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arXiv:2606.02157

Vibrational resonance in a one-dimensional dissipative Bose-Josephson junction

Abhik Kumar Saha

Published Jun 1, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the linear and nonlinear response of a one-dimensional dissipative Bose-Josephson junction subjected simultaneously to a weak low-frequency probe and a rapidly oscillating high-frequency external drive. Starting from the dissipative two-mode Bose-Josephson equations, we derive an effective higher-order nonlinear equation for the population imbalance by retaining the leading nonlinear correction. Using time-scale separation and perturbative analysis, we obtain analytical expressions for both the linear response at the fundamental frequency and the nonlinear response at the second harmonic. We show that the high-frequency modulation modifies the effective potential landscape and dynamically breaks the symmetry around the stationary state, giving rise to a finite second-harmonic response that is absent without the rapidly oscillating field. Both the linear and nonlinear response amplitudes exhibit resonance-like enhancement for optimal values of the high-frequency driving strength. We further analyze the dependence of the resonance characteristics on interaction strength, dissipation, and driving parameters in both the zero-phase and $π$-phase modes and compare the analytical predictions with direct numerical simulations. Our results demonstrate a controllable mechanism toward realizing linear and nonlinear vibrational resonance in a one-dimensional dissipative Bose-Josephson junction and open new possibilities for controlling collective dynamics in driven ultracold bosonic systems.

DOI
10.48550/arxiv.2606.02157

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We investigate the linear and nonlinear response of a one-dimensional dissipative Bose-Josephson junction subjected simultaneously to a weak low-frequency probe and a rapidly oscillating high-frequency external drive. Starting from the dissipative two-mode Bose-Josephson equations, we derive an effective higher-order nonlinear equation for the population imbalance by retaining the leading nonlinear correction. Using time-scale separation and perturbative analysis, we obtain analytical expressions for both the linear response at the fundamental frequency and the nonlinear response at the second harmonic. We show that the high-frequency modulation modifies the effective potential landscape and dynamically breaks the symmetry around the stationary state, giving rise to a finite second-harmonic response that is absent without the rapidly oscillating field. Both the linear and nonlinear response amplitudes exhibit resonance-like enhancement for optimal values of the high-frequency driving strength. We further analyze the dependence of the resonance characteristics on interaction strength, dissipation, and driving parameters in both the zero-phase and πππ-phase modes and compare the analytical predictions with direct numerical simulations. Our results demonstrate a controllable mechanism toward realizing linear and nonlinear vibrational resonance in a one-dimensional dissipative Bose-Josephson junction and open new possibilities for controlling collective dynamics in driven ultracold bosonic systems.
We study Josephson dynamics in a long atomic Bose-Josephson junction formed by two tunnel-coupled coplanar Bose-Einstein-condensate rings. An in-plane linear acceleration breaks the axial symmetry of the trap and transforms a single Josephson plasma oscillation into a multimode population-imbalance response. Gross-Pitaevskii simulations and Bogoliubov-de Gennes analysis show that the additional spectral components arise from collective modes that acquire finite overlap with the population-imbalance operator under symmetry breaking, with their activation governed by reflection symmetry about the acceleration direction. We also propose a mode-resolved Josephson-spectroscopy protocol based on a weak localized periodic perturbation. Frequency scans reveal resonant amplitude peaks and phase shifts at the eigenfrequencies of active Bogoliubov modes, while angular scans of the drive position provide access to the angular structure of the corresponding mode density perturbations. A dissipative time-dependent Bogoliubov theory yields analytical response functions in quantitative agreement with full Gross-Pitaevskii simulations in the linear regime. Our results demonstrate that accelerated dual-ring condensates provide a controllable platform for symmetry-selected Josephson dynamics and spectroscopic probing of collective modes.
Abstract We study the dynamics of a nonlinear dissipative bosonic Josephson junction with a time-dependent sinusoidal perturbation in the interaction term. We demonstrate parametric resonance, where the system undergoes sustained periodic oscillations even in the presence of dissipation. This happens when the frequency of the perturbation is close to twice the frequency of the unperturbed Josephson oscillations and the strength of perturbation exceeds a critical threshold. We have formulated the threshold conditions for parametric oscillations. To explore the nature of the oscillations, we carry out a multiple time scale analysis of the stability boundaries in terms of the V-shaped Arnold tongue in the parameter space. Full numerical simulations have been performed for the zero-, running-, and π -phase modes of the nonlinear Josephson effect. Our results demonstrate that in the π -phase mode the system is capable of making a transition from regular parametric to chaotic parametric oscillations as one crosses the stability boundary. Also, the phase difference undergoes phase slip before executing sustained parametric oscillations.
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The collective oscillations of one-dimensional (1D) repulsive Bose gas with external harmonic confinement in two different regimes are studied. The first regime is the mean-field regime when the density is high. The second regime is the Tonks-Girardeau regime when the density is low. We investigate the resonances under periodic modulations of the trap potential and the effective nonlinearity. Modulations of the effective nonlinear coefficient result from modulations of the atomic scattering length by the Feshbach resonance method or variations of the transverse trap frequency. In the mean-field regime we predict bistability in the nonlinear oscillations of the condensate. In the Tonks-Girardeau regime the resonance has the character of a linear parametric resonance. In the case of rapid strong modulations of the nonlinear coefficient we find analytical expressions for the nonlinearity managed soliton width and the frequency of the slow secondary oscillations near the fixed point. We confirm the analytical predictions by direct numerical simulations of the 1D Gross-Pitaevskii equation and the effective nonlinear Schr\"odinger equation with quintic nonlinearity and trap potential.
We analyze the phase diffusion, quantum fluctuations and their spectral features of a one-dimensional Bose-Josephson junction (BJJ) nonlinearly coupled to a bosonic heat bath. The phase diffusion is considered by taking into account of random modulations of the BJJ modes causing a phase loss of initial coherence between the ground and excited states, whereby the frequency modulation is incorporated in the system-reservoir Hamiltonian by an interaction term linear in bath operators but nonlinear in system (BJJ) operators. We examine the dependence of the phase diffusion coefficient on the on-site interaction and temperature in the zero- and π-phase modes and demonstrate its phase transition-like behavior between the Josephson oscillation and the macroscopic quantum self-trapping (MQST) regimes in the π-phase mode. Based on the thermal canonical Wigner distribution, which is the equilibrium solution of the associated quantum Langevin equation for phase, coherence factor is calculated to study phase diffusion for the zero- and π-phase modes. We investigate the quantum fluctuations of the relative phase and population imbalance in terms of fluctuation spectra which capture an interesting shift in Josephson frequency induced by frequency fluctuation due to nonlinear system-reservoir coupling, as well as the on-site interaction-induced splitting in the weak dissipative regime.
We investigate the excitation properties of finite ultracold bosonic systems in a one-dimensional harmonic trap with a time-dependent interaction strength. The driving of the interatomic coupling induces excitations of the relative motion exclusively with specific and controllable contributions of momentarily excited many-body states. Mechanisms for selective excitation to few-body analogs of collective modes and acceleration occur in the vicinity of resonances. Via the few-body spectrum and a Floquet analysis, we study the excitation mechanisms and the corresponding impact of the driving frequency and strength as well as the initial correlation of the bosonic state. The fundamental case of two atoms is analyzed in detail and forms a key ingredient for the bottom-up understanding of cases with higher atom numbers, thereby examining finite-size corrections to macroscopic collective modes of oscillation.