Spin-dependent Squeezed States Achieve Optimal Displacement Sensing, Saturating the Heisenberg Limit with ~dB Squeezing

Displacement sensing underpins a wide range of precision measurements, yet creating sensors that fully exploit the potential of complex quantum systems remains a significant hurdle. Liam J. Bond from the University of Amsterdam and QuSoft, alongside Christophe H. Valahu and Athreya Shankar et al., now demonstrate a new approach using spin-dependent squeezed states, unique quantum states where squeezed light is linked to an auxiliary spin. Their work proves these states achieve optimal performance, reaching the fundamental limit of precision for displacement sensing, known as the Heisenberg limit. The team also proposes practical methods for preparing and measuring these states, and numerically demonstrates a preparation protocol significantly faster than existing techniques, opening doors to applications ranging from detecting single photons to the search for elusive dark matter particles.

Spin Squeezing via Collective Ion Motion

Scientists are advancing precision sensing by creating spin-dependent squeezed states, a novel type of quantum state where quantum noise is carefully manipulated. This research focuses on generating these states by linking the collective spin of trapped ions to their motion, offering a pathway to enhanced measurement precision. The team employed a mathematical technique called the Magnus expansion to accurately model the evolution of this complex quantum system, ensuring the scalability of their approach. Investigations into the Magnus expansion revealed that higher-order terms introduce errors, but these diminish as the number of ions increases, suggesting the protocol is well-suited for larger systems.

Optimizing the squeezing angle proved crucial, with the most efficient performance achieved at a specific angle related to the system’s underlying quantum properties. The number of repetitions and phase-space loops within the experimental sequence also influenced performance, requiring careful balancing to minimize protocol duration. Detailed analysis, supported by simulations, demonstrated the scalability of this approach and identified key parameters for achieving high fidelity, with significant implications for quantum information processing, precision measurements, and scalable quantum systems.

Spin-Dependent Squeezed States for Precision Sensing

Researchers have developed innovative displacement sensing schemes utilizing spin-dependent squeezed states, achieving the fundamental Heisenberg limit and well-suited for implementation in trapped ion systems. The team demonstrated a scalable protocol for preparing these states, utilizing dynamically modulated interactions to achieve approximately 0. 7 decibels of spin-dependent squeezing. This preparation method is faster than traditional approaches employing second-order sidebands, scaling favorably with the number of ions. Numerical simulations confirmed this speedup, demonstrating a reduction in protocol duration proportional to the inverse square root of the number of ions.

Careful characterization of the stroboscopic protocol revealed excellent agreement with theoretical predictions, validating the approach. The study also investigated the detuning required to achieve target fidelities, demonstrating that increasing the number of ions lowers this requirement. Scaling to larger systems amplifies the displacement signal and holds promise for applications like dark matter searches and advanced atomic clocks.

Spin Squeezing Reaches Heisenberg Limit for Sensing

Scientists have achieved a breakthrough in displacement sensing by developing many-body sensing schemes utilizing spin-dependent squeezed states, a novel type of quantum state linking squeezing to an auxiliary spin. The team proved these states are optimal, reaching the fundamental Heisenberg limit for precision, and proposed practical measurement sequences readily implementable in trapped ion systems. A scalable state-preparation protocol was also developed, demonstrating the creation of approximately 10 decibels of spin-dependent squeezing faster than conventional methods. Experiments reveal that the minimum protocol duration to prepare a spin-dependent squeezed state with 99% fidelity scales favorably with the number of ions and the amount of squeezing.

Specifically, the team demonstrated a minimum time of 3. 48 milliseconds, indicating improved performance with increasing ion number. This speed was achieved by carefully controlling the duration of segments within the stroboscopic sequence, scaling the duration based on system parameters. Measurements confirm that the protocol’s speed is independent of the number of ions when optimized, with a minimum time determined by system characteristics. Numerical simulations with up to 40 ions demonstrate high fidelity and confirm the favorable scaling with ion number. The team also showed that the protocol’s performance is robust, with higher-order error terms remaining manageable under appropriate parameter choices.

Squeezed States Unlock Heisenberg Limit Sensing

This research demonstrates novel approaches to displacement sensing, achieving optimal performance at the fundamental Heisenberg limit. Scientists developed spin-dependent squeezed states and proved their suitability for highly precise measurements of displacement magnitude and components, proposing explicit measurement protocols designed to function effectively with existing quantum hardware. Furthermore, the team established a fast and scalable method for preparing these spin-dependent squeezed states within trapped-ion systems, utilising dynamically modulated interactions that significantly outperform standard approaches. Future research directions include investigating the impact of noise on state preparation and metrological performance, with the potential to engineer robustness through quantum control techniques. The team also plans to explore alternative spin-boson entangling unitaries and compare the performance of various reference states in realistic experimental conditions. Scaling these methods to larger ion crystals promises to amplify displacement signals and reduce preparation times, with potential applications in dark matter searches, atomic clocks, and the study of molecular and highly charged ions.