Detection of pair-superfluidity for bosonic mixtures in optical lattices

We consider a mixture of two bosonic species with tunable interspecies interaction in a periodic potential and discuss the advantages of low filling factors on the detection of the pair-superfluid phase. We show how the emergence of such a phase can be put dramatically into evidence by looking at the interference pictures and density correlations after expansion and by changing the interspecies interaction from attractive to repulsive.

Figure 1

Phase diagram for (top) $N_w=4$ and (bottom) $N_w=6$ and $N=2$. (a, d) Single-particle coherence $N_w\left|{\mathcal{V}}_{2\mathit{SF}}\right|$, as defined in Eq. (2); (b, e) pair-coherence $N_w\left|{\mathcal{V}}_{\mathrm{PSF}}\right|$, as defined in Eq. (3); (c, f) counterpair-coherence $N_w\left|{\mathcal{V}}_{\mathrm{SCF}}\right|$, as defined in Eq. (4). The factor $N_w$ allows a better comparison between the two different lattice sizes. The region of parameters of strong attractive interaction $U_{\mathit{ab}}\lesssim -U$ corresponds to collapse in a large system.

Figure 2

Two-body momentum distribution $n^{(a,b)}(q_a,q_b)$ for $N=2$ and $N_w=4,6$, i.e., filling factor (top) $1/2$ and (bottom) $1/3$. (a, d) Repulsive interparticle interaction $U_{\mathit{ab}}=0.5U$; (b, e) vanishing interparticle interaction $U_{\mathit{ab}}=0$; (c, f) attractive interparticle interaction $U_{\mathit{ab}}=-0.5U$. In all pictures, $J=0.01U.$ Two Brillouin zones are shown for clarity.

Figure 3

Single species momentum distribution $n^{(\sigma )}(q_{\sigma })$ for $N=2$ and $N_w=4,6$, i.e., filling factor (top) $1/2$ and (bottom) $1/3$. (a, d) Repulsive interparticle interaction $U_{\mathit{ab}}=0.5U$; (b, e) vanishing interparticle interaction $U_{\mathit{ab}}=0$; (c, f) attractive interparticle interaction $U_{\mathit{ab}}=-0.5U$. In all pictures, $J=0.01U$. Two Brillouin zones are shown for clarity.

Figure 4

Effect of attractive interspecies interaction $U_{\mathit{ab}}$ on the expansion. (a, c) Two-body density after expansion after a time of flight $E_r{t}_{\mathrm{TOF}}\approx 12$, where $E_r$ is the recoil energy, in the presence of interspecies interaction $U_{\mathit{ab}}$; (b, d) free expansion at the same time of flight (shown for comparison). The strengths of interaction are $\left|U_{\mathit{ab}}\right|/J\approx 20$ in (a, b) and $\left|U_{\mathit{ab}}\right|/J\approx 60$ in (c, d), respectively.