double-body system under consideration, while the other topologies can be viewed as combinations of different separated topologies. In (b), the nested topology can be categorized as a combination of separated topology (i) and separated topology (ii). In (c), the general braided topology can be divided into a strict braided component and a separated component. In the strict braided component, the number of interlaced coupling points is $N = M$, and this component can be further divided into two sets of separated topologies (i) and (ii).
• Figure 4: (Color online) The numerical simulation of the nonreciprocal strength $\sigma(0)$ under strict braided topologies. The gridlines indicate the points $\sigma(0)=\{-1,0,1\}$. Due to destructive interference, the system exhibits reciprocity at the phases $\phi=\{0.5\pi, 1.5\pi\}$.
• Figure 5: (Color online) The numerical simulations of the SNRs $\mathcal{R}_{\alpha} (0)$ and $\mathcal{R}_{\beta} (0)$ in strict braided topologies. Parameters used for plotting are: $\gamma_x=\gamma_y$ and $\kappa=10\gamma_x$. Due to the residual term $\gamma_x+\frac{4\Omega^2}{\gamma_y}$, the SNRs $\mathcal{R}_{\alpha} (0)$ and $\mathcal{R}_{\beta} (0)$ do not strictly overlap at the reciprocal points $\phi=\{0.5\pi, 1.5\pi\}$. In panels (a1)-(a3), the system exhibits right nonreciprocity, except at the reciprocal points, resulting in the SNR $\mathcal{R}_{\beta} (0)$ being greater than the SNR $\mathcal{R}_{\alpha} (0)$. More importantly, the SNR $\mathcal{R}_\beta (0)$ in the interval $\phi \in [0.5\pi, 1.5\pi]$ varies synchronously with the nonreciprocal strength $\sigma(0)$, as shown in Fig. \ref{['SigmaFig1']} (a). This synchronous variation reveals that nonreciprocity can effectively enhance the SNR. Similar results are also observed in the mutual mirroring topology (b1)-(b3), where the roles of the SNRs $\mathcal{R}_\beta (0)$ and $\mathcal{R}_\alpha (0)$ are reversed.