Beyond the Tonks-Girardeau Gas: Strongly Correlated Regime in Quasi-One-Dimensional Bose Gases

We consider a homogeneous 1D Bose gas with contact interactions and a large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using the diffusion Monte Carlo method we show that, for small densities, the gaslike state is well described by a gas of hard rods. The critical density for cluster formation is estimated using the variational Monte Carlo method. The behavior of the correlation functions and of the frequency of the lowest breathing mode for harmonically trapped systems shows that the gas is more strongly correlated than in the Tonks-Girardeau regime.

Figure 1

Energy per particle and inverse compressibility as a function of the gas parameter $n{a}_{1\mathrm{D}}$. Open triangles, DMC results; solid symbols and thick solid line, VMC results and polynomial best fit; thick dashed line, HR equation of state [Eq. (4)]. Statistical error bars are smaller than the size of the symbols. Thin solid and dashed lines, $m{c}^2$ from the variational and HR equation of state, respectively.

Figure 2

Static structure factor $S(k)$ for a gas of HRs at different values of the gas parameter $n{a}_{1\mathrm{D}}$ and for a TG gas (dashed line). Open symbols stand for the DMC result of the super-Tonks (ST) regime at $n{a}_{1\mathrm{D}}=0.1$.

Figure 3

One-body density matrix $g_1(z)$ for a gas of HR at different values of the gas parameter $n{a}_{1\mathrm{D}}$ and for a TG gas (dashed line). Open symbols stand for the DMC result of the super-Tonks (ST) regime at $n{a}_{1\mathrm{D}}=0.1$. The solid line corresponds to the power-law fit $g_1(z)=\mathrm{const}/z^{0.617}$ to the DMC data.

Figure 4

Square of the lowest breathing mode frequency, ${\omega }^2$, as a function of the coupling strength $N{a}_{1\mathrm{D}}^2/a_z^2$ for the LL Hamiltonian ($g_{1\mathrm{D}}>0$) and in the super-Tonks regime ($g_{1\mathrm{D}}<0$). The dashed line refers to the HR expansion (see text).