On the conversion efficiency of ultracold fermionic atoms to bosonic molecules via Feshbach resonances

TL;DR

This paper explains the fundamental limit of 50% efficiency in converting ultracold fermionic atoms to molecules via Feshbach resonances, linking it to the quantum state parity and collision dynamics.

Contribution

It introduces a many-body quantum state model showing how parity and collision rates influence conversion efficiency in ultracold Fermi gases.

Findings

Efficiency limited to 0.5 due to statistical mixture of spin states

Efficiency increases beyond 0.5 when the collision rate exceeds pair decorrelation rate

Parity considerations determine which atom pairs can form molecules

Abstract

We explain why the experimental efficiency observed in the conversion of ultracold Fermi gases of $^{40}$K and $^{6}$Li atoms into diatomic Bose gases is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow to pass adiabatically through the Landau Zener transition but faster than ``the collision rate'' in the gas, and increases beyond 0.5 when it is slower. The 0.5 efficiency limit is due to the preparation of a statistical mixture of two spin-states, required to enable s-wave scattering. By constructing the many-body state of the system we show that this preparation yields a mixture of even and odd parity pair-states, where only even parity can produce molecules. The odd parity spin-symmetric states must decorrelate before the constituent atoms can further Feshbach scatter thereby increasing the conversion efficiency; ``the collision rate'' is the pair decorrelation rate.