Optimal Persistent Currents for Interacting Bosons on a Ring with a Gauge Field

We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subjected to a rotating barrier potential, which induces an artificial $U(1)$ gauge field. We show that, at intermediate interactions, the persistent current response is maximal, due to a subtle interplay of effects due to the barrier, the interaction, and quantum fluctuations. These results are relevant for ongoing experiments with ultracold atomic gases on mesoscopic rings.

Figure 1

Persistent current (a) in the rotating frame and (b) in the nonrotating frame, in units of $I_0=2\pi \hslash /M{L}^2$ for $N=18$, for zero barrier (black dashed line), weak barrier ($\lambda =0.2$, red solid line), and strong barrier ($\lambda =10$, blue dotted line) at fixed interaction strength ($\gamma =0.004$).

Figure 2

Density profiles vs angular coordinate $\theta$ along the ring. (a) GP analytical solution at weak interaction strength $\gamma =0.01$ for a delta barrier for various values of the barrier strength $\lambda$; the inset shows the soliton phase vs $\theta$ for the same values of barrier strength. (b) GP numerical solution (solid lines) at $\gamma =0.01$ for a Gaussian barrier of strength $\lambda =1.9$ for various values of the barrier width $\sigma$ (in units of $n_0^{-1}$) and corresponding barrier potential (dashed lines, in units of $10\times 2{\pi }^2{\hslash }^2/m{L}^2$). (c) MPS solution at intermediate interaction $\gamma =3.3$ and filling 0.15. (d) Analytical TG solution (lines) vs MPS (squares) in the hard-core limit. The other parameters used are $N=18$ and $\mathrm{\Omega }=0.4$ in all the curves.

Figure 3

Persistent current amplitude $\alpha$, in units of $I_0=2\pi \hslash /M{L}^2$, as a function of the interaction strength $\gamma$ at varying barrier strength $\lambda$, for $N=18$, from GP equation (black dotted lines), LL approach (blue solid lines), numerical MPS calculations (red squares, with red thin lines as guides to the eye), and NI and TG exact solutions (green dashes). Orange diamonds and cyan circles are for a Gaussian barrier of width $\sigma =0.5,2(n_0^{-1})$, respectively.