Optical Feshbach resonances in ultra-cold ytterbium

M. Borkowski, A. A. Buchachenko, R. Ciuryło,

P. S. Julienne, Y. Takasu, Y. Takahashi

The project „Precise Optical Control and Metrology of Quantum Systems” is supported

by the Foundation for Polish Science program TEAM cofinanced by the European

Regional Development Fund. This research is a part of the scientific program

of the National Laboratory FAMO in Toruń, Poland.

Support

Two-color photoassociation of Yb

Kitagawa et al, Phys. Rev. A 77, 012719 (2008).

Bound states of Yb2

(11)

(13)

(38)

(18)

(21)

(74)

(26)

(19)

(40)

(50)

(23)

(26)

Borkowski al, Phys. Rev. A 80, 012715 (2009).

Model potential

Exp. Theo.1 Theo.2

C6 [Eh a06] 1.932(30) x103 2.07(20) x103 1.929(39) x103

C8 [Eh a08] 1.9(5) x105 2.02(20)x105

1Zhang and Dalgarno, Mol. Phys. 106, 1525 (2008).2Safronova et al, Phys. Rev. Lett. 109, 230802 (2012)

Scattering length

Gribakin et al, Phys. Rev. A 48, 546 (1993).

Mass scaling

Kitagawa et al, Phys. Rev. A 77, 012719 (2008).

um 7.42

Scattering lengths

Scattering lengths [nm]

Kitagawa et al, Phys. Rev. A 77, 012719 (2008).

Scattering resonances

,10 ,6 ,2

,12 ,8 ,4

g

g

l

aa

l

a

Gao, Phys. Rev. A 62, 050702(R) (2000); 64, 010701(R) (2001).

Kr 100

Spectra

172Yb 176Yb

Borkowski et al, Phys. Rev. A 80, 012715 (2009).

174Yb

T=25 K

Tojo et al, Phys. Rev. Lett. 96, 153201 (2006).

One-color photoassociation

Yb(1S0)+Yb(3P1)

Tojo et al, Phys. Rev. Lett. 96, 153201 (2006).

Two channels model

)1)(2(1212

1

12

)1(

12

)1()1(

12

1

12

1

1

1001

0110

JJBVJ

JV

J

JVV

J

JJ

VVJ

JJJBJV

J

JV

J

J

Jl

Jl

2

2

2 rB

1)1(2)(

)12(441)(

2

1

1)1(2)(

)12(441)(

2

1

2

01

22

01

01101

2

01

22

01

01100

JJBVV

JB

VV

BVVVV

JJBVV

JB

VV

BVVVV

)12(

)12()1( )1(

)12()1(

)12( 2)1(

11

00

-

JJ

JJJBJV

JJ

JJJJBV

01for VVB

Model potential

Wang and Dolg, Theor. Chem. Acc. 100, 124 (1998).

Shape of ab initio potential is very different

Experiment and theory

174Yb ∆e(0u) [MHz]

Je=1 Je=3

Exp. Theor. Exp. Theor.

-4.4(1.0) -4.2 -3.0

-9.5(1.0) -9.7 -7.5

-19.7(1.0) -20.1 -16.1(2.0) -16.7

-37.4(1.0) -38.5 -32.5(2.0) -33.3

-68.6(1.0) -69.1 -61.7

-119.1(2.0) -117.8 -107.5

-191.3(1.0) -192.3 -179.0(2.0) -178.2

-302.3(1.0) -302.5 -284.5(2.0) -283.9

-461.1(1.0) -461.3 -437.4

-684.6(1.0) -684.9 -654.7(2.0) -654.6

-993.7(1.0) -993.7 -955.9

-1412.8(1.0) -1413.0 -1366.7(2.0) -1366.4

-1973.5(1.0) -1973.9 -1918.1(2.0) -1917.3

176Yb ∆e(0u) [MHz]

Je=1 Je=3

Exp. Theor. Exp. Theor.

-3.1 -2.1

-7.9(2.0) -7.5 -5.9(2.0) -5.7

-16.5(2.0) -16.0 -13.9(2.0) -13.1

-32.0(2.0) -31.2 -27.4(2.0) -26.8

-56.2(2.0) -57.0 -50.0(2.0) -50.5

-98.5 -89.4

-162.6 -150.1

-258.2(2.0) -258.3 -242.8(2.0) -241.7

-398.1(2.0) -397.1 -376.4(2.0) -375.5

-594.4(2.0) -593.8 -567.3(2.0) -566.3

-867.6(2.0) -866.7 -832.7(2.0) -832.2

-1240.1(2.0) -1238.9 -1196.2

-1738.5 -1686.5

Borkowski et al, Phys. Rev. A 80, 012715 (2009).

Verification

C6,0u = -2.41(22) 103 Eh a06

C3,0u = -0.1949(11) Eh a03

τ(3P1)= 0.8696(45) μs

Probing ground state

Optical length

22opt

22optbg

21

1)(

2

1),(

21)(),(

IlIb

IlaIa

E pegee

Reduced detuning

Fedichev et al, Phys. Rev. Lett. 77, 2913 (1996).

Bohn, and Julienne, Phys. Rev. A 60, 414 (1999).

Ciuryło et al, Phys. Rev. A 71, 030701 (2005).

Blatt et al, Phys. Rev. Lett. 107, 073202 (2011).

Optical length 174Yb, Je=1

∆e(0u)

[MHz]

lopt/I

[a0/(W cm-2)]

-4.2 1.6×105

-9.7 5.5×104

-20.1 2.0×104

-38.5 7.9×103

-69.1 3.1×103

-117.8 1.2×103

-192.3 466

-302.5 150

-461.3 33

-684.9 1

-993.7 4

-1413.0 17

-1973.9 27.5

I= 1 W

Yamazaki et al, Phys. Rev. Lett. 105, 05045 (2010).

Experiment with 174Yb

ascat=+104 a0

ascat=-594 a0

ascat=-24 a0

ascat=+250 a0

ascat=+63 a0

Optical tuning of scatering length

Experiment with 172YbEnomoto et al, Phys. Rev. Lett. 101, 203201 (2008).

Fatemi et al, Phys. Rev. Lett. 85, 4462 (2000).

Heteronuclear bosonic system

rotA HHH int 2

12121 egge

AAAA

eg

ge

E

E

egge

AA

AA

A

A

AAAA

21

21

2

1

2121

0

0

1

1

2

1

2

12

1

2

1

1 1

2121

2121

EEEE

EEEE

AAAA

AAAA

1

1

0

0

11

u

g

V

V

AH

intH

AH

Heteronuclear bosonic system

222121 )1(

2

1

ugug

EEEEAAAA VVVV

ug

EEAA

VV21for

VEEAA 21

2

1

EE

EEAA

AA ugug

21

21

2)1(

22

)1(1

2

)1(12

VVVV

EEAA

ug

21for VV

EE

C

AA 21

2

3res

6

)(1 C

EEE

p

AA

I21

)1(

C3 [Eh a03]

0u -0.1949(11)

0g +0.1949

1g -0.0974

1u +0.0974

Heteronuclear bosonic system

C3 [Eh a03]

0u -0.1949(11)

0g +0.1949

1g -0.0974

1u +0.0974

EEE

p

AA

I21

)1(

ug

u g

Borkowski et al, Phys. Rev. A 84, 030702(R) (2011).

gerade-gerade transitions

ggug

Meath, J. Chem. Phys. 48, 227 (1968).

Machholm, Phys. Rev. A 64, 033425 (2001).

gerade-gerade transitions

Takasu et al, Phys. Rev. Lett. 108, 173002 (2012).

Ab initio potential

Buchanchenko et al, Eur. Phys. J. D 45, 147 (2007).

174Yb2 N=72

Experiment with kHz accuracy.

Ab initio potential leads to small reduction of

residuals on average from about 83 kHz to 64 kHz

Zhang and Dalgarno, Mol. Phys. 106, 1525 (2008).

High precision data

Zhang and Dalgarno, Mol. Phys. 106, 1525 (2008).

Testing models

Tang and Toennies, J. Chem. Phys. 80, 3726 (1984).

Zhang and Dalgarno, Mol. Phys. 106, 1525 (2008).

12

1

22 )(i

ii EuE

6

66

8

88 )()()(

r

Crf

r

CrfrV

2

6888

2

4666

)(

)(

rWCCrf

rWCCrf

FS

FS

rCrf

rCrf

FS

FS

8

218

6

2

16

16

)0()0(531)(

4

)0(23)(

small r

large r

long range

Summary

• Bosonic and fermionic isotopes of Yb offer large variety of the scattering lengths.

• The simple mass scaling approach works well in case of cold collision of Yb atoms in ground and excited state.

• Results obtained for homo-nuclear systems can be extended for hetero-nuclear.

• Gerade-gerade transitions can be well described and results are consistent with dose for gerade-ungerade transitions

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