1. Direct two-photon excitation of the isomeric transition
Institute of Physics
NAS of Ukraine
Direct two-photon excitation
of the isomeric transition
in Thorium-229 nucleus
Leonid Yatsenko
Institute of Physics
National Academy of Sciences of Ukraine
Kiev, Ukraine
EMMI Workshop
The 229mTh Nuclear Isomer Clock
GSI, Darmstadt, Germany
September 25-27, 2012

2. V.I. Romanenko, Ye.G. Udovitskaya
Coauthors
V.I. Romanenko, Ye.G. Udovitskaya
Institute of Physics of NASU
Kiev, UKRAINE
A.V. Romanenko
Kyiv National Taras Shevchenko University
A.N. Litvinov1, G.A. Kazakov1,2
St. Petersburg State Polytechnical University,
Russia
2. Institute for Atomic and Subatomic Physics TU Wien,
Austria

3. Outlook Why two-photon excitation ?
Spectroscopic data of the Thorium-229 transition
General description of two-photon laser-nucleus interaction
Effective two-level Hamiltonian
Excitation efficiency
conclusions

4. Why two-photon excitation?
One-photon excitation
Two-photon excitation
λ ≈ 160 nm
VUV
λ ≈ 320 nm
Fourth harmonics of 1,24 μm
(fiber lasers)
Problem of background signal
No background signal
One (resonant) spectral component
All spectral components
Doppler shift
No linear Doppler shift for counterpropagating waves
Magneto-dipole transition,
Weak but observable
No intermediate states.
Two-photon transition is extremely weak ?
|e>
|e>
ω≈ω0/2
ω≈ω0
ω≈ω0/2
|g>
|g>

5. Spectroscopic data Level classification – Nilsson (1955)
Radiation lifetime T1/2=3300 s, γ= s-1, ||μeg||=0.65 μN – Ruchovska et al (2006)
Magnetic moments and quadrupole moment in the ground state – Dichne, Tkalya (1998),
Bemis et al (1988)
Estimation of the quadrupole moment for the excited state – Tkalya (2011)

6. Thorium-229 in external magnetic field
Non-zero magnetic dipole moments of the ground and excited states lead to oscillation of the energy of these states in the light field.
g-factor of the level
with momentum F,
F = J + I,
J = L + S
For Th4+ J=0 → gF=gI
For Th3+ ground state is 2F5/2
Fg=0…5, Fe=1...4
gF=3/7 (ground state)
g4=15/28 (excited state)

7. Thorium – laser field interaction
Schrödinger equation
Hamiltonian
Two-photon resonance
Monochromatic field
Sequence of pulses

8. Two-photon excitation without virtual transitions
Phase transformation
Phase-modulated
field ω
ω-Ω
ω+Ω
in our case Ω=ω ω
ω+ ω =2 ω

9. Effective Hamiltonian
where
In both cases Rabi frequencies and light shifts are the same
Monochromatic wave, intensity
Pulse sequence with Gaussian distribution
Intensity

10. Two-photon excitation efficiency: Th3+ in trap
Ground state 52F5/2
Maximal Rabi frequency for
For transition between these hyperfine states
For P=100 mW focused in 1μm (I = 107 W/cm2)
Ω = 0.07 s S = 5·10-6 s-1
saturation (!)
negligible (!)

11. Two-photon excitation efficiency: Th4+ in crystal
Optimal transition
nuclear magneton
Number of photons per second from illuminated region
For n=1018 cm-3 and coherence relaxation rate γ'/2π=1 Hz,
F = 4 photons/s

12. Conclusions
two-photon excitation of the clock transition can be considered as a possible alternative to one-photon probing
the pulsed laser field two-photon excitation provides the same efficiency as CW excitation with the same mean intensity
Th3+ isomer transition can be saturated by the pulsed laser with the averaged power 100 mW
a few fluorescence photons per second from the volume about 100λ3 in crystal doped by Th4+ with density 1018 cm-3 can be obtained