Absence of damping of low-energy excitations in a quasi-two-dimensional dipolar Bose gas

We develop a theory of damping of low-energy, collective excitations in a quasi-two-dimensional, homogenous, dipolar Bose gas at zero temperature, via processes whereby an excitation decays into two excitations with lower energy. We find that owing to the nature of the low-energy spectrum of a quasi-two-dimensional dipolar gas, such processes cannot occur unless the momentum of the incoming quasiparticle exceeds a critical value ${\mathbf{k}}_{\text{crit}}$. We find that as the dipolar interaction strength is increased, this critical value shifts to larger momenta. Our predictions can be directly verified in current experiments on dipolar Bose condensates using Bragg spectroscopy, and provide valuable insight into the quantum many-body physics of dipolar gases.

Figure 1

The data points are the numerically obtained values of the dimensionless ${\tilde{p}}_{\text{crit}}=p_{\text{crit}}/(\hslash \sqrt{2}/l_z)$ plotted as a function of the dimensionless sound velocity ${\tilde{c}}_d=c_d/{\omega }_z{l}_z=\sqrt{g_d{n}_0^{2\mathrm{D}}/\sqrt{2\pi }{l}_z\hslash {\omega }_z}$, defined as the ratio of the interaction energy ($E_{\text{int}}=g_d{n}_0^{\text{2D}}/\sqrt{2\pi }{l}_z$) to the harmonic oscillator energy in the $z$ direction ($E_{\text{ho}}=\hslash {\omega }_z$): $\tilde{c}=\sqrt{E_{\text{int}}/E_{\text{ho}}}$. Collective modes with momenta below $p_{\text{crit}}$ are undamped. The solid line is the analytic result: ${\tilde{p}}_{\text{crit}}=3\sqrt{\pi }{\tilde{c}}_d^2$ obtained using Eq. (6) which works well at small ${\tilde{c}}_d$. For larger ${\tilde{c}}_d$, Eq. (6) underestimates the dipolar dispersion leading to a larger $p_{\text{crit}}$. The contact part of the interaction is set to zero.

Figure 2

Damping rate [normalized to ${\Gamma }_0={(g/\sqrt{2\pi }{l}_z)}^2{n}_0^{\text{2D}}m/4\pi {\hslash }^3$] in a Bose gas with dipolar and contact interactions, plotted vs $p$. The thin dashed curve is the result for purely contact interactions ($\tilde{g}=0$) (cf. Refs. [10, 12]) shown for comparison. The damping rate scales as $p^3$ at low momenta. The remaining curves show the damping rates in a gas with dipolar interactions: $\tilde{g}=g_d/g=0.1$ (solid, black), $\tilde{g}=0.25$ (blue dashed curve starting from $p=0.45\hslash \sqrt{2}/l_z$) and $\tilde{g}=0.5$ (red dotted curve starting from $p=0.7\hslash \sqrt{2}/l_z$). For a dipolar gas, there is no damping until $p$ reaches a threshold value (see Fig. 1). The dip in the damping rate at intermediate momenta is due to the appearance of a slight shoulder in the dispersion relation at intermediate $\tilde{g}$ [25].