Quantum interference phenomenon Quantum interference phenomenon in the cold atomic cascade system $$ : National Science Council and National Space Program

Quantum interference phenomenon Quantum interference phenomenon in the cold atomic cascade systemin the cold atomic cascade system

$$ : National Science Council and National Space Program Office, Taiwan

Ray-Yuan Chang, Wei-Chia Fang, Ming-Da Tsai, and Chin-Chun TsaiNational Cheng Kung University, Tainan, 70148 Taiwan

Classical analogyClassical analogy

Young's interferenceYoung's interference

Fano interferenceFano interference

Quantum interferenceQuantum interference

Autler-Townes splittingAutler-Townes splitting

3

2

1

c

p

2

3

p p

c c

Quantum interference

Abs

orpt

ion

(arb

. uni

t)

EITT

rans

mis

sion

(ar

b. u

nit)

-0.17

-0.12

-0.07

-0.02

-20 -15 -10 -5 0 5 10 15 20

0.00

0.05

0.10

0.15

-20 -15 -10 -5 0 5 10 15 20

p

c

21/ 26s S

23/ 26 p P F=5

F=4

21/ 28s S

Probe laser852nm

Coupling laserCoupling laserTi :SapphireTi :Sapphire

794.4nm794.4nm

133133

CesiumCesiumF=4

Energy level diagram

0

100

200

300

400

500

600

700

-50 -40 -30 -20 -10 0 10 20 30 40 50

Calibration tool and markerCalibration tool and marker for for Rydberg state transitionRydberg state transition

Tra

nsm

issi

on (

arb.

uni

t)

Δc (MHz)

RTEITRTEIT

21/ 26s S

23/ 26 p P

MOT laser

Repump laser

F’=5432

F=4

3

Cs MOT

Experimental Setup

Repump Laser

Cold Cs Atom

Anti-Helmholtz Coil for MOT

Red filter

ND filter

Cs vapor cell PD1

MOTLaser

Ti:Sapphire laser

PD

BS

M

M

AOM

MBS

f

Chopper

MOT fluoEIT res signa cenceBoth and the are monl itored.

Im ρ12 : absorption

Fluorescence

Probe

Probe

Coupling

PDf

Fluorescence

Trap LossTrap Loss

21/ 26s S

23/ 26 p P F=5

F=4

Probe laser852nm

Suppression

21/ 26s S

23/ 26 p P F=5

F=4

Probe laser852nm

Suppression Recovery

21/ 26s S

23/ 26 p P F=5

F=4

21/ 28s S

Probe laser


F=4

MOT LASER

Repump LASER

AH Coil

Ti-Sa LASER

Probe LASER

Ti-Sa LASER

Step

Loading Interaction

suppress recover

Detection

Suppress Recoverfield

B

21/ 26s S

23/ 26 p P F=5

F=4

21/ 28s S

Probe laser


F=4

MOT LASER

Repump LASER

AH Coil

Ti-Sa LASER

Probe LASER

Ti-Sa LASER

Step

Loading Interaction

suppress recover

Detection

Chop ModeChop Mode70kHz

7 s

fieldB

Suppress Recover

-50 0 50 100 150 200

Coupling detuning (MHz)

Probe off

Probe on

RT EIT

Coupling 30 mWCoupling 30 mW

21/ 26s S

23/ 26 p P F=5

F=4

21/ 28s S

Probe laser


F=4

Power dependencePower dependence

-50 -25 0 25 50


0.15 mW

Coupling 10 mW

0.2 mW

0.4 mW

0.8 mW

3 mW

21/ 26s S

23/ 26 p P F=5

F=4

21/ 28s S

Probe laser


F=4

Probe 5μWProbe 5μW


~3.5MHz~3.5MHz


Laser linewidth 0.5 MHzLaser linewidth 0.5 MHz

Laser linewidth 0 MHzLaser linewidth 0 MHz

Conclusion

We've observed the signals by monitoring the

EITMOT fluorescence.

The suppression and recovery method provides a

new way to probe the highly Rydbergexcited states.

Such a quantum interference phenomenon demon sub - naturastrates the linewidth fl eature.

我我是是俊俊哥哥

Absorption EIT/CPT Enhanced

EIT featuresEIT features

-200 -100 0 100 200


-100 0 100


+70 MHz

+26 MHz

-23 MHz

Δp= -53 MHzCoupling 8.3 mW

15.6 mW

38.9 mW

Δp=0 150μW150μW Δp varies

Rb

FrBa

Xe

I am Here!!!I am Here!!!

Periodical TablePeriodical Table

NIST-F1 Frequency standard (9.2 GHz)

~ 6 × 10-16, June 2004).

ImportanceImportance

f

f

Scattering Force

AtomAtom

Vh

k

AtomAtom

kV

m

PhotonPhoton

'

'

Atom Atom

Atom Atom Atom

Atom

P nP P

dP P P nP

dPF

dt

AtomAtom

PhotonPhoton

Spontaneous emissionSpontaneous emissionin a random directionin a random direction

Ultracold Lab.

Doppler Cooling

Hansch and SchawlowOpt. Commun. 13, 68 (1975))

Ultracold Lab.

F v

AtomLaser

Laser Laser

v

c

Laser Laser

v

c

2F kc

z

k

k

zF

zF

zF

zF

V

V

Damp forceDamp force

Magneto-Optical Trap

Steven Chu and D. E. Pritchard Steven Chu and D. E. Pritchard Phys. Rev. Lett. Phys. Rev. Lett. 5959, 2631 (1987), 2631 (1987) F z

Ultracold Lab.

z

00|g> J=0|g> J=0

|e> J=1|e> J=1

-1-1

00

+1+1

+1+1

00

-1-1

mmjj

B=0B=0 B>0B>0B<0B<0

Chin-ChunChin-ChunTsaiTsai

Ultracold Atomic Physics Lab.Ultracold Atomic Physics Lab.

Ray-YuanRay-YuanChangChang

My PHD careerMy PHD career

1. Wavemeter1. WavemeterΔλ/λ～ 10-7

< 50 MHz

My PHD careerMy PHD career2. 2. NaNa22 OODROODR spectroscopy spectroscopy

Δ1g5

1g5

3 1g

4 1g

2 1g

3 1g

6,7,8nd n 1g

7 1g

New observationNew observation

Extend to the higher rovibrational levelsExtend to the higher rovibrational levels

Avoid crossingAvoid crossing

L-uncoupling and Λ doublingL-uncoupling and Λ doubling

Extend to the higher Extend to the higher rovibrational levelsrovibrational levels

3p+3p3s+4p

3s+4d

3s+4f

3s+5d

3s+4d

3s+5p

My PHD careerMy PHD career

3. Precision measurement 3. Precision measurement of the Rydberg statesof the Rydberg states

521621 521622 521623

500

1000

1500

2000

2500

3000

3500

4000

Inte

nsity

(ar

b. u

nit)

Frequency (GHz)

MOT fluorescence

Etalon marker

EIT 2I HFS

Dye Laser : 560nm~630nm

~ 10MHz~ 10MHz

3

21

3

2

1

pcc

p

32

1

pc

Λ - type V - type Cascade

Schematic of EITSchematic of EIT

2

3

233

EIT

p p

c c

p p

c c

p p

c c

Ωc >> ΩpΔc = 0

Δp～

3

2

1

c

p

Our systemOur system

2

3

Phys. Rev. A 59 , 4675 (1999)

p c

Significant siEIT gnals

Cascade

p p

c c

Dressed state approachDressed state approach

D D

Claude Cohen-Tannoudji

Autler-Townes splittingAutler-Townes splittingCPTCPTEITEIT

Pathway CancellationPathway Cancellation

Direct excitationDirect excitation1-19-107 22:04:57

Data set #24642Starting wavelength377281.2(GHz)Data interval 1MHzScan time per segment 1secondsScan distance 1GHzFREQUENCY(GHz) SENSOR 3 FREQUENCY(GHz) SENSOR 8 FREQUENCY(GHz) SENSOR 9

377281.2 73 -399 3779 -3.8E+08 377281.2 -399 163 -3.8E+08377281.2 67 -398 3780 -3.8E+08 377281.2 -398 163 -3.8E+08377281.2 66 -397 3780 -3.8E+08 377281.2 -397 156 -3.8E+08377281.3 67 -396 3777 -3.8E+08 377281.3 -396 158 -3.8E+08377281.3 67 -395 3779 -3.8E+08 377281.3 -395 159 -3.8E+08377281.3 66 -394 3779 -3.8E+08 377281.3 -394 161 -3.8E+08377281.3 67 -393 3779 -3.8E+08 377281.3 -393 160 -3.8E+08377281.3 67 -392 3779 -3.8E+08 377281.3 -392 161 -3.8E+08377281.3 67 -391 3778 -3.8E+08 377281.3 -391 163 -3.8E+08377281.3 65 -390 3778 -3.8E+08 377281.3 -390 160 -3.8E+08377281.3 65 -389 3779 -3.8E+08 377281.3 -389 161 -3.8E+08377281.3 66 -388 3780 -3.8E+08 377281.3 -388 157 -3.8E+08377281.3 66 -387 3779 -3.8E+08 377281.3 -387 162 -3.8E+08

-400 -200 0 200 400

EIT

△c MHz

Trap LossTrap LossLoadingPower broadening

Time sequenceTime sequence

MOT LASER

Repump LASER

AH Coil

Ti-Sa LASER

Ti-Sa LASER

Step

Loading Interaction

fieldB

Detection

Time sequenceTime sequence

21/ 26s S

23/ 26 p P

MO

T la

ser

Rep

um

p la

ser

F=5432

F=4

3

21/ 28s S


F=4

21/ 26s S

23/ 26 p P

MO

T la

ser

Rep

um

p la

ser

F’=5432

F=4

3

21/ 28s S


F’’=4Aulter-Townes splittingAulter-Townes splitting

-150 -100 -50 0 50 100 150


MOT fluorescence

RT EIT

21/ 26s S

23/ 26 p P

MO

T la

ser

Rep

um

p la

ser

F=5432

F=4

3

21/ 28s S

Probe laser


EIT process in MOTEIT process in MOT

133CesiumF=4

MOT LASER

Repump LASER

AH Coil

Ti-Sa LASER

Probe LASER

Ti-Sa LASER

Step

Loading Interaction Detection

Time sequenceTime sequencefield

B

21/ 26s S

23/ 26 p P F=5

F=4

21/ 28s S

Probe laser852nm


794.5nm

F=4

EIT in MOTEIT in MOT

-40 -20 0 20 40


MOT EIT

MOT fluorescence2

1/ 26s S

23/ 26 p P F=5

F=4

21/ 28s S

Probe laser


F=4

Room temperature EIT

Two extreme of probe intensity

10050

050

100

10

20

30

10050

050

100

10

20

30

Δc (MHz)

Tra

nsm

issi

on (

arb.

uni

t)

Ω p(M

Hz)

10050

050

100

10

20

30

10050

050

100

10

20

30

Δc (MHz)

Tra

nsm

issi

on (

arb.

uni

t)

Ω p(M

Hz)

EIT&Raman absorption

Autler-Townes splittingAutler-Townes splittingCPTCPTEITEIT

Doubly dressed statesDoubly dressed states

Doubly dressedDoubly dressed

Doubly dressedDoubly dressed

Splitting of EIT doubletSplitting of EIT doublet

Absorption EIT/CPT Enhanced

21/ 26s S

23/ 26 p P F=5

F=4

21/ 28s S

Probe laser852nm


794.4nm794.4nm

Energy level diagramEnergy level diagram

133133

CesiumCesium


F=4

p

Decay fluorescenceDecay fluorescence

455 456 457 458 459 460

Wavelength (nm)

Flu

ores

cen

ce

inte

nsi

ty

6s

8s

6p

7p

7s

21/ 26s S

23/ 26 p P

MO

T la

ser

Rep

um

p la

ser

F’=5432

F=4

3

21/ 28s S


F’’=4

Excitation

Density matrix approach

Equation of motionEquation of motion

ρ11 ρ13

ρ : density matrix ρ21 ρ22 ρ23

ρ31 ρ32 ρ33

ρ12

3

2

1 p p

c c

c

p

c pH : Interaction Hamiltonian = H + H

2

3

p

p

-iΔ tp

+iΔ tpp

Ω0 - e 0

2Ω

H = - e 0 02

0 0 0

h

h

c

c

-iΔ tcc

+iΔ tc

0 0 0

ΩH = 0 0 - e

2Ω

0 - e 02

h

h

Im ρ12 : absorption dρ 1 1

= H , ρ - γ , ρdt i 2

Density matrix approach

dρ 1 1= H , ρ - γ , ρ

dt i 2

3

2

1

c

p

2 32 22 3 33 12 13

2 2

2 2 321 2 22 23

2 2

3 2 331 32 3 33

2 2

wp wp wc

wp wc

wp wc wc

2

3

1Relaxation process - γ , ρ

2

ρ11 ρ13

ρ : density matrix ρ21 ρ22 ρ23

ρ31 ρ32 ρ33

ρ12


p p

c c

Schematic of EITSchematic of EIT

p piΔ t -iΔ tp p

d 1 1ρ11 = γ2ρ22 + γ3ρ33 - i Ω e ρ12 - Ω e ρ21

dt 2 2

p p piΔ t -iΔ t -iΔ tc p p

d 1 1 1 1ρ12 = - wp + γ2 ρ12 - i Ω e ρ13 + Ω e ρ11 - Ω e ρ22

dt 2 2 2 2

pc -iΔ t-iΔ tc p

d γ3 1 1ρ13 = - wc - wp - - i Ω e ρ12 - Ω e ρ23

dt 2 2 2

p pc iΔ t iΔ t-iΔ tc p p

d 1 1 1 1ρ21 = - wp + γ2 ρ21 - i - Ω e ρ31+ Ω e ρ22 - Ω e ρ11

dt 2 2 2 2

p pc c iΔ t -iΔ tiΔ t -iΔ tc c p p

d 1 1 1 1ρ22 = -γ2ρ22 - i Ω e ρ23 - Ω e ρ32 - Ω e ρ12 + Ω e ρ21

dt 2 2 2 2

pc ciΔ t-iΔ t -iΔ t

c c p

d γ2 + γ3 1 1 1ρ23 = - wc + ρ23 - i Ω e ρ22 - Ω e ρ33 - Ω e ρ13

dt 2 2 2 2

pciΔ tiΔ t

c p

d γ3 1 1ρ31 = -wc - wp - ρ13 - i - Ω e ρ21+ Ω e ρ32

dt 2 2 2

pc c -iΔ tiΔ t iΔ tc c p

d γ2 + γ3 1 1 1ρ32 = - wc + ρ23 - i - Ω e ρ22 + Ω e ρ33 + Ω e ρ31

dt 2 2 2 2

c ciΔ t -iΔ tc c

d 1 1ρ33 = -γ3ρ33 - i - Ω e ρ23 + Ω e ρ32

dt 2 2

Coupled differential equationCoupled differential equation

Steady state


3

2

1

c

p

Our systemOur system

2

3

Phys. Rev. A 59 , 4675 (1999)

p c

Significant siEIT gnals

Cascade

p p

c c

-4 -2 2 4

-0.075

-0.065

-0.06

-0.055

-0.05

-0.045

-4 -2 2 4

-0.075

-0.07

-0.065

-0.06

-0.055

-0.05

-4 -2 2 4

-0.075

-0.07

-0.065

-0.06

-0.055

-0.05

-4 -2 2 4

-0.075

-0.07

-0.065

-0.06

-0.055

-0.05

-4 -2 2 4

-0.075

-0.065

-0.06

-0.055

-0.05

-0.045

-5-2.5

0

2.5

5

-0.08

-0.07

-0.06

-0.05

-5-2.5

0

2.5

5

c

p

Im ρ12

c

c

p

p

2 1

3 0.5

0.1

1

0.2

0.1

p

c

wp

wc

Scan couplingTransmission

Background Free

6s

8s

6p

7p

852.1 nm

7s 794.4 nm

Decay fluorescence

455 456 457 458 459 460

Wavelength (nm)

7p to 6s

Red filter

Cs vapor cell PD1

MOTLaser

Ti:Sapphire laser

M

M

AOM

AOM

AOM

BS

Experimental SetupExperimental Setup

Chopper

fAm orplit theude modu EIT sil gati on nals.


MOT

-4 -2 2 4

-0.075

-0.065

-0.06

-0.055

-0.05

-0.045

-4 -2 2 4

-0.075

-0.07

-0.065

-0.06

-0.055

-0.05

-4 -2 2 4

-0.075

-0.07

-0.065

-0.06

-0.055

-0.05

-4 -2 2 4

-0.075

-0.07

-0.065

-0.06

-0.055

-0.05

-4 -2 2 4

-0.075

-0.065

-0.06

-0.055

-0.05

-0.045

-5-2.5

0

2.5

5

-0.08

-0.07

-0.06

-0.05

-5-2.5

0

2.5

5

c

p

Im ρ12

c

c

p

p

2 1

3 0.5

0.1

1

0.2

0.1

p

c

wp

wc

Calibration tool and markerCalibration tool and marker for for Rydberg state transitionRydberg state transition

SimulationTransmission

Documents

Quantum interference phenomenon Quantum interference phenomenon in the cold atomic cascade system $$ : National Science Council and National Space Program