Stabilization of the $p$-Wave Superfluid State in an Optical Lattice

It is hard to stabilize the $p$-wave superfluid state of cold atomic gas in free space due to inelastic collisional losses. We consider the $p$-wave Feshbach resonance in an optical lattice, and show that it is possible to have a stable $p$-wave superfluid state where the multiatom collisional loss is suppressed through the quantum Zeno effect. We derive the effective Hamiltonian for this system, and calculate its phase diagram in a one-dimensional optical lattice. The results show rich phase transitions between the $p$-wave superfluid state and different types of insulator states induced either by interaction or by dissipation.

Figure 1

Illustration of the dissipation-induced blockade for multiple occupation (more than two) of a single lattice site. Similar to a two-level transition with a detuning ${\Delta }_3$ and a decay rate $\gamma$ for the target level, the effective loss rate of the system is suppressed by a factor $t^2/({\gamma }^2+{\Delta }_3^2)$, where $t$ is the atomic tunneling rate.

Figure 2

Illustration of different atomic hopping processes over the two neighboring sites described by the Hamiltonian (1), where each site has only three possible level configurations.

Figure 3

The dressed molecule number ${\overline{n}}_b$ (the double occupation probability) and the atom number ${\overline{n}}_a$ (the single occupation probability) shown as the function of $\Delta /t$ (with a fixed $\mu /t=-0.5$) in (a) and $\mu /t$ (with a fixed $\Delta /t=-1.5$) in (b). The nonanalyticities of these curves signal a number of quantum phase transitions from the DII state, to a PS state, to a MI state, to a NM, and finally to a NFG phase.

Figure 4

The correlation functions shown for the $p$-wave superfluid phase [(a) and (b)], the Mott insulator phase [(c) and (d)], and the normal mixture phase [(e) and (f)]. Figures (a),(c), and (e) show in $k$ space the Fourier transform $P_k$ of the pair correlation $⟨b_i^{†}{b}_j⟩$. Figures (b),(d), and (f) show the charge density correlations of $⟨n_{bi}{n}_{bj}⟩$, $⟨n_{bi}{n}_{aj}⟩$ and $⟨n_{ai}{n}_{aj}⟩$ in real space. We take $\mu /t=-0.5$ for all the figures.

Figure 5

The complete phase diagram of the system versus two parameters $\mu /t$ and $\Delta /t$. The five different phases are marked with the same notation as in Fig. 3. The black dashed lines a and b correspond to the parameters taken in Figs. 3a, 3b.