Magnetotactic bacterial populations studied with a Pound-Drever-Hall atomic magnetometer

TL;DR

The study addresses measuring the magnetic relaxation of magnetotactic bacteria in bulk under external fields using a compact cavity-enhanced optically pumped magnetometer with Pound-Drever-Hall readout. The authors implement a mm-scale $^{87}$Rb OPM inside a planar optical cavity, achieving a noise floor of $22.2~\text{pT}/\sqrt{\text{Hz}}$ and an Allan deviation minimum of $47~\text{pT}$ at $\tau=6~\text{s}$, suitable for slow biophysical signals, even in open shielding. They observe deviations from exponential relaxation in Magnetospirillum gryphiswaldense MSR-1 suspensions, attributable to distributions in magnetic moment $m$ and rotational damping $\gamma_r$, and show that evaporation-induced concentration broadens these distributions and creates an immobile fraction ($\gamma_r=\infty$), providing direct insight into magnetic inhomogeneities. This work demonstrates the utility of compact, stable OPMs for imaging collective magnetic dynamics in opaque biological media, with potential implications for magnetic microscopy and single-cell or bulk biomagnetism studies.

Abstract

We demonstrate an optically pumped magnetometer that monitors spin polarization using Pound Drever Hall (PDH) technique. The instrument exhibits a noise floor of 22.2 pT/sqrt(Hz) limited by optical photon shot noise, short-term instability of 30.8 pT/sqrt(Hz)/sqrt(τ) for averaging times τ < 0.2 s , instability below 70 pT for 0.2 s < τ < 20 s and a minimum instability of 47 pT at τ = 6 s. We apply the OPM to investigate the ability of magnetotactic bacteria (Magnetospirillum gryphiswaldense, MSR-1) to orient in externally applied magnetic fields. Observing an opaque, concentrated suspension, we detect deviations from exponential relaxation dynamics on second time-scales, which give information about the dispersion of bacterial magnetic moment and rotational damping coefficient. These parameters are observed to evolve as the population further concentrates due to evaporation and settling. To our knowledge, this is the first time such magnetic inhomogeneities and long-term relaxation deviations have been directly observed. This study showcases both the sensitivity and stability of our OPM and its potential for probing biophysical processes.

Figures (6)

• Figure 1: Experimental setup. Pump and probe beams are coupled into a fiber coupler (FC) and reach the atomic vapor within the cavity in the same collinear mode. The probe light is modulated in phase, the pump light is amplified and modulated in amplitude. Pumping scheme is shown with purple continuous line in the diagram. The reflected probe is collected by a 1.4-GHz bandwith photodetector PD, whose output is fed into a Pound-Drever-Hall (PDH) circuit giving an output error signal $\epsilon$. When locking to the zero-crossing point, $\epsilon$ follows atomic precession, as show in the diagram above, where blue line is raw data and black line a fitting to Equation \ref{['Eq:FID']}. $S_H$ in red is the voltage sent to the heater. There are two coils to generate magnetic fields in two perpendicular directions, the shielding coil and the polarizing coil. In the bottom, picture of the optical cavity in the shield with one cap open. The 3D-printed structure is glued to the base of the cavity using epoxy. Positioned above this is the bacteria holder, which incorporates the polarizing coil. This holder is not permanently fixed to the structure, allowing for easy removal and portability. On the right, a photograph displays the opened, bacteria holder containing the solution. LDC - laser diode current controller, TEC - laser diode temperature controller, EOM - electro-optic modulator, TA - tapered amplifier, ISO - optical isolator, AOM - acousto-optic modulator, RFD - radio frequency driver, FG - function generator, VCO - voltage-controlled oscillator, FM - frequency mixer, LPF - low-pass filter, DAQ - digital oscilloscope. Sketch of the cavity with detection in reflection. DWP - dual wavelength wave-plate, PBS - polarizing beam splitter, QWP - quarter wave-plate, BPF - laser line bandpass filter, PD- photo-detector, M1 / M2 - first/second planar cavity mirror.
• Figure 2: Magnetometer sensitivity and stability. Left: measured OPM equivalent magnetic noise (Amplitude spectral density ) for applied DC fields of 17µT (red) and 147µT (blue) along the $z$ direction. Dashed line indicates a noise floor of 22.2pT√Hz. Spectra averaged 10 times. Right: overlapping Allan deviation (OAD). With an applied field of 17µT, a single acquisition of 22.6s duration, filtered with fourth-order, 2Hz-wide IIR bandstop filters at 50Hz, 100Hz, 150Hz and 200Hz. Dashed line shows the OAD of uncorrelated white noise: $\sigma = (30.8pT\per\sqrt Hz ) \tau^{-1/2}$.
• Figure 3: Top plots: Experimental sequence of applied magnetic fields. Bottom: Bacteria alignment towards the resultant field when turning off the polarizing field, in this case $B_\mathrm{DC}=34µT$. Black and gray curves show the field $B_z$ and the inferred magnetization (by Equation \ref{['eq:BzFromCosTheta2']}) $M_\mathrm{full} \langle \cos{\theta} \rangle$ respectively. The dataset consisted of 20 repeated measurements. A moving average with a window of 60ms was applied to each individual trace. Then, the resulting traces were averaged across the 20 measurements to obtain the final signal. Red curve fits the data with $C + A (1-\exp[-t/\tau_B])$. Blue curve fits the data with Equations \ref{['eq:BzFromCosTheta1']} and \ref{['eq:ExpFormB']} to find $B_\mathrm{DC}=34µT$, $|B_\mathrm{MTB}^{(\infty)}|=25.7nT$ and $\tau_B=0.99s$. Pink colored area shows polarization field on and gray area dead time between different measurements.
• Figure 4: Measured magnetic relaxation characteristics of MTB-1. Left: bacteria signal amplitude when changing $B_\mathrm{DC}$. The dots represent experimental data after 20 averages and low pass filter. Right plot shows the inverse of the lifetime $\tau_B$ for different magnetic fields. In both plots dashed line represents computed relaxometry features from Eq. \ref{['eq:ThetaSDEtext']} from initial condition $\theta = \pi/2$ and parameters $m = 0.238e-15Am\squared$, $\gamma_r = 1.28e-20kgm\squared\per s$, $T = 32\celsius$. Simulations averaged a minimum of $10^4$ realizations to compute $\langle \cos \theta \rangle$ versus time, then fit with Eq. \ref{['eq:ExpFormB']} to extract best-fit equilibrium $B_\mathrm{MTB}^{(\infty)} = \lim_{t\rightarrow \infty} B_\mathrm{MTB}(t)$ and relaxation rate $\tau_B^{-1}$. Light blue colored area in the right plot indicates the error from simulation. Left plot error bars are smaller than the plot markers and are not shown.
• Figure 5: Non-exponential relaxation of magnetization from Equation \ref{['eq:ThetaSDEtext']}. Dashed blue curves show average of 1e6 traces starting from $\theta = 0$ with $B = 151.4µT$, $T = 32\celsius$, and $m = x_m \times 0.238e-15Am\squared$ and $\gamma_r = x_\gamma \times 1.28e-20kgm\squared\per s$. Green solid curve shows fit with $\langle \cos\theta \rangle = C + A (1-\exp[-t/\tau_B])$. Red curve shows residuals (simulation minus fit) times ten. Upper left graph shows a monodisperse population with $x_m = x_\gamma =1$, upper right shows a $m$-mixed population with $x_\gamma =1$, $x_m$ log-normal distributed with $E[\ln x_m] = 0.$, $\mathop{\mathrm{var}}\nolimits(\ln x_m) = 4/9$, lower left shows a $\gamma_r$-mixed population with $x_m =1$, $x_\gamma$ log-normal distributed with $E[\ln x_\gamma] = 0.$, $\mathop{\mathrm{var}}\nolimits(\ln x_\gamma) = 4/9$. Lower right shows $x_m$ and $x_\gamma$ independently log-normal distributed with $E[\ln x] = 0.$, $\mathop{\mathrm{var}}\nolimits(\ln x) = 4/9$, for $x\in \{x_m,x_\gamma\}$. The results show that the relaxation in none of the cases is precisely exponential, and that dispersion of $m$ or of $\gamma$ cause similar deviations.