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

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

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

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>

Spectroscopic data Level classification – Nilsson (1955) Radiation lifetime T1/2=3300 s, γ=0.0002 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)

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)

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

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

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

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-1 S = 5·10-6 s-1 saturation (!) negligible (!)

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

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