Novel Quantum Phases of Two-Component Bosons with Pair Hopping in Synthetic Dimension

We study two-component (or pseudospin-$1/2$) bosons with pair hopping interactions in synthetic dimension, for which a feasible experimental scheme on a square optical lattice is also presented. Previous studies have shown that two-component bosons with on-site interspecies interaction can only generate nontrivial interspecies paired superfluid (super-counter-fluidity or pair-superfluid) states. In contrast, apart from interspecies paired superfluid, we reveal two new phases by considering this additional pair hopping interaction. These novel phases are intraspecies paired superfluid (molecular superfluid) and an exotic noninteger Mott insulator which shows a noninteger atom number at each site for each species, but an integer for total atom number.

Figure 1

The relevant physical processes of time-dependent systems. ${\widehat{H}}_{\mathrm{Kin}}$ describes each spin hopping between the nearest neighbor site, ${\widehat{H}}_{\mathrm{rf}}(t)$ is relevant to radio-frequency coupling of the two spin states with periodic Rabi frequency $\mathrm{\Omega }(t)$, and ${\widehat{H}}_{\mathrm{U}}$ represents the on-site interactions.

Figure 2

This two-component boson system in a 1D chain can be mapped to a coupled two-spin chain with SPH interaction $W$. The green arrow indicates intraspecies normal hopping $J$, double both sides dashed arrow indicates SPH interaction $W$, on-site interactions are indicated by both sides dashed arrow.

Figure 3

The phase diagram of two species of Bose gases with SPH interaction in square optical lattice. The interaction parameters are $U_{\mathrm{aa}}^{\mathrm{eff}}=1.0$, $U_{\mathrm{bb}}^{\mathrm{eff}}=0.7$, $U_{\mathrm{ab}}^{\mathrm{eff}}=0.5$, and $W=-0.1$. There are five phases; moreover, the NMI is a new phase.

Figure 4

(a) The total particle number $n_a+n_b$, the number of spin-down (spin-up) components $n_a$ ($n_b$) as a function of chemical potential $\mu$ with $J=0$, 0.008, 0.016. (b) $n_a+n_b$ and $n_a$ and $n_b$ as functions of $W$ with $J=0.008$ and $\mu =2.0$; meanwhile the superfluid order parameter $⟨\widehat{a}\widehat{a}⟩$ and $⟨\widehat{b}⟩$ as a function of $W$ are also shown, where the pink (black) vertical axis represents the value of the superfluid order parameter (particle number). The interaction parameters are $U_{\mathrm{aa}}^{\mathrm{eff}}=1.0$, $U_{\mathrm{bb}}^{\mathrm{eff}}=0.7$, and $U_{\mathrm{ab}}^{\mathrm{eff}}=0.5$.