Population Transfer Resonance: A new Three-Photon Resonance for Small Scale Atomic Clocks Ido Ben-Aroya, Gadi Eisenstein EE Department, Technion, Haifa,

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 WorldThe Quartz Crystal Oscillators (1920stoday)

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.


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)

f0

Δf

•High contrast

•Narrow width

•Fixed f0•Stable during feedback

Principle of Operation


Types of Reliable Frequency Standards

Source: Symmetricom

CSAC:

•Small dimension

•Low power consumption

2’’


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 6000

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]

Am

p [a

rb.

units

]

raw dataLorentzian

f=186Hz

• D2 transition (780nm).

• Resonance width – 186Hz

• Contrast – 0.5% - 1%.


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:


Population Transfer Resonance

2g

1g

e

fhfs

fhfs/2

1 2 3

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

12

3



2g

1g

e

fhfs

fhfs/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.



2g

1g

e

fhfs

fhfs/2

1 2 3

• 3 optically pumps the medium from |g2> to |g1>.

• The two-photon process induced by 1 and 2 transfers the population back from |g1> to |g2> …



2g

1g

e

fhfs

fhfs/2

1 2 3

The absorption of 3 is enhanced due to the repopulation of |g2>

Electromagnetically Induced Absorption (EIA)-type resonance.


The Spectral Constellation87Rb : F=2->F’ F=1->F’

32 112 ~ hfsf

• 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).

2g

1g

e

fhfs

fhfs/2

1 2 3


The Setup

w

vapor cell in -metal

F-P

Spectrum Analyzer

/42 F-P filters

Detector ND Laser

PM and

filters

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

•Parameters: Modulation frequency (12), Total intensity (I), and Carrier to 1st side lobe intensity ratio (C1L).

32 112

32 1


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.


First Observation

• EIA-type resonance for the probe (3) and 1.• EIT-type resonance for 2.

12

3

32 112

3

2

1


The Model

2g

1g

e

fhfs

fhfs/2

1 2 3

Probing 2-ph process: The Population Coupling model

2g

1g

e

p

Γ1→2

2g

1g

eΔ

1 2

Γ2→1

B: Two highly one-photon detuned fields interacting with a three-level -system with a |g2>|g1> coupling channel.

A: One, “on resonance” field interacting with a three-level -system with a |g1>|g2> coupling channel.

Two processes coupled by the population of their states


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.

2g

1g

e

fhfs

fhfs/2

1 2 3

The Coupling of Coherence

2g

1g

e

p

Γ1→2212g

1g

eΔ

1 2

Γ2→1

2g eProcess BProcess A


• The population of |g2> is given by a ratio between two polynomial terms of symmetric (Lorentzian) and anti-symmetric (“dispersion-like”) functions of the modulation frequency ().

• The approximated anti-symmetric and symmetric functions:

2g

1g

e

fhfs

fhfs/2

1 2 3

2g

1g

e

p

Γ1→2212g

1g

eΔ

1 2

Γ2→1

2g e

Process BProcess A

Symmetric

Anti-

Symmetric Fundamental Width:

probe

atom

2-ph

The Model


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:

2g

1g

e

fhfs

fhfs/2

1 2 3

2g

1g

e

p

Γ1→2212g

1g

eΔ

1 2

Γ2→1

2g e

Process BProcess A


The Model2g

1g

e

fhfs

fhfs/2

1 2 3

Results 2g

1g

e

p

Γ1→2212g

1g

eΔ

1 2

Γ2→1

2g e

Process BProcess A

Width (HWHM)

Height


Model versus MeasurementsModel Meas.


The Role of Temperature

• Higher temperatures more atoms and higher velocities.

• Assumption: a change in temperature does not effect 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


The Role of Temperature

• 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.

Vapor Temperature, Beer Law, and PTR

Beer-Lambert :


The Role of TemperatureModel Results

No EIA

Shift in the effect

Higher resonanc

es


The Role of TemperatureExperimental Observations

No EIA

Higher resonanc

es

Shift in the effect


Back to the Experimental Setup

32 1

32 1

32 15 4


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

32 15 4

32 1

No Filters Before Cell


Five Fields87Rb : F=2->F’ F=1->F’

32 112 ~ hfsf

2g

1g

e

fhfs

fhfs/2

1 2 3

87Rb : F=2->F’ F=1->F’

32 1

1245

145 22

12

3

2g

1g

e

fhfs

fhfs/2

1 2 3fhfs/2

54


Experimental ResultsFive Spectral Lines

-75 -50 -25 25 50 750.875

1

1.075

[KHz]

I (n

orm

)

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


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


Summary

• A new type of EIA resonance was introduced.– Resonant population transfer in a three-level

-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?


Acknowledgement

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

• Ramon fellowship of the Israeli ministry of science.

Thank you

Documents

Population Transfer Resonance: A new Three-Photon Resonance for Small Scale Atomic Clocks Ido Ben-Aroya, Gadi Eisenstein EE Department, Technion, Haifa,