Combination of a magnetic Feshbach resonance and an optical bound-to-bound transition

We use laser light near resonant with an optical bound-to-bound transition to shift the magnetic field at which a Feshbach resonance occurs. We operate in a regime of large detuning and large laser intensity. This reduces the light-induced atom-loss rate by 1 order of magnitude compared to our previous experiments [D. M. Bauer et al., Nat. Phys. 5, 339 (2009)]. The experiments are performed in an optical lattice and include high-resolution spectroscopy of excited molecular states reported here. In addition, we give a detailed account of a theoretical model that describes our experimental data.

Figure 1

Level scheme. Pairs of atoms, each in state $|a⟩$, are coupled to a dimer state $|g⟩$ belonging to the electronic ground state. This coupling has a strength $\alpha$ and causes a magnetic Feshbach resonance. Laser light is applied to drive a bound-to-bound transition from state $|g⟩$ to an electronically excited dimer state $|e⟩$ with Rabi frequency ${\Omega }_R$. This causes an ac Stark shift (not shown) of state $|g⟩$ which leads to a shift of the magnetic field at which the Feshbach resonance occurs. Typically, the same light can also drive photoassociation from state $|a⟩\otimes |a⟩$ to state $|e⟩$ with coupling strength $\beta$. The photoassociation is a nuisance for the scheme used here. The light frequency is typically somewhat detuned from both transitions.

Figure 2

(Color online) Predictions for $\text{Re}\left(a\right)/a_{\text{bg}}$ and $K_2$ as a function of $B$ from Eqs. (16, 18). For all curves, we choose $\hslash {\gamma }_e/{\mu }_{ae}=2\text{G}$, $\beta =0$, and $\Delta B=0.2\text{G}$, with $\Delta B$ defined in Eq. (20). The dotted lines (red) are for resonant laser light ${\Delta }_L=0$ and $\hslash {\left|{\Omega }_R\right|}^2/{\gamma }_e{\mu }_{ag}=100\text{G}$. They show two resonances that are symmetrically split around $B_{\text{pole}}$. These resonances represent an Autler-Townes doublet. The solid lines (blue) are for large laser detuning ${\Delta }_L/{\gamma }_e=5$ and $\hslash {\left|{\Omega }_R\right|}^2/{\gamma }_e{\mu }_{ag}=100\text{G}$. They also show two resonances, but their heights, widths, and distances from $B_{\text{pole}}$ are quite different. The dashed line (black) is a reference without any light ${\Omega }_R=0$.

Figure 3

(Color online) Excited-state spectroscopy for ${}^{87}\text{R}\text{b}$. (a) Photoassociation spectrum taken at $B=1000.0\text{G}$. (b) Bound-to-bound spectrum taken at $B=1000.0\text{G}$. Arrows indicate the resonances characterized in Table .

Figure 4

(Color online) Shifting the Feshbach resonance with laser light. (a) Elastic and (b) inelastic two-body scattering properties are shown as a function of magnetic field $B$. Experimental data in the presence (●) and absence (○) of the light are compared. The light power is 11.2 mW and the frequency is ${\omega }_L/2\pi =382048158\text{MHz}$, which is 576 MHz blue detuned from the nearest bound-to-bound transition. The solid lines in (a) and (b) show fits of Eqs. (19, 24b), respectively, to the data. The Feshbach resonance is shifted by $\sim -0.35\text{G}$. At $B=1006.91\text{G}$, we measure $\text{Re}\left(a\right)/a_{\text{bg}}-1\sim 1$ and $K_2\sim 1\times {10}^{-12}{\text{cm}}^3/\text{s}$.

Figure 5

(Color online) Systematic study of the loss resonances. $K_2\left(B\right)$ was measured for certain values of the laser frequency at a fixed laser power of 0.47 mW. (a) The maximum $K_2^{\text{max}}$ and (b) the width $W$ were determined from a fit to Eq. (24b). The experimental data for the resonances that occur at the lower (○) and higher (●) values of $B$ both agree well with the predictions of the full model [Eq. (18)] (solid lines) which is well approximated by Eqs. (35, 38) (dotted lines).