Quantum Sensors’ Noise Limits Mapped across Three Orders of Magnitude in Power

Scientists are increasingly focused on developing highly sensitive sensors capable of simultaneously measuring multiple parameters. Aleksandra Sierant, Diana Méndez-Avalos, and Santiago Tabares Giraldo, all from ICFO, The Barcelona Institute of Science and Technology, alongside Morgan W Mitchell et al., present compelling new research into the fundamental noise limitations of these continuously operating multiparameter sensors. Their experimental investigation, utilising a hybrid radiofrequency-direct current pumped magnetometer, meticulously maps photon shot noise, spin projection noise, and measurement back-action noise across a wide range of power levels. This work is significant because it establishes, for the first time, the precise scaling laws governing noise in such sensors, revealing crucial resource-dependent trade-offs and defining the limits of optimal performance for future devices.

This work details an experimental investigation into the noise mechanisms that constrain the performance of these sensitive devices, revealing critical resource-dependent trade-offs.

Researchers employed a hybrid radio frequency-direct current optically pumped magnetometer to meticulously map photon shot noise, spin projection noise, and measurement back-action noise across a wide range of operating conditions. By varying both probe and pump power, over an order of magnitude in probe power and a factor of three in pump power, while maintaining quantum-noise-limited performance, the study provides unprecedented insight into the behaviour of these sensors.
The investigation demonstrates linear, quadratic, and cubic scaling of the total noise powers with probe photon flux, alongside a quadratic dependence of back-action on pump photon flux. These observations are in quantitative agreement with a stochastic Bloch-equation model, validating the theoretical understanding of noise propagation within the system.

At elevated probe powers, probe-induced relaxation was observed to modify the spin-noise spectrum, though the integrated noise scaling remained consistent. This finding highlights the complex interplay between sensor parameters and their impact on overall performance. This research establishes experimentally the limits governing the optimal operation of continuously monitored multiparameter sensors, such as magnetometers, gyroscopes, and instruments designed to detect physics beyond the standard model.
The team independently varied probe and pump powers to control measurement strength and spin polarization, revealing distinct scaling behaviours for each noise component. Specifically, photon shot noise, spin projection noise, and measurement back-action noise exhibited linear, quadratic, and cubic scaling with probe power, respectively, with measurement back-action noise also showing a quadratic dependence on pump power. These results define fundamental, resource-dependent trade-offs crucial for maximizing the sensitivity of these quantum sensors.

Characterisation of fundamental noise sources in an optically pumped rubidium vapour magnetometer

A hybrid radiofrequency-direct current pumped magnetometer served as the core instrument for investigating noise mechanisms limiting continuously operating multiparameter sensors. The experimental setup utilized an optically pumped 87Rb vapor cell in the Bell, Bloom configuration, generating a collective spin polarization that precessed within an applied magnetic field oriented at 45° relative to the pump-probe axis.

Continuous optical measurement drove the evolution of this collective atomic spin, described to leading order by the stochastic Bloch equation, accounting for magnetic field effects, relaxation rates, and optical pumping. To characterise noise contributions, the research team mapped photon shot noise, spin projection noise, and measurement back-action noise across an order of magnitude in probe power and a factor of three in pump power, maintaining noise-limited operation throughout.

Polarization rotation of the probe beam, prepared in squeezed, coherent, or antisqueezed states, was detected using a Wollaston prism and a balanced photodetector, enabling precise measurement of the Stokes components. Detected signals were demodulated at the pump frequency to obtain polarization noise spectra, revealing the dynamical response of the collective spin.

Single-sided noise power spectral density was then calculated, incorporating squeezing and antisqueezing factors, alongside a Lorentzian response function accounting for magnetic resonance linewidth. This methodology enabled the quantification of photon shot noise, spin projection noise, and measurement back-action noise, establishing experimentally the limits governing optimal sensor operation.

Photon and pump power dependence of quantum noise components in a driven spin ensemble

Researchers mapped photon shot noise, spin projection noise, and measurement back-action noise across a ten-fold range in probe power and a three-fold range in pump power while maintaining quantum-noise-limited operation. The study revealed linear scaling of total noise power with probe photon flux for photon shot noise, quadratic scaling for spin projection noise, and cubic scaling for measurement back-action noise.

A quadratic dependence of measurement back-action noise on pump photon flux was also observed, aligning quantitatively with a stochastic Bloch-equation model. At elevated probe powers, probe-induced relaxation modified the spin-noise spectrum without altering the integrated noise scaling. Specifically, the photon shot noise, spin projection noise, and measurement back-action noise demonstrated linear, quadratic, and cubic scaling with probe power, respectively.

Furthermore, measurement back-action noise exhibited a quadratic dependence on pump power, providing a comprehensive understanding of noise contributions. These findings detail fundamental, resource-dependent trade-offs inherent in continuously monitored multiparameter sensors and experimentally define the quantum limits governing their optimal performance.

The work utilized a hybrid radio frequency-direct current optically pumped magnetometer to independently vary probe and pump powers, controlling measurement strength and spin polarization. Analysis of the demodulated polarization noise power spectral density facilitated the precise determination of noise scaling with both probe and pump flux. This research establishes experimentally the quantum noise behaviors governing the operation of these sensors.

Resource-dependent noise scaling defines sensitivity limits in multiparameter magnetometry

Scientists have mapped the fundamental noise limitations affecting the performance of continuously operating multiparameter sensors. Investigations utilising a hybrid radiofrequency-direct current pumped magnetometer revealed the scaling behaviour of photon shot noise, spin projection noise, and measurement back-action noise across a range of optical power levels.

Observed noise powers scaled linearly with probe photon flux, quadratically with spin projection noise, and cubically with measurement back-action, aligning with predictions from a stochastic Bloch equation model. These findings demonstrate resource-dependent trade-offs inherent in continuously monitored spin systems, specifically a balance between high-frequency sensitivity and low-frequency sensitivity.

The observed cubic scaling of measurement back-action with probe power, alongside its quadratic dependence on pump power, indicates an optimal operating point determined by available optical resources. This optimum is anticipated to be broadly applicable to continuously monitored spin systems, irrespective of specific implementation details.

The authors acknowledge a limitation in not fully exploring the characteristics of this optimal operating point. Future research may focus on identifying and characterising this optimum in greater detail, potentially leading to improved sensor design. These results, combined with previous work on noise scaling with ensemble size, provide a comprehensive understanding of quantum noise in these sensors, offering guidance for their optimisation and development. The study establishes experimentally the limits governing the optimal operation of such devices and provides a full picture of the quantum noise landscape for continuously monitored spin ensembles.