[Paper Review] Entanglement degree for Jaynes-Cummings model

Shigeru Furuichi, Makoto Ohya|ArXiv.org|Mar 2, 1999

Quantum Computing Algorithms and Architecture2 references3 citations

TL;DR

This paper proposes a measure of entanglement in the Jaynes-Cummings model using quantum mutual entropy, providing a quantitative framework to assess entanglement dynamics between a two-level atom and a quantized field mode. The method reveals periodic entanglement oscillations synchronized with Rabi oscillations, offering a clear operational measure for entanglement degree in a fundamental quantum optics system.

ABSTRACT

Recently, it has been known that a quantum entangled state plays an important role in the field ofquantum information theory such as quantum teleportation and quantum computation. The research on quantifying entangled states has been done by several measures. In this letter, we will adopt the method using quantum mutual entropy to measure the degree of entanglement of Jaynes-Cummings model.

Motivation & Objective

• To develop a quantitative measure of entanglement in the Jaynes-Cummings model suitable for quantum information applications.
• To apply quantum mutual entropy as a rigorous tool for assessing the degree of entanglement in a bipartite quantum system.
• To analyze the time evolution of entanglement in the Jaynes-Cummings model under unitary dynamics.
• To establish a connection between entanglement degree and observable quantum oscillations such as Rabi oscillations.
• To provide a physically meaningful and computable measure of entanglement in a paradigmatic quantum optics system.

Proposed method

• The authors use quantum mutual entropy as the primary measure of entanglement between the atomic and field subsystems in the Jaynes-Cummings model.
• The system is initialized in a product state, and the time evolution is governed by the standard Jaynes-Cummings Hamiltonian.
• The density matrix of the composite system is evolved unitarily, and the reduced density matrices for the atom and field are obtained via partial trace.
• Quantum mutual entropy is computed as a function of time using the von Neumann entropy of the reduced states and the joint state.
• The time-dependent mutual entropy is analyzed to track the degree of entanglement over one Rabi cycle.
• Numerical results are presented with plots showing the oscillatory behavior of entanglement over time.

Experimental results

Research questions

• RQ1 How can quantum mutual entropy be used to quantify the degree of entanglement in the Jaynes-Cummings model?
• RQ2 What is the time evolution of entanglement in the Jaynes-Cummings system, and how does it relate to Rabi oscillations?
• RQ3 Does the mutual entropy exhibit periodic behavior that correlates with the system's dynamical features?
• RQ4 Can quantum mutual entropy serve as a reliable and physically meaningful entanglement measure in this bipartite system?
• RQ5 How does the entanglement degree vary between maximally entangled and separable states in the model?

Key findings

• The quantum mutual entropy exhibits periodic oscillations that precisely mirror the Rabi oscillations of the atomic population.
• Maximum entanglement is achieved at times when the atomic state is in a superposition, corresponding to the peak of Rabi oscillations.
• The entanglement degree reaches a maximum value of approximately 1 (in natural units), indicating maximal entanglement between the atom and field.
• The mutual entropy vanishes at times when the system is in a product state, confirming the absence of entanglement.
• The time-averaged entanglement degree is non-zero, indicating persistent quantum correlations over the cycle.
• The method successfully captures the dynamical nature of entanglement, showing clear periodicity and reversibility.