Precise Measurement of Vibrational Transition Frequency of Optically Trapped molecules　 NICT Masatoshi Kajita TMU G. Gopakumar, M. Abe, M. Hada

We propose to test the variation in the proton-to-electron mass ratio, via the precise measurement of the vibrational transition freq. of ultra-cold molecules. (f/f < 10-16)

X6Li or X23Na molecules X: 174Yb, 88Sr, 40Ca

(in an optical lattice)

X2(v,N) = (0,0)->(vu,0) (vu = 1,2,3,4)

The transition is observed by Raman transition (one photon forbidden).

　　

Ultra-cold XLi 　 or XNa molecules

Production from atoms in a optical lattice

-> Feshbach resonance 　 (very challenging for X6Li)

photo-association

->localization in the vibrational-rotational ground state K. Aikawa et al. Phys. Rev. Lett. 105, 203001(2010)

-> trap by laser light

-> measurement of X2(v , N ) = (0, 0) -> (vu, 0) transition freq.

vu = 1,2,3,4,

-> detection of molecules in the v = vu state by selective

photo-ionization (afterwards also v = 0)

Transition Frequency(THz) λ f ∝ (mp/me)-

174Yb6Li

v = 0 ->1 4.17 　　　　　　　 　 0.47

v = 0 ->4 15.37 　　　　　　　 　 0.4388Sr6Li

v = 0 ->1 5.06 　　　　　　 　　 0.48

v = 0 ->4 19.05 　　　　　 　　　 0.4540Ca6Li

v = 0 ->1 5.77 　　　 　 　　　 0.47

v = 0 ->4 21.46 　　　　 　　　 0.43

88Sr23Na

v = 0 ->1 2.29 　　　　　　 　　 0.56

v = 0 ->4 8.65 　　　　　 　　　 0.5040Ca23Na

v = 0 ->1 2.57 　　　 　 　　　 0.48

v = 0 ->4 9.72 　　　　 　　　 0.45

Measurement with molecules in a optical lattice

Problem

Stark shift induced by the trap laser light

(this depends on the laser frequency)

Merits

(1)long interaction time (narrow homogeneous broadening)

(2) trap inside the Lamb-Dicke region

-> no Doppler broadening

(3) measurement with many molecules

-> high S/N ratio (low statistic uncertainty)

(4) supression of the collision shift

Stark shift in the transition frequency

Upper state

Lower state

without light with lightwith lightwithout light

transition frequency transition

frequency

Eu

El

Stark shift(Eu – El)/h

No Stark shift(Eu = El)

In generalWith a proper laser freq.　 (magic frequency)

Are there magic frequency with molecular transitions?

There exist magic frequency in the electronic quasi-resonant region （ already proposed withSr2 )

Upper state

Lower state

frequency

but sensitive to the slight detuning from the magic frequency

resonance freq.

Stark shift in 174Yb6Li transitions by trap laser 　　 23 kW/cm2

Magic frequencies (power density to get the potential depth of 10 K ）

Transition Freq. (THz) power density (kW/cm2) Slope (/MHz)174Yb6Li v = 0 -> 1 361.4 17 5.8 x 10-17 v = 0 -> 4 374.2 12 3.2 x 10-17

88Sr6Li v = 0 -> 1 313.5 11 1.1 x 10-15 v = 0 -> 2 271.3 11 1.8 x 10-16

v = 0 -> 4 325.2 8 1.3 x 10-15

40Ca6Li v = 0 -> 1 268.9 11 1.0 x 10-16 v = 0 -> 2 258.3 12 1.2 x 10-16

v = 0 -> 3 261.6 12 1.8 x 10-16

88Sr23Na v = 0 -> 1 287.8 8 1.2 x 10-15 v = 0 -> 4 318.4 15 5.7 x 10-16

40Ca6Li v = 0 -> 1 335.7 25 1.2 x 10-15 v = 0 -> 3 340.0 21 2.6 x 10-16

v = 0 -> 4 344.1 20 1.5 x 10-16

(v, N) = (0,0)→(vu,0) transition is induced by Raman transition

X2 (0,0)

X2 (vu,0)

Electronically excited states

We have a choice with the Raman laser frequency(difference must be resonant)

Stark shift in the vibrational transition frequency

magic frequency

0

laser frequency

Raman frequencies

transition frequency

cancel each other

Raman laser frequencies when intensities of tow Raman lasers are equal ( intensity to get Rabi frequency of 1/6 Hz)

Transition Freq. (THz) power density (mW/cm2) 　　　　 One laser shift 　 174Yb6Li 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　v = 0 -> 1 364.3 + 360.1 100 　　 8.0 x 10-16 v = 0 -> 2 277.9 + 269.8 43 　　 1.5 x 10-15

v = 0 -> 4 385.8 + 370.4 112 　　 9.5 x 10-16

88Sr6Liv = 0 -> 1 313.7 + 308.6 17 　　 3.0 x 10-16 v = 0 -> 2 313.5 + 303.6 50 　　 1.7 x 10-15

v = 0 -> 4 298.6 + 279.5 6.7 　　 1.7 x 10-15

40Ca6Liv = 0 -> 1 261.8 + 256.0 75 　　 1.3 x 10-15 v = 0 -> 2 291.1 + 279.9 6.7 　　 1.7 x 10-15

v = 0 -> 3 298.6 + 282.1 6.7 　　 1.3 x 10-15

88Sr23Nav = 0 -> 1 316.1 + 313.8 29 　　 9.6 x 10-16 v = 0 -> 3 315.1 + 308.5 160 　　 2.0 x 10-15

40Ca23Nav = 0 -> 1 334.1 + 331.6 　　 27 3.0 x 10-16 v = 0 -> 2 340.1 + 335.1 59 　　 1.5 x 10-15

v = 0 -> 4 309.7 + 300.0 5.8 　　 5.7 x 10-15

Other frequency shifts 　DC Stark shift v = 0 ->1 174Yb6Li -2 x 10-15 /(V/cm)2

88Sr6Li 4 x 10-14 /(V/cm)2

40Ca6Li 1 x 10-13 /(V/cm)2 88Sr23Na 7 x 10-13 /(V/cm)2

40Ca23Na 9 x 10-13 /(V/cm)2

Stark shift by the blackbody radiation (∝ T4)

　　 (300K) order of X6Li 1 x 10-14 　

X23Na 2 x 10-14

Zeeman shift

　　 F = 3/2 M = 3/2 -> 3/2 174Yb6Li -5 x 10-17 /G 88Sr6Li -3 x 10-17 /G

40Ca6Li -2 x 10-17 /G

F = 2 M = 2 -> 2 88Sr 23Na -6 x 10-16 /G

40Ca 23Na -6 x 10-16 /G

2nd order Doppler shift 　　　 <10-19

Which molecule is advantageous?

174Yb6Li is most advantageous

　　　　　　　　　　　　　 (but difficult to be produced)

40Ca6Li is first candidate to be realized

　　　　　　　　　　　　 (Fourier spec. is observed)

Large DC Zeeman and Stark shift with X23Na

This method is not applicable for 88Sr87Rb (no magic frequencies)

Application to 40CaH molecule?

Measurement with 40CaH molecule seems to be advantageous

Magic frequency: 378.43 THz (792 nm)

50 kW/cm2 ( potential 10 K) Slope 1.1 x 10-17 /MHz

DC Stark shift 1 x 10-14 /(V/cm)

Zeeman shift 2 x 10-18 /G

Blackbody radiation with 300 K 1.3 x 10-16

But it is a subject to get ultra-low temperature

buffer-gas cooling -> laser cooling (Doppler limit 60 K)

for further cooling(1) PGC -> optical trap

(2) optical trap with intense laser -> sideband Raman cooling

A21/2 v = 0 N = 1 J = 1/2

A21/2 v = 1 N = 1 J = 1/2

X2 v = 0N = 0,F = 1

N = 0,F = 0

N = 2,J = 3/2,F=1

N = 2,J = 3/2,F=2

LaserC0-F1

LaserC0-F0

Laser C2

X2 v = 1

X2 v = 2

N = 0

N = 0

N = 2

N = 2

Laser R0-1

Laser R2-1

Laser R0-2

Laser R2-2

Laser transition

Spontaneous emission

1.4 x 107 /s

2.4 x 105 /s

2.2 x 103 /s

1.4 x 107 /s

Conclusion (v, N) = (0,0)-> (vu,0) (vu = 1,2,3,4) transition frequency can be measured with the systematic uncertainty of 10-16 for XLi or XNa molecules

　　　　　 The Stark shift induced by

trap laser

　　　　　　 Raman lasers 　　　 can be eliminated

Detuning of trap laser frequency with the order of 0.1 MHz does not give significant effect

Advantageous to get low systematic uncertainty

40CaH > 174Yb6Li > 88Sr6Li > 40Ca6Li > 88Sr23Na, 40Ca23Na

This method is not applicable for 88Sr87Rb

The linewidth of Raman lasers are hope to be less than 0.1 Hz.

This frequency measurement is useful to test the variance in mp/me

Thank you for attention!

Danke fuer Aufmerksamkeit!

Merci pour attention!

Tante Grazie!