EGAS41 - Swansea University

41 st EGAS CP 177 Gdańsk 2009
Feshbach resonances and cold collisions between two alkali
atoms
M. Lysebo ∗ , L. Veseth
Department of physics, University of Oslo, P.O. Box 1048 Blindern, NO-0316 Oslo Norway
∗ Corresponding author: marius.lysebo@fys.uio.no,
Feshbach resonances [1], named after Herman Feshbach, have become very important in
ultracold atomic and molecular physics the last ten years. Feshbach resonances are an
important ingredient in the ongoing exploration of these systems and in the tremendous
progress made after the first successful creation of a Fermi gas [2].
The attractive properties of these systems stems from the possibility of tuning the
interatomic interaction by varying the magnetic field around a Feshbach resonance. The
scattering length is the important parameter which characterizes the atom-atom interaction
in ultracold gases [3] (together with the Pauli principle). The scattering length
behaves in a peculiar way as one pass through a Feshbach resonance - it diverges and
changes sign (see e.g. figure 1). This makes it possible for the experimentalists to attain
full control of the interactions by varying the magnetic field strength. Many systems have
Feshbach resonances that are accessible through relatively low magnetic field strengths.
a s
[a 0
]
600
400
200
0
−200
−400
−600
544 544.5 545 545.5 546
B[G]
Figure 1: Scattering length a s vs. magnetic field showing a narrow Feshbach resonance.
We present a model applicable to cold diatomic collisions and solve the close-coupled
equations for the particular 6 Li 2 and K 2 systems. The calculations are performed ab initio
with the matrix elements for the relevant interactions written in the molecular Hund’s
case (a) basis. The s-wave scattering length is reported for magnetic field strengths
between 0-1000 G for a range of different hyperfine states in both systems. Several
Feshbach resonances, of different widths and characters, are found in both 6 Li 2 and K 2 .
The calculated resonance positions agree very well with the observed resonance positions
for 6 Li 2 [4] and K 2 [5].
In addition, the short range hyperfine interaction has been included in the calculations,
and its effect on the scattering length investigated. Molecular hyperfine parameters were
obtained from separate ab initio calculations.
References
[1] H. Feshbach, Ann. Phys. (N.Y.) 5, 357 (1958)
[2] B. DeMarco, D.S. Jin, Science 285, 1703 (1999)
[3] E. Tiesinga, B.J. Verhaar, H.T.C. Stoof, Phys. Rev. A 47, 4114 (1993)
[4] C.H. Schunck, M.W. Zwierlein, C.A. Stan, S.M.F. Raupach, W. Ketterle, A. Simoni,
E. Tiesinga, C.J. Williams, P.S. Julienne, Phys. Rev. A 71, 045601 (2005)
[5] C. D’Errico, M. Zaccanti, M. Fattori, G. Roati, M. Ignuscio, G. Modugno, A. Simoni,
New Journal of Physics, 9, 223 (2007)
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