Figure 1

Theory of Feshbach resonances. (a) Molecular potentials involved in a Feshbach resonance. Potential A corresponds to the entrance channel and potential B to a closed channel of the scattering process. Potential B supports a bound state (solid straight line), to which the incoming wave function can couple. The energy of an incoming pair of cold atoms is very close to the dissociation threshold (dotted line). For $\Delta E\to 0$, the population of the bound state is resonantly enhanced. (b) Creation of cold molecules using a Feshbach resonance. The energy of the dissociation threshold and the molecular bound state are shown as a function of magnetic field (solid lines). An atomic BEC can be converted into molecules using an adiabatic rapid passage. The experiment uses a negative ramp speed ($dB/dt<0$), as indicated by the arrow. For positive ramp speed, the existence of noncondensate states of atom pairs (dotted lines) would prevent the buildup of a large molecular fraction.Reuse & Permissions

Figure 2

(a) Image of two atomic clouds. The right cloud was temporarily converted into molecules. A Stern-Gerlach field was applied to separate the molecules (right) from the remaining atoms (left). The molecules were converted back into atoms for imaging. The size of the image is $1.3\times 0.34\mathrm{m}\mathrm{m}$. (b) Reference image without application of the Stern-Gerlach field.Reuse & Permissions

Figure 3

Avoided crossing. (a) Energy as a function of magnetic field. The binding energy of the highest-lying bound state in potential A with respect to the dissociation threshold in potential A is $h\times 24\mathrm{M}\mathrm{H}\mathrm{z}$, independent of the magnetic field. The bound state supported by potential B crosses both these energies. The highest-lying bound state is crossed at 1001.7 G, leading to an avoided crossing. The dissociation threshold is crossed at 1007.4 G creating the Feshbach resonance. The energy splitting in the avoided crossing at 1001.7 G is 13 MHz and therefore much larger than the splitting of the Feshbach resonance crossing, which is not visible on this scale. (b) Derivative $dE/dB$ of the upper branch of the avoided crossing. Experimental data for the molecules (circles) extracted from images, such as Fig. 2a, are compared with the theory (solid line) that contains no free fit parameters.Reuse & Permissions

Figure 4

Oscillation of molecules. According to Fig. 3, the molecules are 1001.7-G seekers. With a magnetic field gradient applied in the horizontal direction, the molecules oscillate around a point in space where the magnetic field equals 1001.7 G. The images were recorded for a series of different durations of the Stern-Gerlach field, ranging from 0 to 18 ms (top to bottom). The observed oscillation frequency of 56 Hz agrees well with theory. The anisotropic expansion of the molecular cloud is due to the fact that the one-dimensional trapping potential prevents the cloud from expanding in the horizontal direction. The atomic cloud (top left) is simply accelerated on a parabola. The size of each image is $1.7\times 0.24\mathrm{m}\mathrm{m}$.Reuse & Permissions