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Approach the fluctuation of eigenstates around the avoided levelcrossing by two-level dynamics

Jie Jie, QLWang, SJWei

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

From level dynamics, we show that when two levels come to an avoided From level dynamics, we show that when two levels come to an avoided

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We numerically show the changing of eigenstates of the Hamiltonian as a function of a control parameter governing the strength of a non-integrable perturbation. The eigenstates change abruptly at avoided level crossing. After the avoided level crossing, they tend to restore their original form before the avoided level crossing, and exchange their distribution, especially for those which can he treated as isolated two-body collisions. But in general, the eigenstates have some changings after the avoided crossing, and the symmetries of the system are broken down locally at this kind of avoided level crossings.
Avoided crossings are fundamental phenomena in quantum mechanics and photonics that originate from the interaction between coupled energy levels and have been extensively studied in linear dispersive dynamics. Their manifestation in open, driven-dissipative systems, however, where nonlinear dynamics of quantum fluctuations come into play, remains largely unexplored. In this work, we analyze the hitherto unexplored occurrence of avoided and genuine crossings in the spectrum of quantum noise. We demonstrate that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the associated singular vectors and suggesting the presence of genuine crossings (diabolical points) in nearby systems. We show that these spectral features can be deliberately designed, highlighting the possibility of programming the quantum noise response of photonic systems. As a notable example, such control can be exploited to generate broad, flat-band squeezing spectra - a desirable feature for enhancing degaussification protocols. Our analysis is based on a detailed study of the Analytic Bloch-Messiah Decomposition (ABMD), which we use to characterize the parameter-dependent behavior of singular values and their corresponding vectors. This study provides new insights into the structure of multimode quantum correlations and offers a theoretical framework for the experimental exploitation of complex quantum optical systems.