Feshbach modulation spectroscopy of the Fermi-Hubbard model

In the vicinity of a Feshbach resonance, a system of ultracold atoms in an optical lattice undergoes rich physical transformations which involve molecule formation and hopping of molecules on the lattice and thus goes beyond a single-band Hubbard model description. We explore theoretically the response of this system to a harmonic modulation of the magnetic field, and thus of the scattering length, across the Feshbach resonance. In the regime in which the single-band Hubbard model is still valid, we provide results for the doublon production as a function of the various parameters, such as frequency, amplitude, etc., that characterize the field modulation, as well as the lattice depth. The method may uncover a route towards the efficient creation of ultracold molecules and also provide an alternative to conventional lattice-depth-modulation spectroscopy.

Figure 1

$ab$ Feshbach resonances of the system ${}^{40}\mathrm{K}$ for different lattice depths. The upper panel (a) shows the dependence of the interaction on the magnetic field and the lower panel (b) shows the resulting normalized hopping $j=J_0/U\left(B\right)$.

Figure 2

Doublon production at different values of $B_{\text{max}}$. Each panel represents different values of $V$ and $B_{\text{min}}$. In panels (a), (c), (d), and (e), $B_{\text{min}}$ is chosen such that $j_{\text{max}}=1/24$. The initial temperature is $k_{B}T=0.1U_0$.

Figure 3

Magnetic modulation with the normalized hopping $j$ oscillating within the interval $[j_{\text{min}},j_{\text{max}}]$, with $j_{\text{max}}=1/24$ and $j_{\text{min}}=j_{\text{max}}/2$ for different lattice depths. The corresponding magnetic field intervals $I_B=[B_{\text{min}},B_{\text{max}}]$ are $I_B(V=10E_R)=[212.9G,219.56G], I_B(V=11E_R)=[212.0G,215.52G], I_B(V=12E_R)=[211.4G,213.59G], I_B(V=15E_R)=[210.55G,211.32G]$.