Dissipation as a Resource: Synchronization, Coherence Recovery, and Chaos Control

TL;DR

Open quantum systems traditionally treat dissipation as detrimental, but this work shows dissipation can be a resource to tailor dynamics in a two-component Bose-Josephson junction with incoherent hopping at rate $\gamma$. Using a Lindblad description and a Schwinger-boson mapping to two coupled spins of magnitude $S= N/2$, the authors identify four regimes controlled by the interspecies interaction $V$ and $\gamma$: synchronized phase-locked oscillations for $V<V_c$, a dissipative phase transition to self-trapping at $V=V_c$, transient chaos with coherence recovery for $V>V_c$, and tilt-induced steady-state chaos with irreversible decoherence. They demonstrate that dissipation can temporally scramble quantum information yet enable long-time coherence restoration, and that a tilt converts transient chaos into persistent chaotic dynamics, all while Liouvillian spectra exhibit Ginibre statistics in both chaotic regimes. Overall, the study provides a unified framework where dissipation engineers dynamical phases, controls chaos duration, and supports coherence preservation in open quantum platforms.

Abstract

Dissipation is commonly regarded as an obstacle to quantum control, as it induces decoherence and irreversibility. Here we demonstrate that dissipation can instead be exploited as a resource to reshape the dynamics of interacting quantum systems. Using an experimentally realizable Bose-Josephson junction containing two bosonic species, we demonstrate that dissipation enables distinct dynamical behaviors: synchronized phase-locked oscillations, transient chaos with long-time coherence recovery, and steady-state chaos. The emergence of each behavior is determined by experimentally tunable parameters. At weak interactions, the two components synchronize despite dissipation, exhibiting long-lived coherent oscillations reminiscent of a boundary time crystal. Stronger interactions induce a dissipative phase transition into a self-trapped regime accompanied by chaotic dynamics. Remarkably, dissipation regulates the lifetime of chaos and enables the recovery of coherence at long times. By introducing a controlled tilt between the wells, transient chaos can be converted into persistent steady-state chaos. We further show that standard spectral diagnostics fail to distinguish between the two chaotic regimes, revealing that spectral statistics primarily reflect short-time instability. These results establish dissipation as a powerful tool for engineering dynamical phases, restoring quantum coherence, and controlling the duration of chaotic behavior and information scrambling.

Figures (4)

• Figure 1: Dissipation-controlled dynamical regimes of an open two-component Bose-Josephson junction. (a) Schematic of the system with coherent tunneling, interspecies interactions, and incoherent hopping. (b) Phase diagram in the interaction ($V$)–dissipation ($\gamma$) plane. (c) Weak interactions yield synchronized oscillations even in the presence of dissipation. (d) Stronger interactions lead to transient chaos, where dissipation suppresses long-time scrambling and restores coherence due to the presence of a stable attractor. (e) A tilt destabilizes the attractor, producing steady-state chaos with persistent decoherence.
• Figure 2: Coherent synchronized oscillations. (a,b) Dynamics of the (a) sum $\langle \hat{z}_+\rangle$ and (b) difference $\langle \hat{z}_-\rangle$ of population imbalances of the two species. The standard deviation $\Delta z_{-}$ is plotted in (b) as error bars. (c) The Fourier spectrum $F(\omega)$ of $\langle \hat{z}_{+}(t)\rangle$ reveals a single frequency of oscillation. The vertical dashed line represents the frequency of the corresponding classical orbit. (d) [(e)]: Classical [quantum] oscillatory dynamics on the phase-space portrait of the conjugate plane $z_1-\phi_1$; in (e), the trajectories are plotted within $t\in [0,20]$. We choose $V=0.5$, $\gamma=0.2$, and $S=50$. In this and the rest of the figures, we choose $J=1$.
• Figure 3: Dissipative phase transition from synchronization to self-trapping. Bifurcation diagrams of $s_z^*$ corresponding to (a) transition from fixed point FP-I to FP-III and (b) from FP-II to FP-IV. Solid (dashed) lines indicate stable (unstable) fixed points. (c) Trajectories on the Bloch sphere of one spin exhibiting oscillation around FP-IV and relaxation dynamics to the attractor FP-III. (d) Quantum dynamics of $\langle \hat{z}_-\rangle$, averaged over trajectories, starting close to FP-IV (blue line) and at a generic state (red line). Both trajectories ultimately converge to FP-III. We use $\gamma=0.2$ in all panels and $V=1.7$ in (c,d). For the quantum result in (d), $S=30$.
• Figure 4: Control of chaos and coherence via dissipation and a tilted potential. Left panels (a)-(e): Transient chaos and no tilted traps. (a)-(b): Classical chaos in the absence of dissipation ($\gamma=0.0$, pink) becomes transient chaos in its presence ($\gamma=0.2$, blue) as shown with (a) decorrelator and (b) atomic current of one species. (c)-(d): Corresponding quantum behavior. (c) Von Neumann entropy of one species for $\gamma=0$ and $0.2$; horizontal dashed line represents the maximum value for the open system $\mathcal{S}_{\rm max, open}^{\rm VN} = \ln(2S+1) = \mathcal{S}_{\rm max, closed}^{\rm VN} +1/2$. The time is in the linear scale for $t\in[0,2]$ and in log scale for $t>2$. (d) Dynamics of purity $\mathcal{P}_i$ (right $y$-axis) and phase fluctuation $(\Delta\phi_i)^2$ (left $y$-axis) for $\gamma=0.2$. (e) Reduced density matrix of one species: Off-diagonal elements decay at short times ($t=10$), but coherence is recovered at long times ($t=200$). Right panels (f)-(j): Steady-state chaos in presence of tilted traps, $\omega_z=0.5$. All of these panels include dissipation, $\gamma=0.2$. (f) Long-time classical phase-space density on the chaotic attractor. (g) Husimi distribution $Q(z_1,\phi_1)$ of reduced density matrix $\hat{\rho}_1$ obtained from the long-time density matrix $\hat{\rho}$. (h)-(i) Quantum dynamics for (h) the von Neumann entropy of one species, (i) purity $\mathcal{P}_i$ (right y-axis), and phase fluctuation $(\Delta\phi_i)^2$ (left y-axis); saturating values indicate steady-state chaos. (j) Reduced density matrix of one species: Coherence is no longer recovered at long times. All panels: $V=1.7$. All quantum results are obtained for $S=10$, and the quantities in (c)-(e) and (h)-(j) are computed from $\hat{\rho}(t)$.