Quantum entanglement of a harmonic oscillator with an electromagnetic field

Dmitry N Makarov

doi:10.1038/s41598-018-26650-8

Abstract

At present, there are many methods for obtaining quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of the Schrodinger equation. There is a need for new methods for obtaining quantum-entangled particles and mathematically accurate studies of such methods. In this paper, a quantum harmonic oscillator (for example, an electron in a magnetic field) interacting with a quantized electromagnetic field is considered. Based on the exact solution of the Schrodinger equation for this system, it is shown that for certain parameters there can be a large quantum entanglement between the electron and the electromagnetic field. Quantum entanglement is analyzed on the basis of a mathematically exact expression for the Schmidt modes and the Von Neumann entropy.

Highlights

It is known that quantum entanglement arises when the wave function of a particle system cannot be represented as a product of the wave functions of each particle
It is interesting to note that when δ ~ β, the value is small; in order for the system to have a large quantum entanglement, it takes t ~ 1/β
It is known that the Von Neumann entropy has the maximum value max{SN} = ln N, where N is the number of nonzero eigenvalues; in our case, max{SN} = ln(s1 + s2)

Summary

OPEN Quantum entanglement of a harmonic oscillator with an electromagnetic field

There are many methods for obtaining quantum entanglement of particles with an electromagnetic field. Based on the exact solution of the Schrodinger equation for this system, it is shown that for certain parameters there can be a large quantum entanglement between the electron and the electromagnetic field. On the basis of the exact solution of the nonstationary Schrodinger equation for an atom in a strong two-mode electromagnetic field, it has been shown[17,18] that there is a strong quantum entanglement between photons. As this solution is based upon the assumption that the external electromagnetic field is many times stronger than the Coulomb field of attraction of an electron in an atom, it does not promote an understanding of the influence of the Coulomb. It is shown that for certain parameters of the system under consideration, a large quantum entanglement is possible

Exact solution of the Schrodinger equation

Conclusion

Findings

Additional Information