Recombination of Three Ultracold Fermionic Atoms

Abstract

Three-body recombination of identical, spin-polarized fermionic atoms in the ultracold limit is investigated. The mechanisms for recombination are described in terms of the "scattering volume" Vp in the framework of the adiabatic hyperspherical representation. We have calculated numerically the recombination rate K3 as a function of Vp and have found that K3 scales as |Vp| 8/3 for small |Vp|. A comparison with experimental data is also presented.PACS numbers: 34.10.+x,03.75.Fi Recently, the quantum degenerate regime was attained in ultracold gases of fermionic atoms such as 40 K [1] and 6 Li [2,3]. Part of the motivation for these experiments is to observe a pairing of fermions, leading to a superfluid state. One important factor limiting the achievable density in these degenerate Fermi gases (DFG's) of trapped atoms is the loss of atoms through three-body recombination. Such losses occur when three atoms scatter to form a molecular bound state and a third atom -K + K + K → K 2 + K, for instance. The kinetic energy of the final state particles causes them to escape from the trapping potential.While ultracold three-body recombination of identical, spin-polarized bosons has been theoretically studied because of its importance for Bose-Einstein condensates, recombination of identical fermions has not yet been considered. For bosons, Fedichev et al. [4] predicted that the recombination rate K 3 grows with the two-body s-wave scattering length a s , namely K 3 ∝ a 4 s , for a s > 0. This scaling was later confirmed by Nielsen and Macek [5] who also pointed out that it should hold for negative a s . The a 4 s scaling law for both signs of a s was indeed obtained by Esry et al. [6], Bedaque et al. [7], and Braaten and Hammer [8].In the case of fermions, however, the Pauli exclusion principle prohibits s-wave scattering of atoms in identical spin states, thus leaving only p-wave collisions. The relevant low-energy scattering parameter in this case is the two-body p-wave "scattering volume" defined aswhere δ p (k) is the p-wave scattering phase shift and k is the wave number. The scattering volume V p is related to the p-wave scattering length a p (see, for instance, Ref.[9]) by V p = a 3 p . We choose V p , rather than a p , as the parameter to characterize the three-body recombination of fermions since an artificial nonanalyticity is introduced into a p when taking the cube root of the quantity in the right-hand side of Eq. (1).Even though recombination of identical fermions is suppressed at ultracold temperatures by the Pauli principle, it does not vanish. In fact, it has been shown that the rate is proportional to E 2 at low collision energies [12]. While this rate remains negligible under typical experimental conditions, it can become substantial near a Feshbach resonance. The E 2 threshold law no longer applies, and the recombination rate tends to the limit imposed by unitarity -often comparable to or larger than the rates for boson systems. Feshbach resonances are, of course, extremely useful tools for the expe...

Adiabatic hyperspherical study of triatomic helium systems

“…If needed, the thermal average can be carried out as described in Ref. [49] for K 3 or as described in Ref. [50] for two-body processes.…”

Effective interactions, Fermi–Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides

“…is the odd-wave one-dimensional scattering length, V p = a 3 p = − lim k→0 tan δ p (k)/k 3 is the p-wave "scattering volume" [31], a p is the p-wave scattering length, and ζ(−1/2, 1) = −ζ(3/2)/4π = −0.2079 . .…”

Universal Three-Body Physics for Fermionic Dipoles

“…For short-range, nondipolar interactions, the coefficient C 3 in recombination rate is expected to scale with the scattering volume [9,10] and the effective range [10]. For dipolar interactions, however, the scattering physics is fundamentally different even in the two-body level [17].…”

“…In contrast to bosonic gases whose lifetime is mainly determined by three-body recombination [8], fermionic gases exhibit extraordinary stability against three-body inelastic collisions except when the two-body interaction is tuned near a p-wave resonance [9,10]. Moreover, threebody physics for identical fermions is expected to be nonuniversal, i.e., short-range-dependent [9,11]. Consequently, three-body physics for identical fermions has to some extent been regarded as less exciting and/or difficult to observe.…”