Frequency-selective Quantum Sensing Achieves Weak Signal Detection with Tunable Thresholds

Detecting faint, time-varying signals amidst background noise represents a significant hurdle in precision measurement, particularly when these signals manifest as specific frequency changes within a larger field. Ricard Puig of the Ecole Polytechnique Fédérale de Lausanne, Nathan Constantinides from the University of Maryland, and Bharath Hebbe Madhusudhana of Los Alamos National Laboratory, alongside colleagues, present a novel quantum sensing technique that addresses this challenge. Their research details a method utilising static interactions and quantum entanglement to create a passive, adjustable filter for target frequencies. This innovative approach encodes frequency selection and a sensitivity threshold directly into the quantum system’s behaviour, enabling a response only to signals exceeding a defined amplitude at the desired frequency, thereby simplifying both experimental control and data analysis.

Tunable Quantum Sensor Filters Time-Dependent Signals

Scientists demonstrate a novel quantum sensing technique capable of detecting weak, time-dependent signals with unprecedented efficiency. The research, detailed in a recent publication, introduces a quantum sensor that functions as a passive, tunable frequency filter, circumventing the need for complex control schemes and extensive post-processing typically required in conventional methods. This breakthrough leverages time-independent interactions and entanglement to selectively respond to target frequencies above a defined threshold, effectively isolating desired signals from background noise. The team achieved this by encoding frequency selectivity and thresholding directly into the sensor’s dynamics, creating a system responsive only to specific signal characteristics.

The study reveals a new approach to background cancellation in quantum sensing, addressing a key challenge in detecting subtle perturbations in fields obscured by noise. Researchers designed a two-qubit sensor initialized in a Bell state, where one qubit is exposed to both the signal and background fields, while the other experiences only the background. Through controlled, time-independent interactions, the background field is coherently cancelled, leaving the sensor responsive solely to the target frequency and amplitude of the desired signal. This innovative protocol is effective even with random, fluctuating backgrounds, a unique feature distinguishing it from existing techniques.

Experiments show the sensor’s ability to isolate the Fourier amplitudes of a signal, providing a simple response function that encodes information about the perturbation without relying on detailed assumptions about the signal itself. The research establishes a method for determining the Fourier coefficients of the signal, revealing the presence of specific frequencies and enabling reconstruction of the full signal vector. By expanding the signal vector in the Fourier basis, the sensor accurately identifies and measures time-dependent signals, even in scenarios where the signal’s characteristics are not fully known. This work opens new possibilities for detecting low-probability events in diverse fields, ranging from physics and biology to engineering.

The sensor’s sensitivity to rare occurrences, such as traces of rare molecules or small perturbations in magnetic fields, could facilitate advancements in areas like materials science and medical diagnostics. The ability to sensitively detect signals at a specific frequency with minimal post-processing represents a significant step towards more robust and efficient quantum sensing technologies, paving the way for future applications in fundamental research and practical devices. The probability of obtaining an even-parity outcome is approximately T 2 ∥s ω0 ∥ 2 /2 12, demonstrating the sensor’s capacity for weak signal detection.

Passive Quantum Filtering of Time-Dependent Signals

Detecting weak, time-dependent signals presents a significant challenge in sensing technologies, often requiring intricate dynamical control and extensive post-processing of data. This study pioneers a novel quantum sensing approach that utilizes time-independent interactions and entanglement to create a passive, tunable frequency filter, circumventing the need for complex control schemes. The research team engineered a system responsive only to target frequencies exceeding a defined threshold, effectively reducing computational demands after signal acquisition. Scientists began by considering the most general single qubit signal, defined as HS(t) = s(t) · σ, where s(t) represents the signal’s direction and magnitude, and σ denotes the vector of Pauli operators.

Expanding this signal in the Fourier basis, s(t) = Σω ssω sin(ωt) + scω cos(ωt), allowed the researchers to isolate specific frequency components and reconstruct the full signal vector. The study addresses the inherent difficulty in sensing time-dependent signals, contrasting it with the linear phase accumulation observed in time-independent fields, and highlights the limitations of standard control pulse techniques which demand precise experimental control. The core of this work lies in a two-qubit sensor designed to isolate Fourier amplitudes of the signal while suppressing background contributions. The protocol initiates with the preparation of the system in a Bell state, |Ψ−⟩= 1/√2(|10⟩−|01⟩), where one qubit is exposed to both the signal and background fields, while the second experiences only the background.

Subsequently, the qubits evolve under time-dependent. Measurements are then performed along the direction of the control operator (nω0 ·σ)⊗1+1⊗(nω0 ·σ), revealing a probability of obtaining an even-parity outcome of approximately p ≈ T/2 ∥sω0∥ / 12. This response function demonstrates the sensor’s selectivity, responding only to signals containing a component at the target frequency ω0 and remaining insensitive to the background field, with the squared norm of the signal’s Fourier components calculated as ∥sω0∥ = ∥ssω0∥ + ∥scω0∥. This innovative method not only estimates signal amplitude but also provides a robust detection capability.

Single-shot Detection via Thresholded Frequency Filtering

Scientists achieved a breakthrough in weak signal detection by developing a passive, tunable frequency filter that circumvents the need for complex control schemes and reduces post-processing demands. The research centers on a system leveraging time-independent interactions and entanglement to function as a thresholded frequency filter, responding only to target frequencies exceeding a defined amplitude. Experiments across 200 realizations demonstrated that an even-parity measurement outcome is impossible without the presence of a signal at the target frequency, enabling single-shot detection capabilities. The team measured the response probability as a function of control frequency, revealing that the response vanishes entirely when the signal amplitude is zero.

Analytical calculations bound the estimator error, showing it scales cubically with the perturbation amplitude when the signal strength is comparable to the background noise; specifically, the error |r| is bounded by a function dependent on the integral of the signal’s squared norm over time. Numerical simulations, performed with randomly sampled background and signal functions, confirmed this bound, with polynomial regressions yielding a leading term scaling of 9.78 × 10−4 ε3 + 6.56 × 10−3 ε4 for the average case and 4.57×10−2 ε3 +2.74×10−2 ε4 for the worst case, where ε represents the signal strength. Scaling the protocol to a multi-qubit system, researchers demonstrated the potential for Heisenberg scaling (HS) sensitivity. Calculations of the Classical Fisher Information (CFI) revealed that a system of 2N qubits exhibits a CFI scaling of N2, consistent with the HS limit, where standard deviation decreases proportionally to 1/N. This was achieved by partitioning the qubits into two subsystems and measuring collective spin operators, resulting in a probability scaling quadratically with the number of qubits, approximately N2p, where p is the probability from a single-qubit measurement. This work introduces a quantum sensor functioning as a frequency-selective filter, capable of eliminating background fields and performing in situ information processing.