Two-photon Precision
Spectroscopy of H2+
Jean-Philippe KarrAlbane DouilletVu-Quang Tran, PhDLaurent Hilico
Rachidi Osseni, post docJofre Pedregosa, post docFranck Bielsa, PhDTristan Valenzuela, post doc
Vladimir Korobov
outline
• Motivations
• Experimental status
• Theoretical progress
mp/me measurement Why ?
• Fundamental constant determination
• e- g-2 measurement, G. Gabrielse 2008
mp/me codata 1836.152 672 45 (75) 4.1 10-10
91010122 1024.1101.410.2106.62 b
b
Re
p
p
R
mh
mm
mm
cR
Fine structure constant = 1/137,03…
• h/MRb measurement, F. Biraben 2010
h/mRb : 7. 10-10 → 4.2 10-10
mx/my < 10-10 → 3.5 10-10
-1
• Fundamental constant time-variations
• QED test on simple molecules
yearmmmm
ep
ep /10/
)/( 16
HD+, H2+ Ultra narrow lines
Low polarisabilityLow linear Zeeman effect
mp/me measurement Why ?
Astrophysics and spectroscopy H2, HD, NH3, CO, HCO+, HCN …
red shifts analysis t ~ 1010 years
SF6spectroscopy year/106.58.3 14
Laboratory physics
Proposals on CaH+, MgH+, SrH+, …, GeBr+
at 10-16
mP and me in atomic units are determined separatelythrough RF measurements in Penning traps.
Larmor to cyclotron frequency ratio Electron mass
eC
L
mCmg )(
51
2
512
Accuracy
Proton mass : cyclotron frequencies, using 12C4+.
R.S. Van Dyck, Jr. et al., in Trapped Charged Particles and Fundamental PhysicsAIP Conf. Proc. 457, pp. 101-110 (1999).
mp = 1.007 276 466 812 (90)
me = 0.000 548 579 909 46 (22)
4.1 10-10
4.0 10-10
8.9 10-11
Mp/me = 1836.152 672 45 (75)
Codata 2011
mp/me measurement How ?
C, O, Si
9.2 µm
248 nm
• Doppler-free Two-photon spectroscopy
• 2+1’ REMPD
• Trapped ions
• High precision calculations
Method
Internuclear distance (atomic unit)
Ener
gy (a
tom
ic u
nits
)mp/me Direct optical determination by
H2+ spectroscopy
p+
p+
e-
R e
p
mm
/1
2
e
p
e
p
mmmm
32.6 THz ( 9.1 µm ) (1091 cm-1) ~1600 Hz
...1010 1510
expected
What do we know on H2+ ?
Carrington group, Southampton
Lundeen group, H2 Rydberg states
Jefferts group,Hyperfineor Zeeman
spectroscopy
v
L
from R.E. Moss, Molecular Physics, 80, 1541 1993.
Project challenges state selected H2
+ ion production
H2+ trapping
REMPD lasers High precision calculations
exp mp/me
Two-photon transition probabilities
v=0 → v=1 transitions
2P'v,v
f
2430
'v,v Q4I)1(ca4
2
r
2'v,v
P 'vzEH
1zvQ
How to choose v→v’ ?
9.1 µm
Two-photon transition probabilitiesHow to choose L→L’ ?
L=0, v=0 → L=0, v=1
=9.128µm
L=3, v=0 → L=3, v=1:
=9.205µm
L=2, v=0 → L=2, v=1
=9.166µm
Close to a CO2 laser emission lineQuantum Cascade Laser available
Total nuclear spin I=(-1)L
2 mm
Quantum cascade laser(QCL)
248 nmKrF excimer Pulsed Laser
Hyperbolic Paul trap
Optical cavity
Experimental setup
IR laser source
HITRAN
MH
z
v, L
HCOOH : formic or methanoic acid
IR source
2 mm
HCOOH stabilized
CO2 laser
Quantum cascade Laser
RBW : 10 kHzVBW : 1 kHz
Band width ~ 6 MHz
QCL / CO2 beat note
< 200 Hz
O.I.
-10 -5 0 5 10-95
-90
-85
-80
-75
-70
-65
-60
Am
plitu
de [d
B]
fréquence - 550 [MHz] @ 9R42
QCL / CO2 beat note
Free QCL
5 MHz
IR source
Results
• optical power 54 mW• linewidth ~ 3kHz• high finesse cavity (~1000)• Faraday optical isolator at 9.2 µm
F. Bielsa & al., Optics Letters 32, 1641-1643 (2007)
L. Hilico, Rev. Sc. Instr. 82, 096106 (2011)
2ph~0.3 s-1 polarization
2ph~0.07 s-1 + polarization
• HCOOH stabilized CO2 laser
Absolute frequency measurement
F. Bielsa & al. J. Mol. Spectrosc. 247, 41-46 (2008)LPL, Villetaneuse, France
32 708 391 980.5 (1.0) kHz
U (t)
= 2 x 14 MHzDC -10 / +10 VAC 150 V
r0 = 4.2 mmz0 = 3 mm
The ion trap
T=300K
Vibrational distribution Rotational distributionv=0 : 12 %v=1 : 19 %
L=2 : 12 %
Hyperfine structure J=3/2 40%J=5/2 60%
Result : 0.07 x 0.12 x 0.6 = 0.5 %
Very small !!
G. Werth & Al. Z phys D 28, (1993).
H2+ creation: electron impact
)(
)(
2
2
UVnon
UVnSignal
H
H
1- ion creation (~ 500) 1,0 s2- 1 to 30 UV pulses (20 mJ) 0,3 s3- extraction, time of flight and counting
UV
1 2 3
Laser pulse number n
0.32 mJ
1.10 mJ3.25 mJ11.2 mJ34.0 mJ
114 mJ
sign
alPhotodissociation at 248 nm
1 adjustable parameterion cloud size
experiments 0.85 mmnum. simulations 0.83 mm
30 pulses at 34 mJ, pv=0 - pv=1 ~ 33% 2.4 %30 pulses at 114 mJ, pv=0 - pv=1 ~ 86 % 6.2 % drawback : ion losses
L=2, J=5/2
Results
Photodissociation at 248 nm
11 3 svphotodiss• Photodissociation yield
• v=0 v=1 population difference
J.-Ph. Karr & al., Applied Phys. B (2011)
Can we perform H2+ REMPD
spectroscopy ?
11 3 svphotodiss
Ion number fluctuations
12 3.0 sph
13.0 spiège
Two-photon transitionsPhotodissociationTrap losses
N
-40 -30 -20 -10 0 10 20 300,0
0,2
0,4
0,6
0,8
1,0
1,2
sign
al d
e R
EM
PD
fréquence (kHz)1 10 100
0,01
0,1
écar
t typ
e d'
Alla
n
Nombre de points
Present experimentsignal to noise ratio: 0.27
Improvements • H2+ v=0,L=2 population
• 2phSNR ~ 30
Experimental developments• State selected H2
+ ion creation increase v=0 v=1 population difference
Anderson, & Al, Chem. Phys. Lett. 105, 22 (1984)
H2 : v=0, L=0, 1, 2 à 300 K
H2 X1g+, v=0, L=2
H2 Cu-, v=0, L=2
H2+ X g
+, v=0, L + e-
+ 3 h
+ h
3+1 REMPImJ
303 nm10 ns
L
V. Mac Koy
O’Halloran, J. Chem. Phys. 87, 3288 (1987)
0 0.0052 14 0.01P
hoto
-ele
ctro
n y
ield
H2+ branching ratios
v0 11 0.1
v=0 – v=1L=2, J=5/2pop. diff.
0.8 x 1 x 0.6 = 0.48
Experimental developments
• A linear trap for tighter focussing
waist ÷3 2ph x 81
• H2+ sympathetic cooling by laser cooled Be+ ions
T = 300 KSecond order Doppler effect 7 kHz
T = 20 mK negligible
2
2
2cv
