Page 1
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
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Classical analogyClassical analogy
Young's interferenceYoung's interference
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Fano interferenceFano interference
Quantum interferenceQuantum interference
Autler-Townes splittingAutler-Townes splitting
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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
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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
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21/ 26s S
23/ 26 p P
MOT laser
Repump laser
F’=5432
F=4
3
Cs MOT
Page 7
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
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PDf
Fluorescence
Trap LossTrap Loss
21/ 26s S
23/ 26 p P F=5
F=4
Probe laser852nm
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Suppression
21/ 26s S
23/ 26 p P F=5
F=4
Probe laser852nm
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Suppression Recovery
21/ 26s S
23/ 26 p P F=5
F=4
21/ 28s S
Probe laser
Coupling laserCoupling laserTi :SapphireTi :Sapphire
F=4
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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
Coupling laserCoupling laserTi :SapphireTi :Sapphire
F=4
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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
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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
Coupling laserCoupling laserTi :SapphireTi :Sapphire
F=4
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Power dependencePower dependence
-50 -25 0 25 50
Coupling detuning (MHz)
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
Coupling laserCoupling laserTi :SapphireTi :Sapphire
F=4
Probe 5μWProbe 5μW
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Power dependencePower dependence
~3.5MHz~3.5MHz
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Power dependencePower dependence
Laser linewidth 0.5 MHzLaser linewidth 0.5 MHz
Laser linewidth 0 MHzLaser linewidth 0 MHz
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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.
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Absorption EIT/CPT Enhanced
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EIT featuresEIT features
-200 -100 0 100 200
Coupling detuning (MHz)
-100 0 100
Coupling detuning (MHz)
+70 MHz
+26 MHz
-23 MHz
Δp= -53 MHzCoupling 8.3 mW
15.6 mW
38.9 mW
Δp=0 150μW150μW Δp varies
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Rb
FrBa
Xe
I am Here!!!I am Here!!!
Periodical TablePeriodical Table
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NIST-F1 Frequency standard (9.2 GHz)
~ 6 × 10-16, June 2004).
ImportanceImportance
f
f
Page 24
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.
Page 25
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
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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
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Chin-ChunChin-ChunTsaiTsai
Ultracold Atomic Physics Lab.Ultracold Atomic Physics Lab.
Ray-YuanRay-YuanChangChang
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My PHD careerMy PHD career
1. Wavemeter1. WavemeterΔλ/λ~ 10-7
< 50 MHz
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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
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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
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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~
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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
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Dressed state approachDressed state approach
D D
Claude Cohen-Tannoudji
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Autler-Townes splittingAutler-Townes splittingCPTCPTEITEIT
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Pathway CancellationPathway Cancellation
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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
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Time sequenceTime sequence
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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
Coupling laserCoupling laserTi :SapphireTi :Sapphire
F=4
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21/ 26s S
23/ 26 p P
MO
T la
ser
Rep
um
p la
ser
F’=5432
F=4
3
21/ 28s S
Coupling laserCoupling laserTi :SapphireTi :Sapphire
F’’=4Aulter-Townes splittingAulter-Townes splitting
-150 -100 -50 0 50 100 150
Coupling detuning (MHz)
MOT fluorescence
RT EIT
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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
Coupling laserCoupling laserTi :SapphireTi :Sapphire
EIT process in MOTEIT process in MOT
133CesiumF=4
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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
Coupling laserCoupling laserTi :SapphireTi :Sapphire
794.5nm
F=4
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EIT in MOTEIT in MOT
-40 -20 0 20 40
Coupling detuning (MHz)
MOT EIT
MOT fluorescence2
1/ 26s S
23/ 26 p P F=5
F=4
21/ 28s S
Probe laser
Coupling laserCoupling laserTi :SapphireTi :Sapphire
F=4
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Room temperature EIT
Two extreme of probe intensity
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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
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Autler-Townes splittingAutler-Townes splittingCPTCPTEITEIT
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Doubly dressed statesDoubly dressed states
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Doubly dressedDoubly dressed
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Doubly dressedDoubly dressed
Splitting of EIT doubletSplitting of EIT doublet
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Absorption EIT/CPT Enhanced
Page 50
21/ 26s S
23/ 26 p P F=5
F=4
21/ 28s S
Probe laser852nm
Coupling laserCoupling laserTi :SapphireTi :Sapphire
794.4nm794.4nm
Energy level diagramEnergy level diagram
133133
CesiumCesium
Im ρ12 : absorption
F=4
p
Page 51
Decay fluorescenceDecay fluorescence
455 456 457 458 459 460
Wavelength (nm)
Flu
ores
cen
ce
inte
nsi
ty
6s
8s
6p
7p
7s
Page 52
21/ 26s S
23/ 26 p P
MO
T la
ser
Rep
um
p la
ser
F’=5432
F=4
3
21/ 28s S
Coupling laserCoupling laserTi :SapphireTi :Sapphire
F’’=4
Excitation
Page 53
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
Page 54
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
Im ρ12 : absorption
p p
c c
Schematic of EITSchematic of EIT
Page 55
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
Im ρ12 : absorption
Page 56
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
Page 57
-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
Page 58
6s
8s
6p
7p
852.1 nm
7s 794.4 nm
Decay fluorescence
455 456 457 458 459 460
Wavelength (nm)
7p to 6s
Page 59
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.
Im ρ12 : absorption
MOT
Page 60
-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