Strongly Correlated 2D Quantum Phases with Cold Polar Molecules: Controlling the Shape of the Interaction Potential

We discuss techniques to tune and shape the long-range part of the interaction potentials in quantum gases of bosonic polar molecules by dressing rotational excitations with static and microwave fields. This provides a novel tool towards engineering strongly correlated quantum phases in combination with low-dimensional trapping geometries. As an illustration, we discuss the 2D superfluid-crystal quantum phase transition for polar molecules interacting via an electric-field-induced dipole-dipole potential.

Figure 1

(a) Effective potentials: dipole potential induced by a static electric field $V_{\mathrm{eff}}^{2\mathrm{D}}=D/R^3$ (solid line); potential with a single microwave transition with $\Omega /\Delta =0.1$ (dashed line); attractive potential induced by an additional microwave coupling to the states $|1,\pm 1⟩$ with ${\Delta }_{\perp }=100\Delta$ and ${\Omega }_{\perp }/{\Delta }_{\perp }=0.3$ (dashed-dotted line). (b) Contour plot of the potential $V(\mathbf{r})l_{\perp }^3/D$ [Eq. (1)] in the $(R,z)$ plane. The semiclassical tunneling trajectory is shown as a dashed line.

Figure 2

(a) Energy levels of the rotor in a weak electric field. The microwave transition with detuning $\Delta$ and Rabi frequency $\Omega$ is shown as the arrow. (b) BO potentials for the internal states for $\Omega =0$, where $|g;e{⟩}_{\pm }\equiv (|g;e⟩\pm |e;g⟩)/\sqrt{2}$ denote the first excited states. (c) Avoided level crossing due to the microwave coupling with the effective BO potential $V_{\mathrm{eff}}^{3\mathrm{D}}$ given by the highest eigenenergy state.

Figure 3

(a) Tentative phase diagram in the $T-r_d$ plane: crystalline phase for interactions $r_d>r_{\mathrm{QM}}$ and temperatures below the classical melting temperature $T_m$ (dashed line). The superfluid phase appears below the upper bound $T<\pi {\hslash }^{2}n/2m$ (dotted line). The quantum melting transition is studied at fixed temperature $T=0.014D/a^3$ with interactions $r_d=5–30$ (dashed-dotted line). The crossover to the unstable regime for small repulsion and finite confinement ${\omega }_{\perp }$ is indicated (hatched region). (b) PIMC snapshot of the mean particle positions in the crystalline phase for $N=36$ at $r_d\approx 26.5$. (c) Density-density (angle-averaged) correlation function $g_2(r)$, for $N=36$ at $r_d\sim 11.8$. (d) Superfluid density ${\rho }_s$ and (e) static structure factor $S(\mathbf{K})/N$ as a function of $r_d$, for $N=36$ (circles) and $N=90$ (squares).