Enhancement of on-site interactions of tunneling ultracold atoms in optical potentials using radio-frequency dressing

We show how it is possible to more than double the on-site interaction energy of neutral atoms in optical potentials by the technique of radio-frequency (rf) dressing, while maintaining interwell dynamics. We calculate Bose-Hubbard parameters for rf-dressed optical lattices and arrays of rf-dressed dipole traps. We show that decreasing the distance between wells, by the interpolation of wells confining different $m_F$ states, increases the interaction energy more than decreasing the height of the classically forbidden region between existing wells. The schemes we propose have negligible Landau-Zener losses caused by atomic motion; this was a dominant effect in the first experimental demonstration of the modification of an optical potential by radio-frequency dressing.

Figure 1

(Color online) The types of rf-dressed potentials considered in this paper. Dressed potentials are solid black lines; undressed potentials are dashed lines [$m_F=+1$ and $-1$ (green and red dashed lines), 0 (blue dash-dotted lines)]. The Wannier functions for the lowest state are displayed below the potentials for two of the wells. The $m_F=+1$ state of (a) is at an energy substantially higher than the states shown. The optical lattices of (a) and (b) have ${\sigma }^{+}$ polarization. The recoil energy is defined as $E_r=h^2∕2m{\lambda }^2$. Parameters: (a) $\lambda =790.06\mathrm{nm}$, $B_0=300\mathrm{G}$, ${\nu }_{\mathit{rf}}=213.65\mathrm{MHz}$, ${\Omega }_{\mathit{rf}}∕2\pi =70\mathrm{kHz}$, $P=32\mathrm{mW}$, $w_0=50\mu \mathrm{m}$, ${\nu }_{\perp 1,2}=30\mathrm{kHz}$; (b) $\lambda =790.06\mathrm{nm}$, $B_0=4\mathrm{G}$, ${\nu }_{\mathit{rf}}=3.295\mathrm{MHz}$, ${\Omega }_{\mathit{rf}}∕2\pi =270\mathrm{kHz}$, $P=35\mathrm{mW}$, $w_0=50\mu \mathrm{m}$, ${\nu }_{\perp 1,2}=30\mathrm{kHz}$; (c) $\lambda =800\mathrm{nm}$, $B_0=4\mathrm{G}$, ${\nu }_{\mathit{rf}}=2.78\mathrm{MHz}$, ${\Omega }_{\mathit{rf}}∕2\pi =25\mathrm{kHz}$, $P=25\mu \mathrm{W}$, $w_0=1\mu \mathrm{m}$, ${\nu }_{\perp 1,2}=30\mathrm{kHz}$, $\Delta x=0.6w_0$.

Figure 2

(Color online) Calculated properties of atoms in the ground state of the dressed potentials. The optical power $P$ is the independent variable; dressing parameters ${\nu }_{\mathit{rf}}$ and ${\Omega }_{\mathit{rf}}$ are chosen subject to the conditions that the neighboring wells are the same depth and that the tunneling parameter $J∕h$ is $25\mathrm{Hz}$. These conditions specify ${\nu }_{\mathit{rf}}$ and ${\Omega }_{\mathit{rf}}$ for (b) and (c). For (a) the conditions only specify ${\nu }_{\mathit{rf}}$, so ${\Omega }_{\mathit{rf}}$ can be chosen arbitrarily; two choices are shown. The dashed horizontal line gives the undressed $U$ for comparison, a single value calculated for $J∕h=25\mathrm{Hz}$ in the undressed ${\sigma }^{+}$ or ${\sigma }^{-}$ potential. The scattering rates are from the dressed lattice beams only. Aside from $P$, ${\nu }_{\mathit{rf}}$, and ${\Omega }_{\mathit{rf}}$, the parameters of the potentials are as given in Fig. 1.