Linearly coupled quantum harmonic oscillators and their quantum
entanglement
- URL: http://arxiv.org/abs/2402.00806v1
- Date: Thu, 1 Feb 2024 17:42:17 GMT
- Title: Linearly coupled quantum harmonic oscillators and their quantum
entanglement
- Authors: D.N. Makarov and K.A. Makarova
- Abstract summary: It is shown that quantum entanglement depends on only one coefficient $R in (0,1), which includes all the parameters of the system under consideration.
It has been shown that quantum entanglement can be very large at certain values of this coefficient.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum harmonic oscillators linearly coupled through coordinates and
momenta, represented by the Hamiltonian $ {\hat H}=\sum^2_{i=1}\left( \frac{
{\hat p}^{2}_i}{2 m_i } + \frac{m_i \omega^2_i}{2} x^2_i\right) +{\hat H}_{int}
$, where the interaction of two oscillators ${\hat H}_{int} = i k_1 x_1 { \hat
p }_2+ i k_2 x_2 {\hat p}_1 + k_3 x_1 x_2-k_4 {\hat p}_1 {\hat p}_2$, found in
many applications of quantum optics, nonlinear physics, molecular chemistry and
biophysics. Despite this, there is currently no general solution to the
Schr\"{o}dinger equation for such a system. This is especially relevant for
quantum entanglement of such a system in quantum optics applications. Here this
problem is solved and it is shown that quantum entanglement depends on only one
coefficient $R \in (0,1)$, which includes all the parameters of the system
under consideration. It has been shown that quantum entanglement can be very
large at certain values of this coefficient. The results obtained have a fairly
simple analytical form, which facilitates analysis.
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