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.

Optimization of the resonator-induced phase gate for superconducting qubits

“…where u jk and v jk , j, k = a, b, c, are the flux and charge hybridization coefficients that relate the corresponding bare and normal mode quadratures and are derived via a canonical (Bogoliubov) transformation [42,58,59] (see Appendix C). Moreover, the normal mode harmonic frequencies are shown as ωk in order to distinguish from the renormalized normal mode frequencies (no bar) that contain the static (Lamb) corrections.…”

Dynamical Invariant Applied on General Time-Dependent Three Coupled Nano-Optomechanical Oscillators

“…It includes nano-optomechanical resonances [6,7], electromagnetically induced transparency [8], stimulated Raman effects [9], Josephson phenomena [10], one-half spin dynamics [11], and trapping of different particles [1]. Among various issues related to coupled harmonic oscillators, the entanglement and mixedness are the most remarkable characters which give a theoretical basis for quantum technologies, such as quantum computing and quantum cryptography [12][13][14]. Hence, the entanglement in three coupled harmonic oscillators should be analyzed from the fundamental quantum mechanical point of view.…”

Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators

“…Description and interpretation of coupled systems are of particular interest in physics because the interaction caused by coupling is responsible for novel quantum effects such as entanglement [ 1 , 2 ] and quadrature squeezing [ 3 ]. Coupled oscillatory quantum motions are found in almost all areas of physical sciences, ranging from nanotechnology to biology [ 4 , 5 , 6 , 7 , 8 ]. Coupled oscillatory systems can be used as a model to describe the interactions between atoms in a one-dimensional crystal with spring-like forces under white noise excitations [ 9 , 10 ].…”