Dissipative Superfluidity in a Molecular Bose-Einstein Condensate

Abstract

Motivated by recent experimental realization of a Bose-Einstein condensate (BEC) of dipolar molecules, we develop superfluid transport theory for a dissipative BEC to show that a weak uniform two-body loss can induce phase rigidity, leading to superfluid transport of bosons even without repulsive interparticle interactions. A generalized $f$-sum rule is shown to hold for a dissipative superfluid as a consequence of weak U(1) symmetry. We also demonstrate that dissipation enhances the stability of a molecular BEC with dipolar interactions. Possible experimental signature of dissipative superfluidity are discussed.

Figures (4)

• Figure 1: (a), (b): Density profiles of the order parameter without and with two-body loss at $t=200$ms. (c), (d): Phase profiles of the order parameter without and with two-body loss at $t=200$ms. We start with the ground state of a non-interacting BEC in a pancake-shaped harmonic trap at time $t=0$ and switch on the stirring of the BEC and two-body loss. Here the trap frequencies are $\omega_x=\omega_y=2\pi\times108\mathrm{Hz},\ \omega_z=100\omega_x$, the mass of a boson is $m=2.59\times10^{-22}\mathrm{g}$, and the dissipation rate is $\gamma=3\times10^{-13}\mathrm{cm}^3/\mathrm{s}$. We stir the BEC by introducing slight anisotropy in the trap frequencies ($\omega_x\rightarrow1.03\omega_x$ and $\omega_y\rightarrow1.09\omega_y$) and rotating the potential about the $z$ axis with frequency $\Omega=0.75\omega_x$.
• Figure S1: Spectral function $A(\omega)$ of a dissipative molecular BEC as a function of the kinetic energy $\epsilon=\frac{|\bm{k}|^{2}}{2m}$ and frequency $\omega$ under different regimes and different directions. Here we choose $\epsilon_{dd}=0.833$ and set the polarization of dipole moments along the $z$-axis. Figures a,c,e,g show the weak-dissipation regime where $U_{R}n=1.0$ a.u., and $\gamma n=0.1$ a.u.. Figures b,d,f,h show the weak-interaction regime where $U_{R}n=0.1$ a.u., and $\gamma n=1.0$ a.u.. In Figs. a-f, the directions are $\theta_{\bm{k}}=0,\pi/4,\pi/2$ from top to bottom. In Figs. g and h, we fix $\omega=0.5$ a.u.., where $\epsilon_{kx}:=k_x^2/(2m)$ and $\epsilon_{kz}:=k_z^2/(2m)$.
• Figure S2: Peak frequency of the spectral function (\ref{['eq:spectral_dipoledipole']}) of a dissipative BEC as a function of the kinetic energy $\epsilon=\frac{|\bm{k}|^{2}}{2m}$ in different regimes and different directions. Here we choose $\varepsilon_{dd}=0.833.$ Figures a,c and e show the weak-dissipation regime where $U_{R}n=1.0$ a.u. and $\gamma n=0.1$ a.u.. Figures b,d and f show the weak-interaction regime where $U_{R}n=0.1$ a.u. and $\gamma n=1.0$ a.u.. In a-f, the directions are $\theta_{\bm{k}}=0,\pi/4,\pi/2$ from top to bottom. In the regime $\tilde{U}_{R}\gg\gamma$, $\omega_{\mathrm{peak}}$ exhibits behavior initially following a square-root dependence and subsequently showing a crossover to a linear dependence on $\epsilon$. In the weak-interaction regime, the peak is less sensitive to the direction and shows a bending at $\epsilon=1.0$ a.u. where the real part of the spectrum increases.
• Figure S3: The real part of the Liouvillian spectrum $\omega_1$ in two-dimensional systems. Here we define $k_0:=\sqrt{2mU_Rn}$ as the characteristic wave number and take the parameters $V=0.98\sqrt{U_R/mn}$ for all figures and (a): $\gamma/U_R=0.1$, (b): $\gamma/U_R=0.4$, (c): $\gamma/U_R=0.6$. The critical value above which the roton excitations disappear is given by $\gamma/U_R=0.1456$.