Coupled harmonic oscillators and their quantum entanglement

Physical Review. E
Dmitry N Makarov

Abstract

A system of two coupled quantum harmonic oscillators with the Hamiltonian H[over ̂]=1/2(1/m_{1}p[over ̂]_{1}^{2}+1/m_{2}p[over ̂]_{2}^{2}+Ax_{1}^{2}+Bx_{2}^{2}+Cx_{1}x_{2}) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H[over ̂]Ψ=iℏ∂Ψ/∂t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.

References

Oct 1, 1995·Physical Review. a·P W Shor
Apr 1, 1996·Physical Review. a·C H BennettB Schumacher
Jul 24, 1989·Physical Review Letters·Y S Kim
Jun 10, 1991·Physical Review Letters·F Iachello, S Oss
Aug 5, 1991·Physical Review Letters·A K Ekert
Nov 16, 1992·Physical Review Letters·C H Bennett, S J Wiesner
Jul 23, 2008·Physical Review Letters·Juan Pablo Paz, Augusto J Roncaglia
Jan 15, 2011·Physical Review Letters·Fernando GalveDavid Zueco
Jul 24, 2014·Nature Chemistry·Franklin D FullerJennifer P Ogilvie
Sep 1, 2014·Nature Physics·Elisabet RomeroRienk van Grondelle

❮ Previous
Next ❯

Citations

Nov 20, 2020·Scientific Reports·Dmitry N Makarov

❮ Previous
Next ❯

Related Concepts

Related Feeds

Autoimmune Polyendocrine Syndromes

This feed focuses on a rare genetic condition called Autoimmune Polyendocrine Syndromes, which are characterized by autoantibodies against multiple endocrine organs. This can lead to Type I Diabetes.

Autoimmune Polyendocrinopathies

Autoimmune polyendocrinopathies, also called polyglandular autoimmune syndromes (PGASs), or polyendocrine autoimmune syndromes(PASs), are a heterogeneous group of rare diseases characterized by autoimmune activity against more than one endocrine organ, although non-endocrine organs can be affected. Discover the latest research on autoimmune polyendocrinopathies here.