Lecture 4. Feshbach resonances Ultracold molecules

Transcription

1 Lecture 4 Feshbach resonances Ultracold molecules 95

2 Reminder: scattering length V(r) a tan 0( k) lim k0 k r a: scattering length Single-channel scattering a 96

3 Multi-channel scattering alkali-metal atom: electron spin s=1/2 nuclear spin i total spin f=s+i=i-1/2, i+1/2 example Na: i=3/2: f=1, 2 a 3 S u- : triplet f=2 f=1 m f ~ 100 THz ~10 THz X 1 S g+ : singlet S) Fl, S two alkali-metal atoms (s=1/2) can interact via a singlet S=0 or triplet S=1 potential s s, i i, F S (

4 V(r) Feshbach resonance bound state a coupling incident channel hyperfine interaction r a 3 S u- : triplet Feshbach, Ann. Phys. 5, 357 (1958) in ultracold quantum gases: Tiesinga, Verhaar, Stoof, PRA 47, 4114 (1993) X 1 S g+ : singlet 98

5 Energy scales molecular potential Vibrational states Hyperfine states Rotational states ~ 100 THz ~ 1 GHz ~ 3300 cm -1 (wavenumbers) / ~ 0.4 ev 99

6 Magnetically induced Feshbach resonance (2,1)+(2,1) F=2 E Zeeman effect m F (1,1)+(1,1) F= E B B 100

7 scattering length a/a bg N atoms (x 10 5 ) Feshbach resonance E 0 B two atoms molecule B a( B) a bg 1 B B 0 Feshbach resonances in ultracold gases Chin, Grimm, Julienne, Tiesinga, Rev. Mod. Phys. 82, 1225 (2010) B(G) nouye et al, Nature 392, 151 (1998) 101

8 Near threshold molecular states Na 2 a 3 S u- : triplet X 1 S g+ : singlet M S =+1 M S =0 M S =-1 M S =0 E Zeeman =g S M S m B B 102

9 Hamiltonian of molecular states H H int V Central H int V HFS V Zeeman a HFS i s g J m s B g m i B B V Central V0 r) P0 V1 ( r) ( P 1 Asymptotically: V Central =0 103

10 Zeeman HF,1 0 V V E H HF HF HF HF 2 2 s s i i a s s i i a s i s i a V V HF V HF S S a M M a S a V S HF HF HF HF i S s z B M g M g B V m Zeeman conserves S: no singlet/triplet mixing S F M M M S F ,, ) ( i i s s S Fl S Hamiltonian of molecular states: Moerdijk model 104

11 Example Na+Na: (f=1,m f =1)+ (f=1,m f =1) Spin quantum numbers of relevant singlet and triplet molecular states? m f1 +m f2 =M F =2=M S +M max =3 +S=even (identical bosons) S=0 M S =0 2 2 S=1 M S = M M S =0 3 2 M S = H E0,1 mbb z a 2 a 4 HF HF g M g M M M S S s S i S Diagonal Non-Diagonal 105

12 H E1 mbb z a 2 a 4 HF HF g M g M M M S S s S i S M S=1 M S = M S =0 3 2 M S = M S =1 v=14 M S =0 M S =-1 106

13 H E1 mbb z a 2 a 4 HF HF g M g M M M S S s S i S M S=1 M S = M S =0 3 2 M S = nouye et al, Nature 1998 (Ketterle, MT): F=1, mf=1: 907 G & 853 G Fixes E 1 (v=14) 107

14 Near threshold molecular states Na 2 a 3 S u- : triplet X 1 S g+ : singlet 108

15 a/a bg N atoms (x 10 5 ) Feshbach spectroscopy three-body recombination loss (L 3 ~ a 4 ) B(G) Chin et al, PRA (2004) 109

16 Example: BEC 85 Rb Cornish et al, PRL

17 Quantum chaos in ultracold collisions of Er Frisch et al, Nature 2014 many Feshbach resonances in Er alkali: ns L=0, J=1/2 2 potentials (singlet and triplet) Er: 4f12 6s2 L=6, J=6 91 potentials 111

18 scattering length Feshbach molecules E 0 B two atoms molecule Feshbach resonance B E Ultracold Feshbach Molecules Ferlaino, Knoop, Grimm arxiv: Chapter of Cold Molecules: Theory, Experiment, Applications two atoms molecule (Taylor & Francis, London, 2009) 112 B

19 Adiabatic magnetic field ramp E two atoms dissociation molecule B maging: fast magnetic field backramp Separation: e.g. magnetic field gradient 113

20 Adiabatic magnetic field ramp E two atoms molecule B maging: fast magnetic field backramp Separation: e.g. magnetic field gradient 114

21 Purification E B resonant laser light / microwave pulse 115

22 First Feshbach molecules from BECs Cs 2 Na 2 nnsbruck, Science 301, 1510 (2003) 87 Rb 2 MT, PRL 91, (2003) MPQ, PRL 92, (2004) 116

23 Properties Feshbach molecules single rovibrational quantum state - highly excited vibrational state (n=-1) - rotationally cold s-wave (l=0) even l (BB) odd l (FF) all l (BB,BF,FF ) weakly bound (khz-mhz-ghz)

24 Properties Feshbach molecules atom-molecule, molecule-molecule collisions relaxation to lower vibrational states 118

25 Properties Feshbach molecules atom-molecule, molecule-molecule collisions relaxation to lower vibrational states limited lifetime molecule-molecule atom-molecule MT, PRL 92, (2003) 119

26 Properties Feshbach molecules Scattering length E/(mB) a/a bg E b B Binding energy (B-B 0 )/B Quantum halo state a/2 120

27 Feshbach molecules from fermions Pauli blocking atom-dimer and dimer-dimer relaxation suppressed for large a 6 Li 2 forming Feshbach molecules by three-body recombination trap depth 121

28 molecular BEC gallery ( ) 40 K 2 JLA, Jin et al. 6 Li 2 MT, Ketterle et al. 6 Li 2 6 Li 2 6 Li 2 nnsbruck, Grimm et al. Rice, Hulet et al. ENS Paris, Salomon et 122 al.

29 BEC/BCS crossover T BCS 0.277T F exp 2k a F C a ~ 0. TF T 2 123

30 BEC/BCS crossover Vortices and superfluidity in strongly interacting Fermi gas Zwierlein et al, Science

31 Making ultracold ground-state molecules a 3 S u- : triplet S+P n=0, J=0 X 1 S g+ : singlet Recipe make Feshbach molecules coherent two-photon transfer (STRAP) polar molecules -> atomic mixture S+S r 125

32 Ultracold ground state polar molecules STRAP (Stimulated Raman Adiabatic Passage) KRb Ni et al, Science

33 Key experiments with ultracold polar molecules Quantum-State Controlled Chemical Reactions Ospelkaus et al, Science

34 Key experiments with ultracold polar molecules Dipolar collisions of polar molecules in the quantum regime Ni et al, Nature 2010 De Miranda et al, Nature Physics

35 Key experiments with ultracold polar molecules collisional stability KRb+KRb -> K 2 +Rb 2 Zuchowski & Hutson, PRA 2010 new candidates: NaK, RbCs,... RbCs (Takekoshi et al, arxiv: ) 129