Quantum

Krylov meets Fock: Complementary lenses on quantum dynamics

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Briefings

A new theoretical framework called the Fock state lattice (FSL) extends quantum dynamics analysis from Krylov space to a higher-dimensional lattice using Fock basis vectors. The study applies this to two quantum optics models: the multi-mode Jaynes-Cummings and Dicke models. Key findings include analytical results for Dicke model spread measures in the thermodynamic limit, which detect the superradiant phase transition. The work suggests FSL dynamics offer complementary insights and greater analytical control compared to standard Krylov space methods.

Key points

• The Fock state lattice (FSL) represents quantum dynamics using a higher-dimensional lattice where sites correspond to Fock basis vectors, extending beyond the Krylov basis vectors.
• Analytical results for Dicke model spread measures in the thermodynamic limit were obtained, enabling detection of the superradiant phase transition through time scaling analysis.

Context

This research builds on quantum optics models of light-matter interaction, specifically the multi-mode Jaynes-Cummings and Dicke models, to explore new analytical tools for understanding quantum dynamics in Krylov and Fock spaces.

Limitations

The study focuses on two specific quantum optics models; results for other systems remain unverified. The thermodynamic limit analysis for the Dicke model provides analytical insights but does not cover finite-size effects or specific initial conditions.

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