ODMR short = ODMR, long = optically detected magnetic resonance, tag = abbrev
NMR short = NMR, long = nuclear magnetic resonance, tag = abbrev EM short =
EM, long = electromagnetic radiation, tag = abbrev GSLAC short = GSLAC, long =
ground state level anticrossing, tag = abbrev MRI short = MRI, long = magnetic
resonance imaging , tag = abbrev PID short = PID, long = proportional-
integral-derivative controller, tag = abbrev FCC short = FCC, long = face-
centred cubic, tag = abbrev NV short = NV, long = nitrogen vacancy, tag =
abbrev -NV short = NV-, long = nitrogen vacancy, tag = abbrev SG short = SG,
long = signal generator, tag = abbrev FG short = FG, long = function
generator, tag = abbrev MW short = MW, long = microwave, tag = abbrev LCAO
short = LCAO, long = linear combination of atomic orbitals , tag = abbrev MO
short = MO, long = molecular orbitals , tag = abbrev ISC short = ISC, long =
intersystem crossing , tag = abbrev PL short = PL, long = photo-luminescence,
tag = abbrev cw short = cw, long = continuous wave, tag = abbrev Mandhala
short = Mandhala, long = magnetic arrangement for novel discrete halbach
layout, tag = abbrev HPHT short = HPHT, long = high-pressure high-temperature,
tag = abbrev SQ short = SQ, long = single quantum, tag = abbrev DQ short = DQ,
long = double quantum, tag = abbrev fps short = fps, long = frames per second,
tag = abbrev magnet short = magnet, long = Halbach assembly, tag = abbrev PM
short = PM, long = cylindrical permanent magnet, tag = abbrev LM short = LM,
long = Levenberg-Marquardt, tag = abbrev FWC short = FWC, long = full well
capacity, tag = abbrev FWHM short = FWHM, long = full width at half maximum,
tag = abbrev WF short = WF, long = wide-field, tag = abbrev CVD short = CVD,
long = chemical vapour deposition, tag = abbrev MEG short = MEG, long =
magnetoencephalography, tag = abbrev MCG short = MCG, long =
magnetocardiography, tag = abbrev SQUID short = SQUID, long = superconducting
quantum interference device, tag = abbrev sCMOS short = sCMOS, long =
scientific Complementary Metal-Oxide-Semiconductor, tag = abbrev PSN short =
PSN, long = photon shot-noise, tag = abbrev OPM short = OPM, long = optically
pumped magentometer, tag = abbrev FPGA short = FPGA, long = field progammable
gate array, tag = abbrev ESLAC short = ESLAC, long = excited-state level anti-
crossing, tag = abbrev STED short = STED, long = stimulated emission
depletion, tag = abbrev

# Microwave-free wide-field magnetometry using nitrogen-vacancy centers

Joseph Shaji Rebeirro  Johannes Gutenberg-Universität Mainz, 55128 Mainz,
Germany  Helmholtz-Institut Mainz, GSI Helmholtzzentrum für
Schwerionenforschung, 55128 Mainz, Germany  Muhib Omar  Johannes Gutenberg-
Universität Mainz, 55128 Mainz, Germany  Helmholtz-Institut Mainz, GSI
Helmholtzzentrum für Schwerionenforschung, 55128 Mainz, Germany  Till Lenz
Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany  Helmholtz-Institut
Mainz, GSI Helmholtzzentrum für Schwerionenforschung, 55128 Mainz, Germany
Omkar Dhungel  Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
Helmholtz-Institut Mainz, GSI Helmholtzzentrum für Schwerionenforschung, 55128
Mainz, Germany  Peter Blümler  Johannes Gutenberg-Universität Mainz, 55128
Mainz, Germany  Dmitry Budker  Johannes Gutenberg-Universität Mainz, 55128
Mainz, Germany  Helmholtz-Institut Mainz, GSI Helmholtzzentrum für
Schwerionenforschung, 55128 Mainz, Germany  Department of Physics, University
of California, Berkeley, CA 94720, USA  Arne Wickenbrock  wickenbr@uni-
mainz.de Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
Helmholtz-Institut Mainz, GSI Helmholtzzentrum für Schwerionenforschung, 55128
Mainz, Germany

###### Abstract

A wide-field magnetometer utilizing nitrogen-vacancy (NV) centers in diamond
that does not require microwaves is demonstrated. It is designed for
applications where microwaves need to be avoided, such as magnetic imaging of
biological or conductive samples. The system exploits a magnetically sensitive
feature of NV centers near the GSLAC. An applied test field from a wire was
mapped over an imaging area of [parse-numbers=false]≈500×470. Analysis of the
GSLAC lineshape allows to extract vector information of the applied field. The
device allows micrometer-scale magnetic imaging at a spatial resolution
dominated by the thickness of the NV layer (here
$50\,$\mathrm{\SIUnitSymbolMicro m}$$). For a pixel size of
$4\,$\mathrm{\SIUnitSymbolMicro m}$\times 3.8\,$\mathrm{\SIUnitSymbolMicro
m}$$ the estimated sensitivity is 4.8. Two modalities for visualizing the
magnetic fields, static and temporal, are presented along with a discussion of
technical limitations and future extensions of the method.

##  I Introduction

Negatively charged NV centers in diamond [1] have attracted significant
attention as a promising platform for sensing various physical quantities,
such as temperature, pressure, magnetic and electric fields, at the nanoscale
under various environmental conditions [2, 3, 4]. Magnetometry based on spin-
dependent fluorescence of these NV centers has demonstrated sensitivities down
to [parse-numbers=false]0.6 for ensembles at room temperature [5, 6, 7]. By
employing ODMR with NV centers, one can probe the magnetic fields generated by
a wide range of samples, including biological systems, magnetic materials,
current-carrying wires, and FPGA [8, 6, 9, 10, 11]. In ODMR based
magnetometry, a diamond sample is illuminated with laser light (for example,
at 532 nm) and is subjected to a microwave field to drive population transfer
between the differently bright spin states. When the microwave frequency
matches a transition, there is a decrease of fluorescence. Measuring the
resonant frequencies for transitions between the $m_{s}=0$ and $m_{s}=\pm 1$
states allows reconstruction of the magnetic field projection onto the NV axis
[4, 12, 13].

However, there are scenarios where the use of microwaves is undesirable, such
as when dealing with conductive materials or sensitive biological samples. To
address this, recent developments have focused on microwave-free protocols
that exploit energy-level crossings of NV centers at different magnetic
fields. These protocols include microwave-free magnetometry and vector
magnetometry at zero-field, as well as the exploitation of specific features
like the ESLAC feature at 51.2 mT and the GSLAC feature at 102.45 mT [14, 13,
15]. These kind of magnetically sensitive features have been successfully
utilized for vector magnetometery, measuring eddy currents in conducting
materials and performing NMR [16, 17, 18]. In light of these advancements,
this report presents a microwave-free wide-field magnetic microscope that
leverages the GSLAC feature to probe and image samples where microwaves are
detrimental.

The GSLAC feature originates from the mixing of ground-state levels at 102.45
mT. Due to the Zeeman splitting of the triplet ground state, as illustrated in
Fig. 1a, the $m_{s}=-1$ state becomes degenerate with the $m_{s}=0$ state and
mixing results in population transfer between these states. Mixing occurs due
to hyperfine interaction, cross-relaxation with other defects as well as
static and oscillating transversal magnetic fields. The population transfer is
observed as a drop in fluorescence intensity. Our study aims to explore the
potential of utilizing NV centers without the need for microwaves to map
magnetic fields. We create static magnetic field maps by analyzing the
lineshape of the GSLAC resonance pixel by pixel. Furthermore, in another
sensing modality, we investigate the sensitivity to dynamic field changes
between individual image frames.

To demonstrate the utility of this magnetometer we map the magnetic field
distribution of a direct current (DC) field generated by a straight current-
carrying wire with a diameter of 200 placed on the diamond sample while we
image it from underneath. This proof-of-concept experiment explores the
application of NV centers in a setup without microwaves. The lack of
microwaves increases the usability of the device while reducing its technical
complexity since no microwave components are needed. The results highlight the
viability of diamond-based quantum sensors for a wide range of materials and
biological applications.

Figure 1:  (a) Energy levels of a NV- center [12] also showing the ISC from 3E
$\rightarrow$ 1A1 $\rightarrow$ 1E $\rightarrow$ 3A2 respectively. Two
transition pathways, with and without the ISC, are indicated. The green and
red arrows represent excitation and decay from and to the electronic ground
state triplet; the black curves (“strong” and “weak”) represent decays via the
ISC. Strong and weak in this context means higher and lower rates of decay.
The grey gradient is used to indicate the phonon sidebands of the respective
triplets. (b) The eigenfrequencies of an NV center as a function of Bz of the
electron-spin magnetic sublevels of the ground state triplet neglecting
hyperfine structure.

##  II Experimental Setup

Figure 2:  (a) The WF imaging setup. It includes a diamond,an objective and
the light path. Coils C1 and C2 are used to offset the axial and transverse
magnetic fields. The dichroic mirror is used to separate the collected
fluorescence from the reflected green light, and a flip mirror directs it
either to a camera or a photodiode. The axis of the background and
perpendicular magnetic field are denoted as $B_{\|}$ and $B_{\bot}$
respectively. (b) The [110] sample was made from a [100] cut diamond. The dark
areas are presumably dirt within the crystal that is resistant to acid
cleaning. The unreliable data from these positions were replaced with the mean
of the five nearest reliable pixels. The thickness of the diamond is 50 which
sets the upper limit for spatial field resolution referred to in [19]. (c) An
illustration of the magnetic field arrangement. The magnetic field by the wire
$\vec{B}_{\text{wire}}$ counteracts $\vec{B}$ from the magnet for positive
currents.

The setup incorporates a magnet [20, 21], two pairs of coils, a (110) diamond
plate and collection optics. The cylindrical magnet provides a magnetic field
orthogonal to its bore with minimal stray field external to the magnet. The
diamond is a HPHT grown diamond purchased from Element Six with a
concentration of 3.7 NV centers homogeneously distributed. It was cut
mechanically from a 13C depleted Ib diamond with a (100) face to a (110) face.
The diamond sample dimensions were [parse-numbers=false]1 ×0.5 ×0.05. It had
an initial nitrogen concentration $\leq$ 10\. It was irradiated with electrons
of 5, with a dose of 2e19□ electrons and then annealed at 700 for 8. The
thickness of the NV layer (50) limits the spatial magnetic field resolution
[19]. The diamond is shown in Fig. 2b where the field of view is marked in
blue, the two NV axes of the diamond orthogonal to the cylinder bore usable
for microwave-free magentometry are marked in yellow and violet. We use the
orientation marked in violet.

The sample is positioned in the center of the magnet on a rotatable platform,
with its axis of rotation parallel to the magnet bore perpendicular to the
field. This allowed to align the NV axis in the (110) plane of the diamond to
the magnet background field produced. The sample is set on a sapphire window
with a diameter of 10 and a thickness of 0.25 mm. It permits laser-light
delivery and collection of light from under the diamond sample while acting as
a heat sink.

Figure 3: (a) Experimental sequence: data collection using a camera to capture
pictures at the rising edges of 70 external triggers operating at 185 are
synchronized with a magnetic field sweep. The blue ramp indicated in (a)
represents the field sweep, while the red trace illustrates the GSLAC feature.
(b) Magnetic field maps obtained from a DC field generated with a wire
carrying 0 A and 0.4 A, top and bottom, respectively. Each image is the result
of the analysis of magnetic field scans in each pixel where the signal
profiles are fit with a Lorentzian function. The contrast $C$, center field
($b$) and FWHM ($\Gamma$) are then extracted and displayed. In (c) the GSLAC
was examined at two positions in the diamond and the results compared to the
case without an applied test signal. The blue and orange traces are taken from
the same position beneath the wire with and without a test signal. The green
trace is for a position taken 200 away from the wire center. This indicates
that the axial component of the test field is more prominent closer to the
wire and the transverse component is more prominent further away from the wire
due to the curvature of the field consistent with the illustration in Fig. 2c.
This is also apparent Fig. 4.

As shown in Fig. 2 the magnet is fitted with two sets of Helmholtz coil pairs.
Coil pair C1 is oriented in the direction of the background field and coil
pair C2 is perpendicular to it and parallel to the cylinder axis. The coils
are used to shim the magnetic field of the magnet and optimize the linewidth
and contrast of the GSLAC feature. The diamond mount is attached to the C1
coils. It feature a range of [parse-numbers=false]±1.3. The second Helmholtz
coil pair (C2) is used to remove residual transverse fields. A third coil pair
perpendicular to C1 and C2 would be ideal but was not implemented due to space
constraints in the magnet bore.

A cw 532 nm laser (Laser Quantum, gem532) is used to illuminate the diamond
via a microscope objective (Olympus Plan 10X objective). The fluorescent light
is gathered using the same objective, reflected off a short-pass dichroic
mirror with a cutoff wavelength of 600 nm and passes through a long-pass
filter to remove the remaining green reflection of the laser light.

The collected fluorescence is directed to a sCMOS camera (Andor Zyla 5.5) for
imaging. Alternatively for diagnostic purposes, the light can be directed to a
photodiode (PDA36A2) using a flip mirror.

##  III Results and Discussions

###  III.1 Static Imaging

We demonstrate a static magnetic field imaging modality using the GSLAC by
visualizing the field generated by a wire carrying electric current. The
results are presented in Fig. 3b To image , we illuminated the diamond with cw
532 nm laser light with a Gaussian profile. The laser beam covered an area of
[parse-numbers=false]≈0.5×0.47.

The background magnetic field was swept over a range of [parse-
numbers=false]102.45±1.3, covering the GSLAC feature while images where taken
with the camera. This way the individual pixels contain a magnetic field scan
over the GSLAC feature. The current-carrying wire generates both axial
($B_{\|}$) and transverse components ($B_{\bot}$) in the measurement region,
thereby leading to alterations in the contrast (C), FWHM and the center-field
position of the GSLAC feature.

To analyze and quantify the observed changes, we fitted the experimental data
pixel-by-pixel with a Lorentzian function [22, 23] to extract three fitting
parameters: contrast ($C$), FWHM ($\Gamma$), and center-field ($b$).

To ensure synchronization between the magnetic field ramp and the data
acquisition, we employed an external trigger at 185 Hz. This trigger served as
a timing reference and triggered the camera to capture 70 frames during a 0.4
s magnetic field ramp.

Additionally, to enhance the signal-to-noise ratio, we repeated the
acquisition 20 times and averaged the results.The acquisition procedure, which
is similar to that of [24], is illustrated in Fig. 3a.

During data analysis, we extract the GSLAC feature from individual pixels
within a specific region measuring [parse-numbers=false]≈0.47×0.50□. This
region comprises a total of $625\times 715$ pixels, with each pixel
corresponding to an area of $\approx 0.8\,$\mathrm{\SIUnitSymbolMicro
m}$\times 0.69\,$\mathrm{\SIUnitSymbolMicro m}$$ on the diamond surface. The
extracted data are averaged over a $5\times 5$ pixels grid. This binning
process reduces the optical resolution to approximately $\approx
4\,$\mathrm{\SIUnitSymbolMicro m}$\times 3.4\,$\mathrm{\SIUnitSymbolMicro m}$$
which is not limiting the spatial resolution for magnetic fields.

We utilize the LM algorithm [25] to fit the binned data on a pixel-by-pixel
basis to a Lorentzian function. We extract the fitting parameters for each
pixel, which provides information about the magnetic field distribution. The
fitting of multiple pixels was done in parallel utilizing a threaded Python
script. The resulting data-processing time was 136 per image. This is still
significantly longer than the data acquisition time and requires further
improvement. For example, deploying a parallel fitting routine on a graphics
card or FPGA.

The maps presented in Fig. 3b are reconstructed images of a current-carrying
wire. As the wire field in the sensor is mostly anti-aligned to the background
field (see Fig. 2c), the total magnetic field reduces. The wire field results
in a shift and a broadening of the GSLAC feature. On examination of the maps,
we observe that the width of the feature is smallest at the center of the wire
and increases away from it. This is mirrored in the center maps where the
change in the total magnetic field is largest under the wire, Fig. 2c and Fig.
3c. This is consistent with a model of the wire magnetic field in the diamond.

In the region under the wire, there is no broadening of FWHM caused by
transverse fields. As we move away from the center of the wire, the transverse
components become dominant, leading to an increase in the observed FWHM of the
GSLAC feature. The center maps in Fig. 3c also demonstrate this effect, with
the area nearest to the wire showing a 0.5-shift from 102.4 to 101.9 when a
magnetic field corresponding to a current of 0.4 A is applied. This shift
gradually reduces to 0.1 furthest from the wire.

Additionally, we examine an averaged cross-section of the maps in Fig. 4,
specifically focusing on the FWHM displayed in Fig. 4b. We observe something
peculiar: considering the thickness of the NV layer in the diamond, which is
approximately 50 $\mathrm{\SIUnitSymbolMicro m}$, the spatial resolution for
the magnetic field was expected to be on the order of 50
$\mathrm{\SIUnitSymbolMicro m}$ as well [19]. The wire itself has a diameter
of 200 $\mathrm{\SIUnitSymbolMicro m}$. From observation however, the feature
in the image Fig. 4b corresponding to the wire shows a FWHM of [parse-
numbers=false]≈66 when a field is generated with a wire carrying 0.4 A. Just
directly below the wire its field does not feature a transverse component in
the NV layer. So just there, no broadening is observed. This effect becomes
more pronounced with increasing wire current. It bears some resemblance to
super-resolution imaging techniques like STED [26, 27], albeit in the context
of magnetic fields. In STED, a laser beam with a donut-shaped cross-section is
used to de-excite emitters through stimulated emission for sub-diffraction
resolution images.

Figure 4:  Cross-sections of the center and the FWHM maps in Fig. 3b displayed
for multiple currents, respectively. The cross-section is perpendicular to the
wire. The center shift is maximal under the wire (a), while the width has a
minimum there (b). This is expected from the pattern of the generated field as
the width depends on the transverse component of the field illustrated in Fig.
2c.

###  III.2 Temporal Imaging

To implement dynamic imaging, we captured a video while pulsing current
through the wire. This allows us to observe the magnetic field from the wire
in real time. The results are summarized in Fig. 5. The temporal resolution is
limited by the camera frame rate, which is set at 39 Hz. The camera can
operate at a significantly higher frame rate, however, this reduces the amount
of collected photons.

The experimental procedure is illustrated in Fig. 5a. It involves tuning the
bias field to the slope of the GSLAC feature in at 101.7. We then capture 15
frames for 380 (at a rate of 39 Hz) while turning on a current of 0.4 A
through the wire for the central 100 ms. Post acquisition, we normalize the
contrast of each individual pixel by its maximum value in the 15 images. This
allows a straight-forward comparison of frames taken before and during the
current pulse.

In Fig. 5b and Fig. 5c), we present two frames separated by 25, respectively.
Figure 5b has no current applied through the wire. In figure 5c a current of
0.4 A is applied. We observe changes in contrast in areas away from the wire.
This is a result of the transverse components of the magnetic field
($B_{\bot}$) generated by the wire. It broadens the GSLAC feature. The
broadening leads to a decrease in contrast and the corresponding diamond
region to appear darker. However, directly under the wire, the magnetic field
is aligned with the total field ($B_{\|}$) causing the GSLAC resonance to
shift to 103.2 but not to broaden. This is why this region remains bright. We
have chosen the values of the bias and the wire fields to maximize the
contrast variation between the “on” and “off” frames integrated over the
complete image. Furthermore, we chose these parameters to ensure all pixels
remain within the GSLAC feature and to determine the limit of contrast
variations we can visualize.

An analysis of the temporal cross-section of the acquired frames is shown in
Fig. 6a. The the applied pulse shape is retrieved. An examination of the
cross-section of the wire image is presented in Fig. 6b. We discern maximum
contrast variations of up to 9 at a distance of 100 from the wire center.
Beyond this distance, the contrast variations, which is due mostly to the
transverse field component of the wire, level off. To further improve the
temporal and spatial resolution in this modality, high-frame-rate or lock-in
detection-enabled cameras can be employed.

Figure 5: (a) Illustration of the data acquisition and processing sequence for
temporal imaging. Fifteen frames are taken at 39 Hz, while a current pulse is
applied midst acquisition. The frames are normalized to the maximum value per
pixel in order to visualize dynamics. In (b) and (c) we see the dynamics
between two frames with a temporal separation of 25. (b) The contrast with no
test signal, while (c) displays the contrast variation induced when a current
of 0.4 generates a field. The field below the wire has been shifted to 103.2,
which causes it to appear brighter. The spatial resolution is restricted to
[parse-numbers=false]≈50, which is the resolution limit for magnetic features
that can be attained with the WF sample. In the areas away from the wire the
GSLAC feature is broadened and shifted, which is observed as a reduction in
contrast. (d) An illustration of the expected signal as a function of magnetic
field at three different positions in the acquired frames for clarification of
the involved processes.  Figure 6:  (a) Mean values of the averaged contrast
per frame over the duration of acquisition, showing the applied pulse. (b)
Mean values of the contrast for points in the direction orthogonal to the
wire. We can detect a contrast drop of 9 up to 100 from the center of the wire
after which the contrast variation saturates.

##  IV Conclusion

We developed a microwave-free diamond magnetic field microscope utilizing NV
centers to measure spatially varying magnetic fields over a field of view of
approximately [parse-numbers=false]500 ×470. We analyzed the GSLAC feature and
can reconstruct longitudinal and transverse components of magnetic fields of
samples. We implemented a fitting algorithm to extract the GSLAC feature and
estimate magnetic fields in an image of $125\times 143$ pixels post-binning.

Our results demonstrate the potential of microwave-free vector magnetometry
with temporal resolution enabling recording of magnetic “movies”. We envision
that this approach will have a significant impact across a range of fields,
including materials science, biology, and condensed matter physics.

It is important to acknowledge certain limitations in achieving high-
resolution magnetic maps using the current methodology. One constraint is that
only 1/4 of the NV-center orientations are available for this modality due to
the requirement of on-axis alignment with the bias field. This leads to an
overall drop in signal. Use of preferentially oriented NV centers could
enhance the overall contrast and sensitivity [28].

Another limitation arises from the camera, which imposes constraints in terms
of its Full Well Capacity (FWC) and frames per second (fps). The mean per
pixel shot-noise limit is estimated to be approximately 4.8 for a pixel size
of 4, or 137.35 1.5 for a volume-normalized estimate. This can be compared to
the best-reported volume-normalized sensitivities of comparable cameras using
microwaves (including lock-in cameras) of approximately 31 1.5 [29, 30].
Considering these limits, future improvements may involve lock-in-based
detection to boost sensitivity and pulse sequences for T1 relaxometry [18].

##  V Acknowledgment

This work was supported by the German Federal Ministry of Education and
Research (BMBF) within the Quantumtechnologien program (DIAQNOS, project no.
13N16455) and by the European Commission’s Horizon Europe Framework Program
under the Research and Innovation Action MUQUABIS, project no. 101070546.

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