Dynamical Theory of Superfluidity in One Dimension

A theory accounting for the dynamical aspects of the superfluid response of one dimensional (1D) quantum fluids is reported. In long 1D systems, the onset of superfluidity is related to the dynamical suppression of quantum phase slips at low temperatures. The effect of this suppression as a function of frequency and temperature is discussed within the framework of the experimentally relevant momentum response function. Applications of these results to the understanding of the superfluid properties of helium confined in 1D pores with nanometer diameter, dislocations in solid ${}^4\mathrm{He}$, and ultracold atomic gases are also briefly discussed.

Figure 1

Superfluid response for different probe frequencies $\omega$, which ranges from ${10}^{-2}{\omega }_0$ (dark) to ${10}^2{\omega }_0$ (bright), where ${\omega }_0=2\mathrm{kHz}$ [6]. We used two terms for $H_{\mathrm{PS}}$ [cf. Eq. (5)] setting $\Delta k_{10}=0.007a_0^{-1}$, $\Delta k_{11}/\Delta k_{10}=0.7$, and $g_{10}=g_{11}=1$; ${\chi }_0=M^{2}vK/\pi \hslash$. The inset shows $\mathrm{Im}\chi (\omega ;T)$ (lower part) and the peak temperature dependence on $\omega$ on a log-log scale. Linear density (${\rho }_0$) and cutoff ($a_0$) are chosen so as to conform to the experimental situation in 6. The sound velocity, $v=200\mathrm{m}/\mathrm{s}$, and the Luttinger parameter, $K=8.1$, resulting in onset temperatures comparable to the experimental ones.

Figure 2

Superfluid response vs $T$ for different values of the Luttinger parameter $K$ which ranges in unit steps from 3.2 (dark) to 9.2 (bright), ($g_{10}=g_{11}=1$, $\Delta k_{10}=0.001a_0^{-1}$, and $\Delta k_{11}/\Delta k_{10}=0.7$). The insets ($K=6.2$) show the effect of a larger value of the PS momenta ($g_{01}=g_{11}=1$, $\Delta k_{10}=0.5a_0^{-1}$, and $\Delta k_{11}/\Delta k_{10}=0.7$), resulting in two dissipation peaks.