Dynamics of interacting bosons in a two-leg ring ladder with artificial magnetic flux and ac-driven modulations

TL;DR

We address how to coherently control matter-wave transport in a finite two-leg ring ladder with an artificial magnetic flux and ac-driven local energy shifts. Using a mean-field analysis of a tight-binding model that includes flux-induced Peierls phases, inter-ring coupling, and time-periodic on-site modulation, we map out self-trapping, excitation spectra, and current-direction control. Key findings include the emergence of nonlinear self-trapping at strong interactions, drive-frequency–dependent excitation bands, and precise switching between chiral and antichiral currents via tuning of the drive frequency $\omega$, Peierls phase $\theta$, and bias $\delta J$, complemented by phase diagrams and dynamical observables. The results provide a framework for manipulating persistent currents in closed-loop lattices and inform designs of synthetic quantum devices and atomtronic circuits with potential experimental realization in ultracold atoms.

Abstract

We investigate the nonequilibrium dynamics of interacting bosons in a two-leg ring ladder pierced by an artificial magnetic flux, where the particles are initially localized in the central sites of both rings, and the ac-driven local energy shifts are applied to the remaining lattice sites. Within the mean-field approximation, we demonstrate the emergence of nonlinear self-trapping for strong interparticle interactions, and characterize the distinct excitation regimes in the absence of the inter-ring tunneling. The artificial magnetic flux typically introduces Peierls phase factors, which induces complex-valued hopping amplitudes and leads to directed net particle currents along the chains. By further incorporating the finite inter-ring coupling and biased intra-ring hopping, we reveal that the tuning of the drive frequency and Peierls phase allows the precise control over both the intensity and direction of particle currents, which facilitates the transition between chiral and antichiral dynamics. These findings offer insights into the coherent manipulation of matter-wave transports in closed-loop lattice configurations and the exploration of nonequilibrium synthetic quantum systems in related fields.

Figures (9)

• Figure 1: Sketch of the two-leg ring ladder with an artificial magnetic flux denoted by $\Phi$. The red solid circle and the green solid circle represent the central sites $a$ and $b$, respectively, at which the particles are initially localized. The empty circles labeled by integers $1,2,3,\ldots,L$ correspond to the sites distributed along each lattice chain. The inter-ring coupling strength is characterized by the amplitude $J_{c}$, and the intra-ring hopping from site $\ell$ to $\ell+1$ has matrix element $J_{\nu}e^{-i\theta}$, while the one from $\ell+1$ to $\ell$ is $J_{\nu}e^{i\theta}$, with $\nu=\{a,b\}$.
• Figure 2: Time evolution of the number of particles on the $\ell$th site of ring $\nu$ in the presence of different interaction strengths $U=0$, $2$, $4$ and $6$, respectively, with the Peierls phase $\theta=0$, the inter-ring coupling strength $J_{c}=0$, and the intra-ring hopping amplitude $J_{\nu}=1$. The periodic boundary condition is employed, and the local energy shifts are absent.
• Figure 3: Decay of particles in the central site for different dc amplitude $\mu$, when the ac-driving is absent. Here, the interaction strengths are $U=0$, $2$, $4$ and $6$, respectively, and the Peierls phase is $\theta=0$. The inter-ring coupling strength is $J_{c}=0$, and the intra-ring hopping amplitude is $J_{\nu}=1$.
• Figure 4: The maximum particle number difference $\vert\Delta_{\nu,0}\vert_{\rm{max}}$ vs drive strength $M$ and drive frequency $\omega$ under different interaction strength $U=0$, $2$, $4$, and $6$, respectively. Here, we have taken the dc amplitude $\mu=10$, the intra-ring hopping amplitude $J_{\nu}=1$, the inter-ring coupling strength $J_{c}=0$, and the Peierls phase $\theta=0$. The simulation time is $t_{s}=50$, and the dashed lines delineate the regimes $\omega_{\pm}=\left(\pm2J_{\nu}+\Delta\epsilon\right)/n$ corresponding to the $n$th order excitations.
• Figure 5: Time dependence of the net particle currents with Peierls phases $\theta=\pi/8$, $\pi/4$, $\pi/2$, $5\pi/8$, and $3\pi/4$, respectively. The dashed lines corresponding to $\tau_{-}=19\times \frac{\pi/2}{\omega}$ and $\tau_{+}=21\times \frac{\pi/2}{\omega}$ indicate an exemplified region of the typical oscillation of particle currents within half a driving cycle. Here, we have kept the interaction strength $U=6$ and the dc amplitude $\mu=10$, and taken the driving parameters $M=8$ and $\omega=6$. The intra-ring hopping amplitude is $J_{\nu}=1$, and the inter-ring coupling strength is $J_{c}=0$.