Entanglement in Three Coupled Harmonic Oscillators

Abstract

We develop an approach in solving exactly the problem of three-body oscillators including general quadratic interactions in the coordinates for arbitrary masses and couplings. We introduce a unitary transformation of three independent angles to end up with a diagonalized Hamiltonian. Using the representation theory of the group $SU(3)$, we explicitly determine the solutions of the energy spectrum. Considering the ground state together with reduced density matrix, we derive the corresponding purity function that is giving rise to minimal and maximal entanglement under suitable conditions. The cases of realizing one variable among three is discussed and know results in literature are recovered.

12 pages, references added, typos corrected. Version to appear in Phys. Lett. A

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• Optimization of the resonator-induced phase gate for superconducting qubits
• Dynamics and Redistribution of Entanglement and Coherence in Three Time-Dependent Coupled Harmonic Oscillators
• Magnetic Field Effect on Dynamics of Entanglement for Time-dependent Harmonic Oscillator
• Virtual excitations and entanglement dynamics and polygamy in three ultra-strongly coupled systems
• Tomographic entanglement indicators in a coupled oscillator model
• The Canonical Forms of Matrix Product States in Infinite-Dimensional Hilbert Spaces
• On the diagonalization of quadratic Hamiltonians