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Light-shift-free and dead-zone-free atomic orientation based scalar magnetometry
using a single amplitude-modulated beam
Q.-Q. Yu,1S.-Q. Liu,1C.-Q. Yuan,1and D. Sheng1, ∗
1Department of Precision Machinery and Precision Instrumentation,
Key Laboratory of Precision Scientific Instrumentation of Anhui Higher Education Institutes,
University of Science and Technology of China, Hefei 230027, China
Detection dead zones and heading errors induced by light shifts are two important problems in
optically pumped scalar magnetometry. We introduce an atomic orientation based single-beam
magnetometry scheme to simultaneously solve these problems, using a polarization-reversing and
path-bending Herriott cavity. Here, a reflection mirror is inserted into the cavity to bend the optical
paths in the middle, and divide them into two separated orthogonal regions to avoid the detection
dead zone. Moreover, half-wave plates are added in the center of each optical region, so that the
light polarization is flipped each time it passes the wave plates and the light shift effects are spatially
averaged out. This operation is demonstrated to eliminate the unnoticed heading errors induced by
ac light shifts. The methods developed in this paper are robust to use, and easy to be applied in
other atomic devices.
I. INTRODUCTION
Optically pumped scalar magnetometers resolve
atomic Zeeman splittings to extract the bias field magni-
tude [1]. With developments in experiment schemes,
hardware and techniques, scalar magnetometers have
reached great advances in sensitivities [2–4], stabili-
ties [5], and miniaturization [6]. They have been widely
used in researches on fundamental physics [7, 8], geo-
physics [9], space science [10], and neuroscience [11, 12].
However, due to working principles, they usually suffer
two important problems in practical applications, which
are detection dead zones and heading errors.
As initially studied by Bloom [13], detection dead
zones in scalar magnetometers refer to certain directions
of the target field where the sensor signal-to-noise ratio
is significantly reduced. For example, the detection dead
zones of magnetometers using dc pump beams involve
regions perpendicular to the pump beam direction, and
the dead zones of double-resonance magnetometers in-
clude extra regions near the radio-frequency excitation
field direction. Several methods have been developed to
solve this problem, including the use of pulse laser to
increase the pump beam power [11], employing multiple
vapor cells [10, 14], and combining multi-harmonic infor-
mation [15].
Heading errors correspond to the effect that the mea-
sured field magnitude is correlated with the sensor ori-
entation. Nonlinear Zeeman effects [16, 17] and light
shifts [18] are two main sources of such errors, where
the latter one can be the dominant factor when the bias
field is not large. In optical pumping experiments, light
shifts correspond to the changes of atomic ground state
transition frequencies due to interactions between atoms
with light beams [19, 20]. There are two physical mech-
anism to generate such shifts: one is due to the trans-
∗dsheng@ustc.edu.cn
fer of coherence between ground and excited states in
atomic transitions [19, 21], and the other one is due to ac
Stark shifts [20, 22]. In atomic cell experiments filled with
quenching gases, the former one is largely suppressed [23].
The ac Stark shift can be divided into scalar, vector and
tensor parts [20], among which the vector part is the most
important one in atomic orientation based magnetome-
ters. This vector light shift is determined by the circular
polarization part of the light, and its effect on atoms is
equivalent to an effective magnetic field [22]. It is com-
mon to circumvent this problem by either locking the
beam on resonance, or employing the atomic alignment
based magnetometry [7, 24].
In miniaturized atomic devices [6], it is often preferred
to leave the laser wavelength unlocked, so that both the
power and space can be saved. Moreover, in certain
atomic orientation based magnetometry, such as the one
using a single elliptically polarized light [25], the optical
pumping beam has to be kept off resonance. In these
cases, it requires to develop new methods and schemes
to simultaneously eliminate the detection dead zones and
light shift, even when the light frequency is off resonance
or drifting. A previous successful scheme employs a sin-
gle polarization modulating beam, which can simultane-
ously excite orientation and alignment resonances [26].
While the combination of these two kinds of resonances
can eliminate the detection dead zones, the light shift
effect is time averaged out. However, in practice, the
electrical-optical modulator used for polarization modu-
lations is sensitive to the environment parameters. This
not only is a problem for the device calibration, but also
can cause drifts or fluctuations of the time-averaged light
shift result.
In this work, we present an atomic orientation based
scalar magnetometer, which only uses a single amplitude-
modulated beam. This sensor is assisted by a Herriott
cavity, which is modified to lift the detection dead zones
and suppress light shifts. Following this introduction,
Sec. II introduces the setup and working principle of the
magnetometer employing a conventional Herriott cavity,
arXiv:2205.08136v1 [physics.atom-ph] 17 May 2022
2
Sec. III presents the measurement results and identi-
fies the problems in this conventional magnetometer, Sec.
IV. describes the solutions of these problems by modify-
ing the optical properties of the beams inside the cavity,
and Sec. V concludes the paper.
II. MAGNETOMETER SETUP AND WORKING
PRINCIPLE
A Herriott-cavity-assisted vapor cell, which is made
by the anodic bonding technique [27, 28], is used for the
atomic magnetometer. This cavity consists of two cylin-
drical mirrors with a curvature of 100 mm, a diameter
of 12.7 mm, a thickness of 2.5 mm, and a separation of
19.3 mm. In this work, the multipass cavity increases the
interaction length between light and atoms [29] so that
the cell can be kept at a relatively low working temper-
ature, which is essential for the stability of some opti-
cal elements as discussed in the latter part of the paper.
Such a cavity also provides a platform for manipulating
the optical properties of beams inside. The vapor cell,
filled by Rb atoms with natural abundances and 350 torr
of N2gas, is placed in a 3D printed optical platform,
and heated to a temperature around 55◦C by running ac
currents through ceramic heaters.
Figure 1 shows the optical platform used for a single-
beam Bell-Bloom scalar magnetometer [30]. The pump
beam is amplitude modulated using acoustic-optical
modulators with a duty cycle of 20%, and fiber coupled
to the optical platform. This pump beam, with a diame-
ter of 1 mm and a circular polarization, enters the cavity
from a 2.5 mm hole in the center of the front mirror, and
exits from the same hole after 21 times of reflections.
This magnetometer sensor sits in the middle of five-layer
mu-metal shields, with a 10 µT bias field generated by
solenoid coils inside the shields. The sensor is also con-
nected to a rotation table outside the shields through
a plastic holder, so that the relative angle between the
pump beam direction and the bias field can be precisely
controlled.
Two photodiode signals are sent out from the sensor,
one is the transmitted pump beam signal, and the other
one is the reference signal by recording a part of the in-
put beam before it enters the cavity. This latter one is
also used to lock the time averaged input beam power to
0.14 mW. The current signals from these detectors are
first converted to voltage signals by two transimpedance
amplifiers with feedback resistors of 10 kΩ and band-
widths around 100 Hz. These voltage signals are sent
to a differential amplifier, with a unit gain on the pump
beam signal channel and a variable gain gon the ref-
erence signal channel. The subtractor output is further
amplified by a factor of 200, and recorded as the magne-
tometer signal.
Two coordinates are used to describe the spin dynam-
ics following the notations in Ref. [27]. One is the xyz
coordinate with the zaxis along the center of pump beam
x,y’ y
z
lens
monitor PD
PD
PBS PBS l
_
4
l
_
2
y
!
x’ B
pump beam
FIG. 1: (Color online) Illustration of the optical
platform for a single-beam Bell-Bloom scalar
magnetometer. PBS: polarization beam splitter, PD:
photodiode detector.
directions. The other one is x0y0z0coordinate with the
z0axis along the bias field direction, and y0axis perpen-
dicular to the zoz0plane. We denote the angle between
the zand z0axes as ψz. For this single-beam scalar mag-
netometer, we fix the yaxis in the zoz0plane as shown
in the inset of Fig. 1. The dynamics of the electron spin
polarization Pis described by the Bloch equation [25]:
dP
dt =γP×(B0+BL)+ 1
Q(P)[ROP (s−P)−RdP],(1)
where γis the atomic gyromagnetic ratio, Q(P) is the nu-
clear spin slowing down factor, ROP is the optical pump-
ing rate, sis the photon spin of the light beam [23], Rdis
the atom depolarization rate in the absence of light, and
BLis the effective field induced by the light shift effect.
BLis connected to ROP by the relation [31, 32]
ROP s+i(2I+ 1)γBL=recfΦs/Ar
Γ−i∆ν,(2)
with Ias the nuclear spin, reas the classical electron
radius, cas the speed of light, fas the oscillator strength,
Φ as the light photon flux, Ar as the beam area, Γ as
the atomic transition line width, and ∆νas the light
detuning.
For a pump beam which is amplitude modulated at a
frequency ω, the optical pumping rate can be expressed
as
ROP =a0+
∞
X
n=1
ancos(nωt −αn),(3)
where aiis the corresponding coefficient of the Fourier
expansion series of ROP . With the pump beam duty
3
cycle of 20% in this experiment, we have a1/a0'1.9.
When the pump beam is on resonance with the Rb D1
transition and ωis close to the atomic Larmor precession
frequency ωL, a substantial transverse atomic polariza-
tion can be built as [27, 30]
Px0+iPy0=srna1sin ψz
2[R+iQ(P)(ωL−ω)]e−i(ωt−α1),(4)
where R=Rd+a0,rnis the abundance of the Rb isotope
that is driven by the modulated pump beam. In most
situations, ωRand the ac part of longitudinal atomic
polarization is negligible compared with Px0[27]. The
static part of the longitudinal polarization is:
Pz0=sa0cos ψz/(Rd+a0) (5)
The propagation equation of the pump beam intensity
is:
dI(z)
dz =−I(z)[1 −s·P(z)]nσ, (6)
where σis the photon absorption cross section of atoms,
and nis the atom density. Taking the time average, we
have:
dhI(z)i
dz =−hI(z)inσ [1 −sPz0(z) cos ψz−
srna1(z) sin ψz
2a0(z)A(Px0,s(ω)),(7)
where the operator h· · · i denotes the time average, A(P)
is the amplitude of the oscillating parameter P, and Px0,s
is the part of Px0that is in synchronization with the first
harmonic of the pump beam modulations in Eq. (3),
Px0,s(ω) = sa1cos(ωt −α1) sin ψz
2
R
R2+Q2(P)(ωL−ω)2.
(8)
The analytic solution of Eq. (7) is the principal value
of the Lambert W function [33]. A more convenient way
to effectively express the transmitted beam intensity It
is:
hIti=chI0ie−NdeNd[sP z0cos ψz+srnsin ψzA(Px0,s(ω))a1/2a0],
(9)
where I0is the input beam intensity, the coefficient c
denotes the ratio of It/I0without atoms, and cis deter-
mined by the optical patterns and beam power loss inside
the cavity. The optical depth Ndis equal to nσl, with l
as the length of optical pathes inside the cell, and xis the
spatial average of the parameter xover the whole optical
pathes.
III. MAGNETOMETER RESULTS AND
PROBLEMS
In this scalar magnetometer, the bias field amplitude
is extracted from the atomic Larmor frequency, which is
determined by finding the resonant response of atoms to
ω. Figure 2 shows the experiment results when the pump
beam is resonant with the Rb D1 line. Here, the recorded
signal can be expressed as V=G(hIti − ghIref i), where
Iref is the reference beam intensity recorded by one of the
photodiode detectors in the sensor, gis the variable gain
of the reference signal channel in the differential ampli-
fier mentioned previously, and Gis the converting factor
that connects the recorded beam intensity and the volt-
age output from the sensor electronics. The data shows
symmetrical line shapes, which agrees with predictions
from Eqs. (8) and (9). The exact line shape of the
Herriott-cavity-assisted magnetometer signal is complex,
especially due to the diffusion of atoms among the com-
plicated optical patterns [2, 34, 35]. It has been shown
that [29] we can use a combination of two Lorentzian
functions to describe the atomic polarization in the fre-
quency domain. Therefore, the magnetometer signal can
be fitted by the following equation:
f(ω) = hexp "2
X
i=1
ci(Γi
2)2
(ω−ω0)2+ (Γi
2)2#+b. (10)
Figure 2 shows good fitting results using Eq. (10).
signal (V)
45 46 47 48 49
0
0.05
0.1
0.15
0.2
0.25
0.3
w/2p (kHz)
FIG. 2: Illustration of the magnetometer signal as a
function of the pump beam amplitude modulation
frequency while the pump beam is on resonance with
the Rb D1 line and ψz= 30◦. Here we focus on 85 Rb
atoms, as follows in the rest of the paper. The solid line
is the fitting result using Eq. (10).
To characterize the magnetometer signal amplitude,
we define a parameter Sas the difference between the
magnetometer resonant signal (ω=ωL) and the signal
when ωis far from ωL. In the case that the light is reso-
nant with the Rb D1 line, Sis determined from Eq. (9):
S∝ hIt(ω=ωL)i−hIt(ω→ ∞)i
∝exp −Nd+Nd
s2a0
Rd+a0
cos2ψz×
exp Nd
s2rna1
4a0
a1
Rd+a0
sin2ψz−1.(11)
4
When the cell temperature is low enough, the opti-
cal depth Ndis negligible and the atomic polarization
part in Eq. (7) can be neglected, so that the transmitted
beam intensity is almost independent of the atom polar-
ization. This is the situation of the experiment data at
cell temperature of 35◦C in Fig. 3, where the transmit-
ted beam power has weak angular dependence as shown
in Fig. 3 (a). In this case, Sis determined by the last
line in Eq. (11), which predicts that Sis maximum at
ψz= 90◦and decreases with ψz. This is consistent with
the experiment results at the same cell temperature in
Fig. 3 (b). As the cell temperature and Ndincreases, the
atomic polarization part starts to play an important role
to determine the transmitted beam power. This case cor-
responds to the experiment data at cell temperature of
55◦C in Fig. 3. Due to the cos2ψzterm in Eq. (11), the
maximum amplitude of Sshifts from ψz= 90◦as shown
in Fig. 3 (b). While the two experiment conditions lead
to quite different experiment results when ψzis large, the
magnetometer signal amplitudes show similar rapid de-
cay as ψzapproaches to zero. This is due to the last line
in Eq. (11), which is proportional to sin2ψzwhen ψzis
small. Therefore, the regions near ψz= 0◦are detection
dead zones of current magnetometers.
To better compare the experiment results in different
experiment conditions, we further define the normalized
magnetometer response as the original magnetometer sig-
nals modified by subtracting the signal when ωis far off
resonance, and then normalized by the parameter S. For
the data in Fig. 2, its corresponding normalized magne-
tometer response can be described by:
N(ω) = f(ω)−(h+b)
S
=
exp P2
i=1
ci(Γi
2)2
(ω−ω0)2+( Γi
2)2−1
exp(P2
i=1 ci)−1,(12)
where the parameters in the equation are the same as
Eq. (10). Figure 4 (a) shows the normalized magnetome-
ter responses with three different ψzat a cell temperature
around 55 ◦C. While all the results have symmetric line
shapes, the line width increases as ψzdecreases. This is
due to fact that, as shown in Fig. 3 (a), the transmitted
beam power increases when ψzchanges from 90◦to 30◦,
which leads to a larger power broadening effect.
However, the situation becomes more complicated
when the pump beam is off resonance. In this case, we
need to consider the light shift effects. Similar to ROP ,
the effective field from light shifts can be expanded as
BL= [BL0+PnBLn cos(nωt −αn)]ˆ
z. The first har-
monic part of BLcan excite a part of Pz0to the x0y0
plane, so that there is an additional polarization term
P0
x0along the x0axis besides Px0in Eq. (4). By treating
this effect as a perturbation, we can express P0
x0as [36]:
P0
x0=(ωL−ω)γBL1cos(ωt −α1) sin ψzPz0
2[R2/Q2(P)+(γBL1sin ψz/2)2+ (ωL−ω)2].(13)
S (V)
55 °C
35 °C
transmitted beam power (mW)
yZ (deg)
02010 30 40 50 60 70 80 90
0
0.2
0.4
0.6
0.8
yZ (deg)
02010 30 40 50 60 70 80 90
55 °C
35 °C
(b)
(a)
0
0.02
0.04
0.06
FIG. 3: (Color online) Plot (a) and (b) shows the
transmitted beam power and the Svalue of the
magnetometer response as a function of the ψzat two
different cell temperature.
The transmitted pump beam intensity is now determined
by A(Px0,s+P0x0), instead of A(Px0,s), in Eq. (9). There-
fore, the dispersion relation between P0
x0and ωintroduces
asymmetric magnetometer response results. Similar to
Eq. 10, a combination of two Lorentzian functions and
two dispersion functions are used to describe the atomic
polarization behaviors. The function to fit the magne-
tometer signal with detuned light is:
F(ω) = hexp "2
X
i=1
ci(Γi
2)2+di(ω−ω0)
(ω−ω0)2+ (Γi
2)2#+b, (14)
and the normalized response is described by:
N0(ω) = F(ω)−(h+b)
S
=
exp P2
i=1
ci(Γi
2)2+di(ω−ω0)
(ω−ω0)2+( Γi
2)2−1
exp(P2
i=1 ci)−1.(15)
Figure 4 (b) shows the normalized magnetometer re-
sults, when the pump beam is 6 GHz blue detuned from
the D1 line. It confirms the appearance of asymmetri-
cal line shapes as ψzdeviates from 90◦. On the other
5
45 46 47 48 49
0
0.2
0.4
0.6
0.8
1
normalized response
w/2p (kHz)
45 46 47 48 49
-0.5
0
0.5
1
normalized response
w/2p (kHz)
(a)
(b)
°
y
z
=30
°
y
z
=60
°
y
z
=90
°
y
z
=30
°
y
z
=60
°
y
z
=90
FIG. 4: (Color online) (a) Normalized magnetometer
responses at different ψz, when the pump beam is
resonant with the Rb D1 line and the cell temperature
is around 55 ◦C. The solid lines are fitting results using
Eq. (12). Plot (b) shows the same results as plot (a),
except that the pump beam is 6 GHz blue detuned from
resonance. The solid lines are fitting results using
Eq. (15).
hand, the data also shows that the asymmetry of the line
shapes increases as ψzdecreases. This is because that
the degree of this asymmetry is determined by the ratio
A(P0x0)/A(Px0,s), which is proportional to cos ψz. In or-
der to quantify the degree of the line shape asymmetry,
we introduce a new parameter D, which is the ratio of the
asymmetric part over the symmetric part in the fitting
function:
D(δf ) =
2
P
i=1 RωL+2πδf
ωL−2πδf |di(ω−ω0)
(ω−ω0)2+( Γi
2)2|dω
2
P
i=1 RωL+2πδf
ωL−2πδf |ci(Γi
2)2
(ω−ω0)2+( Γi
2)2|dω
.(16)
The parameters in the equation above are the same as
Eq. (14). Using the fitting results, we have D(3000) =
2.38 for the data at ψz= 30◦in Fig. 4 (b).
IV. SOLUTIONS AND DISCUSSIONS
The field-orientation dependent asymmetric magne-
tometer response, induced by ac light shifts, presents a
new source of heading error in Bell-Bloom magnetome-
try. From Eqs. (8) and (13), we can get that the ac
light shift effect on the transmitted beam intensity is de-
termined by sBL1, the product of the photon spin and
the effective field from the light shift. It is confirmed by
the experiment that the asymmetry of the magnetome-
ter response can be reversed by flipping the pump beam
polarization or detuning. Therefore, to solve this head-
ing error problem without consuming additional power,
a simple way is to reverse the pump beam polarization
inside the atomic cell.
If the optical length of the pump beam inside the cell
with two opposite circular polarizations are same, the ef-
fect of s·P0
x0in Eq. (6) can be cancelled out. In the
same way, the static light shift can also be spatially aver-
aged out. Therefore, the whole light shift effects in this
magnetometry can be eliminated using such a method.
In practice, to maintain the magnetometer signal, it is
also important to reduce the possibility that atoms polar-
ized by one pump beam polarization diffuse into another
region pumped by light with an opposite polarization.
Considering all the requirements, the most suitable way
to implement this scheme in the experiment is to attach
a half-wave plate in the middle of the cavity.
In the experiment, we use a customized true zero-order
half-wave plate, which is attached to a piece of K9 glass so
that the total thickness of the wave plate is 0.6 mm. Due
to the heated environment around the cell, we need to
first check the temperature effect on the performance of
these half-wave plates. For a transverse wave propagating
along the zdirection, the oscillation amplitude of its elec-
tric field can be expressed as Ax,y =Ex,y cos(ωt +δx,y ).
The circular polarization part in this wave can be char-
acterized by an ellipticity parameter η[37]:
sin(2η) = 2ExEysin(δx−δy)
|Ex|2+|Ey|2.(17)
An ideally circularly polarized wave has η= 45◦, and a
linearly polarized wave has η= 0◦.
We attach one of the half-wave plates in the middle of
the cavity as shown in the inset of Fig. 5 (a), use a far-
off-resonance light with ηclose to 45◦as the input beam,
and measure ηof the output beam from the cavity at
different cell temperature. The experiment data in the
same plot shows that the output beam has a weak ellipti-
cal polarization at low temperature, due to 21 reflections
on the cavity mirrors and 22 passes through the wave
plate. ηof the output beam changes slightly when the
temperature is below 80 ◦C, and the circular polariza-
tion of the output beam rapidly degrades when the cell
temperature is above 85 ◦C. Therefore, the customized
half-wave plates are feasible for applications when the
cell temperature is below 80 ◦C, which covers the sensor
operation temperature in this paper.
6
(a)
w/2p (kHz)
(b)
20 40 60 80 100
28
30
32
34
36
(°)
temperature (°C)
normalized response
normal cavity
normal cavity+ l/2 plate
45 46 47 48 49
-0.5
0
0.5
1
FIG. 5: (Color online) Plot (a) shows the ellipticity
parameter ηof the output beam as a function of the cell
temperature, with the cavity configuration shown in the
inset. Plot(b) compares the magnetometer results using
two different cavity configurations. The lines are fitting
curves using Eq. (15).
Using this modified cavity with a half-wave plate in the
middle, we retake the magnetometer results at ψz= 30◦.
The new experiment data in Fig. 5 (b) shows D0(3000) =
0.09. Compared with the results using the conventional
cavity in the previous section, we have eliminated most
of the aforementioned light shift effect, and only 3.7%
of the original effect is left. This residual effect can be
further reduced by tuning the position of the half-wave
plate inside the cavity.
We use the parameter S/N as the magnetometer signal-
to-noise ratio with a 1 Hz bandwidth. Figure 6 (a)
demonstrates that there are two orders of magnitude dif-
ference for the maximum and minimum of S/N in the
magnetometer using a conventional cavity. To lift the
detection dead zones in the sensor, we add a reflection
mirror to the conventional cavity, and arrange the cav-
ity mirrors as shown in the inset of Fig. 6 (a). In this
new configuration, the optical paths are bent by 90◦in
the middle. This path-bending cavity can be treated as
a combination of two separated normal multipass cav-
ities. They can complement each other because their
dead zones are orthogonal.
(a)
normal cavity
path-bending cavity
normalized response
w/2p (kHz)
path-bending cavity
path-bending cavity+ l/2 plates
(b)
S / N
02010 30 40 50 60 70 80 90
0
200
400
600
800
yZ (deg)
45 46 47 48 49
0
0.5
1
FIG. 6: (Color online) Plot (a) shows the magnetometer
S/N as a function of the ψzusing two cavity
configurations with the pump beam resonant with the
Rb D1 line, ω=ωL, and cell temperature around 55
◦C. The inset shows an illustration of the path-bending
cavity. Plot (b) shows the normalized response of the
magnetometers taken at ψz= 45◦, with the pump beam
6 GHz blue detuned from the Rb D1 line. The lines are
fitting curves using Eq. (15), and the inset illustrates a
path-bending cavity vapor cell with half-wave plates.
While it helps to eliminate the detection dead zones,
the introduction of an extra reflection mirror also dou-
bles the interactions between the mirror surfaces and the
beam, which can strongly influence the quality of the
beam circular polarization. In practice, we modify the
cavity mirror parameters by reducing the number of re-
flections inside the cavity to 13 times, and increasing the
length of each optical path inside the cavity to 26.3 mm.
In this way, the magnetometer signal amplitude is kept
almost unchanged, and the polarization of the beam in-
side the cavity is also maintained in a good quality. As
shown in Fig. 6 (a), S/N of the magnetometer using
this path-bending cavity fluctuates within 20% over the
whole range of ψz. This is a significant improvement
compared with the magnetometer using a conventional
cavity, and the remaining orientation dependence of the
7
S/N is mainly determined by the cavity structure.
It is straightforward to combine the two methods de-
veloped above for simultaneous elimination of the dead
zones and light shifts. As shown in the inset Fig. 6 (b),
this is achieved by placing two half-wave plates in the
middle of the optical paths between the reflection mir-
ror and cavity mirrors. Its function is confirmed by the
experiment results in the Fig. 6 (b), which shows simi-
lar success on suppressing the light-shift effect using this
new configuration as the one in Fig. 5 (b).
V. CONCLUSION
In summary, we have demonstrated an atomic orienta-
tion based scalar magnetometer using a single amplitude-
modulated beam and a multipass cell. We suppress the
light-shift effect by more than one order of magnitude,
using a half-wave plate in the middle of the cavity to re-
verse the beam polarization inside the cavity. We also
remove the detection dead zones, and limit the change of
the magnetometer signal-to-noise ratio within 20% over
the whole angular range, by modifying the cavity to a
three-mirror configuration. Combining these two tech-
niques, we reached a light-shift-free and dead-zone-free
scalar magnetometer. The methods developed in this pa-
per are novel in optically pumped magnetometry, robust
to use, and easy to be extended to other atomic devices.
One important application is in the aforementioned
atomic magnetometry using a single elliptically polarized
light [25], where this beam has to be kept off resonance for
both optical pumping and Faraday rotation detections.
The inherent light shift problem limits the application of
this magnetometry in precise scalar field measurements.
The polarization-reversing cavity developed in this paper
can solve this problem by eliminating the first order light
shift effect. Calculations based on Jones calculus have
been performed to confirm the feasibility of this scheme.
If the proposed scheme can be successfully implemented,
this modified magnetometer would be a promising com-
pact single-beam version to replace the widely used two-
beam double-resonance scalar magnetometers [1].
ACKNOWLEDGEMENTS
This work was partially carried out at the USTC Cen-
ter for Micro and Nanoscale Research and Fabrication.
This work was supported by National Natural Science
Foundation of China (Grant No. 11974329), and Scien-
tific Instrument and Equipment Development Projects,
CAS (NO. YJKYYQ20200043).
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