Technion
Population Transfer Resonance:
A new Three-Photon Resonance
for Small Scale Atomic Clocks
Ido Ben-Aroya, Gadi Eisenstein
EE Department, Technion, Haifa, Israel.
FRISNO-11, Aussois, France, Mar. 2011
The Synchronous World
The Quartz Crystal Oscillators (1920stoday)
NIST (NBS) Frequency Standard by
Bell labs, 1929.
4 x 100 KHz crystal oscillators.
stability: 10-7
Source: NIST
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•Resonance frequency
shifted due to aging
•No two crystals with
the same frequency.
2
Frequency/Time Standard
Principle of Operation
• An oscillator with poor long-term stability (hours to
years) is locked on a narrow filter around a fixed
frequency  improved long-term stability.
•High contrast
Local Oscillator
(Quartz Crystal)
f0
•Stable during
feedback
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•Narrow width
Δf
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•Fixed f0
3
Types of Reliable Frequency Standards
CSAC:
•Small dimension
•Low power
consumption
2’’
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Source: Symmetricom
4
CPT based CSAC
• CPT – Two photon coherent process yielding narrow resonances
with low contrast
CPT resonance matching around 3 417.352 499MHz (span 1.5KHz). Resonance width=186Hz
1
raw data
Lorentzian
0.9
• D2 transition (780nm).
• Resonance width – 186Hz
• Contrast – 0.5% - 1%.
Amp [arb. units]
0.8
0.7
0.6
f=186Hz
0.5
0.4
0.3
0.2
0.1
0
-600
-400
-200
0
200
400
f (around 3 417.352 499MHz ; span 1.2KHz) [Hz]
600
• Clocks require complex locking schemes – Multi field FM
spectroscopy
• Large contrast resonances eliminate many of the locking problems
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5
Types of Atomic Resonances
Electromagnetically Induced Electromagnetically Induced
Absorption (EIA) type:
Transparency (EIT) type:
• Important characteristics: width and height (or contrast)
EIA-type: Population Transfer Resonance (PTR)
Inspired by Zibrov and Walsworth group “N-resonance” demonstration.
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6
Population Transfer Resonance
e
fhfs/2 •Three-level L-system
1
interacts with three
phase-locked fields in an
N-type configuration
scheme.

2 3
g2
fhfs
g1
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1 
2
3
7
Population Transfer Resonance
fhfs/2 • The probe 3, is tuned
e
1
on resonance and
therefore is absorbed
by the medium.

2 3
g2
fhfs
g1
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• 1 and 2 are highly
one-photon detuned
and sweep near the
zero two-photon
Raman detuning.
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8
Population Transfer Resonance
fhfs/2 • 3 optically pumps the
e
1
medium from |g2> to
|g1>.

2 3
g2
fhfs
g1
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• The two-photon
process induced by 1
and 2 transfers the
population back from
|g1> to |g2>  …
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Population Transfer Resonance
fhfs/2 The absorption of 3 is
e
1
enhanced due to the
repopulation of |g2>

2 3
 Electromagnetically
Induced Absorption
(EIA)-type resonance.
g2
fhfs
g1
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10
The Spectral Constellation
e
fhfs/2
1
Rb : F=2->F’
F=1->F’
2 3
g2
fhfs
g1
87
2 3 1
12 ~ f hfs
• The interacting frequency components originate from a
laser which is locked to the 87Rb D2 transition (|F=2>|F’=2>)
and modulated by half the 87Rb hyperfine splitting
frequency (fhfs/2=3.417 GHz).
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11
The Setup
Detector
ND
2 F-P vapor cell in /4
filters
-metal
F-P
2 3 1
Laser
w
Spectrum
Analyzer
PM
and
filters
2 3 1
12
•3 main blocks: Source, Medium, and Detection formation.
•Parameters: Modulation frequency (12), Total intensity
(I), and Carrier to 1st side lobe intensity ratio (C1L).
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12
First Observation
Approx. 50 %
contrast.
• The probe (3) intensity (normalized) is measured versus PM
frequency sweeping near 3 417 345 KHz for various C1L ratios.
I=300 W.
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13
First Observation
3
1 
2
3
2
1
2 3 1
12
• EIA-type resonance for the probe (3) and 1.
• EIT-type resonance for 2.
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14
The Model
Probing 2-ph process: The Population Coupling model
Two processes
coupled by the
population of
their states
A: One, “on
resonance” field
interacting with a
three-level Lsystem with a
|g1>|g2>
coupling channel.
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e
fhfs/2
1
2 3
g2
fhfs
g1
e
e
p
Δ
1
g2
2
g2
Γ2→1
Γ1→2
g1
g1
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B: Two highly onephoton detuned
fields interacting
with a three-level
L-system with a
|g2>|g1> coupling
channel.
15
e
fhfs/2
1
The Model (phase II)
2 3
The Coupling of Coherence
g2
fhfs
g1
• The population coupling model is insufficient in describing
the obtained resonance for moderate probe intensities.
• The coupling model neglects the existence of each process
field(s) in the other process.
• The “missing information”: the coherence in both processes.
e
e
p
Process A
g e
2
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g1
1
2
Process B
g2
g2
12
Δ
Γ2→1
Γ1→2
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g1
16
e
fhfs/2
1
2 3
The Model
g2
Process A
Process B
e
e
p
g e
2
g1
1
2
g2
g2
12
fhfs
Δ
Γ2→1
Γ1→2
g1
g1
• The population of |g2> is given by a ratio between two
polynomial terms of symmetric (Lorentzian) and antisymmetric (“dispersion-like”) functions of the modulation
frequency (d).
• The approximated anti-symmetric and symmetric functions:
Fundamental Width:
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17
e
fhfs/2
1
2 3
The Model
g2
Process A
Process B
e
e
p
g e
2
g1
g1
1
2
g2
g2
12
fhfs
Δ
Γ2→1
Γ1→2
g1
• The absorption of the probe, under several assumptions,
is an almost symmetric function of the modulation
frequency:
– Width (HWHM):
– Height:
– Where s is the saturation parameter:
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e
fhfs/2
1
2 3
g2
fhfs
The Model
Results
g1
Process A
Process B
e
e
p
g e
2
g1
1
2
g2
g2
12
Δ
Γ2→1
Γ1→2
g1
Width
(HWHM)
Height
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Model versus Measurements
Meas.
Model
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87
Rb : F=2->F’
F=1->F’
The Role of Temperature
2 3 1
Vapor Temperature, Beer Law, and PTR
• Higher temperatures  more atoms and higher velocities.
• Assumption: a change in temperature does not effect g12.
• 1 and 2 are not absorbed by the medium (due to the
one-photon detuning).
• 3 obeys Beer-Lambert law:
namely, the probe (and only the probe) is absorbed by
atoms in the medium which do not participate in the threephoton process.
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21
87
Rb : F=2->F’
F=1->F’
The Role of Temperature
2 3 1
Vapor Temperature, Beer Law, and PTR
Beer-Lambert :
• At low intensities of the probe, the EIA effect is negligible.
• At higher temperatures the effect is shifted towards higher C1Ls.
• ‘Stronger’ resonances are expected at higher temperatures.
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The Role of Temperature
Model Results
Higher
resonances
Shift in
the effect
No EIA
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The Role of Temperature
Experimental Observations
Higher
resonances
Shift in
the effect
No EIA
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Back to the Experimental Setup
2 3 1
5 2 3 1 4
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2 3 1
25
Back to the Experimental Setup
No Filters Before Cell
m
Detector
F-P
filter
F-P
filter
vapor cell in
-metal
2 3 1
/4
ND
w
Locking
Scheme
PSBP
m
F-P
ECDL
w
PM
Spectrum
Analyzer
5 2 3 1 4
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Five Fields
87
Rb : F=2->F’
F=1->F’
e
1
2 3 1
g2
12 ~ f hfs
g1
87
Rb : F=2->F’
fhfs/2
2 3
1 
2
3
fhfs
F=1->F’
e
4
5 2 3 1 4
12
fhfs/2
fhfs/2
1
2
5
3
g2
fhfs
g1
45  2 12
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Experimental Results
Five Spectral Lines
1.075
I (norm)
EIT
1
C1L ; C2L
AntiSymmetric
Resonance
8.0%;100.0%
12.0%;148.8%
16.2%;200.0%
20.2%;251.2%
EIA
0.875
-75
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-50
24.4%;300.0%
-25
d [KHz]
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25
50
75
28
The Anti-Symmetric Resonance
A Novel Scheme for Atomic Clocks?
• The Local Oscillator should be stable during feedback.
LO
ATOM
RES.
• Employing symmetric resonances requires
peak detection which delays the feedback
• Anti-symmetric resonances provides an
almost instantaneous feedback, therefore
other, less stable oscillators can be used
– Thin Film Resonators
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Summary
• A new type of EIA resonance was introduced.
– Resonant population transfer in a three-level
L-system induced by three electromagnetic fields.
•
•
•
•
A large contrast (~50%) was observed.
A model describing the interaction was introduced.
The role of vapor temperature was discussed.
A first glance over the interaction of five fields
with the same medium.
– A new scheme for atomic clocks?
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Acknowledgement
• This work is partially supported by the Technion
Micro Satellite Program.
• Ramon fellowship of the Israeli ministry of science.
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Thank you