Population Transfer Resonance:

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16 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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Population Transfer Resonance:
A new Three
-
Photon Resonance
for Small Scale Atomic Clocks

Ido Ben
-
Aroya
, Gadi Eisenstein

EE Department, Technion, Haifa, Israel.

Technion

FRISNO
-
11, Aussois, France, Mar. 2011

FRISNO
-
11

Ido B


Technion, Israel.

2

The Synchronous World

The Quartz Crystal Oscillators (1920s

瑯摡礩

NIST (NBS) Frequency Standard by
Bell labs,
1929
.



4 x 100 KHz crystal oscillators.


stability: 10
-
7


Source: NIST


Resonance frequency
shifted due to aging


No two crystals with
the same frequency.

FRISNO
-
11

Ido B


Technion, Israel.

3

Frequency/Time Standard


An oscillator with poor long
-
term stability
(
hours to
years
)

is locked on a
narrow filter

around a fixed
frequency



improved long
-
term stability.

Local Oscillator
(Quartz Crystal)

f
0

Δ
f


High contrast


Narrow width


Fixed f
0


Stable during
feedback

Principle of Operation

FRISNO
-
11

Ido B


Technion, Israel.

4

Types of Reliable Frequency Standards

Source: Symmetricom

CSAC:


Small dimension


Low power
consumption

2’’

FRISNO
-
11

Ido B


Technion, Israel.

5

CPT based CSAC


CPT


Two photon coherent process yielding narrow resonances
with low contrast








Clocks require complex locking schemes


Multi field FM
spectroscopy


Large contrast resonances eliminate many of the locking problems


-600
-400
-200
0
200
400
600
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CPT resonance matching around 3 417.352 499MHz (span 1.5KHz). Resonance width=186Hz
f (around 3 417.352 499MHz ; span 1.2KHz) [Hz]
Amp [arb. units]


raw data
Lorentzian

f=186Hz


D
2
transition (
780
nm).



Resonance width


186
Hz



Contrast


0.5
%
-

1
%.


FRISNO
-
11

Ido B


Technion, Israel.

6

Types of Atomic Resonances


Important characteristics:
width

and
height

(or contrast)



EIA
-
type:
Population Transfer Resonance

(PTR)



Inspired by Zibrov and Walsworth group “
N
-
resonance” demonstration.

Electromagnetically Induced
Transparency (EIT) type:

Electromagnetically Induced
Absorption (EIA) type:

FRISNO
-
11

Ido B


Technion, Israel.

7

Population Transfer Resonance

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3


Three
-
level
L
-
system
interacts with three
phase
-
locked fields in an
N
-
type configuration
scheme.

1

2

3

FRISNO
-
11

Ido B


Technion, Israel.

8

Population Transfer Resonance

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3


The probe

3
, is tuned
on resonance and
therefore is absorbed
by the medium.




1

and

2

are highly
one
-
photon detuned
and sweep near the
zero two
-
photon
Raman detuning.

FRISNO
-
11

Ido B


Technion, Israel.

9

Population Transfer Resonance

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3




3
optically pumps the
medium from |g
2
> to
|g
1
>.


The two
-
photon
process induced by

1

and

2

transfers the
population back from
|g
1
> to |g
2
>




FRISNO
-
11

Ido B


Technion, Israel.

10

Population Transfer Resonance

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3


The absorption of

3
is
enhanced due to the
repopulation of |g
2
>



Electromagnetically
Induced Absorption
(EIA)
-
type resonance.

FRISNO
-
11

Ido B


Technion, Israel.

11

The Spectral Constellation

87
Rb
:
F
=
2
-
>
F’ F
=
1
-
>
F’
3

2

1

12
~
hfs
f


The interacting frequency components originate from a
laser which is locked to the
87
Rb D
2

transition
(|F=2>

|F’=2>
)

and modulated by half the
87
Rb hyperfine splitting
frequency (f
hfs
/2=3.417 GHz).

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3

FRISNO
-
11

Ido B


Technion, Israel.

12

The Setup

w
vapor

cell

in


-
metal
F
-
P
Spectrum
Analyzer

/
4
2
F
-
P

filter
s
Detector
ND
Laser
PM
and
filters

3 main blocks: Source, Medium, and Detection formation.


Parameters: Modulation frequency (

12
), Total intensity
(I), and Carrier to 1
st

side lobe intensity ratio (C1L).

3

2

1

12

3

2

1

FRISNO
-
11

Ido B


Technion, Israel.

13

First Observation


The probe (

3
) intensity (normalized) is measured versus PM
frequency sweeping near 3 417 345 KHz for various C1L ratios.
I=300

W.

Approx.
50
%
contrast.

FRISNO
-
11

Ido B


Technion, Israel.

14

First Observation


EIA
-
type resonance for the probe (

3
) and

1
.


EIT
-
type resonance for

2
.

1

2

3

3

2

1

12

3

2

1

FRISNO
-
11

Ido B


Technion, Israel.

15

The Model

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3

Probing
2
-
ph process: The Population Coupling model

2
g
1
g
e
p

Γ
1

2
2
g
1
g
e
Δ
1

2

Γ
2

1
B
: Two highly one
-
photon detuned
fields interacting
with a three
-
level
L
-
system with a
|g
2
>

|g
1
> coupling
channel.

A
: One, “on
resonance” field
interacting with a
three
-
level
L
-
system with a
|g
1
>

|g
2
>
coupling channel.

Two processes
coupled by the
population of
their states

FRISNO
-
11

Ido B


Technion, Israel.

16

The Model (phase II)


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.

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3

The Coupling of Coherence

2
g
1
g
e
p

Γ
1

2
2
1

2
g
1
g
e
Δ
1

2

Γ
2

1
2
g e

Process B

Process A

FRISNO
-
11

Ido B


Technion, Israel.

17


The population of |g
2
> is given by a ratio between two
polynomial terms of
symmetric

(Lorentzian) and
anti
-
symmetric

(“dispersion
-
like”) functions of the modulation
frequency (
d



The approximated
anti
-
symmetric

and
symmetric

functions:

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3

2
g
1
g
e
p

Γ
1

2
2
1

2
g
1
g
e
Δ
1

2

Γ
2

1
2
g e

Process B

Process A

Fundamental Width:

The Model

FRISNO
-
11

Ido B


Technion, Israel.

18

The Model


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:

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3

2
g
1
g
e
p

Γ
1

2
2
1

2
g
1
g
e
Δ
1

2

Γ
2

1
2
g e

Process B

Process A

FRISNO
-
11

Ido B


Technion, Israel.

19

The Model

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3

Results

2
g
1
g
e
p

Γ
1

2
2
1

2
g
1
g
e
Δ
1

2

Γ
2

1
2
g e

Process B

Process A

Width
(HWHM)

Height

FRISNO
-
11

Ido B


Technion, Israel.

20

Model
versus

Measurements

Model

Meas.

FRISNO
-
11

Ido B


Technion, Israel.

21

The Role of Temperature


Higher temperatures


more atoms and higher velocities.



Assumption: a change in temperature does not effect
g
12
.




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 three
-
photon process.


Vapor Temperature, Beer Law, and PTR

87
Rb
:
F
=
2
-
>
F’ F
=
1
-
>
F’
3

2

1

FRISNO
-
11

Ido B


Technion, Israel.

22

The Role of Temperature


At low intensities of the probe, the EIA effect is negligible.


At higher temperatures the effect is shifted towards higher C
1
Ls.


‘Stronger’ resonances are expected at higher temperatures.

Vapor Temperature, Beer Law, and PTR

Beer
-
Lambert :

87
Rb
:
F
=
2
-
>
F’ F
=
1
-
>
F’
3

2

1

FRISNO
-
11

Ido B


Technion, Israel.

23

The Role of Temperature

Model Results

No EIA

Shift in
the effect

Higher
resonances

FRISNO
-
11

Ido B


Technion, Israel.

24

The Role of Temperature

Experimental Observations

No EIA

Higher
resonances

Shift in
the effect

FRISNO
-
11

Ido B


Technion, Israel.

25

Back to the Experimental Setup

3

2

1

3

2

1

3

2

1

5

4

FRISNO
-
11

Ido B


Technion, Israel.

26

PM
w
vapor

cell

in


-
metal
F
-
P

filter
F
-
P
Spectrum
Analyzer
ND

/
4
m
F
-
P

filter
Detector
ECDL

PSBP
w
Locking
Scheme
m
Back to the Experimental Setup

3

2

1

5

4

3

2

1

No Filters Before Cell

FRISNO
-
11

Ido B


Technion, Israel.

27

Five Fields

87
Rb
:
F
=
2
-
>
F’ F
=
1
-
>
F’
3

2

1

12
~
hfs
f

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3

87
Rb
:
F
=
2
-
>
F’ F
=
1
-
>
F’
3

2

1

12

4

5

1
45
2
2



1

2

3

2
g
1
g
e
f
hfs
f
hfs
/
2
1

2

3

f
hfs
/
2
5

4

FRISNO
-
11

Ido B


Technion, Israel.

28

Experimental Results

Five Spectral Lines

-75
-50
-25
25
50
75
0.875
1
1.075
d
[KHz]
I (norm)


8.0%;100.0%
12.0%;148.8%
16.2%;200.0%
20.2%;251.2%
24.4%;300.0%
C1L ; C2L
EIT

EIA

Anti
-
Symmetric
Resonance

FRISNO
-
11

Ido B


Technion, Israel.

29

The Anti
-
Symmetric Resonance


The Local Oscillator should be stable during feedback.

A Novel Scheme for Atomic Clocks?

ATOM
RES.

LO


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

FRISNO
-
11

Ido B


Technion, Israel.

30

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?

FRISNO
-
11

Ido B


Technion, Israel.

31

Acknowledgement


This work is partially supported by the Technion
Micro Satellite Program.


Ramon fellowship of the Israeli ministry of science.

Thank you