A Bogoliubov-ratio framework for quantum-information diagnostics of time-dependent two-mode Boson Hamiltonian

• URL: http://arxiv.org/abs/2607.24404v2
• Date: Wed, 29 Jul 2026 00:51:30 GMT
• Title: A Bogoliubov-ratio framework for quantum-information diagnostics of time-dependent two-mode Boson Hamiltonian
• Abstract summary: We present a compact and unified framework for quantum-information diagnostics of time-dependent two-mode bosonic systems.<n>We demonstrate the utility of this framework in two distinct non-stationary setups: primordial cosmological perturbations and a chirped-pulse nondegenerate optical parametric amplifier.
• Score: 10.22413990748989
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a compact and unified framework for quantum-information diagnostics of time-dependent two-mode bosonic systems based on the Bogoliubov ratio $λ_k(η) \equiv β_k(η)/α_k(η)$. For a general time-dependent quadratic two-mode Hamiltonian, the state dynamics is exactly reduced to a single complex Riccati equation for $λ_k$. Upon tracing out one partner mode, the spectrum of the one-mode reduced density matrix is determined entirely by the squared magnitude $q_k(η) = \vert{}λ_k(η)\vert{}^2$. Consequently, we could construct the explicit, model-independent formula for the reduced-state purity, linear entropy, Rényi-2 entropy, and von Neumann entropy without reconstructing and diagonalizing the reduced density matrix on a model-by-model basis using coupled squeezing parameters ($r_k, φ_k$). We demonstrate the utility of this framework in two distinct non-stationary setups: primordial cosmological perturbations and a chirped-pulse nondegenerate optical parametric amplifier. In the cosmological context, our formulation clarifies how background-induced phase rotation and frequency softening regulate squeezing growth and state mixedness; in the optical domain, it captures the delayed onset, suppression of squeezing accumulation, and late-time entropy saturation induced by finite pump duration and frequency chirp. By cleanly factorizing model-dependent driving protocols from universal information-theoretic metrics, this framework offers an efficient, standardized diagnostic tool for a broad class of parametrically driven quadratic bosonic systems.

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