+1 - Few

Samuel Lorenzo | Download | HTML Embed
  • Jun 9, 2014
  • Views: 42
  • Page(s): 35
  • Size: 2.30 MB
  • Report

Share

Transcript

1 Lecture 4 Feshbach resonances Ultracold molecules 95

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

3 Multi-channel scattering alkali-metal atom: mf electron spin s=1/2 2 1 nuclear spin i 0 f=2 -1 total spin f=s+i=i-1/2, i+1/2 -2 example Na: i=3/2: f=1, 2 -1 f=1 0 1 a3Su-: triplet ~ 100 THz ~10 THz two alkali-metal atoms (s=1/2) can interact via a singlet S=0 or triplet S=1 X1Sg+: singlet potential (SI ) Fl , S s1 s2 , I i1 i2 , F S I 97

4 Feshbach resonance V(r) bound state a coupling hyperfine interaction incident channel a3Su-: triplet r Feshbach, Ann. Phys. 5, 357 (1958) in ultracold quantum gases: X1Sg+: singlet Tiesinga, Verhaar, Stoof, PRA 47, 4114 (1993) 98

5 Energy scales molecular potential 2+2 1+2 1+1 Vibrational states Hyperfine states 2+2 1+2 1+1 Rotational states ~ 1 GHz ~ 100 THz ~ 3300 cm-1 (wavenumbers) / ~ 0.4 eV 99

6 Magnetically induced Feshbach resonance Zeeman effect E mF 2 1 F=2 0 -1 (2,1)+(2,1) -2 -1 F=1 0 1 (1,1)+(1,1) B E B 100

7 Feshbach resonance scattering length Natoms (x 105) E 0 B two atoms molecule a/abg B a( B) abg 1 B B0 Feshbach resonances in ultracold gases B(G) Chin, Grimm, Julienne, Tiesinga, Inouye et al, Nature 392, 151 (1998) 101 Rev. Mod. Phys. 82, 1225 (2010)

8 Near threshold molecular states Na2 a3Su-: triplet X1Sg+: singlet MS=+1 MS=0 MS=-1 MS=0 EZeeman=gSMSmBB 102

9 Hamiltonian of molecular states H H int VCentral aHFSi s g J m B s g I m B i B H int VHFS VZeeman VCentral V0 (r ) P0 V1 (r ) P1 Asymptotically: VCentral=0 103

10 Hamiltonian of molecular states: Moerdijk model (SI ) Fl , S s1 s2 , I i1 i2 H E0,1 VHF VZeeman F I S MF MI MS VZeeman m B Bz g s M S gi M I aHF aHF VHF aHF i1 s1 i2 s2 i1 i2 s1 s2 i1 i2 s1 s2 2 2 VHF VHF aHF aHF VHF I S MIMS aHF I S I S 2 2 4 conserves S: no singlet/triplet mixing 104

11 Example Na+Na: (f=1,mf=1)+ (f=1,mf=1) Spin quantum numbers of relevant singlet and triplet molecular states? mf1+mf2=MF=2=MS+MI I MI Imax=3 S=0 MS=0 2 2 I+S=even (identical bosons) S=1 MS=1 3 1 1 1 MS=0 3 2 MS=-1 3 3 H E0,1 m B Bz g s M S gi M I I S I S aHF aHF MIMS 2 4 Non-Diagonal 105 Diagonal

12 H E1 m B Bz g s M S gi M I M I M S HF I S I S aHF a 2 4 I MI S=1 MS=1 3 1 1 1 MS=0 3 2 MS=-1 3 3 MS=1 v=14 MS=0 MS=-1 106

13 H E1 m B Bz g s M S gi M I M I M S HF I S I S aHF a 2 4 I MI S=1 MS=1 3 1 1 1 MS=0 3 2 MS=-1 3 3 Inouye et al, Nature 1998 (Ketterle, MIT): F=1, mF=1: 907 G & 853 G Fixes E1(v=14) 107

14 Near threshold molecular states Na2 a3Su-: triplet X1Sg+: singlet 108

15 Natoms (x 105) Feshbach spectroscopy three-body recombination loss (L3 ~ a4) a/abg B(G) Chin et al, PRA (2004) 109

16 Example: BEC 85Rb Cornish et al, PRL 2000 110

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

18 Feshbach molecules scattering length 0 B E two atoms molecule B E Feshbach resonance two atoms Ultracold Feshbach Molecules Ferlaino, Knoop, Grimm molecule arXiv:0809.3920 Chapter of Cold Molecules: Theory, Experiment, Applications B (Taylor & Francis, London, 2009) 112

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

20 Adiabatic magnetic field ramp E two atoms molecule B Imaging: 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 Cs2 Na2 Innsbruck, Science 301, 1510 (2003) MIT, PRL 91, 210402 (2003) 87Rb 2 MPQ, PRL 92, 020406 (2004) 116

23 Properties Feshbach molecules single rovibrational quantum state - highly excited vibrational state (n=-1) - rotationally cold s-wave (=0) even (BB) odd (FF) all (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 MIT, PRL 92, 180402 (2003) 119

26 Properties Feshbach molecules Scattering length B a/abg Binding energy E/(mB) Eb (B-B0)/B Quantum halo state a/2 120

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

28 molecular BEC gallery (2003-2004) 40K JILA, Jin et al. 6Li 2 2 MIT, Ketterle et al. 6Li 2 6Li 6Li 2 2 Innsbruck, Grimm et al. Rice, Hulet et al. ENS Paris, Salomon et 122 al.

29 BEC/BCS crossover TBCS 0.277TF exp 2 k F a TC a ~ 0.2TF 123

30 BEC/BCS crossover Vortices and superfluidity in strongly interacting Fermi gas Zwierlein et al, Science 2005 124

31 Making ultracold ground-state molecules a3Su-: triplet S+P n=0, J=0 X1Sg+: singlet Recipe S+S make Feshbach molecules coherent two-photon transfer (STIRAP) polar molecules -> atomic mixture 125 r

32 Ultracold ground state polar molecules STIRAP (Stimulated Raman Adiabatic Passage) KRb Ni et al, Science 2008 126

33 Key experiments with ultracold polar molecules Quantum-State Controlled Chemical Reactions Ospelkaus et al, Science 2010 127

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 2011 128

35 Key experiments with ultracold polar molecules collisional stability KRb+KRb -> K2+Rb2 Zuchowski & Hutson, PRA 2010 new candidates: NaK, RbCs, ... RbCs (Takekoshi et al, arXiv:1405.6037) 129

Load More