Controlled acoustic-driven vortex transport in coupled superfluid rings

TL;DR

The paper addresses how angular momentum is coherently exchanged between two density-coupled ring Bose-Einstein condensates via vortex dynamics in atomtronic circuits. It combines a dissipative quasi-2D Gross-Pitaevskii framework in an accelerating frame with Bogoliubov-de Gennes analysis and a reduced 1D acoustic description to characterize low-energy phonon-like normal modes that govern persistent-current oscillations. Key findings include the identification of a phonon-mediated mechanism, quantitative agreement between the acoustic model, BdG results, and full Gross-Pitaevskii simulations, and the discovery of a critical dissipation $\\gamma_{cr} \\approx 0.015$ that marks a transition to overdamped localization; plus, a resonant barrier-modulation protocol enabling controlled vortex transfer within a finite frequency window (e.g., $22$–$26$ Hz). The work provides a hydrodynamic, parameter-free framework for circulation exchange in double-ring atomtronic devices and demonstrates a practical control knob for vortex transport via barrier modulation.

Abstract

Atomtronic quantum sensors based on trapped superfluids offer a promising platform for high-precision inertial measurements where the dynamics of quantized vortices can serve as sensitive probes of external forces. We analytically investigate persistent current oscillations between two density-coupled Bose-Einstein condensate rings and show that the vortex dynamics is governed by low-energy acoustic excitations circulating through the condensate bulk. The oscillation frequency and damping rate are quantitatively predicted by a simplified hydrodynamic model, in agreement with Bogoliubov-de Gennes analysis and Gross-Pitaevskii simulations. We identify the critical dissipation separating persistent oscillations from overdamped vortex localization. Furthermore, we demonstrate that periodic modulation of the inter-ring barrier at resonant frequencies enables controlled vortex transfer even when the condensates are well separated in density. These results clarify the role of collective hydrodynamic modes in circulation transfer and establish a framework for employing vortex dynamics in atomtronic quantum technologies.

Figures (9)

• Figure 1: Schematic representation of possible persistent current oscillation regimes. Left column: (a) The prepared initial state with a closed gate and an anti-vortex in the left ring. (b) The state with an open gate, demonstrating the anti-vortex's free oscillation between rings. (c) The open-gate state, which exhibits decaying oscillations due to dissipation. This results in vortex pinning at the center of the system. (d) Biased oscillation due to the presence of acceleration, which shifts the anti-vortex equilibrium position to the right ring. The right column (i) shows the dynamics of the barrier amplitude, where the vertical dot-dashed magenta lines represent the open-gate part of the protocol. The other parts on the right are examples of dynamics for the winding number of the left ring ($\rm{n_L}$) and the angular momentum per particle difference between the rings ($\Delta L_z$) of the corresponding regimes: (ii) and (iii) correspond to the conservative regime (b); (iv) and (v) correspond to the weakly dissipative regime (b-c); (vi) and (vii) correspond to the highly dissipative, overdamped regime (c); and (viii) and (ix) correspond to the biased regime with weak dissipation (d). Yellow dashed lines indicate zero angular momentum difference.
• Figure 2: Analytical and numerical predictions of beating effects in vortex oscillations. (a) Population imbalance between rings and (d) angular momentum per particle difference dynamics for the opening gate protocol at $V_0=1.2 \mu$, obtained in numerical simulations of conservative GPE \ref{['eq:dGPE2D']}. (b) and (c) corresponding Fourier spectra, normalized to the maximum value, of population imbalance (a), at different frequency ranges. Note how much smaller the scale of (c) is relative to (b). (e) and (f) similar normalized Fourier spectra of angular momentum difference (d). Vertical lines denote the corresponding elementary excitation \ref{['eq: BdG system']} of the open-gate stationary solution. Red lines denote visible, while grey lines denote inactive modes.
• Figure 3: Oscillations and beating effects of multiply charged persistent currents. (a) initial phase, (b) population imbalance, and (c) angular momentum per particle difference dynamics for the opening gate protocol for two (left column) and four (right column) vortices in the system.
• Figure 4: The frequency split (envelope frequency) dependence on the present vorticity in the system ($m$), for different acoustic waves $\rm{n}$. The points present the solution of \ref{['eq: BdG system']}; while the lines show the acoustic model approach, whenever filled points correspond to quantized vorticity values.
• Figure 5: The normalized Fourier spectrum of the GPE \ref{['eq:dGPE2D']} without dissipation ($\gamma=0$). Shown is the particle imbalance dynamics, as a function of the present acceleration along the main axis in the system. Yellow crosses present numerical results of respective BdG eigenfrequencies \ref{['eq: BdG system']} of the open-gate stationary solution, at given acceleration. More pinkish regions correspond to more active modes. The vertical (frequency) axis is normalized to $\omega_0=2\pi \times 20.57 \, \rm{Hz}$, which is the average frequency of the lowest phonon modes.