A Rydberg atom based system for benchmarking mmWave automotive radar chips

Abstract

Rydberg atomic sensors and receivers have enabled sensitive and traceable measurements of RF fields at a wide range of frequencies. Here we demonstrate the detection of electric field amplitude in the extremely high frequency (EHF) band, at 131 GHz131\ \mathrm{GHz}. In our approach we propagate the EHF field in a beam, with control over its direction and polarization at the detector using photonic waveplates. This way, we take advantage of the highest detection sensitivity, registered for collinear propagation and circular polarization. To exhibit the potential for applications in this kind of Rydberg-atom based detection, we perform test measurements on the EHF field emitted from an on-chip radar, planned to be used in automotive industry as a vital sign detector. Our work elucidates practical applications of Rydberg-atom media as well as photonic metamaterial elements.

Full text

A Rydberg atom based system for benchmarking mmWave automotive radar chips
Sebastian Borówka,1, 2, ∗Wiktor Krokosz,1, 2 Mateusz Mazelanik,1 , †Wojciech Wasilewski,1, 2 and Michał Parniak1, 2, ‡
1Centre for Quantum Optical Technologies, Centre of New Technologies,
University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
2Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
Rydberg atomic sensors and receivers have enabled sensitive and traceable measurements of RF
fields at a wide range of frequencies. Here we demonstrate the detection of electric field amplitude in
the extremely high frequency (EHF) band, at 131 GHz. In our approach we propagate the EHF field
in a beam, with control over its direction and polarization at the detector using photonic waveplates.
This way, we take advantage of the highest detection sensitivity, registered for collinear propagation
and circular polarization. To exhibit the potential for applications in this kind of Rydberg-atom
based detection, we perform test measurements on the EHF field emitted from an on-chip radar,
planned to be used in automotive industry as a vital sign detector. Our work elucidates practical
applications of Rydberg-atom media as well as photonic metamaterial elements.
I. INTRODUCTION
Rydberg microwave electrometry was proposed as a
means to measure weak RF fields with reference traceable
to atomic transition dipole moments, the values of which
can be derived from quantum atomic theory. The ad-
vantages of atomic measurements include direct measure-
ment of E-field, intrinsic calibration, tunability to various
bands, prospects for integration, and weak scattering, en-
abling stealthy measurements [1,2]. The developments in
detection with Rydberg atomic vapors enabled great sen-
sitivity [3–6] and expanded the measurement schemes to
imaging [7,8] and photon-counting [9]. A lot of research
was devoted to analyses of atomic receivers [10–18] and
various demonstrations presented solutions adjacent to
real-world applications, such as transmission of recorded
sound through atomic media [19], spectral analysis [20],
multifrequency recognition [21], sensing at distance [22]
and satellite radio reception [23].
The realisations presented to date involved working in
the extremely high frequency (EHF) band, entering the
regime of millimeter waves [24–29]. In this research area,
specific solutions included imaging via Autler-Townes (A-
T) splitting [8] and fluorescence [30], proposal for trans-
duction to optical frequencies [31], later realized in cryo-
genic vacuum [32] and heated vapor cell [33] environ-
ments and recently an EHF band receiver [34].
Here we propose a measurement scheme for the cal-
ibration and testing of an on-chip sensor operating in
the EHF band (131 GHz). Because on-chip radars are
expected to be implemented as in-cabin vital sign de-
tectors in automotive industry, we hope that this proof-
of-concept demonstration takes Rydberg atom based
mmWave detection a step further towards industrial ap-
plications, allowing measurement of electric field and
frequency in a band notorious for difficulties in cali-
∗s.borowka@cent.uw.edu.pl
†m.mazelanik@cent.uw.edu.pl
‡mparniak@fuw.edu.pl
5S1/2
5P3/2
34D5/2
32F7/2
probe
780nm
384THz
coupling
481nm
623THz
EHF field
2.29mm
131GHz

Figure 1. Energy level structure utilized in the experimental
setup. The two-photon (probe-coupling) excitation path is
used to access one of the Rydberg states, enabling Rydberg
transitions in the EHF regime. The probe field is scanned near
the atomic resonance, while the EHF field has an additional
variable detuning, indicated by the value ∆(defined here non-
canonically as a detuning below the energy level, for further
convenience).
bration. The setup is based on 3D-printed high im-
pact polystyrene (HIPS) diffractive and metamaterial el-
ements, acting as lenses and waveplates, enabling prop-
agation of the measured field in beam, and control of
its polarization. With the use of a parabolic mirror, the
beam is focused inside a rubidium vapor cell, where the
EHF field can be detected near a Rydberg state transi-
tion.
II. PRINCIPLE AND METHOD
The detection of EHF field relies on the rubidium
energy level structure visualized in the Fig. 1. The
342D5/2→322F7/2transition is addressed with the
EHF field at 131 GHz (2.29 mm wavelength). To ac-
cess this transition, a standard probe-coupling excitation
scheme is used, where absorption spectrum of scanning
probe field is utilized as a detection readout. The coun-
terpropagation of probe and coupling fields allows par-
arXiv:2406.04021v1 [physics.app-ph] 6 Jun 2024

2
QWP
POL
HWP
f = 75 mm
f = 50.8 mm
PM
DM
PD
DUT
beam
dump
780 nm
481 nm
2.29 mm
(131 GHz)
d = 50.8 mm
87Rb
POL
Figure 2. The proposed setup used for the calibration of DUT (device under test). The EHF field is directionally emitted
and collimated into a beam with diameter 2” = 50.8 mm via a lens with focal length f= 75 mm. The beam is passed via a
setup of POL (linear polarizer), HWP (half-waveplate), POL and QWP (quarter-waveplate), allowing control of intensity and
polarization of the EHF field, nominally set for circular polarization. The EHF field is focused with a PM (parabolic mirror),
with reflected focal length f= 2” = 50.8 mm, into a quartz 87Rb vapor cell. There, a probe-coupling Rydberg electrometric
detection scheme is realized with counter-propagating circularly polarized optical beams combined with DM (dichroic mirrors)
and focused to an interaction region corresponding to Gaussian beams with matching waists w0= 250 µm. The readout of
probe field absorption in 87 Rb is facilitated with a PD (photodiode).
tial Doppler effect cancellation and enables operation in
room-temperature atomic vapors. Furthermore, taking
advantage of circular polarizations of fields, allows better
addressing the most sensitive transitions in the degener-
ated hyperfine structure of the energy levels.
To explain atom-light interaction in the depicted 4-
level ladder scheme, a density matrix approach can be
used, yielding particularly simple results in the form
of nested Lorentz-type resonances, where weak probe
field approximation is assumed [35]. This approach,
even expanded to the Doppler-broadened case for room-
temperature atoms, shows that the A-T splitting induced
by the EHF field can be directly observed in the probe
field absorption as the splitting of electromagnetically in-
duced transparency (EIT) resonance [36]. In this realiza-
tion, the splitting sA−Tobserved in probe field detuning
can be expressed as
sA−T=λc
λp
Ω,(1)
where λp,λcare wavelengths of probe and coupling fields
and Ωis the Rabi frequency of the EHF field. This pa-
rameter is directly proportional to the amplitude of the
EHF electric field E:
Ω = d·E
h,(2)
where dis the transition dipole moment. In further con-
sideration, we assume that for the chosen EHF transition
d= 542a0e[37], where a0is Bohr radius and eelemen-
tary charge.
Typically in Rydberg detection schemes, the EHF
fields have been treated as RF fields emitted from a horn
antenna. However, as the wavelengths are significantly
smaller than with typical RF fields, it is possible to treat
the EHF fields akin to optical or terahertz fields, that is,
to propagate them in beams with finite apertures. This
enables better control of the direction, which the detected
field comes from, and is a first step in Rydberg atom
based measurement of not only electric field amplitude,
but also power. Additionally, to achieve the greatest sen-
sitivity, control over the polarization of the EHF field is
paramount. This mandates the usage of optical compo-
nents that can shape, polarize and attenuate the EHF
field generated by the source.

3
(a)
lens HWP QWP
-0.5 0.0 0.5
x [mm]
-4.0
-2.0
0.0
2.0
4.0
z [mm]
(b)
-0.5 0.0 0.5
x [mm]
-4.0
-2.0
0.0
2.0
4.0
z [mm]
(c)
-0.5 0.0 0.5
x [mm]
-4.0
-2.0
0.0
2.0
4.0
z [mm]
(d)
0.40 mm
1.00 mm
5.17 mm
0.0
0.2
0.4
0.6
0.8
1.0
|
Ex
|2
0.0
0.2
0.4
0.6
0.8
1.0
|
Ey
|2
0.0
0.2
0.4
0.6
0.8
1.0
arg(
Ey
/
Ex
) [ rad]
Figure 3. (a) A photograph of lens, HWP (half-waveplate) and QWP (quarter-waveplate) used in the experimental setup.
The elements are 3D-printed from HIPS filament. The holder enables slide-in type mounting and rotation of waveplates, made
easier by tart-like shapes of waveplates’ edges. (b) Results of the 2D numerical FDTD simulation showing the |Ex|2of electric
field vector in space around a single fin of the QWP, with the EHF field propagating in the −zdirection. (c) The corresponding
results for the |Ey|2. (d) The corresponding results for the phase shift between Eyand Ex. Note the π/2shift. The dimensions
of the fin and fin pitch of the QWP are noted on the colormap. For the HWP the fin is twice as high with the other dimensions
unchanged.
80 60 40 20 0 20 40 60 80
Probe field detuning [MHz]
0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Probe field transmission
= 0 MHz
E = 0 V/m
= 9.38 MHz
E = 0.215 V/m
= 41.3 MHz
E = 0.948 V/m
= 94.2 MHz
E = 2.16 V/m
Figure 4. A-T splitting arising from the EHF field. The EHF
frequency was picked to be in resonance with the Rydberg
states transition, which manifests itself in the split peaks be-
ing of equal height for each signal. The visible signals present
a normalized probe field transmission spectrum, where each
measurement was divided by the measured background, i.e.
the one-photon probe transmission spectrum. The legend
presents parameters derived from the measurements, where Ω
is the Rabi frequency of the EHF driven state transition and
is equal to the separation between the split peaks multiplied
by λp/λc, and Eis the corresponding electric field amplitude,
calculated from the dipole moment relation (2).
III. EXPERIMENTAL SETUP
The experimental setup, presented in the Fig. 2, re-
lies on three fields, which are directed into a 87Rb vapor
cell. The probe transmission spectrum is observed us-
ing an avalanche photodiode (Thorlabs APD430A). The
coupling beam counterpropagates to offset the Doppler
effect within the atomic vapors, and dichroic mirrors are
utilized to combine both beams. Subsequently, the EHF
field is focused inside the vapor cell with a gold-coated
off-axis parabolic mirror. The mirror has a hole drilled
to enable a collinear introduction of optical beams.
The device under test emits the signal at a wide an-
gle (over 20◦), which necessitates the use of a collimat-
ing lens. For this purpose, a dielectric lens with a fo-
cal length of f= 75 mm was 3D-printed from HIPS
filament. The material has been shown to offer reason-
able parameters to be used as a refractive material in
the low THz regime, in particular its refractive index for
EHF and THz fields is n≈1.5[38] and its absorption
coefficient @131GHz is around α= 0.15 cm−1, which
was confirmed in our test measurements. The lens has
been verified to create a collimated beam with a diam-
eter of around 2” = 50.8 mm. It is propagated through
a linear polarizer, half-waveplate, linear polarizer and a
quarter-waveplate. This part of the setup is responsi-
ble for offering continuously variable attenuation of the
EHF field and inducing a circular polarization at the en-
try to the vapor cell. The half-waveplate as well as the
following quarter-waveplate are also 3D-printed HIPS el-
ements, photographed in the Fig. 3, with the details con-
cerning their shapes denoted. Their waveplate properties
arise from their fin-based metamaterial structure [39–41],
designed and verified using finite difference time domain
(FDTD) software [42], the results of which are also shown
in the Fig. 3. The use of 3D-printing enables custom solu-
tions for diffractive elements and waveplates, and is par-
ticularly low-cost, even in comparison to standard, non-
custom lens and waveplates for EHF and THz fields. On
the other hand, the polarizers used in the setup are PCB
boards of sub-mm spaced copper paths (width 0.25 mm
and pitch 0.6mm).
The automotive radar chip presented as the device
under test in this experiment is Indie Semiconductor

4
TRA_120_045. It can be driven to emit EHF frequen-
cies from 114–134 GHz range, though in this demonstra-
tion it is tuned narrowly around 131 GHz. Its power
reduction function (by −3 dB) and disabling the built-
in amplifier (after which we still observed weak emitted
field at around −21 dB relative to high power mode) were
used as a means to attenuate the EHF field at the detec-
tor, in addition to attenuating with a half-wave plate and
polarizers.
IV. RESULTS AND DISCUSSION
For the demonstration of the benchmarking setup, we
first measure the resonant frequency of the 342D5/2→
322F7/2transition at 130.728 GHz. This can be com-
pared to the simulated prediction of 130.726 GHz [37].
At this resonant frequency we perform a standard A-T
splitting measurement of the EHF electric field for var-
ious levels of this field, applying the relations (1) and
(2). These results are presented in the Fig. 4in the do-
main of probe field detuning, where zero detuning is de-
fined as two-photon EIT resonance. For weak field the
splitting becomes unresolvable with the standard tech-
nique, therefore, other methods have to be used for an
absolute calibration [5,6]. On the other end, for strong
fields diffusion-like properties of the split peaks are ex-
hibited. These may be attributed to the different sen-
sitivities of degenerated sublevels to non-zero magnetic
fields (e.g. the Earth’s magnetic field in this case). Nev-
ertheless, the A-T splitting method in the presented case
offers around 20 dB of the absolute calibration range.
Next, we use the setup to estimate the overall effi-
ciency of the control over polarization. We rotate the
HWP and QWP in the experimental setup and mea-
sure the Rabi frequency with the A-T splitting method,
assuming d= 542a0efor the 342D5/2(F=4,mF=4) →
322F7/2(F=5,mF=5) transition (we can assume hyper-
fine splitting despite the degeneration as the circular po-
larizations drive a closed transition which has the largest
dipole moments). The results are presented in the Fig. 5.
Note that the results are presented as Ω2, effectively in
the domain of field intensities. We fit cosine functions
to the results to estimate the contrast and visibility. For
the HWP we arrive with the contrast (ratio between the
maximum and minimum) of 420 (26 dB), that trans-
lates to the interferometric visibility of 0.995. For the
QWP we get the contrast of 9.2. The minimal achiev-
able splitting remains substantial, which is the result
of the A-T splitting still being induced, although via a
different transition, induced by the reverse polarization,
with different dipole moment. Although various transi-
tions may be considered, and the definite answer requires
the full consideration of the state evolution model, the
most obvious candidate is the 342D5/2(F=4,mF=4) →
322F7/2(mJ=3/2) transition, having a dipole moment of
d′= 118a0e[37]. With that assumption, the contrast for
a perfect QWP should yield 21. In that case, in relation
to the maximal contrast, we achieve the visibility of 0.88.
Consequently, we demonstrate that using this setup,
an estimation of EHF field’s frequency, in particular the
∆detuning, is possible as well. For the set EHF electric
field, we perform measurements for different ∆detunings,
and present the results for chosen detunings in the Fig. 6.
In this case, a crude estimation is provided by the relation
describing the separation between the peaks
sA−T,∆=λc
λp
pΩ2+ ∆2,(3)
where the parameters are defined as in the Eq. (1), with
∆corresponding to the detuning from the Fig. 1. The
comparison between the presented relation and obtained
results is presented in the inset to the Fig. 6. In this con-
sideration Ωis considered set and constant, measured at
∆=0detuning as Ω = 41 MHz. When the set ∆are
taken as ground truth, the estimation results from the
±100 MHz range yield an average deviation of 1.1 MHz.
This method is not suitable for precise estimation of fre-
quency, that instead should be obtained from wavemix-
ing with a known local oscillator [4], however, it gives a
reasonable estimate.
V. SUMMARY AND PERSPECTIVES
This proof-of-concept demonstration underlines the
control of EHF field direction and polarization, and
presents the detection scheme in a collinear configura-
tion. The practicality of this approach is further empha-
sised by the demonstration of a calibration procedure for
an automotive radar chip, bringing this technique a step
closer towards real-world applications. Our work demon-
strates a unique combination of the usage of Rydberg
media, photonic metamaterial elements in a practical ap-
plication. There are a few aspects that escaped the scope
of this work, though. In particular, the absolute estima-
tion of measured EHF power is missing. This is, however,
a persisting problem, coming down to the estimation of
the relation between the atomic interaction region and
region, where the EHF field is focused.
We anticipate further development will be focused
around adding resonant structures to the detection setup.
This may enhance the detection sensitivity and provide
additional degree of freedom for frequency tuning. This
is particularly feasible, as on the one hand for the EHF
wavelengths the sizes of the resonant structures, e.g. cav-
ities, can be manageable around a typical optical setup,
on the other hand, the manufacturing precision required
is low enough that the elements allow for integration with
optics, e.g. with through-holes for optical beams.
In principle, this detection setup can be repurposed for
other modes of operation, such as single-photon count-
ing, enabled by EHF-to-optical conversion. We expect
that due to predicted directionality of the converting re-
ceiver, it can be used efficiently for quantum temperature
detection in the EHF band, as the thermal radiation in

5
0/2 3 /2 2
Angle [rad]
02
202
302
402
502
602
702
2 [MHz2]
HWP
0/2 3 /2 2
Angle [rad]
QWP
Data
Fit
Figure 5. EHF Rabi frequencies squared, Ω2, measured via A-T splitting and corresponding to the rotation angles of the HWP
and QWP in the experimental setup. We fit cosine functions to both of the results and estimate their contrasts, i.e. the ratio
between the maximum and minimum. For the HWP we obtain contrast of 420 and for QWP – 9.2.
80 60 40 20 0 20 40 60 80
Probe field detuning [MHz]
0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Probe field transmission
[MHz]
-100
-70
-40
40
70
100
100 0 100
[MHz]
40
60
80
100
sA T
, [MHz]
Theory
Data
Figure 6. A-T splitting arising from various detuned EHF
fields. The Rabi frequency is constant throughout the series
and measured at ∆ = 0 as Ω = 41 MHz.Each line corresponds
to a different EHF field detuning ∆, which results in increas-
ing splitting between the peaks, as well as increasing difference
in the height of the peaks. All signals were normalized in the
same manner as was the case with the results in the Fig. 4.
The inset presents results of peak separation sA−T,∆measure-
ments in relation to ∆. The measurements are compared to
the theoretical estimation based on the Eq. (3), yielding an
average deviation of 1.1 MHz.
the super high frequency (SHF) band has already been
directly observed in a similar system [9].
DATA AVAILABILITY
Data underlying the results presented in this paper are
available in the Ref. [43].
CODE AVAILABILITY
The codes used for the numerical simulation are avail-
able from M.M. upon request.
ACKNOWLEDGMENTS
We thank K. Banaszek for the generous support. This
research was funded in whole or in part by National Sci-
ence Centre, Poland grant no. 2021/43/D/ST2/03114.
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