Test of The Gravitational Inverse- Square Law Using Photo Association Spectroscopy of Ytterbium hashi A, A, B , Hirotaka Ya Yamada B , Yu uchi B , Yosu Kaker eru Ta Takaha Yu Kikuchi suke ke Taka kasu su B , Katsuna Enomoto C , Ma ki Ando B , Yo hi B, B, D unari Eno Masa saki Yoshi hiro Ta Takaha hashi University of Tokyo A , Kyoto University B , Toyama University C , JST-CREST D 201 2011/2/ 2/21 21 GCOE E Symposium 1/9 /9
Test of the Gravity Square-Inverse Law at Takahashi Lab. λ: 1 nm ~ 10 nm Our target: Science Extra large dimensions New gauge boson, Light dark matter Nesvizhevsky put an upper limit of | α | ~ 10 22 at 1 nm using neutron scattering (PRD., 77, 034020 (2008)) α : ~10 21 Experimental method Measuring the Yb 2 inter atomic potential Poster: “ High resolution photoassociation spectroscopy of ultra-cold Yb atoms for testing the square inverse law of the gravity ” Hirotaka Yamada 2011/2/ 201 2/21 21 GCOE E Symposium 2/9 /9
Inter Atomic Potential The inter atomic potential of Yb is decided at Takahashi Lab. by Kitagawa (for Ev ~ 300 MHz) (PRA., 77 , 012719 (2008)) E h =4.35974 × 10 -18 J (Hartree energy) C6=1931.7 E h a 0 6 C8=1.93 × 10 6 E h a 08 a 0 =0.52917 Å (Bohr radius ) C12=1.3041 E h a 012 (at 1 nm) | α |~10 20 , λ ~ a few µ m will affect to potential measurement 2011/2/ 201 2/21 21 GCOE E Symposium 3/9 /9
Measurement of the Inter Atomic Potential Inter atomic potential Molecular binding energies Molecular spectroscopy Inter atomic potential BEC Yb gas 2 color photo association Ratio of Yb Isotopes Inter atomic potential shape is studied well 168 Yb: 0.13% 172 Yb: 21.9% BEC has been achieved 170 Yb: 3.05% 173 Yb: 16.1% Narrow linewidth 171 Yb: 14.3% 174 Yb: 31.8% No thermal shift 176 Yb: 12.7% Many isotopes No electronic spin No hyper fine structure 2011/2/ 201 2/21 21 GCOE E Symposium 4/9 /9
Two Color Photo Association Spectroscopy Two laser light near the atom resonance frequency (f0) illuminate atoms When the frequency difference ∆ f = Ev, PA light make molecule from two atoms We can get absorption spectrum by counting remaining atom number GPS locked synthesizers control ∆ f within 1 Hz accuracy The frequency fluctuation of original laser doesn’t affect to ∆ f measurement 2011/2/ 201 2/21 21 GCOE E Symposium 5/9 /9
Noise Sources Shift of f 0 Light shift of PA light Resonant frequency shift by input PA power Mean field energy Mean field energy can be different between atom and molecule. Problem of analyze Calculating error of potential parameter Model irregularity (especially Born-Oppenheimer approximation) 2011/2/ 201 2/21 21 GCOE E Symposium 6/9 /9
201 2011/2/ 2/21 21 GCOE E Symposium 7/9 /9
Binding Energy Measurement We have not established analyzing flow yet Especially, we need careful evaluation of error 201 2011/2/ 2/21 21 GCOE E Symposium 8/9 /9
Summary and Future Works Summary An experiment to limiting alpha at 1 nm ~ 10 nm of λ , α ~10 21 is operated at Takahashi lab We measure inter atomic potential of Yb 2 molecule to limit α We decide inter atomic potential with measuring binding energy of Yb 2 molecule We use 2 color photo association to measure binding energy precisely Now we have got 4 binding energies to fit 3 potential parameter and α The calculating method have not been established completely... Future works We can put better upper limit of α with measuring other binding energies Especially, measuring binding energy of 168 Yb can improve α largely Using optical lattice to suppress collision loss for more accurate measurement 2011/2/ 201 2/21 21 GCOE E Symposium 9/9 /9
予備スライド 201 2011/2/ 2/21 21 GCOE E Symposium 10 10/9 /9
Inter Atomic Potential of Yb 2 Atom Kitagawa (2008) C 6 : Second order perturbation of dipole–dipole interaction C 8 : Second order perturbation of dipole-quadrapole interaction C 12 : Repulsive ....... He has measured 12 binding energy from 6 isotopes of Yb. He decided potential parameters and confirmed that its eigenstates match experiments well We can put gravitational correction term and limit it with operating same method! Kitagawa’s result is not enough for limiting alpha to 10 21 . 201 2011/2/ 2/21 21 GCOE E Symposium 11/9 11 /9 We measure binding state using BEC Yb gas with 2 color photoassociation
Example of data ( 174 Yb, J=0, v=2) Light shift cancellation Measuring resonant frequency with changing PA power (using fixed I1/I2 ratio) to extrapolate canceling light shift. For all eigenstate, we measured spectrum for more than two ∆ parameter to confirm they cross at extraporating point Mean field energy cancelation グラフは実験の進行状況を見ながら分かりやすいものに差し替える Measuring resonant frequency with changing density of atoms to extrapolate mean field energy 201 2011/2/ 2/21 21 GCOE E Symposium 12/9 12 /9
Experimental Setups We use AOMs to make frequency difference ∆ f = ∆ f 1 - ∆ f 2 The laser frequency shift or fluctuation has small effect to this experiment GPS locked synthesizers control ∆ f within 1 Hz accuracy PA light power stabilization A PBS converts polarization rotation to power fluctuation to suppress differential power fluctuation 201 2011/2/ 2/21 21 GCOE E Symposium 13 13/9 /9
Analysis flow Measure spectrums with changing atom number Canceling the effect of mean field energy Measure spectrums with changing PA power Canceling light shift Operating for each eigenstate Search good potential parameter set which generate eigenstates matches to experiment 201 2011/2/ 2/21 21 GCOE E Symposium 14/9 14 /9
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