# An optically pumped magnetic gradiometer for the detection of human
biomagnetism

Harry Cook  School of Physics and Astronomy, University of Birmingham,
Edgbaston, Birmingham, B15 2TT, United Kingdom  Yulia Bezsudnova  School of
Physics and Astronomy, University of Birmingham,
Edgbaston, Birmingham, B15 2TT, United Kingdom  Lari M. Koponen  Centre for
Human Brain Health, School of Psychology, University of Birmingham,
Edgbaston, Birmingham, B15 2SA, United Kingdom  Ole Jensen  Centre for Human
Brain Health, School of Psychology, University of Birmingham,
Edgbaston, Birmingham, B15 2SA, United Kingdom  Giovanni Barontini  School of
Physics and Astronomy, University of Birmingham,
Edgbaston, Birmingham, B15 2TT, United Kingdom  Centre for Human Brain Health,
School of Psychology, University of Birmingham,
Edgbaston, Birmingham, B15 2SA, United Kingdom  Anna U. Kowalczyk
<EMAIL_ADDRESS>Centre for Human Brain Health, School of Psychology,
University of Birmingham,
Edgbaston, Birmingham, B15 2SA, United Kingdom

###### Abstract

We realise an intrinsic optically pumped magnetic gradiometer based on non-
linear magneto-optical rotation. We show that our sensor can reach a
gradiometric sensitivity of 18 fT$/\text{cm}/\sqrt{\text{Hz}}$ and can reject
common mode homogeneous magnetic field noise with up to 30 dB attenuation. We
demonstrate that our magnetic field gradiometer is sufficiently sensitive and
resilient to be employed in biomagnetic applications. In particular, we are
able to record the auditory evoked response of the human brain, and to perform
real-time magnetocardiography in the presence of external magnetic field
disturbances. Our gradiometer provides complementary capabilities in human
biomagnetic sensing to optically pumped magnetometers, and opens new avenues
in the detection of human biomagnetism.

##  I Introduction

Highly sensitive magnetometers [1] have a diverse range of applications that
span from geophysics and exploration [2], to non-destructive magnetic
materials testing [3, 4, 5], archaeology and palaeomagnetism [6],
environmental monitoring [7], navigation and positioning [8], space
exploration [9], biology, neuroscience [10, 11, 12], and fundamental physics
research [10, 13]. Over the past few decades, advances in quantum science
spurred the development of various types of magnetometers with very different
operating principles: from electron spin resonance magnetometers such as
SQUIDS to optically pumped magnetometers with NV centers in diamond or thermal
atoms.

Optically pumped magnetometers (OPMs) based on thermal atoms are able to
achieve subfemtotesla sensitivities [14] and do not require cryogenics, so
that they are compact, portable and inexpensive. Therefore, they are emerging
as the preferred sensors in biomagnetism applications previously dominated by
SQUIDs [15, 16, 17, 18, 19, 20]. In human brain imaging in particular, new
capabilities have been demonstrated when OPMs are used for
magnetoencephalography (MEG) [21, 22, 23, 24]. MEG normally requires the
detection of both magnetic fields and magnetic field gradients, with these
latter enabling higher spatial resolution and better localization of the
biomagnetic source [25, 26, 27, 28]. In general, the measurement of the small
magnetic fields produced by the human body is strongly affected by
environmental magnetic field noise, whose cancellation and shielding is
expensive and cumbersome [21, 29, 30, 31]. Measuring magnetic field gradients
can help in circumventing or simplifying this problem.

Several types of optically pumped magnetic gradiometer (OPMG) have been
realised. In the so-called synthetic gradiometers, signals from two or more
closely spaced sensors are subtracted digitally or electronically. Such a
configuration suppresses the common mode magnetic field noise, but enables
only reduced sensitivity [32]. Semi-intrinsic OPMGs use a single laser beam
split into either two [33] or multiple measurement channels [34]. The signals
produced are electronically subtracted enabling superior sensitivity.
Intrinsic OPMGs directly subtract common-mode magnetic field noise before
converting the magneto-optical rotation signal to a photocurrent. This
eliminates the need of post-processing and does not degrade the sensor’s
sensitivity [35, 36, 37, 38, 39, 40].

In this work, we realise an intrinsic OPMG based on non-linear magneto-optical
rotation (NMOR). We show that our OPMG can reach sensitivities of 18
fT$/\text{cm}/\sqrt{\text{Hz}}$ while being resilient to fluctuations of
external magnetic fields, that can be suppressed up to 30 dB. We demonstrate
that such an OPMG is sufficiently sensitive and resilient to be employed in
human biomagnetic applications such as MEG and magnetocardiography. In
particular, we are able to measure the magnetic field gradient produced by the
auditory evoked field in the human brain, and the magnetic field gradient
produced by cardiac activity in the presence of external magnetic field
disturbance.

This work is organised as follows: in section II we describe the working
principle of our OPMG, in section III we detail the design of our sensor, in
section IV we report the testing of the performance of our sensor in a
controlled environment, in section V we present the applications of our sensor
in MEG and magnetocardiography experiments, and in in section VI we report our
conclusions.

##  II Working principle

In an NMOR magnetometer, amplitude or frequency-modulated linearly polarised
resonant light is used to induce spin precession in an atomic gas. A static,
homogeneous bias magnetic field applied along the direction of propagation of
the light sets the Larmor frequency. Changes in the external magnetic field
increase or decrease the Larmor frequency, and are detected by monitoring the
rotation of the light polarisation that happens synchronously with the
modulation [41].

Figure 1:  Intrinsic gradiometer operating principle. (a) A laser beam passes
through two cells (C1 and C2) with equal bias fields $\vec{B}_{0}$ pointing in
opposite directions and is retroreflected on a mirror. The half-waveplate
($\lambda$/2) between the cells flips the sign of the resonance generated in
C2 allowing constructive addition of NMOR resonances. (b) Magnetic fields
along the sensitive axis of the gradiometer: $B_{e}$ is the homogeneous
external field and $b$ is the differential magnetic field between two cells
separated by the gradiometer baseline $d$. (c) The continuous line is the
total phase of the gradiometer in (a) as a function of the frequency, in the
presence of the magnetic field in (b). The dotted lines show the behaviour of
the phase in the case the cells were probed independently.

The working principle of our OPMG is an extension of the NMOR technique. Fig.
1(a) shows the basic elements of the gradiometer: a near-resonant laser beam
passes through two vapour cells and is retroreflected. The bias fields in the
two cells have the same magnitude $B_{0}$ but opposite directions. A waveplate
between the two cells rotates the polarisation by $\pi$, ensuring constructive
addition of the NMOR resonances. Supposing that, as shown in Fig. 1 (b), the
gradiometer is immersed in an external magnetic field with amplitude
$B=B_{e}+B^{\prime}z$ directed along the direction of propagation of the light
$z$, the signal produced is the sum of the NMOR signals in each cell:

$Q_{G}+iP_{G}=[Q_{C1}+Q_{C2}]+i[P_{C1}+P_{C2}]$ (1)

where $Q_{G}$ and $P_{G}$ are the total quadrature and in-phase signals, and
$Q_{Ci}$ and $P_{Ci}$ denote the quadrature and in-phase components of the
signal produced in each cell. By writing the two contributions explicitly, we
obtain:

$\displaystyle Q_{G}(\omega)$ $\displaystyle=$ $\displaystyle
A_{1}\left(\frac{\Gamma_{1}}{2}\right)^{2}\frac{1}{[\omega-\omega(B_{0}+B_{e}+b)]^{2}+(\Gamma_{1}/2)^{2}}$
(2) $\displaystyle+$ $\displaystyle
A_{2}\left(\frac{\Gamma_{2}}{2}\right)^{2}\frac{1}{[\omega-\omega(B_{0}-B_{e})]^{2}+\left(\Gamma_{2}/2\right)^{2}}$

$\displaystyle P_{G}(\omega)$ $\displaystyle=$ $\displaystyle
A_{1}\frac{\Gamma_{1}}{2}\frac{\omega-\omega(B_{0}+B_{e}+b)}{[\omega-\omega(B_{0}+B_{e}+b)]^{2}+(\Gamma_{1}/2)^{2}}$
(3) $\displaystyle+$ $\displaystyle
A_{2}\frac{\Gamma_{2}}{2}\frac{\omega-\omega(B_{0}+B_{e})}{[\omega-\omega(B_{0}-B_{e})]^{2}+\left(\Gamma_{2}/2\right)^{2}},$

where $A_{i}$ and $\Gamma_{i}$ are the amplitude and width of the NMOR
resonance in cell $i$, $\omega(B)=g\mu_{B}B/\hbar$ are the NMOR resonance
frequencies, $\mu_{B}$ the Bohr magneton, $g$ the Landé g-factor, $\hbar$ the
reduced Planck constant, and $b=B^{\prime}d$, with $d$ the separation between
the cells. Assuming that $A_{1}=A_{2}$ and
$\Gamma_{1}=\Gamma_{2}>\omega(b+2B_{e})$, we find the zero of the total phase

$\Phi(\omega)=\textrm{arctan}\left(\frac{P_{G}}{Q_{G}}\right)=\frac{P_{G}}{Q_{G}}$
(4)

to be at

$\omega=\omega(B_{0}+b/2).$ (5)

The position of the gradiometric NMOR resonance is therefore independent on
$B_{e}$, and depends only on the differential magnetic field between the cells
$b$ (Fig. 1 (c)). If the separation between the cells $d$ is known, the
gradiometer provides a direct measurement of $B^{\prime}$.

##  III The NMOR gradiometer sensor

The sensor head of our OPMG is an evolution of the NMOR magnetometer described
in [42]. All the components of the sensor and the optical path are shown in
Fig. 2. The laser light is delivered by a polarisation-maintaining optical
fibre, and is collimated to a 1.8 mm beam diameter using a non-magnetic GRIN
(graded-index) lens. The polarisation of the beam is cleaned with a Wollaston
prism (W) that also aligns the beam along the sensor axis. The beam passes
through a 10/90 non-polarizing beam splitter cube (BSC), and then through the
two sensing cells, that are separated by a half-waveplate ($\lambda$/2). The
beam is retro-reflected by a plane mirror and, after passing through the cells
a second time, is reflected by the BSC to the polarimeter. This consists of
another Wollaston prism, rotated by 45∘, and a balanced photodiode (PD). The
PD signal is delivered to a transimpedance amplifier, which is then fed to a
lock-in amplifier. To track the changes of the measured magnetic field in
real-time, we use a combination of lock-in detection and a phase-locked loop
(PLL) that ensures that the resonance condition is always fulfilled.

Figure 2: Sensor layout: exploded view. The laser beam (represented with a red
line) is delivered with an optical fibre and collimated using a GRIN lens (not
shown). The beam is deflected on a Wollaston prism (W), 10% of the beam passes
through the beam splitting cube (BSC), cell 1 (C1), half-wave plate
($\lambda/2$), cell 2 (C2) and is retroreflected with a mirror (M). After
passing through the cells the second time, 90% of the beam is reflected by the
BSC and then a right-angle mirror to the polarimeter formed by a second
Wollaston prism and two photodiodes (PD). The coils surrounding both cells are
identical but are expanded around C2 for better visualisation.

The two sensing cells (C1 and C2) are paraffin-coated and have cylindrical
internal dimensions of 1.00 cm in length and 0.95 cm in diameter [43]. The
centres of the two cells are separated by $d$ = 4 cm. The baseline was chosen
as a compromise between measuring magnetic field gradients originating from
the brain and keeping the sensor compact. Each cell is held in place with a
polyjet 3D-printed mount made of thermoset acrylic resin. To produce the bias
field in each cell we use a pair of _self-shielded_ bias coils, that generate
reduced external stray fields and are also least sensitive to external
electromagnetic noise due to reciprocity. The first feature is especially
important in the case of gradiometers, which have two adjacent cells with bias
fields that can affect each other. Each bias coil is made from a rigidised
flexible PCB, consisting of 4 elements, placed symmetrically around each cell
(Fig. 2). Each element has two layers of copper. The spacing between the
elements and the geometry within each layer are optimised numerically for the
best possible balance between field homogeneity and self-shielding factor.
Compared to a solenoid of the same diameter and length, the optimised bias
coils produce a more homogeneous field (mean magnetic field inhomogeneity over
the cell volume 1.2% versus 6.0% for our earlier solenoid) and reduce the
stray field by 20 dB at 4.0 cm (i.e., at the other cell of the gradiometer or
for two adjacent sensors) and by $>$ 40 dB at $>$ 8 cm. Consequently, the mean
magnetic field of bias coil 1 on cell C2 is reduced from $-11\%$ to $-1.2\%$
and the mean magnetic field inhomogeneity in the gradiometer configuration is
improved to 1.8% (versus 8.2% for a pair of our earlier solenoids).

Because of the light absorption within the cells, the power of the laser beam
decreases after each pass. Since the amplitude of the NMOR signals depends on
the light intensity, this results in $A_{1}\neq A_{2}$, voiding a necessary
condition for the correct functioning of the gradiometer. To equalise the
amplitude of the individual NMOR signals, we independently control the optical
density of the atomic vapour in each cell with the temperature. This is
achieved with ac current heating and dedicated thin two-layer flexible PCB
coils (Fig. 2). The winding pattern for the heating coils is optimised to
produce the lowest possible magnetic field at each cell (i.e., a bifilar coil
with winding number zero for both filaments). Coincidentally, a coil in such
configuration produces internal stray fields approximately orthogonal to the
sensitive axis of the gradiometer. In NMOR, fields normal to the bias field
and of smaller amplitude do not significantly affect the sensitivity [44].
Additionally, we drive the coils with low-noise audio amplifiers at 21 kHz,
which is far detuned from the NMOR resonance at $\sim$1.5 kHz. The temperature
in each cell is measured with a non-magnetic PT1000 resistance temperature
detector, which is connected to a low-noise readout amplifier. This readout is
delivered to a microcontroller which outputs a digital signal of the measured
temperature to a PC. The amplitude of the two 21 kHz sinuoids is stabilized
with a digital feedback loop. The signals are passed through an audio
amplifier to generate the current needed to heat the cells. Due to the
proximity of the temperature sensor to the cells, probing the temperature
generates spurious magnetic field noise, therefore we sample the temperature
only every 15 s. This allows us to control the temperature with 0.1 ∘C
precision.

##  IV Performance

Figure 3:  Amplitude spectral density (ASD) of our sensor as a function of
frequency. The data shown are averaged over 30 one-second experimental traces.
Figure 4:  (a) Rejection coefficient $R$ of our sensor as a function of the
frequency, for two different amplitudes of the magnetic field noise $\delta$B,
measured in a controlled environment. The amplitude of the external magnetic
field for this measurement was set to 0.9 nT and 5.1 nT, the set width of the
gradiometer signal was 55 Hz. The inset shows the averaged rejection
coefficient $\overline{R}$ over 1-20 Hz as a function of the amplitude of the
applied magnetic field noise in experimental conditions (i) $B_{e}$ =0 nT and
$\Gamma$=55 Hz (pink squares), (ii) $B_{e}$ =100 nT and $\Gamma$=55 Hz (yellow
dots), (iii) $B_{e}$ =0 nT and $\Gamma$=75 Hz (green triangles). (b) Signal-
to-noise ratio of a detected sinusoidal gradient field oscillating at 6 Hz for
the gradiometer (filled points) and magnetometer (empty points) as a function
of the amplitude of the applied magnetic field noise.

To characterise the performance of our sensor, we placed it at the centre of a
cylindrical 4-layer $\mu$-metal shield that has an internal coil system for
precise control of the magnetic fields (Twinleaf MS-2). To obtain equal
resonance amplitudes, we first warm up C1 to 42 ∘C and C2 to 38 ∘C, and then
fine-tune the temperatures until the amplitudes are equal within 5$\%$ error.
Finally, we overlap the resonances at a single frequency in the range of 1.5-2
kHz by adjusting the bias fields in each cell. In this work, the lock-in
detection is performed using a third-order digital low-pass filter with a time
constant of 1.61 ms. The signal acquired from the PLL is sampled with a rate
of 837.1 Hz.

In line with convention, we define the sensitivity of our sensor as the
measured average noise floor of the amplitude spectral density. Specifically
we measure the noise floor in the 2-48 Hz band, which is the band relevant for
biomagnetic measurements. We determine the experimental sensitivity of our
sensor by recording 30 one-second traces in the absence of any applied
magnetic fields. We convert the signal time-course to amplitude spectral
density for each trace and then average these traces. The result is shown in
Fig. 3. We measured a sensitivity of (17.9 $\pm$ 1.4)
fT$/\text{cm}/\sqrt{\text{Hz}}$, which is mainly limited by the electronic and
PLL noise.

Another important parameter of the sensor is its insensitivity to temporal
variations of homogeneous magnetic fields. To determine the resilience of our
sensor, we measured its common mode rejection coefficient
$R=20\textrm{log}_{10}\left[ASD_{g}(\omega)/ASD_{m}(\omega)\right]$, with
$ASD$ the amplitude spectral density, and with the subscripts $g$ and $m$
indicating the sensor operating in gradiometer or magnetometer mode
respectively 111Operating the sensor in magnetometer mode was done by
switching off the bias field of C1. To measure $R$, we applied a homogeneous
magnetic white noise of amplitude $\delta B$ along the sensor’s sensitive
direction. This was produced with a low-noise voltage-driven current source
controlled by an arbitrary waveform generator. The applied white magnetic
field noise had a bandwidth of 1 - 100 Hz, and $\delta$B was varied in the 0.5
- 10.1 nT range. For each $\delta$B, we recorded 10 traces of 3 s, and
repeated the measurements for 3 sets of operating conditions:

  * •

Setup (i): we tuned the laser power and detuning to achieve the best possible
sensitivity. The resulting minimum full width at half maximum of the
gradiometer resonance $\Gamma$ was (55 $\pm$ 3) Hz.

  * •

Setup (ii): to investigate the resilience of our sensor to high external
magnetic fields, we additionally applied a DC offset of $B_{e}$ = 100 nT along
the sensitive direction. This procedure did not affect $\Gamma$ which remained
$\sim$55 Hz.

  * •

Setup (iii): to explore the relation between bandwidth and sensitivity of NMOR
and light intensity, $\Gamma$ was increased to 75 $\pm$ 3 Hz.

For each trace, we calculated the amplitude spectral density and then we
performed the average over 10 traces. These averages were then used to
evaluate $R$. We also calculated the averaged rejection $\bm{\overline{R}}$ by
averaging $R$ across the 1 - 20 Hz band.

Fig. 4 summarises the performance of the OPMG in all 3 operating conditions.
In panel (a) we show $R$ for $\delta B$ = 0.9 nT (pink line) and $\delta B$ =
5.1 nT (green line), obtained in the best sensitivity condition (i). For each
$\delta B$, $R$ remains fairly constant over the entire frequency range:
$\bm{\overline{R}}$ is $\sim$ 31 dB for $\delta$B = 0.9 nT and $\sim$ 23 dB
for $\delta$B and 5.1 nT. In the inset of Fig. 4 (a), we show the dependence
of $\bm{\overline{R}}$ on $\delta B$ for the 3 operating settings. The pink
squares are data collected in settings (i). The attenuation for $\delta B>$
1.5 nT linearly decreases. This is because the overlap between the C1 and C2
resonances is reduced by $\sim$ 30%, and therefore the condition
$\Gamma_{1}=\Gamma_{2}>\omega(b+2B_{e})$ is no more well verified. Beyond
$\delta B~{}\simeq$ 1.5 nT, such a condition is no more satisfied and the
noise rejection of the sensor rapidly degrades. The absolute maximum $\delta
B$ that our gradiometer can tolerate in settings (i) is $\sim$ 5 nT. The
yellow circles represent the data in settings (ii). Since increasing the
background field does not significantly affect $\Gamma$, the performance of
the gradiometer is similar to (i), with slightly worse $\bm{\overline{R}}$ at
higher $\delta$B. This demonstrates the ability of our sensor to operate in
high external magnetic fields, a characteristic ‘inherited’ by the underlying
NMOR physics. The green triangles are the data in settings (iii). Here the
rejection range is increased up to $\delta B~{}\simeq$ 10.1 nT, and
$\bm{\overline{R}}$ is increased above 30 dB for $\delta$B $<$ 2.5 nT. This is
a result of wider $\Gamma$, so that the condition
$\Gamma_{1}=\Gamma_{2}>\omega(b+2B_{e})$ is stringently verified over a
broader range.

To determine the ability of the sensor to measure a magnetic field gradient in
the presence of external magnetic field noise, we repeated the above
measurements additionally applying a small sinusoidal magnetic field gradient
$B^{\prime}$ = 5 pT$/$cm, oscillating at 6 Hz. To extract the signal-to-noise
ratio (SNR) we divide the amplitude of the measured signal at 6 Hz with the
measured average noise in the 10 - 50 Hz range, and then average over 10
repetitions. The results are reported in Fig. 4 (b). The solid points are the
data collected in the gradiometer mode, while the open points in magnetometer
mode. For all the settings investigated, the SNR computed for the OPMG
outperforms the one of the OPM by more than one order of magnitude for $\delta
B~{}<~{}1$ nT. For higher values of $\delta B$, it is not possible to identify
a measurable signal at 6 Hz when operating in magnetometer mode.

##  V Biomagnetic sensing

Measurement of human biomagnetism is very demanding as it requires both high
sensitivity and substantial shielding from external perturbations. These
requirements are often met by employing a combination of highly sensitive
magnetic gradiometers inside a magnetically shielded room. Our OPMG has the
potential to intrinsically satisfy both requirements because, as we show in
the following, it is sufficiently sensitive to detect human brain activity,
and sufficiently resilient to detect human cardiac activity in a substantially
perturbed environment.

###  V.1 Magnetoencephalography

MEG is a non-invasive neuroimaging technique that measures weak magnetic
fields produced by neural activity in the brain [46]. To test the response of
our gradiometer to brain signals we measured event-related fields (ERF) in the
human brain. The experiment took place at the University of Birmingham, Centre
for Human Brain Health. The participant was seated inside a 2-layer
magnetically shielded room. We recorded the auditory evoked field (AEF) to a
binaural oddball paradigm [47] commonly used in benchmarking OPM sensors [48,
49, 50]. The research protocol was approved by the Science, Technology,
Engineering and Mathematics Ethical Review Committee at the University of
Birmingham. The participant was informed about the experimental method and a
written consent was obtained.

The participant was seated in a custom-made wooden chair with an adjustable
platform to attach the sensor. The auditory stimulus produces a strong
response in the brain, with a well-defined activity region making it easy to
position the sensor around the head. Similarly to [42], we have first
determined the location on the subject’s scalp with the highest AEF using a
conventional MEG system. The gradiometer was then positioned at this location.
During both sessions, the participant was listening to two auditory stimuli. A
1 kHz pure tone was played for 80% of the trials, whilst during the remaining
20%, the oddball 40 Hz thump was played. The oddball tone not only induces the
AEF itself, but it also increases the brain response from the subsequent
normal 1 kHz tone. The duration of the stimuli was 100 ms followed by an
interval randomly varied between 911 ms and 1111 ms. This randomised time gap
between stimuli was introduced to prevent the adaptation of the brain to the
repeated noise. The sound was generated using a SOUNDPixx system and was
delivered to the participant binaurally using MEG-compatible air-tubes and
disposable ear-pieces. No active response from the participant was required.
The participant was asked to concentrate on the tone, fixate eyes on the
target placed on the wall and minimise any movement. We recorded 445 trials
with 837 Hz sampling rate. Along with the gradiometer signal, we recorded an
analogue trigger signal to timestamp the presentation of the tone.

Figure 5:  Time course of the event-related field (a) The purple line is the
Auditory Evoked Response averaged over 445 epochs, the shading represents the
standard error of the mean. (b) Inter-trial coherence across all epochs in the
time-frequency domain. The gray shaded area in (a) and the vertical grey lines
on (b) show the onset and duration of the auditory tone.

The raw data were detrended and epoched. A pre-tone interval of 200 ms was
used to perform baseline correction, which subtracted all values within an
epoch by the average baseline value, correcting for dc offsets. The line noise
was removed by fitting and subtracting a single sinusoidal component near 50
Hz from each epoch. All epochs were filtered with a 20 Hz first-order
Butterworth infinite impulse response filter (operating in both forward and
reverse directions to achieve an acausal response with zero phase shift) and
averaged.

The typical time course of the AEF obtained with our gradiometer is shown in
Fig. 5 (a). The purple line shows the averaged signal while the purple shaded
area represents the standard error of the mean calculated across all epochs.
The grey shaded area indicates the stimulation duration. At about 100 ms a
strong deflection can be noticed that corresponds to the N100m peak [46],
followed by another one at 150ms corresponding to P150m. The total amplitude
of the detected N100 and P150 peaks is 60 fT/cm , yielding an averaged signal-
to-noise ratio of 5.7 within this region. The inter-trial coherence (ITC) was
calculated for all AEF epochs and the results are shown in Fig. 5 (b). ITC in
MEG signals provides information about the consistency or phase-locking of
neural activity across different trials of an experiment. ITC is acquired here
by applying time-frequency decomposition on each trial with a single taper
applied to each 250 ms long sliding window. The higher coherence values
represent a correlation in the phase of the signal across epochs. The spectral
leakage into neighbouring frequency intervals is a side-effect of the tapering
method and windowing parameters used in order to maintain good temporal
resolution. Nonetheless, there is a clear increase in ITC during the same 100
- 200 ms period after stimulus onset which confirms consistent synchronisation
in the activity of neural ensembles in response to auditory stimuli during the
task.

###  V.2 Magnetocardiography

To test the performance of our sensor in real-time recordings, and to
demonstrate the attenuation of environmental magnetic noise, we measured the
heartbeat of a human participant during a time in the day when there was
intense activity in the building. Our magnetically shielded room is located in
the basement of a 7-story building in the vicinity of lifts that create up to
5 nT peak-to-peak magnetic field changes when running the full distance. In
this experiment, the gradiometer was fixed on the platform of the wooden chair
while the participant was leaning over the sensor keeping a 5 cm distance from
the sensor surface. The data acquisition was carried out with the same lock-in
parameters as in the MEG session, however, no filtering or averaging has been
applied. During recording, the building lifts were in use and the created
magnetic disturbance was recorded using commercial sensors (FieldLine V2).

Fig. 6 shows our magnetocardiography results. The purple line in panel (a) is
a 400 s recording with our gradiometer, while the green line is the background
magnetic field fluctuations measured with the reference sensor positioned in
the same direction as the gradiometer. The peak at around 50 s is caused by
opening and closing our laboratory entrance door which has a magnetic lock.
This door is about 5 m from our magnetically shielded room. The rest of the
peaks and dips are due to the lift movements between various floors. After 250
s the lifts traveled larger distances creating also substantial magnetic field
gradients, that are therefore picked up by our sensor. Overall, we achieved
attenuation of external magnetic field disturbances up to 27 dB. Fig. 5 b
shows a zoom over the shaded area of figure 5(a) and shows the recorded
heartbeats (purple line) together with the reference signals. Note the
different vertical scales. There are three expected cardiography signals: the
P wave, the T wave, and the QRS complex. The latter is responsible for a large
spike in signal, which should be most clear. The P wave is a smaller waveform
that precedes QRS complex, whilst the T wave is a similar, more powerful
signal that occurs afterwards [51]. The QRS complex is clearly visible, and
for most trials so is the T wave. The P component is not so clear to notice.

Figure 6:  Magnetocardiogram recording in the gradiometer mode with the nearby
lifts running: (a) full duration of the recording, (b) zoomed-in area
highlighted in grey in figure (a). The purple trace is the gradiometer signal
$b=B^{\prime}d$ and the green trace is the reference magnetometer showing the
magnetic field component in the gradiometer’s sensitive axis direction. At 50
s, the impact of a magnetic lock while opening and closing door is visible.
After 70 s, the operation of the building’s lifts has started. The arrows
indicate the QRS complex and T wave of the measured heartbeat.

##  VI Conclusion

In summary, we have discussed a scheme for the realisation of an OPMG based on
NMOR, and shown that it is insensitive to external homogeneous magnetic field
noise and sensitive to magnetic field gradients. We have detailed our methods
to practically implement the scheme discussed and build up a compact magnetic
gradiometer sensor. We have tested the performance of our sensor in controlled
conditions, allowing us to measure its best sensitivity to magnetic field
gradients and the optimal resilience to external magnetic fields. The
amplitude of the magnetic noise range here investigated, $\delta$B $<$ 5 nT,
is typical for light magnetically shielded rooms close to strong noise sources
such as lifts or urban traffic. We have shown that our sensor can be adapted
to work in different conditions, depending on the amplitude of the magnetic
field noise present. We have demonstrated that our OPMG has sufficient
sensitivity to measure human biomagnetism. In particular we have been able to
record the auditory evoked response of a human brain with excellent signal-to-
noise ratio, and we show that the measured brain response remains phase-locked
to the stimulus over the duration of the recording. Finally we have
demonstrated the ability to measure cardiac signals in real-time, even in the
presence of significant transient magnetic field fluctuations. Our work
provides new opportunities in measuring human biomagnetism, complementing the
features of OPMs. The capabilities of atomic vapour sensors now match those of
SQUIDS, but with enhanced performance, portability and reduced costs.
Particularly interesting is the ability of combining our OPMG, whose head does
not contain any magnetizable part, with transcranial magnetic stimulation.
This could open new avenues in understanding brain connectivity and in
development of drug-free treatments for various brain disorders.

## Acknowledgments

This work was supported by EPSRC (grant number EP/T001046/1). LK is supported
by European Union’s Horizon 2020 programme (No 101027633). OJ is supported by
the Wellcome Trust Discovery Award (grant number 227420). AK is supported by
EPSRC Quantum Technology Career Development Fellowship (grant number
EP/W028050/1).

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