Nonlinear Adiabatic Passage from Fermion Atoms to Boson Molecules

We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction $\Gamma$ on the sweep rate $\alpha$ varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number $N$. The power law is linear, $\Gamma \propto \alpha$, when the initial molecular fraction is smaller than the $1/N$ quantum fluctuations, and $\Gamma \propto {\alpha }^{1/3}$ when it is larger. Experimental data agree well with a linear dependence, but do not conclusively rule out the Landau-Zener model.

Figure 1

Many-body collective dynamics of adiabatic passage from a fermionic atomic gas into a molecular BEC for five pairs of fermionic atoms. (a) Sweep rate $\alpha =2g^{2}N$. (b) Sweep rate $\alpha =g^{2}N/4$. Overall efficiency is independent of atomic dispersion in both (a) and (b).

Figure 2

Equal-energy contours of Hamiltonian (6) plotted as a function of $w$ and $\theta$ for different detunings $\delta$. $w=1$ is all atoms and $w=-1$ is all molecules. The various fixed points corresponding to adiabatic eigenvectors are marked by (blue) squares, (red) circles, and (black) stars.

Figure 3

Many-body calculations for the fraction of remnant atoms, $\Gamma$, versus dimensionless inverse sweep rate for various particle numbers in the range $N=2$ to 800. The many-body results for a large number of particles converge to the mean-field results (solid green line) of Fig. 4.

Figure 4

Fraction of remnant atoms, $\Gamma$, versus inverse ramp speed $1/\dot{B}$ across the 543 G resonance of ${}^6\mathrm{Li}$. The experimental data (black squares) of 2, which saturate at a remnant of $1/2$ [20], and the mean-field calculations obey a linear dependence on sweep rate beyond $0.5\mathrm{ms}/\mathrm{G}$. $\frac{g^2}{\alpha N}$ is multiplied by $0.5\mathrm{ms}/\mathrm{G}$ to scale the abscissa for the calculated results. Also shown as a dashed line is the best exponential fit to the data, $\Gamma =0.479\exp (-\alpha /1.3)+0.521$.