Universal Aspects of Dipolar Scattering Christopher Ticknor. May 15 at INT UNCLASSIFIED

Transcription

1 Universal Aspects of Dipolar Scattering Christopher Ticknor May 15 at INT 1

2 Outline of Talk Universal Dipolar Scattering Theory of a long range scattering potential D Universal and tilted dipolar scattering Interplay of interaction and geometry Universal 3-body dipolar recombination (not included) 4 L3 D, a D

3 Ultracold Scattering Feshbach resonances s-wave p-wave = 4 k sin Regal et al. PRL (003) 3

4 Ultracold Scattering Threshold laws for partial waves s-wave, energy independent p-wave, suppressed s 1/ r l 1 s ~ k k p l E p=min l, s 3 4

5 Ultracold Scattering But dipoles are different Long range Anisotropic Strong s=3 0 l E d d 3 R d V dd = 3 R 1 3cos V dd ~ d 3 R 5

6 Dipolar Scattering The system can be magnetic or electric. Dipolar length scale D= d m r /ℏ Energy scale E D = d / D =ℏ / d m 3 r Strong interactions, many exotic theories. 6

7 Ultracold Scattering Long Range energy 1/ R 3 full 7

8 Dipolar Scattering Equation of Motion 1 3cos =E 3 m r R y=r/ D R = l Y lm F l R 8

9 Dipolar Scattering Equation of Motion Universal! Except for short range y0=r0 / D 1 Cll' l l 1 d E F l l ' 3 F l ' = F l ED dy y y C l l ' = lm 1 3cos l ' m 9

10 Dipolar Scattering Semi-classical solution from Eikonal approximation line V dd z, b, dz E 1 ED 8 D = k Bohn, Cavagnero, and Ticknor NJP (009) Ticknor PRL 100, 1330 (008) 10

11 Dipolar Scattering E 1 ED Threshold behavior Born Approximation: all dipolar coupled partial waves have an energy independent cross section! 3 l l ' F l 1 /R F l ' lm 1 3cos l ' m e=1.117 D o =3.351 D Bohn, Cavagnero, and Ticknor NJP (009) 11

12 Dipolar Scattering Experimental observation from Innsbruck. Threshold universality universal D=100 a 0 E D =00 K From K. Aikawa et al. PRL (013) 1

13 D dipolar scattering with a tilt Christopher Ticknor May 15 at INT 13

14 D dipolar scattering Long range Anisotropic Strong d d 3 R d V dd = 3 R R d cos z sin x 1 3cos sin V dd = d 3 14

15 D Universal Dipolar Scattering =0 d = / D d m 1/4 1 E 3 m= m ED d Universal Repulsive diagonal potential for m=0 Diagonal in partial wave Short range not really important 15

16 D Universal Dipolar Scattering Semi-classical regime E 1 ED 4 sc= Dk k Ticknor, PRA (009) 16

17 D Universal Dipolar Scattering E 1 ED Threshold regime m=0 m 0 a / D=e ln Dk m= k m 1 /4 Ticknor, PRA (009) m k 4m 1 17

18 Interplay of geometry and interaction 0 d 1 3cos sin V dd = d 3 18

19 Breakdown of superfluidity in a BEC An amazing BEC experiment. 19

20 Interplay of geometry and interaction D dipolar gas with tilted polarization Anisotropic superfluid character! Ticknor et al. PRL

21 Interplay of geometry and interaction 1 3cos sin 1 3cos V dd = 3 3 = / y x 1

22 Interplay of geometry and interaction cos V dd 3 = / 4 y x

23 Interplay of geometry and interaction Binding Energies as function of a/d and α = / 4 1/ a = / Ticknor PRA

24 Interplay of geometry and interaction ei / 4 i m i m' f i, f = e T mm ' e mm' k i i = d f f i, f f 1 = mm ' T mm ' k 4

25 Interplay of geometry and interaction Fermions with tilted polarization / =0.315 cos m sin m 5

26 Interplay of geometry and interaction i / =0.315 y x 6

27 Conclusions Universal dipolar scattering in 3D. Many partial waves always contribute. Dipolar scattering in D is universal. If polarization is tilted then: Tune anisotropy of system. Money from LANL and LDRD. 7

28 Interplay of geometry and interaction y x f i, f 8

29 Interplay of geometry and interaction f i, f / =0.315 y x i=0, / 9

30 3-body dipolar recombination Studied formation of body molecule from 3 body dipolar system. Ticknor and Rittenhouse, PRL (010) 30

31 3-body dipolar recombination a/d bound states Shape Also see: Wang and Greene PRA (01) 31

32 3-body dipolar recombination Example wave functions. 3

33 3-body dipolar recombination Now use Fermi Golden Rule (FGR) 3 body plane wave V dd molecule third V dd k m m 1 k 3 k R R [Y k, m Y k, m ]0 1 33

34 3-body dipolar recombination a 4 a D D 4 34

35 Interplay of geometry and interaction / =0.5 / =0.35 / =0.5 a / D=0.1 a / D=1 a / D=10 a / D=100 35

36 Interplay of geometry and interaction Fermions in D with tilted polarization / =0.315 ±i m e 36

37 Interplay of geometry and interaction 0 d m 1 3 d m' 3 3 = 1 sin mm ' sin mm ' ± 4 37

38 Interplay of geometry and interaction m 1 3 d m' cos m sin m 9 3 = 1 sin mm ' = 1 sin mm ' sin mm ' ± sin mm ' ±

39 Dipolar Scattering Semiclassical Universality first predicted numerically True of Fermions and Bosons and distinguishable particles. k Ticknor PRL 100, 1330 (008) E/ED 39

40 Interplay of geometry and interaction k sc=4 Dk 40

41 Interplay of geometry and interaction 0 d 4 Dk 3 k m m' = 1 sin 4 m 1/4 4 Dk 3 k m' m = sin m 1/ m 3/ 4 4 Dk 3 k 1 ±1= sin m 1/4 4 41