Squeezing light boosts sensor precision in quantum magnetometers

Asghar Ullah of Koç University and Özgür E. Müstecaplıoğlu of Koç University and TÜBITAK Research Institute for Fundamental Sciences report a method for significantly enhancing the precision of quantum sensors. Their work demonstrates that a coupled two-resonator system, used to estimate both temperature and magnetic fields with measurements taken on a single resonator, can surpass fundamental precision limits imposed by vacuum fluctuations. The researchers found that within the system’s quadratic interactions naturally induce squeezing, yielding orders-of-magnitude enhancement in sensitivity in low-temperature and weak-field regimes compared to standard approaches.

Quadratic Interactions Enhance Squeezing in Coupled Resonators

Counter-rotating terms within the interaction between coupled resonators naturally induce squeezing, a phenomenon that enhances the precision of quantum sensors at low temperatures. This effect arises from the specific characteristics of quadratic interactions, differing from conventional radiation-pressure couplings typically used in optomechanical systems. Researchers have demonstrated that this induced squeezing generates non-Gaussian features in the probe state, improving its ability to detect subtle changes in external conditions.

A coupled two-resonator system is the core of this enhanced sensing capability, designed to simultaneously estimate both the temperature of a thermal bath and the strength of an external magnetic field. While one resonator experiences the influence of a weak magnetic field, measurements are performed on a single resonator acting as the probe, streamlining the sensing process.

This system uses superconducting circuit optomechanical architectures, where nonlinear couplings between microwave resonators are engineered using SQUID-mediated interactions, allowing for strong single-photon coupling and tunable interactions. These improvements are particularly pronounced in low-temperature and weak-field regimes, where conventional sensors struggle with limitations imposed by vacuum fluctuations. Specifically, the counter-rotating terms function as an effective parametric drive, inducing equilibrium squeezing at moderate coupling strengths and driving the probe into a highly non-Gaussian, cat-like state at stronger coupling.

This intrinsic non-Gaussian mechanism persists even as temperature approaches zero, allowing higher-order correlations to enhance the probe’s susceptibility to small temperature variations. This approach offers a pathway toward more sensitive and precise quantum sensors, potentially impacting fields ranging from materials science to fundamental physics research. The system’s ability to achieve orders-of-magnitude enhancement in sensitivity represents an advancement in quantum metrology.

Non-Gaussian Correlations Improve Thermometry Precision

Non-Gaussian correlations within coupled microwave resonators offer a pathway to significantly improve the precision of temperature measurements, surpassing the limitations of conventional methods. Unlike earlier thermometry approaches relying on spectral asymmetry or auxiliary probe modes, this new technique uses quadratic interactions to directly induce squeezing in the probe resonator without external driving. This intrinsic squeezing, particularly prominent at intermediate coupling strengths, alters the structure of the probe state and enhances its sensitivity to subtle temperature variations.

The ability to generate non-Gaussian features in the probe mode is a key advantage, becoming increasingly pronounced as coupling strength increases. Analysis of the Wigner function, a quantum representation of the probe’s state, reveals momentum squeezing at intermediate coupling, a phenomenon not typically observed in systems relying on radiation-pressure couplings.

The study demonstrates a trade-off in simultaneously estimating both temperature and an external magnetic field, with the structure of this trade-off dependent on the interaction model employed. Although quadratic coupling substantially improves single-parameter estimation, it introduces statistical correlations between the temperature and magnetic-field estimators, potentially degrading performance in multiparameter estimation. Despite these correlations, the optimal measurements for both parameters remain compatible, meaning the reduction in joint-estimation precision stems from information redistribution rather than measurement incompatibility.

The analysis of the quantum Fisher information reveals that the degradation in joint-estimation precision is not due to incompatible measurements, but rather to the way information is distributed among correlated parameters. Understanding this is important for optimizing measurement strategies and mitigating the effects of these correlations.

Optomechanical System Models Temperature & Magnetic Field

The interaction between the resonators is defined by a coupling strength, g, and is mathematically described by a quadratic interaction that links the squared field quadrature of one resonator to the displacement of the other. This type of interaction, formally similar to higher-order optomechanical couplings, arises in hybrid bosonic platforms. Specifically, the QFI, used as a measure of estimation precision, varies significantly with different coupling strengths, g, set to 0.02 and 0.08.

These calculations assume parameters of ω_A = 1 and ω_B = 0.04, demonstrating the system’s sensitivity to these values. The researchers found that statistical correlations, originating from the off-diagonal elements of the QFIM, do not prevent compatible measurement operators for both temperature and magnetic field, despite the induced squeezing and non-Gaussianity enhancing single-parameter sensitivity.

Radiation-Pressure vs. Quadratic Coupling Comparison

Specifically, squeezing emerges as the dominant resource for precise magnetic field determination, while stronger non-Gaussian features contribute more significantly to enhanced temperature sensitivity. A comparison of joint estimation of temperature and magnetic field with single-parameter estimation reveals a reduction in precision when both parameters are targeted simultaneously. This reduction stems from the non-diagonal structure of the quantum Fisher information matrix, indicating statistical correlations between temperature and magnetic field. These correlations redistribute the available information, limiting the achievable precision in joint estimation.

Low-Temperature & Weak-Field Precision Gains

Analysis of the quantum Fisher information (QFI) demonstrates that quadratic interactions outperform radiation-pressure couplings, particularly when operating in low-temperature and weak-field conditions. This advantage stems from the generation of non-Gaussian features in the probe state, redistributing fluctuations to improve estimation accuracy. The researchers state that these probe features offer a more direct route to quantum sensing enhanced by non-Gaussianity in the low-temperature and weak field regimes, highlighting the potential for future sensor development.

The study’s findings demonstrate that carefully controlling system parameters allows for maximized precision in magnetic field estimation at low temperatures. This is a critical step toward developing sensors capable of operating in environments where traditional methods are limited by vacuum fluctuations. The observed improvements are not merely incremental; the data suggest orders-of-magnitude enhancement in sensitivity.

Resonator System Design for Quantum Magnetometry

A coupled two-resonator system offers a pathway to surpass fundamental precision limits in quantum magnetometry by moving beyond conventional radiation-pressure interactions. Rather than measuring the temperature of individual resonators, the design estimates the temperature of a shared thermal bath while simultaneously detecting a weak magnetic field applied to one resonator.

The researchers found that single-parameter estimation remains the most effective strategy for achieving high-precision thermometry and magnetometry with this system. The system’s design allows for the estimation of both parameters using a single probe resonator, simplifying the experimental setup and potentially reducing noise. The data supporting these findings are not publicly available but can be requested from the authors. The study’s findings provide a clear demonstration of how carefully controlling system parameters can maximize precision in quantum sensing applications.

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