Ramsey Fringes in a Bose-Einstein Condensate between Atoms and Molecules

In a recent experiment, a Feshbach scattering resonance was exploited to observe Ramsey fringes in a ${}^{\mathrm{85}}\mathrm{R}\mathrm{b}$ Bose-Einstein condensate. The oscillation frequency corresponded to the binding energy of the molecular state. We show that the observations are remarkably consistent with predictions of a resonance field theory in which the fringes arise from oscillations between atoms and molecules.

Figure 1

Binding energies as a function of magnetic field. The solid line is the coupled channels result for the most accurate rubidium interactions. This is compared with the binding energy resulting from the contact scattering model as defined in 8, with $a_{\mathrm{b}\mathrm{g}}=-450a_0$ (where $a_0$ is the Bohr radius), $\Delta \mu =-2.23{\mu }_B$ (with ${\mu }_B$ the Bohr magneton), and $g_0=3.11\times {10}^{-38}\mathrm{J}{\mathrm{m}}^{3/2}$ (open squares).

Figure 2

A typical magnetic field pulse sequence as a function of time. The interval $t_{\mathrm{e}\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{v}\mathrm{e}}$ is modified in the experiment. The position of the resonance is indicated by the dashed line.

Figure 3

Fraction of the atomic condensate as a function of time. We identify these atoms as the remnant of Donley et al. [3]. The calculation is done for the pulse sequence given in Fig. 2, for a density $n=3.9\times {10}^{12}{\mathrm{c}\mathrm{m}}^{-3}$. The inset shows the analogous graph for the molecular condensate.

Figure 4

Normal field $G_N(r)$ as a function of time and distance for the same calculation illustrated in Fig. 3. We identify these atoms as the burst atoms of Donley et al. [3]. The spread in $r$ space is a measure of the energy of these noncondensate atoms.

Figure 5

Oscillations between the atomic condensate (solid line) and the normal field $G_N(0)$ (dashed line). These two numbers add up to the total number of recovered atoms (squares), which excludes the molecular component. The calculation is performed for a mean density of $⟨n⟩=3.9\times {10}^{12}{\mathrm{c}\mathrm{m}}^{-3}$.