Spin damping in an rf atomic magnetometer

Under negative feedback, the quality factor $Q$ of a radio-frequency atomic magnetometer can be decreased by more than two orders of magnitude, so that any initial perturbation of the polarized spin system can be rapidly damped, preparing the magnetometer for detection of the desired signal. We find that noise is also suppressed under such spin damping, with a characteristic spectral response corresponding to the type of noise; therefore magnetic, photon shot, and spin-projection noise can be measured distinctly. While the suppression of resonant photon shot noise implies the closed-loop production of polarization-squeezed light, the suppression of resonant spin-projection noise does not imply spin squeezing, rather simply the broadening of the noise spectrum with $Q$. Furthermore, the application of spin damping during phase-sensitive detection suppresses both signal and noise in such a way as to increase the sensitivity bandwidth. We demonstrate a threefold increase in the magnetometer's bandwidth while maintaining 0.3 fT/$\sqrt{\mathrm{Hz}}$ sensitivity.

Figure 1

Experimental setup (a) and schematic (b) of the spin-damping mechanism. A perturbing magnetic field $B_1$ sets the optically pumped potassium atoms precessing around $B_0$. The resulting transverse atomic polarization $P_x$ rotates the probe beam's polarization, which is detected and converted to an electrical signal $V_{\mathrm{out}}$ by a balanced polarimeter. Part of this electric signal is phase corrected and fed back through electromagnetic saddle coils to produce a damping field $B_{\mathrm{fb}}$ that is antiparallel to $B_1$, resulting in an active damping of the K transverse polarization. The strength of the damping is characterized by the open loop gain, $D=\alpha \beta P_z{\gamma }_{\mathrm{K}}{T}_2/2$.

Figure 2

Spectra of measured magnetometer noise (dotted lines) for various damping factors (lower curves are at higher damping factors), showing suppression of on-resonance noise amplitude $A_n$ at the higher damping factors to well below photon shot noise, which is the measured noise with no pump beam (flat red solid curve). Also plotted is the expected photon shot noise (black dashed line). The noise spectra for each damping factor is fitted to Eq. (27) (solid lines). The inset shows similar suppression of the magnetometer output to an applied reference rf magnetic field of $209\mathrm{fT}$ (points with error bars), fitted to a Lorentzian function (solid lines). Acquisition time was 16.4 ms, more than an order of magnitude larger than K $T_2$. This data is expressed both in volts from the polarimeter output, left axis, and rotation angle of the probe polarization, right axis.

Figure 3

The magnetometer signal amplitude suppression, defined as $A_s^0/A_s$ (solid navy circles), and linewidth expansion, defined as ${\Gamma }_s/{\Gamma }_s^0$ (open navy circles), scale as $(1+D)$ (black line). The on-resonance noise amplitude suppression, $A_n^0/A_n$ (solid orange squares), is linear at low damping factors ($<20$) but clearly reaches a noise limit at higher $D$, while the expansion of noise width, ${\Gamma }_n/{\Gamma }_n^0$ (open orange squares), is linear for the range of damping factors measured.

Figure 4

For cell 1 (open navy circles) and cell 2 (solid orange squares), the plot of resonant noise power $A_n^2$ as a function of suppression, fitted to a quadratic polynomial (solid lines). The values of all parameters for the two cells are given in Table .

Figure 5

Plot of the measured magnetometer $\mathrm{SNR}$ (open points) and bandwidth (solid points), for both cell 1 (navy squares) and cell 2 (orange circles), shows good agreement to the predicted (lines) values. The inset is the magnetometer $\mathrm{SNR}$ for three damping factors (larger widths correspond to higher damping factors) as a function of frequency for cell 2, and shows that sensitivity bandwidth can be broadened with little loss of SNR for $D\le 20$.

Figure 6

Plots (a) and (b) demonstrate the application of spin damping with the magnetometer initially in a perturbed state, a state created by a resonant rf pulse of amplitude $1.13\mathrm{pT}$ applied for $t\le 0$. (a) The magnetometer response to a $0.37\mathrm{pT}$ rf signal, applied at $t=60\mu \mathrm{s}$, is obscured by the transient ringing from the initial perturbed state (dashed line). Application of spin damping during a short window quickly eliminates the transient and permits the clear observation of the signal (solid line) as compared to when there is no initial perturbation (dotted line). (b) The ringing transient naturally decays with a time constant of $T_2=0.7\mathrm{ms}$ (dashed line), but under damping, the transient decays in less than $60\mu \mathrm{s}$ (solid line). However, due to inhomogeneity in $B_0$ across the K cell, a small feedback hump arises after the damping field is turned off.

Figure 7

Results showing that application of spin damping can reduce the negative effects of perturbation noise and recover the magnetometer sensitivity. Two forms of damping are tested. Both start with $D=150$ for the first $20\mu \mathrm{s}$ of the $60\mu \mathrm{s}$ feedback window, but in one the damping is smoothly reduced to zero, while in the other, the damping is reduced to 10 and kept at this value throughout the acquisition window. SNR is measured for a $24\mathrm{ms}$ (sparse hatching) and a $1.5\mathrm{ms}$ (dense hatching) window in the absence, columns 1–3, and in the presence, columns 4–8, of ringing created by a perturbing pulse three times larger than the detected signal. As shown in 1–3, the switching off of damping adds noise, but with damping retained during acquisition the SNR is regained. Measurement 4 shows the significant loss of SNR due to noise from an initial perturbation of the K spins. The SNR is partially regained with damping (5). The addition of phase cycling (6) or damping during the window (7) further increases the SNR, and with the combination of the two techniques (8) the SNR for both window sizes is in agreement with the SNR when ringing is not present (1).