Effective control of cold collisions with radio-frequency fields

We study ${}^{87}\mathrm{Rb}$ cold collisions in a static magnetic field and a single-color radio-frequency (RF) field by employing the multichannel quantum defect theory in combination with the Floquet method to solve the two-body time-dependent Schrödinger equation. Our results show that RF fields can modify the two-body scattering length by a large scale through Feshbach resonances in both low- and high-static magnetic-field regimes. Such RF-induced Feshbach resonances can be applied to quenching experiments or control of interactions in spinor condensates. Here, we also show that, analogously to photoassociation, RF fields can also associate cold atoms into molecules at a useful rate.

Figure 1

Resonant interactions between RF fields and cold atoms. In the ultracold regime, collisions are always near channel thresholds as denoted by the dashed horizontal lines. The solid horizontal lines represent the weakly bound states of each channel. There are three major processes of RF-induced transition between ${}^{87}\mathrm{Rb}$ hyperfine levels: (i) free-free transitions in the asymptotic region, (ii) bound-free transitions in the Franck-Condon overlapping area, and (iii) bound-bound transitions in the Franck-Condon overlapping area and also at short distances.

Figure 2

(a) Resonance profile as a function of the magnetic field and the frequency of the RF field with amplitude $B_{\mathrm{RF}}=5$ G for scattering channel $|1,1\rangle +|1,1\rangle$ at $1\mu \mathrm{K}$. Thin red line: positions where the scattering length is nearly divergent. Thick blue line: positions where the scattering length vanishes. The avoided crossing indicates an RF-induced transition between two bound states. (b) The real part of the scattering length as a function of the magnetic field at $\nu =745$ MHz, as shown by the vertical line in (a). For comparison, the dashed line shows the results without RF fields. (c) The real part of the scattering length as a function of the RF frequency at $B=1009.2$ MHz, as shown by the horizontal line in (a).

Figure 3

Tuning Feshbach resonances with the RF amplitude and the static magnetic-field strength. All collisions are from the $|1,-1\rangle +|1,-1\rangle$ channel at 1 $\mu \mathrm{K}$. (a) The tunability of the scattering lengths $\mathrm{\Delta }a$ (thin red line) and the inelastic width ${\mathrm{\Gamma }}_{\mathrm{in}}$ (thick blue line) as a function of the RF amplitude square in a static magnetic field, $B=6$ G. The dashed blue line indicates a linear fitting of ${\mathrm{\Gamma }}_{\mathrm{in}}$ at a low RF amplitude. (b) The tunability of scattering lengths and the inelastic width as a function of the magnetic-field strength with a fixed RF amplitude $B_{\mathrm{RF}}=5$ G.

Figure 4

RF association rate for collisions between $|1,1\rangle$ states in the BEC regime as a function of the collision energy for various RF amplitudes: $B_{\mathrm{RF}}=4.99$ G (dotted red line), 5.00 G (dashed green line), and 5.01 G (solid blue line) at $\nu =6841.59$ MHz and $B=15$ G.