Shell Models for Alkali Metal Trimersphysics.usc.edu/Shells/Talks/Ernst_Part_II_ShellEffects... ·...
Transcript of Shell Models for Alkali Metal Trimersphysics.usc.edu/Shells/Talks/Ernst_Part_II_ShellEffects... ·...
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Institute of Experimental Physics
1Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Shell Models for Alkali Metal Trimers:Electronic Level Structure and Magnetic
Properties from Experimental and Theoretical Investigations
Lecture II■ introduction: helium droplets, doping with foreign
species, spectroscopy■ alkali atoms and molecules on helium droplets■ spectra, absorption and magnetic circular
dichroism■ identification of high spin trimers■ ab initio K3 and Rb3, K2Rb and KRb2 quartet states■ quartet state shell structure, harmonic oscillator
states■ the ultimate resolution: electron spin resonance
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Institute of Experimental Physics
2Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPHelium nanodroplets
cooling clusters evaporative(adiabatic expansion) grow cooling
■ Excellent cryostat, at T~0.4K■ Weak interactions■ Liquid (in fact superfluid)■ Confinement (r = 20-100 Å)■ “Natural selection” of weakly bound species
HeN
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3Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPSuperfluid helium droplets as nanocryostat
Spectroscopic linewidths?
Rotational (microwave) and vibrational (infrared)excitation of a dopantin a superfluid
No friction, only inertia
1 cm-1
300 cm-1
Electronic excitation (visible or UV)of a dopant
Electron repulsionby helium
Broadenedandblue-shifted
K 4s-4p
Details: C. Callegari and W. E. Ernst in: Handbook of High Resolution Spectroscopy, eds. F. Merkt and M. Quack, Wiley 2010
Grebenev, Toennies, Vilesov(Science 1998)
Trot=0.37 K
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4Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
KCl:O-2 luminescence spectrum at 4.2K.
From: Freiberg & Rebane in „Zero-Phonon Lines“ (eds. Sild & Haller (Springer))
Comparison of LIF spectra of dopants on/in helium nanodroplets (Na2 singlet vs. glyoxal):
Superfluid helium droplets as nanocryostatSpectroscopic linewidths?
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5Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPExperiment
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6Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Alkali n-mers on HeN: High-spin selectivity
E
+ =
+ =
E
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7Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPHomonuclear & heteronuclear alkali molecules
11500 12000 12500 13000 13500 14000 14500 15000 15500 16000 16500 17000 17500
K2 K2
Rb2
K3 K3
KRb
KRb
KRb
Rb3
Rb3
wavenumber
Rb3
KRb
K3Rb K Rb2
KRb
LIF spectra of K + Rb attached to He nanodroplets
K Rb
1 2 0 0 0 1 3 0 0 0 1 4 0 0 0 1 5 0 0 0 1 6 0 0 0 1 7 0 0 00
5 0 0
1 0 0 0
1 5 0 0
2 0 0 0
2 5 0 0
3 0 0 0
3 5 0 0
w a v e n u m b e r
LIF
sign
al /
arb.
u.
R b 3R b
R b 2 :1 3 g
R b 3
R b 3
R b 2 :2 3 g
Rb only
1 2 0 0 0 1 3 0 0 0 1 4 0 0 0 1 5 0 0 0 1 6 0 0 0 1 7 0 0 0 1 8 0 0 00
2 0 0 0
4 0 0 0
6 0 0 0
8 0 0 0
K 3:
LIF
sign
al
w a v e n u m b e r
K 3:
2 4E ' - 1 4A '2
K
K 2:
1 3 g
K 2 :
2 3 g
K 3 : K only
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8Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
12000 13000 14000 15000 16000 170000
1000
2000
3000
4000
5000
6000
7000
8000
wavenumber spektrenKRbcollected
23
33+3
KRb
KRb
K2Rbor
KRb2
K2Rbor
KRb2
Johann Nagl and Carlo Callegari
heteronuclear alkali molecules
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9Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
11500 12000 12500 13000 13500 14000 14500 15000 15500 16000 16500 17000 17500
K2 K2
Rb2
K3 K3
KRb
KRb
KRb
Rb3
Rb3
wavenumber
Rb3
KRb
K3Rb K Rb2
KRb
LIF spectra of K + Rb attached to He nanodroplets
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10Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPAlkali-HeN pseudo diatomic: atomic excitation ns-np
1) Treat He droplet as a giant closed-shell atom
2) Calculate (vdW) molecular potential by integrating vdW pair potentials over He density
3) Approximate spectrum with F-C Factors
23/2
21/2
21/221/2 5s
5p
HeNRb
HeNRb
HeNRb
Rb 5s on HeN surface,DFT calculation (help by F. Toigo) in:Brühl, Trasca, Ernst JCP 115, 10220 (2001)
● ● ● ● ●
●●●●●
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11Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
HeN
Key questionsDopants with spin in external B-field
inside
surface
Create spin precession:
Spin relaxation due tohelium environment?
For atoms?
For molecules?
Related topic: helium buffer gas cooling of oriented atoms or molecules
B
LASER
Carlo Callegari
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12Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
linear
+
Add magnetic field and exploit dichroism:
Rb 5s-5p
/4
B= 2.9 kG
field free
excitedstate(2P1/2)
with magnetic field
TS TS=0.37K
ground state(2S1/2)
- +linear
0.37 K
T
Spin temperature
Phys. Rev. Lett. 98, 075301-1-4 (2007)
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13Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPHighly excited states and ionization of atomsFor example: two step processes in HeN-Rb
~12817 cm-1
~12579 cm-1
Fixed
~25700 cm-1 52D manifold
52P3/2
52S1/2
52P1/2
2-step excitation
Scanned ~13175cm-1
12601cm-1
12606cm-1
12611cm-1 52S1/2 (2Σ1/2)
52P3/2 (2π3/2, 2Σ1/2)52P1/2 (2π1/2)
12607cm-1
21911cm-1
33691cm-1bare Rb
Moritz Theisen and Florian Lackner
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14Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Florian Lackner
Moritz Theisene-
Rb+
He
Rb+
He
Rb+
Hee-
Goal: High-lying Rydberg state
Rb+
Hee-
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15Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Cold chemistry in confinement
initiate reactions with laserexcited atoms, e.g. Cs 7p + H2
dope dropletwith H2 or HCl
H2
add alkali
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16Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
11500 12000 12500 13000 13500 14000 14500 15000 15500 16000 16500 17000 17500
K2 K2
Rb2
K3 K3
KRb
KRb
KRb
Rb3
Rb3
wavenumber
Rb3
KRb
K3Rb K Rb2
KRb
LIF spectra of K + Rb attached to He nanodroplets
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17Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Rb on He nanodroplets: Rb2 1 3g 1 3u+
13200 13400 13600 138000
100
200
300
400
500
600
700
800
LIF
/ arb
.u.
Wavenumber / cm-1
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18Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Comparison of Frank-Condon factors to LIF spectrum
4 6 8 10 12 14 16
12800
13000
13200
13400
0
500
1000
1500
2000
2500
13200 13300 13400 13500 13600 13700 138000,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
FC
F
Wavenumber / cm-1
LIF
/ ar
b.u.
1g
0g-
0g+
2g
ground state: only v” = 0 populatedexcited state v’=0–9 for each SO substate
+43 cm-1
ab-initio potential energy curves from O. Dulieu (Orsay)
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19Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPSpin-orbit coupling: alkali 3Π on helium
H = Hmol + Hd + HSOBasis: Eigenstates of Hmolcomponents of angular momenta along z: Hd interaction with helium(determined by integrating alkali-He pair potentials(Pascale) weighted by the helium density distribution)
HSO: Well known spin orbit Hamiltonian in basis (approximated R independent)In general: 12x12 matrix
y
z
Gerald Auböck
J. Phys. Chem. A111, 7404 (2007), in memory of Roger Miller
Tendencies:Cs2 at left end,others between 1 and 3 on horizontal scale
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20Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPOur model incl. Zeeman effect
(G. Auböck, J. Nagl, C. Callegari, and W.E. Ernst, J. Phys. Chem. A, 2007)
Rb2: LIF, MCD with Simulation K2: LIF, MCD with Simulation
Zeeman populationscorrespond to 0.37 K
temperature, i.e thesame as inside the
droplet.τ
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21Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Na2 Na3
First observation of trimers on droplets(collaboration with G. Scoles, Princeton)
PRL 74, 3592 (1995)
PRL 77,4532 (1996)
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22Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
relaxation
spin flip
h h h
h1850 cmE
trimerzedspinpolari
bind
(~ 700 cm-1three-body int.)
4.4 Å
Photoinduced Spin Dynamics
Science 273, 629 (1996)
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Institute of Experimental Physics
23Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
11500 12000 12500 13000 13500 14000 14500 15000 15500 16000 16500 17000 17500
K2 K2
Rb2
K3 K3
KRb
KRb
KRb
Rb3
Rb3
wavenumber
Rb3
KRb
K3Rb K Rb2
KRb
LIF spectra of K + Rb attached to He nanodroplets
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24Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPDepletion spectra with mass selective detection
(use quadrupole mass spectrometer)
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25Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPAlkali trimer quartet state excitations
(Phys. Rev. Lett. 100, 063001-1-4 (2008))
Calculations:
MOLPRO,Complete Active Space Self Consistent Field(CASSCF) & CASPT2
Andreas W. Hauser
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26Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Quartet trimers: Electronic structure
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27Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPHomonuclear Alkali Trimers K3 and Rb3
3
Geometry optimization at the RHF-CCSD(T) level of theory
strongly boundlow-spin2E´ ground state
K3 Rb3
b = 4.1 A b = 4.4 A= 77°
= 79°
K3 Rb3
b = 5.05 A b = 5.5 A= 60°
= 60°
More weakly bound(van der Waals) high-spin4A2´ ground state
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28Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
3
Geometry optimization at the RHF-CCSD(T) level of theory
Introduction of normal coordinates Scan over Qx coordinate
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29Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
A borrowed approximation: harmonic oscillator eigenfunctions
yes, but not as good as for doublet
Check CI vectors
MOs are delocalized and show typical s,p,d character
Make density plots of canonical MOs
We observe a close similarity with the energy ordering of a harmonic oscillator
No, it is more complicated
Compare the harmonic osci eigenenergieswith the observed bands of the ab inito calculation
This model offers a qualitative description of state energies
Fit MO energies with 5-parameter formulaincluding anharmonicity and cross terms
Is the state pattern comparable to atomic s,p,d energies?
How localized are the MOs?
Does a single-electron approximation hold?
A shell model for the quartet states
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30Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Time-independend Schrödinger equation in N dimensions:
Apply factorization method:
Choose isotropic harmonic oscillator potential:
Solutions:
dimension !
A shell model for the quartet states
N=2 (x,y)N=1 (z)
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31Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPA shell model for the quartet states
(x,y) (z)
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32Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
(0,0,0)
(0,±2,0)
(1,0,0)
(0,0,1)
(0,±1,1)E=h(2n+l)+hznz+anharm.
(0,±1,0)
A shell model for the quartet states
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33Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP ×104
(0,±1,0)+
(0,0,1)
(0,±2,0)(1,0,0)
B2
B2
A2 B1
A2
(0,0,0)
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Institute of Experimental Physics
34Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
A borrowed approximation: harmonic oscillator eigenfunctions
yes, but not as good as for doublet
Check CI vectors
MOs are delocalized and show typical s,p,d character
Make density plots of canonical MOs
We observe a close similarity with the energy ordering of a harmonic oscillator
No, it is more complicated
Compare the harmonic osci eigenenergieswith the observed bands of the ab inito calculation
This model offers a qualitative description of state energies
Fit MO energies with 5-parameter formulaincluding anharmonicity and cross terms
Is the state pattern comparable to atomic s,p,d energies?
Are the MOs comparable to AOs?
Does a single-electron approximation hold?
A shell model for the quartet states
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35Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Vibronic spectra
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36Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPFurther refinement: SO-coupling
CASPT2 + ECP-LS
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37Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPJahn-Teller effect theory
Qx Qy
Energy
Two-fold vibrational degeneracy
Two-fold electronic degeneracy
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38Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Adiabatic energy surfaces are obtained by diagonalizationof He +HSO:
Relativistic Jahn-Teller effect theory
Harmonic force term
SO splitting
Linear JT parameter
Quadratic JT parameter
potential surfaces !
= f(Qx,Qy)
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39Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Parameters in dimensionless units:
Jahn-Teller parameters
D
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40Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Vibronic spectra: the 14A2’24E’ transition
V = 0
V = 1V = 2
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41Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPAlkali trimer quartet state excitations
K3 and Rb3(quartet):Hauser, Auböck, Callegari, Ernst,J. Chem.Phys. 132,164310 (2010)
(doublet):Hauser, Callegari,Soldan, Ernst,J. Chem. Phys. 129,044307 (2008)andspectral predictions:Chem.Phys.(in print)
heteronuclear:in preparation
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42Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPLevel Structure and Magnetic Properties
from One-Electron Atoms to Clusterswith Delocalized Electronic Orbitals:
Shell Models for Alkali Trimersby A.W. Hauser, C. Callegari, W.E. Ernst
in: P. Piecuch et al. (eds.), Advances in the Theory of Atomic and Molecular Systems, Progress in Theoretical Chemistry and Physics 20, DOI
10.1007/978-90-481-2985-0 30, Springer Science+Business Media B.V. 2009
Doublet states:Electronic shell model,
See e.g. Cocchini, Upton,Andreoni, J. Chem. Phys. 1989
Quartet states:Our model relating the electronicstructure to the eigenstatesof the harmonic oscillator,cf. single particle states inquantum dots
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Institute of Experimental Physics
43Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPMagnetic Resonance
Superfluid helium nanodroplets
a cold container for single
particles (0.38 K)
study exotic, ‘unstable’ species
(e.g. K3, Rb3)
preparation probingmanipulation
A C
dBdz
dBdz
B
single atoms long spin lifetime create spin polarization
low optical density indirect detection
Rabi: spatial separation
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Institute of Experimental Physics
44Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
High resolution mw or rf spectroscopy?
How about polarization methods?
Narrow linewidth on mw and IR transitions
Large linewidth on optical transitions
Molecules in/on helium droplets:
LIF Detection of Microwave Absorption e.g. W. E. Ernst, S. Kindt, and T. Törring, Phys. Rev. Lett. 51, 979(1983)
W. E. Ernst, J. Kändler, C. Noda, J. S. McKillop and R. N. Zare,Hyperfine Structure of BaI, J. Chem. Phys. 85, 3735-3743 (1986).
RTPI Detection of Microwave AbsorptionNa3, W.E. Ernst and O. Golonzka (1999)
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Institute of Experimental Physics
45Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Pumping and probingThe optical 2S1/2 2P1/2 transitions can be used to manipulate and probe spin states
2P1/2
+1/2
-1/2
+3/2
+1/2
-1/2
+1/2-1/2-3/2
+-
mj2P3/2
2S1/2
Zeeman
K can be spin polarized by depletion
Rb can be spin polarized by optical pumping G. Auböck, J. Nagl,
C. Callegari,and W. E. ErnstPRL 98, 075301(2007)PRL 101, 035301(2008)
12600 12800 13000 132000
50
100
150
200
LIF
(103
cou
nts p
er se
cond
)
wavenumber (cm-1)
Rb K
D2
D1
12600 12800 13000 132000
50
100
150
200
LIF
(103
cou
nts p
er se
cond
)
wavenumber (cm-1)
Rb K
D2
D1 D2D1
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46Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
A C Bpump mw probe
Markus Koch
Optically Detected ESR
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47Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
0 100 200 300 400 500
-8-6-4-202468
Ener
gy /
h (G
Hz)
Magnetic field B0 (mT)
2S1/2F=3
F=2I=5/2
85Rb
linear,|S,I;F,mF ›
linear,|S,I;mS,mI ›
Breit-Rabi formula
ESR on helium droplets
g
aHFS
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48Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
0 100 200 300 400 500
-8-6-4-202468
Ener
gy /
h (G
Hz)
Magnetic field B0 (mT)
2S1/2F=3
F=2I=5/2
85Rb
0 100 200 300 400 50002468
1012141618
Tran
sitio
nene
rgy
/ h (G
Hz)
Magnetic field B0 (mT)
|∆mS| = 1, ∆mI = 0
trans
ition
ene
rgy
/ h (G
Hz)
9.4
GH
z
free atomdroplet free atom B0droplet
magnetic field shift (µT)
LIF
sign
al (1
03cp
s)
magnetic field (mT)200 300 400
ESR on helium droplets
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Institute of Experimental Physics
49Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
0 100 200 300 400 500
-8-6-4-202468
Ener
gy /
h (G
Hz)
Magnetic field B0 (mT)
2S1/2F=3
F=2I=5/2
0 100 200 300 400 50002468
1012141618
Tran
sitio
nene
rgy
/ h (G
Hz)
Magnetic field B0 (mT)
85Rb
9.4
GH
zfree atom droplet
|∆mS| = 1, ∆mI = 0
trans
ition
ene
rgy
/ h (G
Hz)
magnetic field (mT)200 300 400
magnetic field shift (µT)
LIF
sign
al (1
03cp
s)
ESR on helium droplets
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50Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
Modeling: Breit-Rabi formula
• droplet: variations δaHFS, δgS free parameters
• 39K: δaHFS/aHFS = 325 ± 40 ppm, δgS/gS = 0 ± 3 ppm
• 85Rb: δaHFS/aHFS = 412 ± 8 ppm, δgS/gS = 0 ± 3 ppm
• δaHFS/aHFS = δ|0|2/|0|2
varies with droplet size!dropletfree atom
magnetic field shift (µT)
LIF
sign
al (1
03cp
s)
magnetic field (mT)200 300 400
magnetic field shift (µT)
LIF
sign
al (1
03cp
s)
200 300 400
magnetic field shift (µT)
LIF
sign
al (1
03cp
s)M. Koch, J. Lanzersdorfer, C. Callegari, J.S. Muenter, and W. E. ErnstJ. Phys. Chem. A 113, 13347-13356(2009)
M. Koch, G. Auböck, C. Callegari and W. E. ErnstPhys. Rev. Lett. 103, 035302-1-4(2009)
ESR on helium droplets
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51Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPElectron spin density at alkali nucleus
Following Adrian [J. Chem. Phys. 32 (4), 972–981 (1960)], the relative change of hfs consists of two parts:
Relative change of electron spin density at alkali nucleus in ppm for HeN droplet
see M.Koch, C. Callegari, and W. E. Ernst, Mol. Phys. 108 (7), 1005 (2010), issue in honor of R. N. Zare
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52Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPRabi oscillations
decoherence time T2 > 50 µs
MW magnetic field BMW (µT)
ES
R a
mpl
itude
|c1|2
ES
R a
mpl
itude
cavity position, x=vt
MW magnetic field BMW (µT)
ES
R a
mpl
itude
dephasing time T2 ≥ 50 µs
kxa
x
aAB
sin1
… detuning
… Rabi frequency
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53Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPESR on droplets: conclusions & future• first demonstration of MR (ESR) on doped HeN • hyperfine resolved ESR spectrum of 39K, 85Rb
• shifts (~400 ppm), droplet-size dependent: Fermi contact term
• coherent population transfer: Rabi oscillations
Currently in progress:
Cr:S = 6/2I = 0
vd WaalsXe
129Xe: I = 1/2 131Xe: I = 3/2
rest: I = 0
K, Rb
Poster by Martin Ratschek and Markus Koch (yesterday)
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54Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EPThe HeDrop Team
Dr. Andreas W. Hauser
Dr. Carlo Callegarinow Elettra, Trieste Dr. Markus Koch
Johann Naglnow MIBLA Co
Gerald Auböcknow EPFL
Florian Lackner
Moritz Theisen
Martin Ratschek
Research funded by
Fonds zur Förderung der wissenschaftlichen Forschung
& EU Network „Cold Molecules“
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55Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
WE-Heraeus-Seminar No. 343
Helium Clusters– Finite-Size Superfluid and Nano-Size Cryostat
Physikzentrum Bad Honnef, GermanyMarch 30 to April 1, 2005
Scientific Organizers:Wolfgang E. Ernst and Carlo Callegari
WE-Heraeus-Seminar No. 482
Helium Nanodroplets– Confinement for Cold Molecules and Cold Chemistry
Physikzentrum Bad Honnef, GermanyMay 29 to June 1, 2011
Scientific OrganizersWolfgang E. Ernst and Markus Koch
Institute of Experimental PhysicsGraz University of Technology
Petersgasse 16A-8010 Graz, Austria, Europe
E-mail: [email protected]
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56Wolfgang E. Ernst Shell Models, Erice, July 26-30, 2010
EP
THE END