Hydrogen 1s-2s experiment
13
Hydrogen 1s - 2s experiment Possible goals of improving laser system • Improving resolution by decreasing the linewidth. For this purpose we need to improve reference cavity. • Possibility of new experiments – 1s-2s spectroscopy of Tritium in Karlsruhe. Carrier collapse problem of ECDL laser.
Transcript of Hydrogen 1s-2s experiment
Hydrogen 1s-2s experiment
Possible goals of improving laser system
• Improving resolution by decreasing the
linewidth. For this purpose we need to
improve reference cavity.
• Possibility of new experiments – 1s-2s
spectroscopy of Tritium in Karlsruhe.
Carrier collapse problem of ECDL laser.
Vertical cavity
Horizontal cavity Vertical cavity
The idea of vertical cavity by Mark Notcutt:
M.Notcutt et al., Opt. Lett. 30, 1815 (2005)
( )g g t
Spectrum of ECDL locked to the cavity
12 13 14 15 16 17 18
-80
-70
-60
-50
-40
-30
-20
-10
Sp
ec
tra
l p
ow
er
de
ns
ity
, d
B
Frequency, MHz
Power in central peak 93%
N.Beverini, M. Prevedelli, F. Sorrentino, B. Nushkov, A. Ruffini
Quantum electronics 34, 559-564 (2004)
PDH Lock
Phase inside the
cavity φ0
Phase of laser φ0+φ
If laser frequency is in resonance with cavity mode then Error Signal
errorU
Beam from ECDL
RF Error signal for
feedback
errorU f
Carrier collapse - theory
• Consider the process
with phase jitter :
If random phase is distributed normally:
Then spectrum of the process contains δ-function
(carrier). Fraction of power in carrier:
Consequently after frequency doubling:
In 8-photon process
0 cos( ( ))E E t t
( )t ( ) 0i t
te
( )t2
2( ) exp
2 rms
p
2exp rms
2 2 4exp (2 ) exp 4( )rms rms
64
eff IR
Carrier collapse in pictures
14 16 26 28 30 32 34 36
-80
-70
-60
-50
-40
-30
-20
Feedback depth -11 dB P
ow
er
sp
ectr
al d
en
sity, d
B
Frequency, MHz
93% 75%
14 16 26 28 30 32 34 36
-80
-70
-60
-50
-40
-30
-20
Feedback depth -10 dB P
ow
er
sp
ectr
al d
en
sity, d
B
Frequency, MHz
92% 78%
14 16 26 28 30 32 34 36
-80
-70
-60
-50
-40
-30
-20
Feedback depth -9 dB P
ow
er
sp
ectr
al d
en
sity, d
B
Frequency, MHz
91% 78%
14 16 26 28 30 32 34 36
-80
-70
-60
-50
-40
-30
-20
Feedback depth -8 dB P
ow
er
sp
ectr
al d
en
sity, d
B
Frequency, MHz
95% 80%
14 16 26 28 30 32 34 36
-80
-70
-60
-50
-40
-30
-20
Feedback depth -7 dB P
ow
er
sp
ectr
al d
en
sity, d
B
Frequency, MHz
95% 76%
14 16 26 28 30 32 34 36
-80
-70
-60
-50
-40
-30
-20
Feedback depth -6 dB P
ow
er
sp
ectr
al d
en
sity, d
B
Frequency, MHz
95% 75%
14 16 26 28 30 32 34 36
-80
-70
-60
-50
-40
-30
-20
Feedback depth -5 dB P
ow
er
sp
ectr
al d
en
sity, d
B
Frequency, MHz
95% 74%
14 16 26 28 30 32 34 36
-80
-70
-60
-50
-40
-30
-20
Feedback depth -4 dB P
ow
er
sp
ectr
al d
en
sity, d
B
Frequency, MHz
93% 70%
14 16 26 28 30 32 34 36
-80
-70
-60
-50
-40
-30
-20
85% 69%
Feedback depth -3 dB P
ow
er
sp
ectr
al d
en
sity, d
B
Frequency, MHz
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-80
-70
-60
-50
-40
-30
-20
52%81%
Feedback depth -2 dB P
ow
er
sp
ectr
al d
en
sity, d
B
Frequency, MHz
14 16 26 28 30 32 34 36
-80
-70
-60
-50
-40
-30
-20
72% 28%
Feedback depth -1 dB Y
Po
we
r sp
ectr
al d
en
sity, d
B
Frequency, MHz
14 16 26 28 30 32 34
-80
-70
-60
-50
-40
-30
-20
Full collapse
243 nm beatnote
Pow
er
spe
ctr
al d
en
sity, d
B
Frequency, MHz
486 nm beatnote
Feedback depth 0 dB
44%
Feedback depth
-12 -10 -8 -6 -4 -2 0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0P
ow
er
in c
arr
ier
Feedback depth, dB
Blue light
UV light
Feedback influence on fraction of power in carrier
Check of carrier collapse formula
-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
Lo
g(
24
3)
, U
V lig
ht
be
atn
ote
Log(486
), blue light beatnote
Check of 4 theory.
Graph contain all points gathered
9.02.2006 and 13.02.2006
Fit y=Bx
B =3.89 +/- 0.18
Central peak of small horizontal cavity
15.000 15.005 15.010
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
Po
we
r s
pe
ctr
al d
en
sit
y, V
2/H
z
Frequency, MHz
Beat signal
Gauss fit
Central peak of beatnote at 486 nm.
Small horizontal cavity - Huge horizontal cavity.
Width 470 Hz
30.005 30.010 30.015 30.020 30.025
0.00E+000
2.00E-009
4.00E-009
6.00E-009
8.00E-009
1.00E-008
1.20E-008
1.40E-008
1.60E-008
Beat signal
Gauss fit
Central peak of beatnote at 243 nm.
Small horizontal cavity - Huge horizontal cavity.
Po
we
r s
pe
ctr
al d
en
sit
y, V
2/H
z
Frequency, MHz
Width 985 Hz
Central peak with vertical cavity
0 100 200 300 400
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
Am
plitu
de
sp
ec
tra
l d
en
sit
y, V
/Hz
1/2
FFT Frequency, Hz
18 FFT Spectra of beatnote at 486 nm.
-600 -400 -200 0 200 400 600
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
Am
plitu
de
sp
ec
tra
l d
en
sit
y, V
/Hz
1/2
Frequency detuning, Hz
FFT Averaging of 18 Onosokki Spectra.
Measurement A (Dye laser pump box open)
-800 -600 -400 -200 0 200 400 600 800
0.000
0.005
0.010
0.015
0.020
0.025
0.030
Am
plitu
de
sp
ec
tra
l d
en
sit
y, V
/Hz
1/2
Frequency detuning, Hz
Lorentz fit of 18 averaged spectra of beatnote at 486 nm
Width 14 Hz
-1500 -1000 -500 0 500 1000
0.000
0.002
0.004
0.006
0.008
0.010
0.012
Am
plitu
de
sp
ec
tra
l d
en
sit
y, V
/Hz
1/2
Frequency detuning, Hz
Width 71 Hz
Lorentz fit of 16 averaged spectra of beatnote at 243 nm.
Why 2? Why 4?How to estimate linewidth
0( ) cos ( )E t E t t
( )t ( )t
t
The moment :
( ) 1
1
The linewidth could be
estimated as:
Why 2? Why 4?Frequency noise model
( )p
t
0 cosE E t dt
Two important parameters
modulation depth
and correlation time
0
corrT
0
corrT
Why 2? Why 4?
Linear phase drift and phase diffusion
......t
( )t
corrTt
N t
1 rad
/ 2
/ 4
Summary: Two principal cases:
Deep frequency noise. Gaussian profile. After frequency doubling
linewidth increases twice.
Fast frequency noise. Lorentz profile. After frequency doubling
linewidth increases by the factor 4.
1corrT
1corrT
