Density-Dependent Synthetic Gauge Fields Using Periodically Modulated Interactions

We show that density-dependent synthetic gauge fields may be engineered by combining periodically modulated interactions and Raman-assisted hopping in spin-dependent optical lattices. These fields lead to a density-dependent shift of the momentum distribution, may induce superfluid-to-Mott insulator transitions, and strongly modify correlations in the superfluid regime. We show that the interplay between the created gauge field and the broken sublattice symmetry results, as well, in an intriguing behavior at vanishing interactions, characterized by the appearance of a fractional Mott insulator.

Figure 1

Scheme of the $AB$ set up: (a) for $0<t<T/2$ Raman assisted hopping couples an $A$ site with the $B$ site at their right; for $T/2<t<T$, it couples an $A$ site with the $B$ site at their left; (b) the $U_{A1}(t)$ function is $\sin ({\omega }_{AB}t)$ for $0<t<T/2$ and $-\sin ({\omega }_{AB}t)$ for $T/2<t<T$, with ${\omega }_{AB}=4\pi /T$.

Figure 2

(a) Ground-state quasimomentum distribution for model (2) for a homogeneous distribution in 24 sites with ${\mathrm{\Omega }}_{AB}=\pi /4$, $U=0.2J$, and a density $⟨\widehat{n}⟩$; (b) same for a harmonically trapped gas as a function of $V_T$ (see text) for ${\mathrm{\Omega }}_{AB}=\pi /4$, $U=J$, and 24 particles in 24 sites. Both figures show density-matrix renormalization group (DMRG) [48] results with 500 states, and a maximal occupation per site $n_{\text{max}}=10$.

Figure 3

Mott phases at half-integer and integer fillings of model (2). (a) MI lobes for ${\mathrm{\Omega }}_{AB}=\pi /2$, $\mathrm{\Phi }=\pi$. (b) Varying the relative phase $\mathrm{\Phi }$ may induce phase transitions in the ground state. Here, we choose ${\mathrm{\Omega }}_{AB}=\pi /2$ and change $\mathrm{\Phi }$ [46] for $J/U=2$ (dashed lines indicate a closing gap). (c) Lines of constant density and MI phase at half-filling for vanishing on-site interactions $U=0$. In the DMRG-calculation system size $L$ and maximal occupation number of bosons per site $n_{\text{max}}$ have been scaled carefully (up to $n_{\text{max}}=12$ and $L=144$ sites) till a convergence was reached.

Figure 4

Behavior of the Luttinger parameter $K$ as a function of ${\mathrm{\Omega }}_{AB}$ for $U=J/2$ for ${\rho }_0=1.75$ (upper curves) and ${\rho }_0=0.75$ (lower curves). Dashed lines indicate the analytical estimation (5) in the weakly interacting regime, whereas the circles denote our results obtained from DMRG calculations of the single-particle correlation function.

Figure 5

Quasimomentum $k_{\text{max}}$ at which the quasimomentum distribution of the $B$ sublattice is maximal as a function of ${\mathrm{\Omega }}_{AB}⟨\widehat{n}⟩$ for $\omega =20J$ and $U=J$. Solid (dashed) lines denote the results obtained from the effective model (2) with $⟨\widehat{n}⟩=3/2$ (1). The error bars denote the uncertainty (time average and standard deviation for $200<t/T<400$) of $k_{\text{max}}(t)$ for the case of a linear ramp of ${\tilde{U}}_{A1}$ with a ramp time of $\tau =200T$ (see text). Inset: Solid and dashed-dotted lines show $k_{\text{max}}(t)$ for $⟨\widehat{n}⟩=3/2$ with ${\mathrm{\Omega }}_{AB}=0.4$ and 0.8, whereas the dotted line indicates the value of $k_{\text{max}}$ for the effective model (2). We depict, with a dashed line, the ramp ${\tilde{U}}_{A1}(t)$.