Observability of Quantum Criticality and a Continuous Supersolid in Atomic Gases

We analyze the Bose-Hubbard model with a three-body hard-core constraint by mapping the system to a theory of two coupled bosonic degrees of freedom. We find striking features that could be observable in experiments, including a quantum Ising critical point on the transition from atomic to dimer superfluidity at unit filling, and a continuous supersolid phase for strongly bound dimers.

Figure 1

Phase diagram for the Bose-Hubbard model with a three-body hard-core constraint, and $U<0$. The black curve represents the mean field phase border, while red (light gray) and blue (dark gray) curves include shifts due to quantum fluctuations in $d=2$, 3.

Figure 2

Ground state computations on 60 lattice sites with $U/J=-20$ using $t$-DMRG. (a) Correlation functions characterizing the CDW and DSF orders for open boundary conditions at unit filling on a log-log scale as a function of distance $x$. (b) Fitted algebraic decay exponents $K_{\mathrm{DSF}}$ and $K_{\mathrm{CDW}}$ for varying $n$ (error bars show estimates of the fitting error). (c) Density $n(x)$ for a system with a harmonic trapping potential $V(x)/J=(x-30.5{)}^2/900$, $N=60$ particles. (d) Shaded plot of the DSF correlation function $⟨b_x^{†}{b}_x^{†}{b}_y{b}_y⟩$ with interpolated shading, indicating substantial DSF order where $n\sim 1$.