Test of The Gravitational Inverse- Square Law Using Photo - - PowerPoint PPT Presentation
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
GCOE E Symposium 201 2011/2/ 2/21 21 1/9 /9
Kaker eru Ta Takaha hashi A,
A, B, Hirotaka Ya
Yamada B, Yu Yu Kikuchi uchi B, Yosu suke ke Taka kasu su
B, Katsuna
unari Eno Enomoto C, Ma Masa saki ki Ando B, Yo Yoshi hiro Ta Takaha hashi hi B,
B, D
Test of The Gravitational Inverse- Square Law Using Photo Association Spectroscopy of Ytterbium
University of Tokyo A, Kyoto University B, Toyama University C, JST-CREST D
201 2011/2/ 2/21 21 GCOE E Symposium 2/9 /9
Test of the Gravity Square-Inverse Law at Takahashi Lab.
λ: 1 nm ~ 10 nm
Measuring the Yb2 inter atomic potential Nesvizhevsky put an upper limit of |α| ~ 1022 at 1 nm using neutron scattering (PRD., 77, 034020 (2008)) Our target: Science Experimental method
α: ~1021
Poster: “High resolution photoassociation spectroscopy of ultra-cold Yb atoms for testing the square inverse law of the gravity ” Hirotaka Yamada
Extra large dimensions New gauge boson, Light dark matter
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Inter Atomic Potential
C6=1931.7 Eha0
6
C8=1.93×106 Eha08 C12=1.3041 Eha012 Eh=4.35974×10-18 J (Hartree energy) a0=0.52917 Å (Bohr radius )
The inter atomic potential of Yb is decided at Takahashi Lab. by Kitagawa (for Ev ~ 300 MHz)
(PRA., 77, 012719 (2008))
|α|~1020 , λ ~ a few µm will affect to potential measurement
(at 1 nm)
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Measurement of the Inter Atomic Potential
BEC Yb gas 2 color photo association
Inter atomic potential shape is studied well BEC has been achieved
Narrow linewidth No thermal shift
Many isotopes No electronic spin No hyper fine structure
172Yb: 21.9% 173Yb: 16.1% 174Yb: 31.8% 176Yb: 12.7% 168Yb: 0.13% 170Yb: 3.05% 171Yb: 14.3%
Inter atomic potential Molecular binding energies Molecular spectroscopy Inter atomic potential
Ratio of Yb Isotopes
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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
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Noise Sources
Light shift of PA light Mean field energy Calculating error of potential parameter Model irregularity (especially Born-Oppenheimer approximation) Resonant frequency shift by input PA power Mean field energy can be different between atom and molecule. Shift of f0 Problem of analyze
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Binding Energy Measurement
We have not established analyzing flow yet Especially, we need careful evaluation of error
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Summary and Future Works
An experiment to limiting alpha at 1 nm ~ 10 nm of λ, α ~1021 is
We measure inter atomic potential of Yb2 molecule to limit α We decide inter atomic potential with measuring binding energy of Yb2 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...
Summary Future works
We can put better upper limit of α with measuring other binding energies Especially, measuring binding energy of 168Yb can improve α largely Using optical lattice to suppress collision loss for more accurate measurement
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Inter Atomic Potential of Yb2 Atom
Kitagawa (2008) C6 : Second order perturbation of dipole–dipole interaction C8 : Second order perturbation of dipole-quadrapole interaction C12: 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 1021. We measure binding state using BEC Yb gas with 2 color photoassociation
201 2011/2/ 2/21 21 GCOE E Symposium 12 12/9 /9
Example of data (174Yb, J=0, v=2)
Light shift cancellation 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 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 Measuring resonant frequency with changing density of atoms to extrapolate mean field energy
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Experimental Setups We use AOMs to make frequency difference ∆f = ∆f1 - ∆f2 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
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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