Entanglement-Enhanced Magnetic Induction Tomography

Magnetic induction tomography (MIT) is a sensing protocol exploring conductive objects via their response to radio-frequency magnetic fields. MIT is used in nondestructive testing ranging from geophysics to medical applications. Atomic magnetometers, employed as MIT sensors, allow for significant improvement of the MIT sensitivity and for exploring its quantum limits. Here, we propose and verify a quantum-enhanced version of the atomic MIT by combining it with conditional spin squeezing and stroboscopic backaction evasion. We use this quantum enhancement to demonstrate sensitivity beyond the standard quantum limits of one-dimensional quantum MIT detecting a conductive sample.

Figure 1

Setup for entanglement-enhanced MIT. (a) Configuration of rf coils, the probing direction, the bias magnetic field, the conductive sample, and the vapor cell inside the magnetic shield. (b) Simplified experimental setup (top view), where $\lambda /2$ and $\lambda /4$ indicate half- and quarter-wave plates, (P)BS indicates a (polarizing) beam splitter. (c) Illustration of the trajectory of the spin projection ${\overrightarrow{J}}_{\perp }$ (dashed green line) in the presence of the MIT signal, together with the PN of the CSS state (red) and the squeezed state (blue). The insets show the time sequences for the continuous and stroboscopic probing. More visualizations of spin dynamics and quantum noise can be found in Supplemental Material [20].

Figure 2

Generation of a spin-squeezed state of the magnetometer. (a) Pulse sequence used for squeezing demonstration consisting of optical pumping and a train of stroboscopic probing pulses modulated at twice the Larmor frequency. (b) Experimental demonstration of squeezing versus preparation duration ${\tau }_A$ and verification duration ${\tau }_B$ for 15% duty cycle. Green horizontal line (solid): slice for ${\tau }_B=40\mathrm{\mu }\mathrm{s}$ used in subfigure (c). Blue vertical line: slice for ${\tau }_A=220\mathrm{\mu }\mathrm{s}$ used in subfigure (d). Green horizontal line (dashed): slice used for inset in subfigure (d). (c) Achievable squeezing versus ${\tau }_A$ for ${\tau }_B=40\mathrm{\mu }\mathrm{s}$ for 15% (blue), 50% (red), and 90% (green) duty cycle. (d) Projection noise (red), unconditional variance (blue), and conditional variance (green) versus ${\tau }_B$ for optimal ${\tau }_A=220\mathrm{\mu }\mathrm{s}$. The noise is normalized to light shot noise units (SNU). The inset shows squeezing for ${\tau }_B=100\mathrm{\mu }\mathrm{s}$ versus ${\tau }_A$. The error bars in subfigures (c) and (d) are obtained from statistical analysis of eight datasets, each containing 4000 repetitions.

Figure 3

Entanglement-enhanced eddy current measurement. (a) Pulse sequence with rf pulse between stroboscopic probing pulses. (b) Eddy current signals (${\mathrm{S}}_{\mathrm{ec}}$), the difference between sample and background signals, as a function of the rf phase. Each point is averaged over 16 000 measurements, while error bars represent single-shot uncertainty. Blue and red points represent unconditional and conditional results, respectively. The green error bars represent the quantum noise $\sqrt{{\mathrm{SN}}_B+{\mathrm{PN}}_B}$, corresponding to the backaction evaded measurement without squeezing, horizontally shifted for clarity. The inset shows the unconditional (blue) and conditional (red) signal distribution for the rf phase of 90°.

Figure 4

Entanglement-enhanced 1D MIT. The statistical distribution of the sample center found from 1D MIT scanning 50 mm in 1 mm steps. One hundred red (blue) points corresponding to the results for the position of the center of the sample obtained with (without) spin entanglement. Each point is averaged over 40 measurement repetitions. The red (blue) shaded areas cover the red (blue) data points within one standard deviation.