Abstract
The coupled quantum harmonic oscillator is one of the most researched and important model systems in quantum optics and quantum informatics. This system is often investigated for quantum entanglement in the environment. As a result, such studies are complex and can only be carried out using numerical methods that do not reveal the general pattern of such systems. In this work, the external environment is considered to be two independent particles interacting with coupled harmonic oscillators. It is shown that such a system has an exact analytical solution to the dynamic Schrödinger equation. The analysis of this solution is carried out, and the main parameters of this system are revealed. The solutions obtained can be used to study more complex systems and their quantum entanglement.
Highlights
A coupled harmonic oscillator is the most important model system in quantum optics and computer science
A model of linear beam splitter in quantum optics can be represented by two coupled harmonic oscillators [1]
Reducing the quantum decoherence of a system when it interacts with a classical system is one of the important problems in quantum informatics on the way to creating quantum computers
Summary
A coupled harmonic oscillator is the most important model system in quantum optics and computer science. A model of linear beam splitter in quantum optics can be represented by two coupled harmonic oscillators [1] This model is used to explain the problem of photosynthesis based on quantum entangled states [2,3,4]. Study of properties of coupled harmonic oscillators, mainly quantum entanglement, is a separate direction in quantum physics. Oscillators are used as quantum entangled particles, which interact with the system of oscillators (thermal bath) modeling the classical medium (e.g., References [16,17,18]). This choice is justified because oscillators are the simplest model for studying complex systems. The obtained solution can be used to analyze quantum entanglement and decoherence of bound harmonic oscillators
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