Radio-frequency dressing of multiple Feshbach resonances

We demonstrate and theoretically analyze the dressing of several proximate Feshbach resonances in ${}^{87}\text{R}\text{b}$ using radio-frequency (rf) radiation. We present accurate measurements and characterizations of the resonances, and the dramatic changes in scattering properties that can arise through the rf dressing. Our scattering theory analysis yields quantitative agreement with the experimental data. We also present a simple interpretation of our results in terms of rf-coupled bound states interacting with the collision threshold.

Figure 1

Schematic of rf-induced Feshbach resonances for the $M_F=0a+e$ entrance channel (black circles). At 9.1 G the $a+e$ channel is coupled by spin exchange to the $\left(cg\right)$ bound state (broad arrow). Seven other bound states are, in turn, coupled by rf induced magnetic dipole transitions (dashed arrows) to the $\left(cg\right)$ state. The rf photons, linearly polarized perpendicular to the magnetic field, can drive transitions with $\Delta M_F=\pm 1$. The inset shows the energies and labelings of the atomic Zeeman states of ${}^{87}\text{R}\text{b}$ at a small, nonzero magnetic field, along with the two-photon $a\leftrightarrow e$ transition. The energy splitting between hyperfine levels $f=1,2$ is not drawn to scale. The bound state labels are explained in the text.

Figure 2

Atom loss data from the $a+e$ entrance channel in the vicinity of the 9.1 G resonance with applied rf radiation. (a) For ${\nu }_1=6.0303\text{MHz}$ the rf dressing splits the undressed 9.1 G $a+e$ Feshbach resonance into two separated features as a result of an avoided crossing. (b) For ${\nu }_2=6.1343\text{MHz}$ the coupling of three bound states leads to two narrow features (arrows) in addition to the primary loss feature. The bound states $|\left(\gamma \delta \right),N^{\prime }⟩$ that contribute to the loss features are listed in the boxes within each panel.

Figure 3

(Color) Locations of experimental resonance features (solid points), and theoretical spin relaxation loss rate coefficient $K_2$ (pseudocolor intensity), for collisions in the $|a+e,N⟩$ entrance channel as a function of magnetic field and rf frequency. Dotted lines indicate where the bound state assignments $|\left(\gamma \delta \right),N^{\prime }⟩$ cross the $|a+e,N⟩$ threshold. Vertical lines labeled ${\nu }_{1,2}$ correspond to the loss profiles in Fig. 2. No data could be taken close to the region labeled “atomic Zeeman resonances,” where atomic transitions occur among several entrance channels.