MAGNETOMETRY USING ELECTROMAGNETICALLY INDUCED
TRANSPARENCY IN A ROOM TEMPERATURE VAPOUR CELL
Developing an Optical Magnetometer that Utilises the Steep Dispersion Curve
Observed in EIT to Detect Time Varying Magnetic Fields
Melody R. Blackman and Benjamin T. H. Varcoe
School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, U.K.
Keywords:
Magnetometry, EIT.
Abstract:
The physiological importance of magnetic signals within biological systems has been investigated with ever in-
creasing sensitivities over the last decade. Currently superconducting quantum interference devices (SQUIDs)
are at the forefront of bio-magnetic diagnostics. In this research we aim to build an optics based magnetometer
that can compete with the sensitivity of the SQUID but that runs at a lower start up and operational cost. To
do this we intend to use the steep dispersion curve observed in the atomic physics effect electromagnetically
induced transparency. This magnetometer can operate at room temperature, its design is a convenient method
for monitoring bio-magnetic fields, making this technology an affordable technique for further bio-magnetic
diagnostics.
1 INTRODUCTION
Bio-magnetism is a fast developing field of research
as its non-invasive applications make it a very desir-
able diagnostic tool. The presence of time varying
electric fields in the human body has been greatly
studied over the last hundred years. Electrocardio-
graphs (ECG) measure these fields as potential dif-
ferences on the skin’s surface, with emphasis on the
torso (Nash et al., 2002; Ramanathan et al., 2004).
However each of these electric fields is accompanied
by a weak magnetic field that also holds information
on the condition of the organ. Unlike electric fields
the magnetic, do not suffer from varying attenuation
at they travel through the different types of tissue. An-
other advantage of measuring the magnetic field is
the ability to make direct measurements of an organ’s
field map instead of the potential difference between
two points.
The largest magneto-physiological signal in the
body is created by the heart’s QRS peak which corre-
sponds to the contraction and relaxation of the cardiac
muscle during a single heart beat. The magnetic fields
associated with this process are of the order of tens
of picotesla, although the more clinically important
signals that are unobservable with ECG are formed
by the cardiac conducting system, which are super-
imposed on the field and are less than 1 pT (Fenici
et al., 1983).
Currently at the forefront of magnetometer clini-
cal trials are Superconducting Quantum Interference
Devices(SQUIDs), which have displayed sensitivities
as high a few fT/
Hz (Vodel and Makiniemi, 1992).
Since their implementation they have been used to
form dynamic mapping of both the brain and heart’s
magnetic fields (H¨am¨al¨ainen et al., 1993; Fagaly,
2006). The limitations with SQUIDs come from their
operational requirements, starting with their need for
a cryostat, crucial for the 4 Kelvin cooling of the su-
perconducting materials that make up the Josephson
junctions used in the detector heads. This causes the
overall cost of the SQUIDs to be very high (in the
order of hundreds of thousands of pounds) meaning
there is a place in the market for cheaper alternatives.
It is in the field of optical magnetometry where
the most promising competition to SQUIDs can be
found (Bloom, 1962; Cohen-Tannoudji et al., 1969;
Nagel et al., 1998; Budker et al., 2000; Bison et al.,
2003; Kominis et al., 2003) and it is in this field that
our research is based. These methods allow for low
cost, non-invasive, non-contact highly sensitive mag-
netic field detectors that can be made and operated
at a fraction of the cost of a SQUID. The ability to
measure bio-magnetic signals without contact makes
173
R. Blackman M. and T. H. Varcoe B. (2009).
MAGNETOMETRY USING ELECTROMAGNETICALLY INDUCED TRANSPARENCY IN A ROOM TEMPERATURE VAPOUR CELL - Developing an
Optical Magnetometer that Utilises the Steep Dispersion Curve Observed in EIT to Detect Ti.
In Proceedings of the International Conference on Biomedical Electronics and Devices, pages 173-177
DOI: 10.5220/0001434501730177
Copyright
c
SciTePress
it very useful for fetal cardiac diagnostics (Comani
et al., 2004) as well as the more standard magneto-
cardiographs (MCG) and in the case of burns victims
where contact is not an option.
When making observations of magnetic fields us-
ing atom-light interactions one may start by thinking
of the Zeeman effect. The Zeeman effect explains the
perturbation of atomic energy levels by means of an
applied magnetic field, which couples to the magnetic
moment of the atomic electrons. Here we still utilise
the Zeeman effect but we need to go further into the
detail of the energy level shifts by discussing the ac-
Stark shift (also called the Autler-Townes effect) as
these are essential to the mechanism needed for mak-
ing our magnetometer more sensitive than a device
utilising just the Zeeman effect.
In this experiment we use a form of coherent pop-
ulation trapping (CPT) (Belfi et al., 2007) called Elec-
tromagnetically Induced Transparency (EIT) (Boller
et al., 1991; Scully, 1991; Harris, 1997). EIT is
a quantum interference effect whereby an opaque
medium is made transparent to a probe laser under
certain resonance conditions. To understand how the
many mechanisms that create EIT work together we
shall start by considering a three level system in the Λ
configuration. A depiction of the Λ transition used in
this experiment is displayed in figure 1. In this case
the ground states are degenerate, resulting in a sym-
metric transition so the coupling and probe beams can
be resonant with either m
F
= ±1 levels by switching
the sign of the circular polarisation (σ
+/
).
The intense coupling beam drives the transition
into the excited state; at this point an ac Stark shift
occurs at the upper energy level, whereby the atomic
absorption line splits into an Autler-Townes doublet,
symmetric about the transition’s unshifted resonance.
We now consider the processes of EIT in more de-
tail. We are fortunate that a thorough mathematical
understanding of EIT is available allowing us to sim-
ulate the system before building an experiment. This
is presented in the following paragraphs.
The following time dependent interaction Hamil-
tonian describes the atom-light coupling for a system
with EIT;
H
int
=
~
2
[
p
(t)
ˆ
σ
eg
1
e
i
1
t
+
c
(t)
ˆ
σ
eg
2
e
i
2
t
+ H.c]
(1)
where the
c/p
(t) are the Rabi frequencies of the
coupling and probe fields respectively,
ˆ
σ
ij
= |iihj| is
the atomic projection operator, is the detuning and
H.c is the Hermitian conjugate. It is this Hamilto-
nian that is inserted into the Master equation and al-
lows us to calculate the atomic density operators (ρ).
The solutions of the Master equation are fundamental
Figure 1: The Λ configuration for our
87
Rb transition show-
ing the possible detuning () of the m
F
levels in the pres-
ence of a coupling and probe beam. σ
+/
denotes the sign
of the circular polarisation. As the applied magnetic field
oscillates our system will rotate through these three Λ sys-
tems.
to understanding how the photons are no longer ab-
sorbed at the resonance peak, showing us that when
the coupling and probe beams interact they can cancel
each others absorptive terms producing a dark state by
means of destructive quantum interference. How this
affects the absorption can be seen by looking at the
real and imaginary parts of the linear susceptibility
(χ), given by;
χ(ω
p
,ω
p
) =
|µ
13
|
2
ε
0
~
N
atom
V
×
"
4δ(||
2
4δ∆) 4γ
2
g
1
g
2
|||
2
+ (γ
eg
1
+ i2)(γ
g
1
g
2
+ i2δ)|
2
+i
8δ
2
γ
eg
1
+ 2γ
g
1
g
2
(||
2
+ γ
g
1
g
2
γ
eg
1
)
|||
2
+ (γ
eg
1
+ i2)(γ
g
1
g
2
+ i2δ)|
2
#
(2)
where the two photon detuning, δ =
1
2
=
ω
g
1
g
2
(ω
p
ω c) and is derived from the single
photon detuning, =
1
= ω
eg
1
ω
p
. The coherent
decay between states is γ, in this case γ
g1
γ
g2
= 0. The
probe beam term (γ
e
γ
g2
) is neglected from the equa-
tion as it is assumed it has no observable effect on the
atom’s behaviour, this is in part due to the two photon
Raman resonance which occurs in the presence of the
dark states (Fleischhauer et al., 2005).
The linear susceptibility, as seen in equation 2
holds all the important information about the atom’s
absorption and refractive index and as these are both
BIODEVICES 2009 - International Conference on Biomedical Electronics and Devices
174
−1 −0.5 0 0.5 1
−0.02
−0.01
0
0.01
0.02
Linear susceptibility (χ) of a system with EIT
/γ
31
Re[χ]
−1 −0.5 0 0.5 1
0
0.01
0.02
0.03
/γ
31
Im[χ]
Figure 2: This figure shows rst the real Re[χ] then the
imaginary Im[χ] parts of the susceptibility calculated for the
D1 line of
87
Rb using equation 2.
altered in a EIT system it gives us a clear picture of
how the atom-light interaction has changed. Figure 2
displays how all these effects alter the real (Re[χ]) and
the imaginary (Im[χ]) part of χ.
B
V
V
Figure 3: The top line is a representation of Re[χ] for a
standard saturation spectroscopy dispersion curve, while the
lower is Re[χ] in the presence of EIT. The figure displays
how the sensitivity to magnetic eld is increased propor-
tionally to the gradient of the dispersion curve, where B is
the amplitude of the input and V is the amplitude of the
response.
The key to why a system with EIT makes for a
good magnetometer is the steep dispersion curve. Fig-
ure 3 shows a representation of the difference that the
steep dispersion curve has on the atom’s response to
magnetic fields. Therefore the steeper one can make
the dispersion curve the better the magnetic detector
will be produced from it.
2 EXPERIMENTAL SETUP
The experiment currently runs using free space op-
tics and a diode laser. The laser is tuned to
794.985nm, which is the transition frequency of
the D1 (5
2
S
1/2(F=2)
5
2
P
1/2(F=1)
) line of rubidium 87
(
87
Rb). The
87
Rb is contained within vapour cell with
a buffer gas of, neon at 30Torr. We use
87
Rb as it al-
lows us the run the experiment at room temperature
with low powered laser beams. Figure 4 displays the
apparatus used in this experiment.
The laser is a commercially available diode laser,
from which beams are tapped off and sent to the di-
agnostic and stabilisation section of the experiment.
Contained within this setup is the reference
85/87
Rb
vapour cell, arranged in a saturation spectroscopy
retro-reflection configuration. Using this along with
a wavemeter and a lock-in amplifier we can lock the
laser to the resonance peak of the transition, stabilis-
ing the laser system.
Laser
Amplifier
Lock−in
Wavemeter
Lock−in
Oscilloscope
Signal
Generator
Diagnostics
&
Laser Stabilisation
50:50
PBS
50:50
Rb cell
ND filter
Data Collection
λ/2
λ/4
ND
filter
Amplifier
3 layer
− metal
µ
Rb cell
2 solenoids
Figure 4: A schematic of the apparatus used in this experi-
ment.
The main design of the experiment is a Sagnac in-
terferometer, which starts a single beam that is then
split, these two beams then counterpropagate around
a ring. The beams return to their entry point and leave
the interferometer where they interact and produce in-
terference fringes.
Before the light enters the interferometer it is cou-
pled into a single mode optical fibre to clean the mode
MAGNETOMETRY USING ELECTROMAGNETICALLY INDUCED TRANSPARENCY IN A ROOM
TEMPERATURE VAPOUR CELL - Developing an Optical Magnetometer that Utilises the Steep Dispersion Curve
Observed in EIT to Detect Time Varying Magnetic Fields
175
for the experiment. We use a series of optics to pre-
pare the polarisations before splitting the circular po-
larised light with a 50:50 beam splitter into the in-
terferometer. It is here we obtain the σ
+/
terms as
displayed in figure 1. Before entering the vapour cell
one of the beams is attenuated with a neutral density
filter (ND filter), making it into our weak probe beam.
Two solenoids surround the vapour cell within
three layers of µ-metal shielding. These are driven by
an arbitrary signal generator. The first (modulation)
solenoid is driven with a square wave correspond-
ing to approximately 1nT of between 250-300KHz,
which is used as the reference for the signal recovery
lock-in amplifier. The second solenoid is also con-
nected to the arbitrary signal generator and is driven
with a sine wave with frequencies between 2-8Hz.
The human heart has a frequency range of 1-1.67Hz,
with higher frequency components.
The raw signal is collected via a photodiode and
then connected to the input of the signal recovery
lock-in amplifier. The lock-in amplifier allows very
small signals to be extracted from the large amounts
of noise, using this system we have gained sensitiv-
ities in the range of a fetal heart beat. An example
of test data taken using a simulated heartbeat is dis-
played in figure 5.
Figure 5: A sceen dump of data take on the experiment.
The centre trace is the raw input signal, a simulated QRS,
the lower trace is the raw data from the photodiode and the
upper trace is the 20 trace avarage.
3 CONCLUSIONS
With current data we can measure magnetic fields of
the order of a fetal heart beat. The experiment is
still at a very early stage of development, therefore
the current data acquisition method is not suitable for
clinical applications. However even at this stage the
experiment has shown a great deal of promise as a
potential MCG device. We expect, with some calibra-
tion, to obtain at least femtotelsa sensitivities (Fleis-
chhauer and Scully, 1994), with the possibility of us-
ing more optical fibres and replacing the modulation
solenoid with an alternative scheme such as an acous-
tic or electro-optic modulator (AOM/EOM). These
improvements will move this research closer to being
a competitive device for performing clinical MCG tri-
als.
ACKNOWLEDGEMENTS
This work is funded by an EPSRC DTA.
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MAGNETOMETRY USING ELECTROMAGNETICALLY INDUCED TRANSPARENCY IN A ROOM
TEMPERATURE VAPOUR CELL - Developing an Optical Magnetometer that Utilises the Steep Dispersion Curve
Observed in EIT to Detect Time Varying Magnetic Fields
177