Solid-State Spin Measurements Reach Fundamental Precision Limit, Boosting Quantum Technology
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Researchers are continually seeking methods to improve the precision of spin measurements in solid-state systems. Mikhail Mamaev, Jayameenakshi Venkatraman, and Martin Koppenhöfer, alongside Ania C. Bleszynski Jayich and Aashish A. Clerk, demonstrate a novel protocol for detecting quantum noise in a solid-state spin ensemble using dispersive measurement techniques. This work addresses a significant challenge in the field, as conventional optical methods often suffer from limited readout fidelity. By analysing fluctuations in microwave resonator signals, the team derive conditions under which measurements are limited by fundamental spin-projection noise, and propose an experimental method for directly detecting spin squeezing, a crucial resource for enhancing metrological precision. Resonator-mediated homodyne detection of spin ensembles and limits to precision measurement are explored Scientists have developed a theoretical framework for measuring the spin polarization of solid-state spin ensembles with a precision at or below the standard quantum limit. Conventional methods relying on optical fluorescence often suffer from limited readout fidelity, creating a need for alternative approaches. This work explores indirect microwave resonator-mediated measurements as a promising solution, providing a detailed analysis of the noise sources inherent in this technique. Researchers studied dispersive readout of an inhomogeneously broadened spin ensemble coupled to a driven resonator, utilising homodyne detection to analyse the signals. The study derives analytic conditions defining when homodyne measurements are limited by fundamental spin-projection noise, rather than being dominated by microwave-drive shot noise or resonator phase noise. By meticulously examining fluctuations in the measurement record, a novel experimental protocol for directly detecting spin squeezing has been proposed. Spin squeezing represents a reduction of the intrinsic projection noise of the spin ensemble, originating from entanglement. This protocol offers a means to benchmark states suitable for quantum-enhanced metrology, potentially improving the sensitivity of sensors beyond classical limits. Specifically, the research focuses on a dispersive readout scheme where the collective spin polarization of a solid-state spin ensemble modulates a microwave resonator. This modulation is then detected via homodyne measurement of the reflected microwave signal. The analysis accounts for the effects of both inhomogeneous broadening, a common characteristic of solid-state systems, and the finite lifetime of the spin states, denoted as T1, which influences both the signal and noise during measurement. By carefully considering these factors, the team established parametric requirements for achieving spin-projection-noise-limited detection. The proposed protocol not only enables the detection of spin squeezing but also provides a pathway to characterise entangled states for applications in quantum-enhanced metrology. This advancement addresses a critical challenge in the field, where technical noise often overshadows the benefits of entanglement in solid-state spin sensors. The study addresses challenges in solid-state measurements, where conventional optical fluorescence techniques often suffer from poor readout fidelity. Researchers implemented dispersive readout of an inhomogeneously broadened spin ensemble by coupling it to a driven resonator, subsequently measured using homodyne detection. This work details the construction of a circuit-QED setup comprising N spin-1/2 degrees of freedom coupled to a resonator, with individual couplings denoted as gj. The resonator experiences decay at a rate κ, while individual spins decay at a rate γ−, and is driven by an input microwave field, ain. Quadratures of the output light field, aout, are then passed through an I-Q mixer to obtain a time-integrated homodyne current, M. The system spectrum features spins with inhomogeneous frequencies δj, and the resonator is detuned by ∆ from the spins’ center frequency. The experimental protocol involves analyzing fluctuations in the measurement record to directly detect spin squeezing, a reduction of the spin ensemble’s intrinsic projection noise from entanglement. By studying the distribution of measurement outcomes, M(T), after a collection time T, the mean value reveals the collective spin polarization, while the variance, ∆M(T)², is targeted for spin-projection-noise limitation. This approach provides a method for benchmarking entangled states for quantum-enhanced metrology, enabling the assessment of states suitable for high-precision measurements. The research derives analytic conditions determining when homodyne measurements are limited by fundamental spin-projection noise, rather than microwave-drive shot noise or resonator phase noise. Resonator and spin dynamics in a diamond nitrogen-vacancy centre ensemble are explored A system comprising a superconducting microwave resonator inductively coupled to an ensemble of nitrogen-vacancy centers in diamond has been theoretically explored, revealing parameters for precision spin polarization measurements. Numerical calculations utilized a system with 10 6 atoms, a spin-resonator coupling of 2π × 50s −1 , and an inhomogeneous broadening width of 2π × 10 6s −1 . Spin decay rates were established at 2π × 1s −1 , while the resonator loss rate reached 2π × 10 5s −1 . The resonator-spin detuning was set to 2π × 5 × 10 6s −1 , with a resonator mean photon number of 10 5 . The research details a renormalized spin decay rate of 2π × 1s −1 , calculated by considering both intrinsic spin decay and coupling to the resonator. Dispersive coupling between individual spins and the resonator was quantified at 2π × 5 × 10 −4s −1 . Homodyne measurement time, a crucial parameter for signal acquisition, was shown to vary depending on experimental conditions. A parameter, λ, characterizing the dispersive measurement quality for homogeneous systems, was determined to be 16χ 2 nN/(κγ), where χ represents the spin dispersive coupling, n the resonator photon number, N the atom number, κ the resonator loss rate, and γ the spin decay rate. The study establishes conditions under which homodyne measurements can be limited by fundamental spin-projection noise, rather than microwave-drive shot noise or resonator phase noise. Fluctuations in the measurement record were analyzed to propose a protocol for directly detecting spin squeezing, a reduction of the spin ensemble’s intrinsic projection noise. This protocol offers a method for benchmarking states suitable for enhanced metrology, potentially improving the sensitivity of spin-based sensors. The zero-point current in the resonator, operating at millikelvin temperatures and a frequency of approximately 5GHz, was calculated to be around 50 nanoamperes. Homodyne detection of spin squeezing surpasses standard quantum limits in precision measurement Scientists have demonstrated a method for measuring the spin polarization of solid-state spin ensembles with precision at or below the standard quantum limit. Conventional optical fluorescence techniques are often hampered by low readout fidelity when assessing these systems, prompting investigation into indirect, microwave resonator-mediated measurements. This work details an analysis of dispersive readout, utilising a driven resonator and homodyne detection to assess inhomogeneously broadened spin ensembles. The research establishes analytic conditions under which homodyne measurements are limited by fundamental spin-projection noise, rather than technical noise sources like microwave drive fluctuations or resonator phase noise. Furthermore, a protocol for directly detecting spin squeezing, a reduction in the intrinsic projection noise of the spin ensemble, has been proposed and benchmarked for enhanced metrology. Results confirm applicability to both squeezed and anti-squeezed states, offering flexibility in experimental design. The authors acknowledge a limitation in their analysis stemming from the use of the dispersive approximation, which may not hold for non-detuned resonators where spins decay directly at the coupling rate. Additionally, the current model neglects spin flip-flop interactions, which could become significant in very dense ensembles. Future research directions include exploring the behaviour of resonant spins and incorporating spin flip-flop interactions through coarse-graining techniques to simplify the analysis and broaden the model’s applicability. These developments promise improved precision in spin measurements and a pathway towards more sensitive quantum sensing technologies. 👉 More information 🗞 Detecting quantum noise of a solid-state spin ensemble with dispersive measurement 🧠 ArXiv: https://arxiv.org/abs/2602.03734 Tags: