Nonuniversal beyond-mean-field properties of quasi-two-dimensional dipolar Bose gases

We study a quasi-two dimensional gas of bosonic dipoles, calculating the beyond-mean-field corrections to the ground-state energy and chemical potential neglecting the transverse mode structure. We show that the corrections are sensitive to the high-momentum part of the interaction and cannot be expressed solely in terms of the scattering length and the dipole strength. While nonuniversal, the correction is found to be negative, which provides an additional attractive term in the extended Gross-Pitaevskii equation, enhancing the roton instability.

Figure 1

Bogoliubov dispersion for different dipole strength $C_{\mathrm{dd}}=0$ (black dashed), $1/3\sqrt{g/n}$ (blue), $2/3\sqrt{g/n}$ (green dotted), and the critical value $\sqrt{g/n}$ (magenta) for which the spectrum has a roton minimum which touches zero.

Figure 2

Energy of the system as a function of the cutoff parameter $\kappa$ for the density $n={10}^{-10}$ and $\epsilon ={10}^{28}$. The dashed line shows the result given by (9). Here $k_0=\sqrt{g_{0}n}$ and $g_0=4\pi /ln\left(\epsilon /n\right)$.

Figure 3

Energy of the system as a function of the cutoff parameter $\kappa$ for different dipole strengths $C_{\mathrm{dd}}=0$ (black dashed), $1/3\sqrt{g_0/n_0}$ (blue), $2/3\sqrt{g_0/n_0}$ (green dotted), and $\sqrt{g_0/n_0}$ (magenta). Density and $\epsilon$ are the same as in Fig. 2.

Figure 4

Correction to the chemical potential as a function of the density for various dipole strengths $C_{\mathrm{dd}}=0$ (black dashed), $2/3\sqrt{g_0/n_0}$ (green dotted), and $\sqrt{g_0/n_0}$ (magenta). The cutoff at each point is chosen to minimize the derivative $\frac{\partial E}{\partial \kappa }$.

Figure 5

Ground-state energy of the gas as a function of the density in the vicinity of the roton with $C_{\mathrm{dd}}=\sqrt{g_0/n_0}$. The purple dashed line shows the result with the cutoff minimizing the derivative $\frac{\partial E}{\partial \kappa }$, while for the red line the $\kappa$ value was shifted to $1.06k^{★}$ to cover the roton.

Figure 6

Correction to the chemical potential as a function of the density for strong dipolar interaction $C_{\mathrm{dd}}=\sqrt{g_0/n_0}$ and the cutoff chosen as in Fig. 5.

Figure 7

Correction to the chemical potential for strong dipolar interaction $C_{\mathrm{dd}}=\sqrt{g_0/n_0}$ at the critical density $n_0$ as a function of the cutoff $\kappa$.