Dynamical instability in parametrically driven bosonic systems is generally associated with diverging occupations and the absence of a stationary state, but its implications for long-time entanglement remain unclear. We investigate this question in a dissipative bosonic dimer with beam-splitter and two-mode-squeezing interactions, local loss, and a tunable common bath. The non-Hermitian dynamical spectrum governing the Gaussian moments partitions the parameter space into distinct regimes and provides a unified description of population and entanglement dynamics across both stable and unstable regions. We find that dynamical instability does not imply unbounded entanglement growth: although the bosonic population diverges, the logarithmic negativity remains bounded and approaches a finite asymptotic value. We further characterize the finite asymptotic entanglement and show that asymmetric local dissipation shifts both the stability boundary and the threshold for nonzero asymptotic entanglement. For identical local dissipation, the presence of a common bath leaves the dynamical-region boundaries unchanged while qualitatively reshaping the long-time entanglement landscape, producing broad enhancement regions within the stable regimes and a narrow enhancement region within the unstable regime. In the common-bath-only limit, this enhancement is attributed to an exact dark-mode (bound-state-in-the-continuum, BIC) protection mechanism, which reduces to a quasi-BIC remnant under independent dissipation. Our results establish the non-Hermitian dynamical spectrum as a framework for connecting stability, nonequilibrium dynamics, and asymptotic entanglement in open quadratic bosonic systems.
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The paper asks whether dynamical instability in an open parametric bosonic system necessarily entails unbounded entanglement growth. It studies a two-mode quadratic model with beam-splitter coupling $g$, two-mode squeezing $J$, local losses $\Gamma_{1,2}$, and collective loss $\kappa\mathcal D[a_1+a_2]$. Starting from the two-mode vacuum, it derives analytical Gaussian-moment dynamics and evaluates logarithmic negativity from the partially transposed covariance matrix.
For equal local losses $\Gamma$ without collective loss, the drift spectrum separates unstable, nonoscillatory stable, and oscillatory stable regimes. Writing $s=2\sqrt{J^2-g^2}$, instability occurs for $s\geq\Gamma$, while $g=J$ marks an exceptional point separating the stable regimes. In the exponentially unstable region, occupations diverge but logarithmic negativity approaches $E_N^\infty=\max\{0,-\log[2J\Gamma/(s(s+\Gamma))]\}$. This follows from cancellation of leading exponential factors in covariance-matrix invariants, rather than convergence to a stationary state.
Analytical asymptotics and parameter diagrams show that unequal local losses shift both stability and entanglement thresholds. With equal local losses, a common bath leaves the regime boundaries unchanged but enhances asymptotic entanglement over broad stable regions and a narrow unstable window. Without local losses, the antisymmetric normal mode is exactly dark: entanglement grows without bound for $g<J$ and oscillates persistently for $g>J$.
The analysis is restricted to a Markovian quadratic Gaussian dimer. Multimode systems and interaction-driven non-Gaussian entanglement are identified as directions for further study.
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Central claim may not hold: The abstract's finite-asymptotic-entanglement claim omits the common-bath-only exception, for which the paper itself demonstrates unbounded logarithmic negativity in the amplifying regime.
Appendix C3 switches dominant asymptotic exponentials at s=Γ+κ instead of s=Γ+2κ, producing an unsupported discontinuity and incorrect common-bath entanglement predictions over part of the unstable regime.
Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.
Dynamical instability in parametrically driven bosonic systems is generally associated with diverging occupations and the absence of a stationary state, but its implications for long-time entanglement remain unclear. We investigate this question in a dissipative bosonic dimer with beam-splitter and two-mode-squeezing interactions, local loss, and a tunable common bath. The non-Hermitian dynamical spectrum governing the Gaussian moments partitions the parameter space into distinct regimes and provides a unified description of population and entanglement dynamics across both stable and unstable regions. We find that dynamical instability does not imply unbounded entanglement growth: although the bosonic population diverges, the logarithmic negativity remains bounded and approaches a finite asymptotic value. We further characterize the finite asymptotic entanglement and show that asymmetric local dissipation shifts both the stability boundary and the threshold for nonzero asymptotic entanglement. For identical local dissipation, the presence of a common bath leaves the dynamical-region boundaries unchanged while qualitatively reshaping the long-time entanglement landscape, producing broad enhancement regions within the stable regimes and a narrow enhancement region within the unstable regime. In the common-bath-only limit, this enhancement is attributed to an exact dark-mode (bound-state-in-the-continuum, BIC) protection mechanism, which reduces to a quasi-BIC remnant under independent dissipation. Our results establish the non-Hermitian dynamical spectrum as a framework for connecting stability, nonequilibrium dynamics, and asymptotic entanglement in open quadratic bosonic systems.
The paper asks whether dynamical instability in an open parametric bosonic system necessarily entails unbounded entanglement growth. It studies a two-mode quadratic model with beam-splitter coupling g, two-mode squeezing J, local losses Γ1,2, and collective loss κD[a1+a2]. Starting from the two-mode vacuum, it derives analytical Gaussian-moment dynamics and evaluates logarithmic negativity from the partially transposed covariance matrix.
For equal local losses Γ without collective loss, the drift spectrum separates unstable, nonoscillatory stable, and oscillatory stable regimes. Writing s=2J2−g2, instability occurs for s≥Γ, while g=J marks an exceptional point separating the stable regimes. In the exponentially unstable region, occupations diverge but logarithmic negativity approaches EN∞=max{0,−log[2JΓ/(s(s+Γ))]}. This follows from cancellation of leading exponential factors in covariance-matrix invariants, rather than convergence to a stationary state.
Analytical asymptotics and parameter diagrams show that unequal local losses shift both stability and entanglement thresholds. With equal local losses, a common bath leaves the regime boundaries unchanged but enhances asymptotic entanglement over broad stable regions and a narrow unstable window. Without local losses, the antisymmetric normal mode is exactly dark: entanglement grows without bound for g<J and oscillates persistently for g>J.
The analysis is restricted to a Markovian quadratic Gaussian dimer. Multimode systems and interaction-driven non-Gaussian entanglement are identified as directions for further study.
We provide a framework for understanding dynamical metastability in open many-body systems of free bosons, whereby the dynamical stability properties of the system in the infinite-size (thermodynamic) limit may sharply differ from those of any finite-size truncation, and anomalous transient dynamics may arise. By leveraging pseudospectral techniques, we trace the discrepancy between asymptotic and transient dynamics to the non-normality of the underlying quadratic bosonic Lindbladian (QBL) generator and show that two distinct flavors of dynamical metastability can arise. QBLs exhibiting type I dynamical metastability, previously discussed in the context of anomalous transient amplification [Phys. Rev. Lett. 127, 245701 (2021)], are dynamically unstable in the infinite-size limit yet stable once open boundaries are imposed. In contrast, type II dynamically metastable QBLs, which we uncover in this work, are dynamically stable for infinite size but become unstable under open boundary conditions for arbitrary finite system size. We exhibit representative models for both types of metastability in the dissipative, as well as the closed-system (Hamiltonian) settings, and analyze distinctive behavior they can engender. We show that dynamical metastability manifests itself in the generation of entanglement entropy by way of a transient which reflects the stability phase of the infinite (rather than the actual finite) system and, as a result, is directly tied to the emergence of supervolume entanglement scaling in type I systems. Finally, we demonstrate how, even in Hermitian, and especially in highly non-normal regimes, the spectral properties of an infinite-size QBL are reflected in the linear response functions of the corresponding finite QBLs by way of resonant pseudospectral modes.
Zero modes, understood here as degrees of freedom with vanishing confining frequency, play a central role in the nonequilibrium dynamics of bosonic systems. In Gaussian models, however, they lead to an unbounded, logarithmic growth of entanglement entropy. We show that this divergence is not an intrinsic property of zero modes themselves, but arises specifically for non-compact zero modes. Their non-compact configuration space allows unbounded spreading in position space, while their continuous spectra enable indefinite dephasing in momentum space. By contrast, compact zero modes in compact bosonic systems behave fundamentally differently: Spreading and dephasing are eventually halted, so that compactness caps the entanglement entropy at a finite value, making its dynamical role most transparent in the presence of a zero mode. We demonstrate this mechanism in a minimal setting by comparing two coupled harmonic oscillators with two coupled quantum rotors. We then show that the same physics persists in many-body systems by contrasting an N-site compact rotor chain with the non-compact harmonic chain. Finally, we relate these insights to ultra-cold-atom realizations of compact quantum field theories. In particular, we clarify when a compact free-boson (Tomonaga-Luttinger liquid) description is required and when the commonly used non-compact massless Klein-Gordon model breaks down. Even when the initial state is accurately captured by a non-compact Gaussian description, compactness ultimately governs the late-time quench dynamics, curbing entanglement growth rather than allowing a dynamical divergence.
Abstract Unlike their fermionic counterparts, the dynamics of Hermitian quadratic bosonic Hamiltonians are governed by a generally non-Hermitian Bogoliubov-de Gennes effective Hamiltonian. This underlying non-Hermiticity gives rise to a dynamically stable regime, whereby all observables undergo bounded evolution in time, and a dynamically unstable one, whereby evolution is unbounded for at least some observables. We show that stability-to-instability transitions may be classified in terms of a suitably generalized P T symmetry , which can be broken when diagonalizability is lost at exceptional points in parameter space, but also when degenerate real eigenvalues split off the real axis while the system remains diagonalizable. By leveraging tools from Krein stability theory in indefinite inner-product spaces, we introduce an indicator of stability phase transitions, which naturally extends the notion of phase rigidity from non-Hermitian quantum mechanics to the bosonic setting. As a paradigmatic example, we fully characterize the stability phase diagram of a bosonic analogue to the Kitaev–Majorana chain under a wide class of boundary conditions. In particular, we establish a connection between phase-dependent transport properties and the onset of instability, and argue that stable regions in parameter space become of measure zero in the thermodynamic limit. Our analysis also reveals that boundary conditions that support Majorana zero modes in the fermionic Kitaev chain are precisely the same that support stability in the bosonic chain.
Entanglement phase transitions driven by quantum measurements have emerged as a central paradigm in open quantum many-body physics. Such phase transitions are well established for systems with finite local Hilbert-space dimensions, such as qubits and fermions, while their realization in bosonic systems with unbounded local occupation numbers remains poorly understood. Even in the absence of interactions, number states of bosons are intrinsically non-Gaussian, preventing the use of standard correlation-matrix approaches. To address this problem, we develop a replica-free Keldysh field-theoretic framework that expresses the Renyi entropy of bosonic systems initialized in on-site Fock states in terms of permanents of matrices constructed from single-particle Green's functions. Applying this framework to a continuously monitored one-dimensional cross-stitch lattice conditioned on the no-click trajectory, we uncover a transition from volume-law to logarithmic entanglement scaling. We show that the transition is controlled by a restructuring of the non-Hermitian spectrum that changes the number of long-lived modes from extensive to finite. In the strongly monitored regime, bosons dynamically condense into a microscopic number of slowest-decaying modes, producing logarithmic entanglement scaling, whereas an extensive manifold of long-lived modes at weak monitoring gives rise to volume-law entanglement. Our results establish a distinct mechanism for measurement-induced entanglement transitions in free bosonic systems and provide a computationally efficient diagnostic of the measurement-induced bosonic condensation.
We describe the evolution of the quantum entanglement of an open system consisting of two bosonic modes interacting with a common thermal environment, described by two different models. The initial state of the system is taken of Gaussian form. In the case of a thermal bath, characterized by temperature and dissipation constant which correspond to an asymptotic Gibbs state of the system, we show that for a zero temperature of the thermal bath an initial entangled Gaussian state remains entangled for all finite times. For an entangled initial squeezed thermal state, the phenomenon of entanglement sudden death takes place and we calculate the survival time of entanglement. For the second model of the environment, corresponding to a non-Gibbs asymptotic state, we study the possibility of generating entanglement. We show that the generation of the entanglement between two uncoupled bosonic modes is possible only for definite values of the temperature and dissipation constant, which characterize the thermal environment.
Entanglement in continuous-variable Gaussian systems is a key resource, and common reservoirs can both suppress and generate correlations. Existing work focused on pre-entangled states or Markovian baths, leaving open whether separable squeezed inputs entangle in structured environments or under modulation. We study two bosonic modes coupled to a common reservoir, each initialized in a separable squeezed vacuum. Dynamics are analyzed utilizing Gaussian covariance methods, evolved under approximate Non-Markovian quantum state diffusion (QSD), finite-temperature pseudomode embeddings, and Bures-based non-Markovian diagnostics. We identify three mechanisms absent in Markovian dynamics: (1) A detuning condition that freezes entanglement trajectories across reservoir correlation times; (2) birth, death, and revival of entanglement from orthogonal inputs; and (3) integer-locked beating with square-wave oscillations produced by periodic detuning. All mechanisms persist at finite temperature, with deviations bounded within 5% in cryogenic regimes and 20% at moderate occupations. These deviation bounds align with cryogenic cavity, phononic, and optomechanical platforms, where structured spectral densities and detuning modulation are already accessible. Structured reservoirs are shown to emerge as tunable entanglement resources for continuous-variable quantum technologies.