Universal trimer states in a three-component Fermi gas. Selim Jochim Max-Planck-Institute for Nuclear Physics and Heidelberg University

Transcription

1 Universal trimer states in a three-component Fermi gas Selim Jochim Max-Planck-Institute for Nuclear Physics and Heidelberg University

2 A three-component mixture

3 Many different phases are expected A gas of fermionic trions

4 Many different phases are expected A color superfluid?

5 Outline 1. Universal few-body physics: The Efimov effect 2. Adapting the Efimov effect to fermions, understanding the few-body physics in a threecomponent Fermi gas 3. Our ideas of observing many-body physics in this system

6 The Efimov effect An infinite number of 3-body bound states exists when the scattering length diverges: (3 identical bosons) At infinite scattering length: E n = E n+1 Scattering length values where Efimov trimers become unbound a n+1 =22.7a n Drawing: V. Efimov Position of the series fixed by a three-body parameter, a * the infinite series is limited for small scattering lengths by the effective range, in alkali atoms ~ 10s of a 0

7 What is observed? three-body recombination deeply bound molecule

8 Enhanced recombination With an (Efimov) trimer at threshold recombination is enhanced: deeply bound molecule Drawing: V. Efimov Decay rate, width of Efmov state: Inelastic three-body parameter h *

9 What has been seen 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) An Efimov spectrum: Zaccanti et al., nature physics 5, 586 (2009) K-Rb-Efimov states Barontini et al., PRL (2009) 7 Li: particularly universal trimer Gross et al., arxiv: (2009)

10 Efimov physics with fermions Need three distinguishable fermions with (in general) different scattering lengths: 1 a 11 1 a 11 a 13 a 12 1 a a 23

11 How to obtain a three-component gas Cooling is performed on a two-component mixture of 6 Li (established technology) Mix all three states with RF fields RF 23 RF 12

12 Challenges to obtain three components 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: Two-component gas Three-component gas symmetry forbidden allowed

13 Prepare a stable mixture Feshbach resonances in 6 Li Prepare the mixture where all scattering lengths are small Current status: atoms in each state T/T F ~ 0.37 (mildly degenerate) zero crossings lifetime > 30 s near zero crossings M. Bartenstein et al., PRL 94, (2005) for a review, see: C. Chin et al., arxiv:

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

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

16 Inelastic rate vs. magnetic field Three-body coefficient: n K n 3 3 Similar experiments at: Penn State: J. Huckans et al., PRL 102, (2009), also at Tokyo University and MIT T. Ottenstein et al., PRL 101,

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

18 Decay of the trimer state The trimer decays rapidly into a dimer plus a free atom: What dimer does the trimer decay into? What s the rate?

19 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:

20 Vary η * with binding energy η * is determined by the lifetime of the trimer state Try to scale it as h const * 1 E B A. Wenz et al., arxiv:

21 High field region Can we also observe Efimov states at large a? 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 a 0 (B 880 G) continuum atom dimer thresholds trimer states what happens here? For a quantitative treatment, see: Braaten et al.: arxiv: (2009)

22 Preliminary results Expectation from low-field experiments Similar results at Penn State: J.R. Williams et al., arxiv: (2009)

23 High field region Can we also observe Efimov states at large a? 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 a 0 (B 880 G) continuum atom dimer thresholds trimer states what happens here? Braaten et al.: arxiv: (2009)

24 Preliminary results prepare a mixture of molecules (out of states 2> and 3>) and atoms (state 1>) theory prediction 1

25 Conclusion 1. We are able to create degenerate mixtures of three distinguishable fermions 2. Stability depends strongly on the magnetic field and is governed by Efimov physics. A generic three-component Fermi system with tunable interactions! Next steps: 1. Complete understanding of few-body physics 2. Observe many-body physics: color superfluid?

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