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arXiv:2606.26394

Non-ergodic dynamical phase transition via a zero-mode exceptional point in a non-Markov atomic Josephson junction

Koichiro Furutani

cond-mat.quant-gascond-mat.stat-mechquant-phSubmitted Jun 24, 2026• Announced Jun 26, 2026• 0 citations
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Abstract

Open quantum systems typically lose their initial memory due to the environmental decoherence resulting in thermalization. We demonstrate a striking breakdown of this paradigm in a head-to-tail Bose-Josephson junction, which is described by an intrinsically momentum-coupled Caldeira-Leggett model. Through exact non-Markov Langevin simulations, we discover a novel type of non-ergodic dynamical phase transitions into a running state, which has no counterpart in Markov limit. Crucially, we reveal that this transition is fundamentally governed by a zero-mode exceptional point emerging from the non-Markov friction. This topological origin is characterized by the winding of the response function. Finally, numerical quantum simulations of an equivalent driven XXZ spin chain confirm that this exceptional-point-induced signature robustly survives as a dynamical crossover against strong quantum fluctuations and the dynamical backreaction of the environment. This macroscopic robustness offers a promising platform for long-lived quantum memories in dissipative environments.

Comments
7+5 pages, 4+2 figures

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Open quantum systems typically lose their initial memory due to the environmental decoherence resulting in thermalization. We demonstrate a striking breakdown of this paradigm in a head-to-tail Bose-Josephson junction, which is described by an intrinsically momentum-coupled Caldeira-Leggett model. Through exact non-Markov Langevin simulations, we discover a novel type of non-ergodic dynamical phase transitions into a running state, which has no counterpart in Markov limit. Crucially, we reveal that this transition is fundamentally governed by a zero-mode exceptional point emerging from the non-Markov friction. This topological origin is characterized by the winding of the response function. Finally, numerical quantum simulations of an equivalent driven XXZ spin chain confirm that this exceptional-point-induced signature robustly survives as a dynamical crossover against strong quantum fluctuations and the dynamical backreaction of the environment. This macroscopic robustness offers a promising platform for long-lived quantum memories in dissipative environments.
We propose a dissipative phase transition in a head-to-tail Bose Josephson junction. The quantum phase transition has the same origin as the one in a resistively shunted Josephson junction, but the intrinsic momentum coupling between the Josephson mode and the bath modes enables us to observe the dissipative phase transition without any synthetic dissipation. We show that the interatomic interaction strength plays the role of the damping parameter. Consequently, in contrast to a resistively shunted Josephson circuit, the Bose Josephson junction can exhibit an insulating phase in a wider parameter region by increasing the repulsive interaction strength, which is robust against nonperturbative effects. We argue that tight transverse confinement of the quasi-one-dimensional atomic gas allows us to reach the insulating phase.
We consider a model describing Bose-Josephson junction (BJJ) coupled to a single bosonic mode exhibiting a quantum phase transition (QPT). Onset of chaos close to QPT is observed from semiclassical dynamics of collective modes and from spectral statistics. A detailed analysis of entanglement entropy and multifractal nature of states reveals a non-ergodic to weakly ergodic crossover at a critical energy. We identify the imprint of collective π\piπ-oscillation as many body quantum scar (MBQS), which leads to the deviation from ergodicity. Persistence of phase coherence in non-equilibrium dynamics of such initial state corresponding to the π\piπ-mode is an observable signature of MBQS which can be relevant for experiments on BJJ.
Using state-of-the-art numerical techniques, we investigate how quantum phase fluctuations and quasiparticle tunneling shape the behavior of a small-capacitance Josephson junction across Ohmic, sub-Ohmic, and super-Ohmic dissipation regimes. We show that increasing the Ohmic dissipation strength drives a Berezinskii-Kosterlitz-Thouless quantum phase transition at thermodynamic equilibrium. Deviations from Ohmic behavior profoundly alter this scenario: the super-Ohmic regime exhibits no phase transition, whereas the sub-Ohmic regime displays a continuous second-order transition, consistent with the universality classes of the spin-boson model. Within the Ohmic regime, real-frequency linear-response calculations reveal that the phase particle does not undergo the commonly assumed diffusive-to-localized crossover. Instead, finite resistance progressively suppresses the singular zero-frequency response, producing a ballistic-to-localized change in the dynamics. At finite frequencies, coupling to the environment generates a long-lived excitation in the charge response, which evolves into a resonance as the subgap and shunt resistances are reduced.
We investigate the effect of dissipation in a Bose-Josephson junction (BJJ) coupled to baths of bosons at its two sites. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within a Holstein-Primakoff approximation, which exhibits vanishing of the energy gap and enhanced quantum fluctuations at the critical point. We study the dynamics of BJJ using a time-dependent variational method and analyze stability of different types of steady states. As a special case we study in detail the phase space dynamics of BJJ coupled to a single mode, which reveals diffusive and incoherent behavior with increasing coupling to the bath mode. The dynamical steady states corresponding to the π oscillation and self-trapped state become unstable when their oscillation frequencies are in resonance with the bath modes. We study the Josephson dynamics in the presence of an Ohmic bath with Gaussian noise to incorporate the thermal fluctuations and obtain the Josephson oscillation frequency and damping analytically. We also observe the transition to the symmetry-broken state for strong coupling as well as decay of π oscillation and a self-trapped state to the ground state due to dissipation. Variation of the phase fluctuation with temperature of the bath shows similar behavior as observed in experiment. Finally we discuss the experimental setup to study the observable effects of dissipation in BJJ.
Exceptional points in non-Hermitian quantum systems give rise to novel genuine quantum phenomena. Recent explorations of exceptional-point-induced quantum phase transitions have extended from discrete-variable to continuous-variable-encoded quantum systems. However, quantum phase transitions driven by Liouvillian exceptional points (LEPs) in continuous-variable platforms remain largely unexplored. Here, we construct and investigate a Liouvillian exceptional structure based on a driven-dissipative Kerr-cat qubit. Through numerical simulations, we reveal a quantum phase transition occurring at the LEP characterized by a sudden change in dynamical behavior from underdamped oscillations to overdamped relaxations as visualized via Wigner functions and Bloch sphere trajectories. Notably the negativity of the Wigner function serves as a direct signature of genuine quantum coherence unattainable in conventional single-qubit non-Hermitian systems. Furthermore, we introduce the phase difference between the off-diagonal elements of the Liouvillian eigenmatrices as a novel parameter to quantify the transition. Our results establish the Kerr-cat qubit as a novel continuous-variable setting for exploring dissipative quantum criticality and intrinsic non-Hermitian physics.
We theoretically investigate the state evolution and decoherence of Bell states in a two-qubit system coupled to local bosonic thermal baths. By employing a hybrid Liouvillian formalism with a tuning parameter , we systematically explore the transition from purely non-Hermitian coherent evolution ( ) to complete Lindblad master equation dynamics ( ) in a bosonic environment. Our results demonstrate that at , dynamically encircling a second-order exceptional point (EP) enables a near-perfect chiral transfer between the Bell states and . This phenomenon is shown to be globally robust against variations in the bosonic thermal occupation numbers of the environment. However, the introduction of quantum jump processes ( ) significantly suppresses the directional selectivity, and the chirality completely disappears in the full Liouvillian limit ( ). Furthermore, we find that the dissipative protocol is unable to generate entanglement starting from a maximally mixed state, highlighting the role of initial state purity. This work elucidates the interplay between non-Hermitian topology and bosonic decoherence, providing insights for state evolution in realistic open quantum systems.