Dynamically generating superflow in a bosonic ring via phase imprinting

TL;DR

The paper studies dynamic superflow generation in a ring-shaped Bose gas using phase imprinting, addressing how angular momentum is injected and how quantized circulation emerges. By solving the time-dependent Schrödinger equation for a noninteracting gas and the Gross-Pitaevskii equation for interacting cases, with an angular imprinting potential $U(\theta)$ applied for time $\tau$, it shows that density depletion from the imprint injects angular momentum via $l^{\rm tot}_z(t)$ while azimuthal phase slips drive quantized currents $l^{\varphi}_z(t)$, with phase slips marked by nodes in the density and jumps in the winding number. The final winding number can be tuned by $\tau$, but stronger interactions suppress both angular-momentum growth and phase slips by favoring density homogeneity. These results provide a microscopic understanding and practical guidance for experimentally realize dynamic superflow and atomtronic components in ring Bose gases.

Abstract

Phase imprinting enables the dynamic generation of superflow in bosonic atoms, effectively overcoming traditional limitations such as vortex number constraints and heating effects. However, the mechanisms underlying superflow formation remain insufficiently understood. In this work, we reveal these mechanisms by studying the time evolution of the transferred total angular momentum and the quantized current throughout the phase imprinting process, achieved through numerically solving the time-dependent Schrödinger and Gross-Pitaevskii equations. We demonstrate that the Bose gas dynamically acquires angular momentum through the density depletion induced by the phase imprinting potential, whereas quantized currents emerge from azimuthal phase slips accompanied by complete density depletions. Regarding the impact of system parameters, such as interactions, we find that interactions hinder superflow formation, as the azimuthal density distribution becomes less susceptible to the phase imprinting potential. Our findings offer microscopic insights into the dynamic development of superflow during the phase imprinting process and provide valuable guidance for ongoing experimental efforts.

Figures (3)

• Figure 1: (a) Schematic illustration of $V(r, \theta)$, which generates the ring-shaped potential. The blue dots represent the confined Bose atoms in the ring. (b) Angular density profile $n(\theta,t)/n_0$ of a noninteracting Bose gas for $tE_0/ \hbar=0$ (red dashed curve) and $tE_0/\hbar=0.5$ (blue solid curve), respectilvely. The inset shows the profile of $U(\theta)/U_0$ (red solid curve). (c) Time evolution of $l^{\rm tot}_z(t)/\hbar$ (blue dashed curve) and $l^{\varphi}_z(t)/\hbar$ (red solid curve). In (b)(c), we set $E_0=\hbar^2 /(M a^2)$ as an energy scale, where $a$ serves as the characteristic length scale. Here, parameters are $U_0=5E_0, \Delta \theta=0.01\pi, R=10a, \tau E_0 /\hbar=5$, $n_0=1/(2\pi)$ and $n(\theta,t)$ satisfies $\int d\theta n(\theta,t)=1$.
• Figure 2: (a) Time evolution profile of $\Delta \varphi(\theta,t)$ for $tE_0/\hbar=0.5$ (blue dashed curve) and $t E_0 /\hbar=1.5$ (red solid curve) with a fixed quench time $\tau E_0/\hbar$. (b) Time evolution of $(|\psi(\theta,t)|/f_0)_{\text{min}}$ (blue dashed curve) with a fixed $\tau E_0/\hbar$. The inset shows the time evolution of $l^{\varphi}_z(t)$ (red solid curve). (c) Profile of $|\psi(\theta,t)|/f_0$ at $tE_0/\hbar=0.5$ (blue dashed curve), $tE_0/\hbar=0.98$ (red solid curve) and $tE_0/\hbar=1.5$ (black dash-dotted curve). (d) The injected angular momenta $l^{\rm tot}_z(t)$ and $l^{\varphi}_z(t$) at a long time. Here, $f_0=1/\sqrt{2\pi}$; other parameters are the same as those in Fig. \ref{['Fig1']}.
• Figure 3: (a) Time evolution of $l^{\rm tot}_z(t)/\hbar$ and $l^{\varphi}_z(t)/\hbar$ under different interaction strengths with a fixed $\tau E_0/\hbar$. The blue dashed (gray dashed) curve and red solid (gray dash-dotted) curve denote $l^{\rm tot}_z(t)/\hbar$ and $l^{\varphi}_z(t)/\hbar$, respectively, for $g=10E_0$ ($g=0$). (b) Time evolution of $[\bar{n}_L(t)-\bar{n}_R(t)]/n_0$ under different interaction strengths, the red solid (blue dashed) curve denotes the time evolution of $[\bar{n}_L(t)-\bar{n}_R(t)]/n_0$ for $g=10E_0$ ($g=0$). (c) Density profile under different interaction strengths at the same time. The blue solid (red dashed) curve denotes the profile of $|\phi_0(\theta,t)|/f_0$ for $g=10E_0$ ($g=0$) at $tE_0/\hbar=0.8$. Here, other parameters are the same as those in Fig. \ref{['Fig1']}.