Controlling Correlated Tunneling and Superexchange Interactions with ac-Driven Optical Lattices

The dynamical control of tunneling processes of single particles plays a major role in science ranging from Shapiro steps in Josephson junctions to the control of chemical reactions via light in molecules. Here we show how such control can be extended to the regime of correlated tunneling of strongly interacting particles. Through a periodic modulation of a biased tunnel contact, we have been able to coherently control single-particle and correlated two-particle hopping processes. We have furthermore been able to extend this control to superexchange spin interactions in the presence of a magnetic-field gradient. Such photon-assisted superexchange processes constitute a novel approach to realize arbitrary $XXZ$ spin models in ultracold quantum gases, where transverse and Ising-type spin couplings can be fully controlled in magnitude and sign.

Figure 1

(a) Schematics of the superlattice potential created by overlapping the short (dashed line) and the long lattice (solid line) with relative phase $\varphi$. A periodic modulation of the long lattice (gray shaded area) is used to resonantly drive different tunneling processes, e.g., single-atom tunneling (b) or effective superexchange (c).

Figure 2

Fraction of atoms transferred to the right well $n_{R\sigma }$ as a function of the driving frequency $\omega /2\pi$ with fixed modulation time $T=2.5\mathrm{ms}$ and driving amplitude $\delta V=8.2(3)E_r^{xl}$ [24]. The lattice parameters given in the figure correspond to a tilt $\Delta /h=4.3(2)\mathrm{kHz}$. Single atoms (black circles) are resonantly transferred for $\omega /2\pi =5.2(1)\mathrm{kHz}$ (gray vertical line), in agreement with ${\Delta }^{\prime }=h\times 5.0(2)\mathrm{kHz}$, where the value $J/h=1.30(5)\mathrm{kHz}$ was obtained from independently measured single-particle tunnel oscillations in undriven symmetric double wells. In the case of atom pairs (blue circles), this resonance is shifted to $\omega /2\pi =3.9(1)\mathrm{kHz}$ due to interactions. In both cases, the resonance around $\omega /2\pi =7.5\mathrm{kHz}$ can be attributed to a two-photon transfer to the third Bloch band. Finally, the resonance for atom pairs at $\omega /2\pi =10.8(2)\mathrm{kHz}\simeq 2{\Delta }^{\prime }/h$ corresponds to the directly driven cotunneling of the pair. Inset: Time evolution of $n_{R0}(T)$ for the single-particle resonance measured with $\delta V=16.4(5)E_r^{xl}$, together with a fit using a damped sine wave. The Rabi frequency provides the coupling $K/h=153(10)\mathrm{Hz}$, in reasonable agreement with the value of 166(10) Hz obtained from a single-particle band structure calculation.

Figure 3

(a) Sketch of the resonantly driven superexchange coupling via four possible intermediate states with different detunings $U\pm \Delta \pm G$, reached either by bare ($J$, solid arrows) or driven tunneling ($K$, dashed arrows). (b) Fraction of atoms $n_{R\uparrow ,\downarrow }$ in the right well as a function of the modulation frequency $\omega /2\pi$. The lattice parameters were $V_z=192(6)E_r^z$, $V_y=142(5)E_r^y$, $V_{xl}^0=35(1)E_r^{xl}$, $V_{xs}=7.0(2)E_r^{xs}$, $\varphi =0.35(1)\mathrm{rad}$, and $G/h=1.2(1)\mathrm{kHz}$. The simultaneous transfer of both spins for $\omega /2\pi \simeq 2.6\mathrm{kHz}$ (gray line) corresponds to a single-photon-driven superexchange, while the one for $\omega /2\pi \simeq 1.5\mathrm{kHz}$ is driven by the absorption of two photons. (c) Time evolution of the mean population imbalance $X(t)$ and spin imbalance $N^z(t)$ at the superexchange resonance $\omega /2\pi =2.6\mathrm{kHz}$, fitted with a damped sine (solid line). The fit yields a superexchange coupling of $J_{\mathrm{ex}}^{\perp }/h=0.56(2)\mathrm{kHz}$ and a damping time ($1/e$) of $\tau =9(1)\mathrm{ms}$.

Figure 4

Strength of the driven superexchange interaction $|J_{\mathrm{ex}}^{\perp }|$ as a function of $\Delta$. The lattice parameters were the same as in Fig. 3c, except for $V_{xs}=10(2)E_r^{xs}$ and $V_z=120(4)E_r^z$. The measured values (circles) are compared to second-order perturbation theory (dotted line) and a numerical calculation including the five lowest Bloch bands (solid line). The error bars represent the standard deviation of the Rabi frequency as obtained by a damped sine-wave fit.