Sensing high-frequency ac fields via a two-qubit sensor

TL;DR

The paper addresses the challenge of sensing high-frequency oscillating fields with quantum sensors, where single-qubit pulsed schemes demand unrealistically short intervals and suffer from pulse-width errors. It introduces a two-qubit sensor that leverages a field-induced modification of the inter-qubit coupling; in the high-frequency frame, the Hamiltonian becomes effectively time-independent, and the field amplitude is inferred from the interaction shift. The authors derive that the measurement observable $M$ yields a Fisher information $I(b) = \left(\frac{8gt}{\omega}\right)^2 \left[J_1\left(\frac{4b}{\omega}\right)\right]^2$, which matches the quantum Fisher information, indicating an optimal readout; the scheme remains robust to unknown phase $\phi$ and can accommodate noise. While noise imposes a finite ceiling on the information, applying XY4-like pulses in a toggling frame substantially mitigates decoherence effects, extending viable interrogation times even when pulse spacing is not ultra-short. Overall, this two-qubit approach offers a practical path to precise high-frequency field metrology with intrinsic phase robustness and noise-resilience.

Abstract

Quantum sensors allow us to measure weak oscillating fields with incredible precision. One common approach is to use the time evolution of a single two-level system (or a qubit) in conjunction with applied control pulses to measure the oscillating field. For high-frequency fields, the time interval required between the applied pulses decreases, meaning that errors due to the finite width of the pulses can become important. This paper presents an alternative scheme that does not rely on applying pulses with short time intervals. Our scheme uses two interacting qubits. In the presence of an oscillating field, the interaction strength changes. The oscillating field can be estimated by measuring the change in this interaction strength. We quantify the precision of this estimate by calculating the Fisher information. We show the effect of noise on our scheme and discuss how control pulses can be applied to mitigate the impact of noise. Importantly, the time interval between these pulses need not be very short.

Figures (6)

• Figure 1: $\langle M(t) \rangle$ as a function of time $t$ with the full time-dependent Hamiltonian (solid, black curve), the effective time-independent Hamiltonian (dashed, red curve), and the original Hamiltonian with no oscillating field present (dot-dashed, blue curve). As usual, we are working in dimensionless units with $\hbar = 1$, and we have set $g = 1$. We have used $b = 1$ and $\omega = 10$.
• Figure 2: Plot of the Fisher information $I(b)$ as a function of time $t$. The solid, black curve is the Fisher information with our two-qubit sensor, while the dashed, red curve is the Fisher information with a single qubit sensor. As usual, we are working in dimensionless units with $\hbar = 1$, and we have set $g = 1$. Also, $b = 1$ and $\omega = 10$. The figure in the inset is the same as the main figure, except that we have zoomed in to show the behavior of the Fisher information at small times.
• Figure 3: $\langle M(t) \rangle$ as a function of time $t$ with the full time-dependent Hamiltonian with $\phi = 30^\circ$ (solid, black curve), the effective time-independent Hamiltonian in Eq. \ref{['a3']} (dashed, red curve), and the original Hamiltonian with no oscillating field present (dot-dashed, blue curve). As usual, we are working in dimensionless units with $\hbar = 1$, and we have set $g = 1$. We again have $b = 1$ and $\omega = 10$.
• Figure 4: $I(b)$ as a function of time $t$. Here we are using $f_1(t) = \frac{1}{2}\left(1 + e^{-t/T_1}\right)$ and $f_2(t) = e^{-t/T_2}$. The dashed, black curve shows the behavior of the Fisher information with $T_1 = 300$ and $T_2 = 200$, while the solid, red curve shows the behavior with $T_1 = 200$ and $T_2 = 100$. The dot-dashed magenta curve is the Fisher information in the absence of noise. As usual, we are working in dimensionless units with $\hbar = 1$, and we have set $g = 1$. Also, $b = 1$ and $\omega = 10$. The figure in the inset is the same as the main figure, except that we have zoomed in to show the smooth oscillations of the Fisher information [see Eq. \ref{['fishereqwithnoise']}].
• Figure 5: $\langle M(t) \rangle$ (in the toggling frame) as a function of time $t$ without noise (solid, black curve), with noise (dot-dashed, blue curve), and with noise but with pulses also applied (red, dashed curve). For the noise (see the main text), we have used $\mu = 0$, $\sigma = 0.2$, and $\tau = 50$. We have taken an average of $50$ simulations. As usual, we are using dimensionless units with $\hbar = 1$, and $g = 1$, $b = 1$, and $\omega = 10$.