Quantum Systems Harness ‘scars’ for Far More Precise Field Sensing

Matheus Fibger of the Fluminense Federal University (UFF) and colleagues show that these scars, displaying unusual coherent behaviour, enable resonant processes when the driving frequency aligns with the scar gap. This results in a quantum Fisher information that grows quadratically with time, offering a pathway to improved sensing performance. Their analysis of probe operator connectivity reveals that staggered magnetization outperforms homogeneous magnetization in scaling the quantum Fisher information with system size, establishing a method for using non-ergodic dynamics in quantum sensing protocols.

Quantum many-body scars enable quadratically scaling precision in quantum sensing

A substantial leap forward was demonstrated by the quantum Fisher information (QFI), achieving quadratic-in-time growth, a rate previously unattainable with conventional coherence-based methods. Overcoming limitations imposed by rapid decoherence in many quantum systems, this quadratic scaling signifies that sensing precision improves proportionally to the square of the measurement time. Quantum many-body scars within the PXP model enabled this enhanced sensitivity, representing unusual quantum states exhibiting prolonged coherent dynamics.

Employing staggered magnetization as a probe operator yielded a more favourable scaling of the QFI with system size than homogeneous magnetization, establishing a pathway to optimise sensor performance. Resonant driving, matching the frequency to multiples of the scar gap, sustained this growth of the QFI for extended periods. Collective transitions occurring across the scar tower, a series of closely-spaced energy levels, underpin this enhancement. A compact analytical expression was successfully derived using a single-tower approximation, capturing both the time dependence and system-size scaling of the QFI, further validating the theoretical understanding of this improved sensing capability and offering insights into the underlying mechanisms.

Enhanced sensor precision via durable quantum many-body scar states

Researchers, led by David Awschalom, are increasingly focused on exploiting quantum phenomena to build sensors capable of detecting incredibly faint signals, promising to revolutionise fields from medical diagnostics to materials science with unprecedented precision. Maintaining the delicate quantum states needed for accurate measurements remains a significant hurdle, as signal degradation over time often plagues current methods. This work demonstrates a potential solution by utilising quantum many-body scars, unusual states that resist typical thermal behaviour, though further investigation is needed to confirm applicability beyond the specific model used.

The PXP model served as the focus of this work, but it establishes a principle for using structured, non-random behaviour within quantum systems to enhance sensing capabilities, potentially applicable to more complex scenarios. This finding demonstrates substantial improvements in quantum Fisher information, a measure of a sensor’s ability to distinguish between very similar inputs, using these durable states. Moving beyond reliance on fragile entangled states, exploiting the unusual behaviour of these scars offers a new approach to quantum sensing. Sustained responses to external stimuli are enabled by these states, allowing for more reliable detection of weak signals over time. A quadratic increase in sensing precision was observed by driving these systems with precisely tuned frequencies, a rate previously unattainable with standard methods, potentially broadening the scope of sensitive measurements beyond the specific model investigated.

Quantum many-body scars (MBS) represent a fascinating departure from the typical behaviour of isolated quantum systems. Normally, systems evolve towards thermal equilibrium, losing coherence and making precise measurements challenging. However, MBS exhibit weak ergodicity breaking, meaning they do not fully explore all possible states, and retain long-lived coherent dynamics even within a thermalising background. These scars arise due to specific, non-random structures within the system’s energy spectrum, forming what is known as a ‘scar tower’, a series of approximately equally spaced energy levels. The PXP (Periodic Potential with X-shaped interactions) model, a one-dimensional spin chain, provides a tractable platform for studying these phenomena. It is characterised by interactions between neighbouring spins, leading to collective behaviour and the emergence of MBS under certain conditions.

The core of this research lies in leveraging the metrological properties of these MBS. Metrology, the science of measurement, benefits greatly from quantum enhancements, and the QFI serves as a crucial figure of merit. It quantifies the maximum achievable precision in estimating a parameter, in this case, the amplitude of a weak alternating current (AC) field applied to the PXP model. Traditional coherence-based sensing methods are limited by decoherence, which degrades the quantum signal over time. The researchers found that the approximately uniform energy spacing within the scar tower facilitates collective resonant processes when the driving frequency of the AC field matches integer multiples of the scar gap. This resonance amplifies the signal and allows the QFI to grow quadratically with time, meaning the precision increases with the square of the measurement duration. This t² scaling represents a significant advantage over conventional methods.

The choice of probe operator, the observable used to extract information about the parameter being estimated, is critical. The researchers compared two options: staggered magnetization and homogeneous magnetization. Staggered magnetization measures the difference in magnetization between adjacent sites, while homogeneous magnetization measures the total magnetization. Their analysis revealed that staggered magnetization exhibits superior scaling with system size in terms of the QFI. This suggests that designing sensors based on staggered magnetization will yield better performance, particularly for larger systems. The connectivity of the probe operator to the scar states dictates this improved scaling, with staggered magnetization being more effectively coupled to the collective excitations within the scar tower. This provides a concrete design principle for optimising quantum sensors based on MBS.

To further understand the underlying mechanisms, the researchers derived a compact analytical expression for the QFI using a single-tower approximation. This simplification allows for a clear understanding of the time dependence and system-size scaling of the QFI. The analytical result confirms the quadratic time dependence and provides insights into the role of the scar gap and the driving frequency. This theoretical framework not only validates the numerical findings but also offers a roadmap for exploring similar phenomena in other quantum systems. The ability to accurately predict and control the QFI is essential for realising practical quantum sensors based on MBS. The observed quadratic scaling of the QFI with time, coupled with the optimised probe operator selection, represents a substantial advancement in the field of quantum sensing, potentially enabling the detection of signals previously beyond the reach of current technologies.

While the study focuses on the PXP model, the principles established here are broadly applicable. The demonstration of enhanced sensing capabilities through the exploitation of non-ergodic dynamics opens up new avenues for designing robust and high-precision quantum sensors. Future research will likely focus on extending these findings to more complex systems and exploring the potential for implementing these sensors in real-world applications, ranging from detecting gravitational waves to improving medical imaging techniques.

The research demonstrated that quantum many-body scars can be leveraged to improve the precision of weak AC field estimation using the quantum Fisher information. Specifically, utilising staggered magnetization as a probe operator resulted in a more favourable scaling of the quantum Fisher information with system size compared to homogeneous magnetization. This improvement arises from the stronger connectivity between staggered magnetization and the collective excitations within the scar tower, offering a design principle for optimising quantum sensors. Researchers also developed an analytical expression to accurately predict the time dependence and system-size scaling of the quantum Fisher information.