Phases of dipolar bosons in a bilayer geometry

We study, by first-principles computer simulations, the low-temperature phase diagram of bosonic dipolar gases in a bilayer geometry as a function of the two control parameters, i.e., the in-plane density and the interlayer distance. We observe four distinct phases, namely, paired and decoupled superfluids, as well as a crystal of dimers and one consisting of two aligned crystalline layers. A direct quantum phase transition from a dimer crystal to two independent superfluids is observed in a relatively wide range of parameters. No supersolid phase is predicted for this system.

Figure 1

Phases of a bilayer bosonic dipolar system. There are two superfluid phases, one consisting of a single superfluid of dimers (a), the other one comprising two independent 2D superfluids (b); (c) shows a crystal of dimers, while (d) two aligned crystal layers.

Figure 2

Schematic ground-state phase diagram of bosonic dipolar gases on a bilayer geometry as a function of the interparticle distance $r_s$ and the interlayer separation $d$. Boxes refer to actual simulation results. 2SF stands for two decoupled 2D superfluids, PSF 2D pair superfluid, PC for a pair crystal, and 2CR for two separate 2D crystals. (a)–(d) Points for which pair-correlation functions are shown in Fig. 3. The open square along the $d=0$ line represents the single-layer crystal-superfluid phase transition as estimated in Ref. [9]

Figure 3

Pair-correlation functions $g_{\alpha \alpha }\left(r\right)$ (black dashed line), $g_{\alpha \beta }\left(r\right),\alpha \ne \beta$ (solid line), with $\alpha ,\beta =1,2$ plane indices. The interlayer distance $d=0.1$. Panel (a) refers to the pair superfluid phase (PSF) with $r_s=0.6$, (b) to the pair crystal (PC) with $r_s=0.2$, and (c) to two independent superfluids (2SF) with $r_s=0.1$. All of the curves shown here are representative of the $T=0$ limit.

Figure 4

Snapshot of many-particle configurations (world lines) for a bilayer system with mean interparticle distance $r_s=0.2$ and interlayer separation $d=0.1$, at temperature $T=0.1$ in the units adopted here (see text). Different colors refer to particles in different layers.

Figure 5

Pair-correlation function $g_{\alpha \beta }\left(r\right),\alpha \ne \beta$ at different temperatures, for $d=0.1$. Left: $r_s=0.2$, and $T=1$, 100 in the units utilized in this work. Right: $r_s=0.05,T=40,125$. Lower peaks correspond to higher $T$. Also shown is the corresponding $g_{\alpha \alpha }\left(r\right)$ at the lowest temperature for each case (arrows). In the results shown in the left panel, $g_{\alpha \alpha }$ cannot be distinguished from $g_{\alpha \beta }$ at the same temperature, for $r\gtrsim 0.1$.