Informational Topology of Quantum Resonances: From Dark-State Entanglement to Vacuum Tunneling in 2D Superfluids
Abstract
Recent experimental advances --- the stabilization of long-lived entanglement through dark states in nanocavities and the observation of vacuum tunneling in 2D superfluids --- highlight a common principle: quantum coherence is not absolute but tunable through environmental and topological parameters. We develop the Informational-Topological (InterTop) framework, in which quantum states are modeled as holonomies across informational manifolds. Within this geometry, dark states correspond to holonomies with suppressed leakage, while vortex--antivortex tunneling in superfluids realizes emergent informational nodes with variable holonomy mass. We derive explicit mathematical formalisms connecting InterTop amplitudes to experimental observables, including oscillatory visibility laws V()V(\omega), synthetic phase shifts proportional to trap or flow parameters, and holonomy-induced anisotropies. Our analysis maps these predictions onto resource-theoretic measures of coherence and formulates falsifiable experimental tests, distinguishing InterTop from standard decoherence theory. By integrating photonic and superfluid platforms, this work positions InterTop as a geometrical alternative to collapse, branching, and hidden-variable models, offering predictive power for quantum technologies and foundational insights into the ontology of resonance.
Main BackgroundÂ
1. Dark-State Entanglement
Experimentally, entanglement lifetimes were extended by ~600 by tuning cavity loss rates.
Dark states act as "optically invisible" modes with minimal leakage, stabilizing coherence.
This demonstrates that entanglement coherence is controllable and engineerable, not fixed.
In InterTop terms: dark states = holonomies with suppressed variance, representing stable informational loops.
2. Vacuum Tunneling in 2D Superfluids
Vortex--antivortex pairs created spontaneously under superflow mimic Schwinger pair creation.
The vortex mass is not constant, but depends on motion and environment.
This introduces a variable holonomy mass, directly aligning with InterTop's concept that coherence stability depends on the geometry of the informational manifold.
The controllability of tunneling and stability suggests that holonomies can be tuned, just like entanglement in dark states.
3. Synthesis into InterTop
Both experiments converge on a shared principle: quantum coherence is resonance in an informational-topological space, tunable via environmental and structural parameters.
This motivates a rigorous mathematical framework where amplitudes are decomposed into holonomies, stability criteria define pointer states, and predictive functions for visibility/phase can be derived.
Outline
I. Introduction
Motivation: foundational puzzles of superposition & entanglement.
Context: recent breakthroughs in dark-state entanglement & 2D superfluid tunneling.
Need for a unifying theoretical framework beyond decoherence.
II. InterTop Mathematical Formalism
Definition of informational manifold, nodes, and holonomies.
Gauge-like informational connections.
Synthetic phase and holonomy invariants.
Embedding visibility--distinguishability tradeoff in geometry.
III. Dark-State Entanglement as Holonomy Stabilization
Mapping cavity tuning to holonomy variance suppression.
Prediction: oscillatory visibility functions beyond monotonic decoherence.
Synthetic phase shifts under cavity parameter cycling.
IV. 2D Superfluid Tunneling as Holonomy Creation
Vortex--antivortex pairs as informational nodes.
Variable vortex mass holonomy variance.
Predictive laws for coherence vs. superflow velocity.
Geometric loop phases under parameter cycling.
V. Unified Resource-Theoretic Mapping
