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Millimeter Wave Detection via Autler-Townes Splitting in Rubidium Rydberg
Atomsa)
Joshua A. Gordon,1, b) Christopher L. Holloway,1Andrew Schwarzkopf,2Dave A. Anderson,2Stephanie Miller,2
Nithiwadee Thaicharoen,2and Georg Raithel2
1)National Institute of Standards and Technology (NIST), Electromagnetics Division, U.S. Department of Commerce,
Boulder Laboratories, Boulder, CO 80305
2)Department of Physics, University of Michigan, Ann Arbor, MI 48109
(Dated: 16 June 2014)
In this paper we demonstrate the detection of millimeter waves via Autler-Townes splitting in 85Rb Rydberg
atoms. This method may provide an independent, atom-based, SI-traceable method for measuring mm-wave
electric fields, which addresses a gap in current calibration techniques in the mm-wave regime. The electric-
field amplitude within a rubidium vapor cell in the WR-10 wave guide band is measured for frequencies of
93 GHz, and 104 GHz. Relevant aspects of Autler-Townes splitting originating from a four-level electromag-
netically induced transparency scheme are discussed. We measure the E-field generated by an open-ended
waveguide using this technique. Experimental results are compared to a full-wave finite element simulation.
The detection of millimeter waves (mm-waves) has
proven useful for a broad range of applications, includ-
ing weapons stand-off detection1, aeronautics2, remote
sensing3, next generation wireless communications4and,
stand-off human vital sign monitoring5to mention a few.
Each of these applications may be appropriately suited
to one or more of the myriad of sensor types available.
Traceability for both electric field and power measure-
ments at these frequencies is through power. Typical
sensors are Schottky diodes, bolometers, and calorime-
ters, all of which are traceable to calorimeter measure-
ments. Calorimeter and bolometer measurements are
traceable to DC voltage and resistance measurements6.
The sensors and the calorimeters measure power at a ref-
erence plane (often a connector) of a rectangular wave
guide. If a direct measurement of the electric field is
desired, then models and or measurements, such as near-
field antenna pattern techniques7, are needed to ob-
tain the relationship between the desired electric field
and the power at the reference plane. However, spec-
ifying reliable models and performing antenna pattern
measurements becomes difficult at mm-wave frequencies
because the mechanical tolerances and repeatability of
such components may vary such that they are a signif-
icant fraction of the operating wavelength. For these
reasons we are investigating more direct and traceable
techniques for mm-wave electric field and power calibra-
tions. Here we present on an atomic-based technique
which allows direct measurement of the magnitude of the
electric field, |E|, at mm-wave frequencies via Autler-
Townes (AT) splitting in Rydberg atoms. This split-
ting is inversely proportional to Planck’s constant, ~pro-
viding a link to the SI. We obtain data for a range of
electric field levels in the WR-10 band (75-110 GHz) at
a)This work was partially supported by DARPA’s QuASAR pro-
gram. Publication of the U.S. government, not subject to U.S.
copyright.
b)Electronic mail: josh.gordon@nist.gov
93.71 GHz and 104.77 GHz. Fundamentally this tech-
nique also lends itself to measurements beyond 110 GHz,
which may address a current lack of traceable methods
for calibrating mm-wave systems above 110 GHz. Fur-
thermore, it does not rely on a priori knowledge of an
antenna pattern for determining the electric field. In ad-
dition this technique has many novel properties useful
for measurements of |E|that we have recently reported
on, such as extremely large bandwidth8(1-500 GHz),
sub wavelength imaging9and two-photon AT interac-
tions at microwave frequencies for potential use in high
power microwave sensing10
Rydberg atoms have a single valence electron in a
highly excited state, where the principal quantum num-
ber is typically n>10. The dipole moment, ℘, in Ryd-
berg atoms scales as n2, and at the nrequired for a mm-
wave transition (n∼30), it can be several orders of mag-
nitude greater than for a ground state atom ∼1000ea0,
where eis the electron charge and a0is the Bohr radius.
Therefore Rydberg atoms can have significant response
to mm-wave electric fields. In this paper we will focus on
the 85Rb isotope of rubidium excited to n= 28,29, be-
tween the nD5/2to (n+ 1)P3/2manifolds, corresponding
to Rydberg transitions in the WR-10 mm-wave band. As
has been well established in the literature11 the energy,
W(n∗), of Rydberg states may be modeled as,
W(n∗) = −RRb
(n∗)2,(1)
where RRb is the Rydberg constant for the reduced elec-
tron mass in rubidium, n∗=n−δis the effective prin-
ciple quantum number determined using the quantum
defect11,13,δ. The quantum defects from13 were used
to determine the specific mm-wave frequencies for each
transition.
Although a thorough discussion of electromagnetic in-
duced transparency (EIT) is beyond the scope of this
paper, a brief description of the phenomena is give. In
a gas of rubidium atoms an incident probe laser beam
arXiv:1406.2936v1 [physics.atom-ph] 11 Jun 2014
2
FIG. 1. Energy levels used in the experiment for generating
Autler-Townes splitting from 85Rb Rydberg atoms.
experiences large absorption when tuned to the D2tran-
sition, at λp= 780.241 nm. However, in the presence
of a second coupling laser at, λc≈480 nm this gas
will be rendered partially transparent to the probe laser
and a transmission peak will result in the spectrum of
the probe laser. This quantum interference effect be-
tween the ground state and states excited by the probe
and coupling laser is known as Electromagnetic Induced
Transparency14. This has been widely studied for both
Rydberg atoms as well as alkali atoms at lower nand was
first demonstrated by Boiler et. al. . Later the effects of
adding a fourth level to the EIT scheme (see Figure 1)
were theoretically investigated18. In this scheme the the
transition to this fourth level is taken to be a radio fre-
quency (RF) transition of either a hyper fine transition or
a Rydberg state transition18. In the case we present here,
the transition to the fourth level is a mm-wave Rydberg
transition. To be clear, in keeping with popular nomen-
clature in the literature, the use of the term RF will be
used interchangeably to mean mm-wave frequencies in
the rest of this paper. When Rydberg atoms are used in
a four level system, the strength of the RF transition at
modest electric field strengths is sufficient to transition
this four level system from the EIT regime into the AT
regimes15,16 where the RF electric field causes the EIT
peak to split into two peaks.
With the coupling laser on resonance, and the probe
frequency swept, the EIT peak is observed to split into
two equal peaks separated by the Rabi frequency, ΩRF ,
of the RF transition,
ΩRF =℘RF |ERF |
~(2)
In actuality the frequency splitting, ∆fprobe, that is
measured on the probe laser EIT spectrum, must be
scaled by the ratio of laser wavelengths. This is in or-
der to take into account the effects of Doppler mismatch,
which occurs due to the different wavelengths of the
counter propagating probe and coupling laser beams in-
teracting with the thermal vapor (room temperature) of
atoms17. The measured splitting on the probe laser is
FIG. 2. Experimental setup for generating EIT and AT spec-
tra. Counter-propagating 780 nm probe laser (dotted line)
and 480 nm coupling beam (solid line) are shown, as well as
the Rb vapor cell, dichroic beam splitter and bandpass filter.
thus related to ΩRF in terms of the wavelengths of the
coupling laser, λc, and probe laser, λp, by
∆fprobe =λc
λp
ΩRF
2π(3)
From (2) we see that this splitting is linearly pro-
portional to the RF electric field strength, |ERF |, the
dipole matrix element, ℘RF of the Rydberg RF transi-
tion, and ~. This direct relationship of the measured
Rabi frequency to the electric field, the dipole matrix el-
ement and Planck0s constant is at the heart of the trace-
ability of this technique. Sedlacek et. al.19 used this
technique for the 53D5/2−54P3/2Rydberg transition in
87Rb to measure the electric field strength at 14.23 GHz
inside a vapor cell. In this paper we extend this technique
for measuring electric fields in the mm-wave regime.
Frequencies in the WR-10 band of f0= 93.71 GHz, and
f0= 104.77 GHz corresponding to the, 29D5/2−30P3/2,
and 28D5/2−29P3/2transitions respectively, are mea-
sured over a range of electric field strengths. Data
are presented comparing the electric field determined
via this AT splitting technique to numerical simulations
performed using a three dimensional finite element ap-
proach.
Our experimental setup is shown in Figure 2.
Two counter-propagating lasers beams were used, the
probe laser tuned to the D2 transition of 85Rb at
780.241 nm and the coupling laser tuned to approxi-
mately 480 nm for exciting Rydberg states are incident
on the room temperature vapor cell. This is depicted in
Figure 2. The full-width half-max beam diameters at the
center of the vapor cell for the probe and the coupling
laser are 80 µm and 100 µm respectively. The beam pow-
ers were nominally 28 mW for the coupling laser and 100
nW for the probe laser. The line widths for both probe
and coupling lasers were ≈1 MHz.The probe laser does
not need to be broadband tunable because it is always
probing the same transition (i.e. 85 Rb D2 line). For the
coupling laser it is advantageous to have broadband tun-
ability over a range of at least several hundred GHz to
be able to optically excite a selection of Rydberg levels.
The mm-waves were produced using an RF signal
3
generator (SigGen) with 0.1 Hz resolution to drive a
WR-10 6x frequency multiplier. The output of the fre-
quency converter was coupled to a WR-10 open ended
rectangular wave guide (OEG) placed approximately 140
mm from the vapor cell. The cell is a 25 mm x 75 mm
hollow glass cylinder containing 85Rb vapor commonly
used in saturation absorption spectroscopy. The vapor
cell was mounted on a low permittivity foam block to iso-
late mm-wave scattering from surrounding metal optics
mounts and microwave absorber was used to cover ex-
posed surfaces of the optics bench. A variable in-line at-
tenuator was used to vary the mm-wave power. The mm-
wave power was verified for each dial position of the vari-
able attenuator using a WR-10 power meter connected
directly to the output of the OEG. Because the attenu-
ator uses a mechanical vane to achieve attenuation, the
equal dial settings did not necessarily correspond to equal
steps in mm-wave power. Therefore, the power output
from the OEG, POEG , was calibrated using the WR-10
power meter for each frequency, and at each increment on
the variable attenuator. The reflection coefficient, |S11|,
between the OEG aperture and free space was measured
on a vector network analyzer. Since the power meter is
impedance matched to the OEG, the power actually leav-
ing the OEG when coupled to free space is determined
by modifying the power meter reading by (1 − |S11 |2) so
as to take in account the aperture reflection missing in
the matched power meter reading.
The full range of the variable attenuation was used,
however the mm-wave power range at each frequency
was not the same because the power produced by the
mixer decreased as the frequency increases. Therefore the
power range at 93.71 GHz is larger than at 104.77 GHz.
This results in a variation of achievable dynamic range
between the mm-wave frequencies. The maximum power
measured at the OEG aperture was -0.83 dBm at 104.77
GHz, and +1.95 dBm at 93.71 GHz. The minimum power
measured at the OEG aperture which gave unambigu-
ous AT splitting was -11.58 dBm and -12.71 dBm, at
104.77 GHz and 93.71 GHz respectively. For each level
of POEG the AT signal was measured on the probe laser
using a silicon photodiode and lock-in amplifier. The
probe laser was separated from the coupling laser us-
ing a dichroic beam splitter followed by a 10 nm wide
line filter in front of the photo diode see Figure 2. The
lock-in signal was generated by chopping the coupling
laser beam using an acousto-optic modulator to produce
a 30 KHz square wave modulation. With the probe laser
sweeping across the Doppler spectrum of the D2 tran-
sition, the coupling laser was tuned to the wavelength
for the desired Rydberg state. The coupling laser wave-
length was determined using the 85Rb ionization energy
and D2 transition energy from12, and the calculated Ry-
dberg state energy using (1), fine-tuning was done by
observing the three-level EIT signature (with mm-wave
power off). Once the EIT signal was established the cou-
pling laser was locked to a stabilizing cavity.
To produce the AT signal, the SigGen was tuned to
FIG. 3. EIT peak with mm-wave power off and and AT split-
ting for POEG =−2.43 dBm for the 28D5/2−29P3/2transi-
tion, f0= 104.77 GHz.
the mm-wave frequency that was determined again using
(1) for the desired Rydberg transition. With the variable
attenuator set to half of the power range, the mm-wave
frequency was fine-tuned so as to result in AT peaks of
equal heights. Both the laser fields and mm-waves were
(linear) π-polarized and aligned so as to minimize excita-
tion of the 3-level EIT pathway21. The mm-wave power
was then varied using equal increment dial settings on
the attenuator. The Doppler-free saturation absorption
spectrum of the probe laser was obtained simultaneously
with the AT spectrum. This was used to calibrate the
measured AT splitting from the known frequency spac-
ing of the Doppler-free hyperfine features present in the
D2 saturation spectrum. Equation(2) was then used to
determine the ΩRF , where the dipole moment ℘RF , was
calculated using the methods described in11 and the ap-
propriate Clebsch-Gordan coefficients. Figure 3 shows
scans taken for the 28D5/2−29P3/2transition for the
EIT signal with mm-wave power off, along with the AT
signal with the power at the OEG set to -2.43 dBm.
Electric fields were using the experimental setup de-
scribed above. For each power setting of the vari-
able attenator the splitting was calculated using (2)
and (3) and compared to simulated results. At a
distance of 140 mm from the aperture of the OEG,
the vapor cell was well beyond the farthest far-
field distance calculated for the mm-wave frequencies
that were measured (i.e. ≈5.63 mm, the value at
104.77 GHz). The far-field distance was calculated us-
ing the dimension of the OEG aperture diagonal and the
conventional definition given in20. Simulations were per-
formed to determine the electric field radiated by the
OEG using the far-field calculator in the electromagnetic
4
FIG. 4. AT splitting in MHz versus √POEG for the 29D5/2−
30P3/2,f0= 93.71 GHz, and 28D5/2−29P3/2f0= 104.77
GHz transitions. Linear fits are shown as solid lines.
finite element solver HFSS (mention of this software is
not an endorsement but is only intended to clarify what
was done in this work). These field values were then used
to compare with those measured using the vapor cell.
First, we established that the measured splitting scales
linearly with the electric field as expected from (2). Given
that the electric field at the vapor cell is proportional to
the √POEG , if the splitting indeed follows the behavior
in (2), then a linear relationship would be apparent by
plotting ΩRF versus √POEG. This is clearly shown in
Figure 4 for both frequencies. Figures 5 and 6 show a
comparison of the electric field values determined from
the vapor cell measurements to those obtained from the
HFSS far-field simulation. The error bars in these plots
show the expected range of electric field values within
the vapor cell due to field variations that are present be-
cause of the dielectric boundary of the cell. We discuss
this further next.
From Figures 5 and 6, we see that there is a
noticeable difference between the measured and simu-
lated electric field values. Also, the agreement of the
measured electric field to simulated results is not con-
sistent between frequencies. A strongly observable effect
which alters the electric field inside the vapor cell results
from standing waves set up by the dielectric boundary of
the cell walls interacting with the mm-waves. The dimen-
sions of the vapor cell used are ≈25 mm x 75 mm and
the operating wavelengths are 3.22 mm and 2.88 mm at
93.71 GHz and 104.77 GHz respectively. Therefore, the
vapor cell, in terms of wavelengths is ≈7.7λx 23.4λ
and ≈8.7λx 26.3λfor these two cases. Since the laser
beams were not moved between measuring the two mm-
wave frequencies, the observed frequency dependence is
attributed to the difference in mm-wave mode structure
of the vapor cell as a result of the difference in wave-
FIG. 5. Electric field values at 93.71 GHz measured using the
vapor cell and compared to HFSS far-field simulation. Solid
line shows HFSS simulation. Error bars indicate the possible
20% field variation range due to resonant mm-wave scattering
effects of the vapor cell.
FIG. 6. Electric field values at 104.77 GHz measured using the
vapor cell and compared to HFSS far-field simulation. Solid
line shows HFSS simulation. Error bars indicate the possible
%20 field variation range due to resonant mm-wave scattering
effects of the vapor cell.
length between the 93.71 GHz and 104.77 GHz frequen-
cies. As the wavelength changes, the standing wave struc-
ture changes, and thus the electric field amplitude at the
location of the laser beams in the vapor cell will depend
on the mm-wave frequency. We have reported on this
5
effect in detail in9, where we show the ability to image
these standing waves at extreme sub-wavelength resolu-
tion using AT splitting at both microwave (17.04 GHz)
and mm-wave (104.77 GHz) frequencies. From imaging
these standing waves we determined a ±20% variation
about the mean field strength as a function of measure-
ment location in the vapor cell at 104.77 GHz. The error
bars in Figures 5 and 6 indicate this ±20% variation for
the measurements we present here. This perturbing ef-
fect of the electric field by the presence of the dielectric
vapor cell is something we are currently addressing.
In this paper we demonstrate the detection of mil-
limeter waves via Autler-Townes splitting in 85Rb
Rydberg atoms. This method may provide an indepen-
dent, atomic-based, SI-traceable method for measuring
mm-wave electric fields, which addresses a gap in current
calibration techniques in the mm-wave regime. The elec-
tric field amplitude within a rubidium vapor cell in the
WR-10 waveguide band was measured for frequencies of
93.71 GHz, and 104.77 GHz. Experimental results are
presented where we measure the far-field electric field
generated by an open ended waveguide using this tech-
nique. A comparison to far-field electric field values ob-
tained from a finite element simulation is made. The
experimentally observed scaling behavior follows closely
the expected linear behavior of Autler-Townes splitting.
The electric fields measured agree to within ±20% of the
far-field simulations due to standing wave effects.
I. ACKNOWLEDGMENTS
Special thanks to David R. Novotny, and Galen H.
Koepke of the Electromagnetics Division at NIST,
Boulder for assistance with equipment.
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