Restoring Narrow Linewidth to a Gradient-Broadened Magnetic Resonance by Inhomogeneous Dressing

We study the possibility of counteracting the line broadening of atomic magnetic resonances due to inhomogeneities of the static magnetic field by means of spatially dependent magnetic dressing, driven by an alternating field that oscillates much faster than the Larmor precession frequency. We demonstrate that an intrinsic resonance linewidth of 25 Hz that has been broadened up to hundreds of hertz by a magnetic field gradient can be recovered by the application of an appropriate inhomogeneous dressing field. The findings of our experiments may have immediate and important implications, because they enable the use of atomic magnetometers as robust, high-sensitivity sensors to detect in situ the signal from ultralow-field NMR-imaging setups.

Figure 1

Simplified schematics of the magnetometer and the field arrangement. The optical axis of the sensor is $x$. A static magnetic field—oriented in the $z$ direction—with the main component dependent on the $x$ coordinate due to a static quadrupolar term, producing a gradient $G=\mathrm{\partial }{B}_z/\mathrm{\partial }x$. The concomitant $\mathrm{\partial }{B}_x/\mathrm{\partial }z$ term has no first-order effects on the atomic precession [the presence of a small $x$ component of the field, amounting to ($\mathrm{\partial }{B}_x/\mathrm{\partial }z)\mathrm{\Delta }z\ll B_z$ over the beam radius $\mathrm{\Delta }z$, has only second-order effects, as also discussed in the Appendix, Eq. (A2)]. An electromagnetic dipole (D) oriented along $x$ produces an oscillating (dressing) magnetic field $B_D$ at a frequency well above the Larmor frequency, oriented along $x$, the strength of which decreases along that direction. Cs, cesium cell; F, interference filter stopping the pump radiation; ${\mathrm{L}}_1$, pump laser; ${\mathrm{L}}_2$, probe laser; P, balanced polarimeter.

Figure 2

Atomic magnetic resonance under different conditions. The plot with open circles shows the unperturbed resonance. The plot with solid circles is obtained in the presence of a static magnetic field gradient. The plot with solid squares is obtained with no static gradient but in the presence of a strong, transverse, inhomogeneous field that oscillates much faster than the Larmor precession ($\omega =2\pi 32$ kHz). This dressing field (amplitude of about 2.4 $\mu \mathrm{T}$) produces a resonance shift that broadens the resonance due to its inhomogeneity (600 nT/cm). With opportune amplitude and frequency values of the dressing field, the two broadening mechanisms compensate each other, and a shifted but narrow resonance can recorded, as shown in the plot with open squares. PS, power spectrum.

Figure 3

Resonance profile under suppressed-broadening conditions for different values of $G$. The circles are the amplitudes measured and the lines are best fits targeted to a Lorentzian profile. A progressive shift toward lower frequencies occurs, consistent with Eq. (3). Simultaneously, the profile width increases slightly. Above 100 nT/cm, some deviations from the Lorentzian model, due to the higher-order terms [Eq. (5)], appear as an increase in the low-frequency wing. The leftmost plot (recorded at 140 nT/cm) would appear as a 1-kHz broadened resonance in the absence of the dressing field. PS, power spectrum.

Figure 4

NMR signal from a 4-ml ${\mathrm{H}}_2\mathrm{O}$ sample. (a) The NMR signal in a homogeneous field with neither $G$ nor $B_D$ applied. The trace is obtained by our averaging over 100 shots. (b) The NMR signal recorded in the presence of $G=50$ nT/cm and $B_D=3\mu \mathrm{T}$. The trace is obtained by our averaging over 400 shots.

Figure 5

Tap-water proton NMR spectra of the signals under different gradient conditions. (a) Spectrum obtained with $G=0$ and $B_D=3\mu \mathrm{T}$: a narrow NMR is recorded, with low signal-to-noise ratio, because the protons are not affected by $B_D$, while $\mathrm{Cs}$ atoms are, so only a slice of the sensor is effectively pumped. (b) Spectrum obtained from the data shown in Fig. 4: $G=0$ and $B_D=0$ produce a narrow NMR with high signal-to-noise ratio. (c) Spectrum corresponding to the trace shown in Fig. 4: here the static gradient $G$ broadens the NMR spectrum. The IDEA method allows the same spectrum to be recorded with a high signal-to-noise ratio. ASD, amplitude spectral density.

Figure 6

Plots of the measured $\rho (x)\eta (x)$ (blue), the estimated $\eta (x)$ (red), and the inferred $\rho (x)$ (black), which can be compared with the sample shape represented in the upper part. The data are the same as shown in the plots in Figs. 4 and 5. Some position jitter of the sample occurs and is detected shot by shot by the camera. To limit the consequent image blurring, only traces corresponding to sample positioning within a $\pm 3$-mm interval are selected.

Figure 7

Arrangement of the sensor and sample. Both have cylindrical shapes with axes oriented along $x$. The sensor is a differential one and gradiometrically measures the $\mathrm{\partial }{B}_z/\mathrm{\partial }z$ term of the field generated by the sample. To this aim, the two halves of the probe beam—represented by the two-colored cylinder within the cell—are analyzed separately. Each slice of the sample (characterized by its $x$ coordinate) produces a signal at its specific frequency (MRI frequency encoding). Each slice of the sensor ($x^{\mathrm{\prime }}$ coordinate) is differently coupled with various slices of the sample (slices are represented by dashed boxes). The coupling factor $\eta$ is evaluated on the basis of a model in which all the sample slices are modeled as dipolar field sources, and all the sensor slices contribute additively to the polarimetric signal.