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2009

A Universal Trimer in a Three-Component Fermi Gas

Wenz, A. N., Lompe, T., Ottenstein, T. B. et al.

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We show that the recently measured magnetic field dependence of three-body loss in a three-component mixture of ultracold $^6$Li atoms [1,2] can be explained by the presence of a universal trimer state.

Previous work suggested a universal trimer state as a probable explanation, yet failed to get good agreement between theory and experiment over the whole range of magnetic fields.
For our description we adapt the theory of Braaten and Hammer [3] for three identical bosons to the case of three distinguishable fermions by combining the three scattering lengths $a_{12},$ $a_{23}$ and $a_{13}$ between the three components to an effective interaction parameter $a_m$.
We show that taking into account a magnetic field variation of the lifetime of the trimer state is essential to obtain a complete understanding of the observed decay rates.

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J. von Stecher, J. P. D’Incao, and C. H. Greene, Nature Physics 5

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In the case of identical bosons or non-identical fermions with the same mass and similar scattering lengths s 0 = 1.00624 s_{0}=1.00624

Cited in the paper.

We use the term deep dimer for all non-universal two-body bound states. This means that their binding energy is ≳ ℏ / ( m r 0 2 ) \gtrsim\hbar/\left(m\,r_{0}^{2}\right) , where r 0 r_{0} is the range of the interaction potential

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From here on we assume to be in the low-energy ( k → 0 k\rightarrow 0 ) and zero-range ( r 0 → 0 r_{0}\rightarrow 0 ) limit

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P. S. Julienne (private communication), calculated using the model described in [ 29 ]

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The binding energies of the molecular states were calculated using formulas derived in [ 30 ]

Cited in the paper.