1. Efimov Physics with Ultracold Atoms Selim Jochim Max-Planck-Institute for Nuclear Physics and Heidelberg University

2. Outline 1.Summary of the Efimov effect 2.Experimental observations 3.Efimov physics with distinguishable particles: three fermions

3. The Efimov effect An infinite number of bound states exists when the scattering length diverges: the infinite series is limited for small scattering lengths by the effective range, in alkali atoms ~ 10s of a 0 At infinite scattering length: E n =22.7 2 E n+1 Scattering length values where Efimov trimers become unbound a n+1 =22.7a n Drawing: V. Efimov

4. Realization in ultracold atoms for a review, see: C. Chin et al., arXiv:0812.1496 example: Feshbach resonances in 6 Li tune the scattering length using Feshbach resonances → simply apply a magnetic field!

5. What has been done in experiments? Observe and analyze collisional stability in ultracold gases pioneering experiment with ultracold Cs atoms (Innsbruck): T. Krämer et al., nature 440, 315 (2006)

6. What is observed? three-body recombination deeply bound molecule

7. Enhanced recombination With an (Efimov) trimer at threshold recombination is enhanced: deeply bound molecule Drawing: V. Efimov

8. Suppressed recombination two interfering pathways lead to suppression deeply bound molecule Drawing: V. Efimov

9. Quest to observe the logarithmic periodicity of the Efimov states Major challenge: - at low a, the series is truncated by the effective range - at large a, measurements require extremely low temperature/density: Observing an Efimov Spectrum Drawing: V. Efimov D‘ Incao et al., PRL 93, 123201 (2003)

10. What has been done in experiments? Observe and analyze collisional stability in ultracold gases pioneering experiment with ultracold Cs atoms (Innsbruck): T. Krämer et al., nature 440, 315 (2006)

11. Observing an Efimov spectrum Spectrum observed in 39 K: two loss minima, one loss maximum at negative scattering length Rather strong variation from universal scaling is observed Zaccanti et al., nature physics 5, 586 (2009)

12. A universal Efimov trimer An Efimov state is observed on both sides of the resonance, with the same three-body parameters, indicating a universal trimer Gross et al., arXiv:0906.4731 (2009)

13. Efimov physics with fermions Identical fermions do not interact in s-wave collisions need three distinguishable particles! SU(3) symmetry reminds us of the color symmetry in quarks! Our original motivation: Study many-body physics! Cooper pairs 1 32 a 12 a 13 a 23 a 12

14. Many different phases are expected A gas of fermionic “trions”, “baryons”

15. Many different phases are expected A “color superfluid”?

16. Many different phases are expected Will we get a mixture of pairs?

17. Many different phases are expected …. or will we get a phase separated state of dimers?

18. Laser cooled atoms ~10 9 fermionic 6 Lithium atoms at 200µK, phase space density ~10 -5

19. Crossed-beam optical dipole trap Rotate polarization Vacuum windows Atoms are trapped where the two beams cross Fiber laser 200W @ 1070nm Atoms trapped in conservative potential (off-resonant laser beam)

20. BEC of molecules Create BECs of ≈10 5 molecules repetition rate ~4s S. Jochim et al., Science 302, 2101 (2003) M. Greiner et al., Nature 426, 537 (2003) M. Zwierlein et al., PRL 91, 250401 (2003) Original work: Starting point for experiments with very cold fermions! Density distribution of atoms after time-of-flight

21. How to obtain three components Cooling is performed on a two-component mixture (established technology) Mix all three states with RF fields RF 23 RF 12

22. Challenges to obtain three components allowedsymmetry forbidden Two-component gasThree-component gas 1.RF fields couple the three states coherently, need to make sure that incoherent mixture is realized (mag. field gradient across the trap does the job!) 2. Is the three-component gas stable against inelastic decay? Formation of deeply bound dimers:

23. Prepare a stable mixture zero crossings → Prepare the mixture where all scattering lengths are small M. Bartenstein et al., PRL 94, 103201 (2005) for a review, see: C. Chin et al., arXiv:0812.1496 Feshbach resonances in 6 Li

24. Collisional stability studies Loss feature at B = 127 G Holding the mixture for 250 ms at different magnetic fields: Mixture is stable if two- particle scattering lengths are small Rapid decay close to the two- particle Feshbach resonances (expected!) T ≈ 200 nK T. Ottenstein et al., PRL 101, 203202

25. Inelastic rate vs. magnetic field T. Ottenstein et al., PRL 101, 203202 Similar experiments at: Penn State: J. Huckans et al., PRL 102, 165302 (2009), also at Tokyo University and MIT Three-body coefficient:

26. a B For a certain interaction strength, three particles become bound E continuum Borromean state Do we observe an Efimov state? A three-body resonance should occur a*a*

27. Do we observe such a borromean state? assume everything we observe can be described only by the scattering lengths: for a thorough treatment see: E. Braaten et al., arXiv:0811.3578 (2008) To make our life easier: Average all three scattering lengths in a meaningful way!

28. An experimentalist’s model … Theoretical model for bosons: E. Braaten and H. Hammer, Phys. Rep., 428, 259 (2006) what‘s the discrepancy at higher fields? η * : resonance width a * : resonance position Braaten et al. arXiv:0811.3578 Naidon et al. arXiv:0811.4086 Schmidt et al. Phys. Rev. A 79, 053633 Similar work

29. Decay of the trimer state The trimer decays rapidly into a dimer plus a free atom: What dimer does the trimer decay into? Is the rate of the decay governed by the binding energy of the dimer?

30. Feshbach molecules are important! A (weakly) bound state is associated with large, pos. scattering length! Our trimers decay into weakly bound Feshbach molecules: Their binding energy strongly depends on mag. field! A. Wenz et al., arXiv:0906.4378

31. Vary η * with binding energy η * is determined by the lifetime of the trimer state Try to scale η * as A. Wenz et al., arXiv:0906.4378

32. High field region Assume a * to be insensitive to the magnetic field Then the lowest trimer state remains bound due to the large background scattering length Loss resonance expected for a m ≈ -6600 a 0 (B ≈ 880 G) Can we also observe Efimov states at large a? For a theoretical treatment, see: Braaten et al.: arXiv:0908.4046 (2009)

33. Preliminary results More quantitative results: J.R. Williams et al., arXiv:0908.0789 (2009), see also: Ken O‘Hara‘s talk!

34. While evidence for the existence of Efimov states in ultracold gases is compelling, they have not been directly observed One way would be to measure the binding energy as a function of the scattering length: Observe for example: Dimer + free atom + RF photon → trimer state To observe a logarithmic series of Efimov states, heteronuclear systems are very promising as the universal scaling factor is reduced. First results: Barontini et al., PRL 103 043201 (2009) Outlook

36. 3-body decay analyzed Determine 3-body decay coefficient: Density dependent loss leads to heating Density depends on temperature: Need to model numerically! Use code by T. Weber et al. (PRL 2003)

37. Naidon et al. (arXiv:0811.4086v1) numerically solve hyperspherical equations Schmidt et al. Phys. Rev. A 79, 053633 (2009) functional renormalization group theory Braaten et al. (arXiv:0811.3578v1) effective field theory Recent theory publications

38. Connection to Efimov‘s scenario Universal trimer states on a Feshbach resonance. In our case: scattering length does not go through infinity! 22.7 22.7 2 unstable decays into deeply bound dimer and free atom

39. Connection to Efimov‘s scenario Universal trimer states on a Feshbach resonance. In our case: scattering length does not go through infinity! 22.7 22.7 2 unstable decays into deeply bound dimer and free atom