In this study, we investigated the properties of entanglement of an optomechanical system including two mechanical oscillators, where two mechanical oscillators are coupled with the cavity field in different coupling modes: the interaction between one mechanical oscillator and cavity field is first-order coupling, and the interaction between the other and the cavity field is quadratic coupling. On the one hand, the entanglement between two mechanical oscillators is studied. The influence of the frequency of the cavity field, the mass of mechanical oscillators, and the temperature of mechanical oscillators on the entanglement between two mechanical oscillators are investigated. On the other hand, for the given parameters of the system, we also obtained the entanglement between the cavity field and the mechanical oscillator that has a quadratic coupling. Compared with the entanglement between microscopic particles, the stable macroscopic quantum entanglement between two mechanical oscillators has the characteristics of long existence life and can be reused, and it also plays an important role in quantum information processing and quantum network construction.In this study, we investigated the properties of entanglement of an optomechanical system including two mechanical oscillators, where two mechanical oscillators are coupled with the cavity field in different coupling modes: the interaction between one mechanical oscillator and cavity field is first-order coupling, and the interaction between the other and the cavity field is quadratic coupling. On the one hand, the entanglement between two mechanical oscillators is studied. The influence of the frequency of the cavity field, the mass of mechanical oscillators, and the temperature of mechanical oscillators on the entanglement between two mechanical oscillators are investigated. On the other hand, for the given parameters of the system, we also obtained the entanglement between the cavity field and the mechanical oscillator that has a quadratic coupling. Compared with the entanglement between microscopic particles, the stable macroscopic quantum entanglement between two mechanical oscillators has the characteristics of long existence life and can be reused, and it also plays an important role in quantum information processing and quantum network construction.

Frontiers in PhysicsJun 15, 20224 citations

The Quantum Mechanics of Coupled Oscillators.

B. R. Mollow

Jan 1, 19660 citations

Quantum Mechanics of Harmonic Oscillators

Thomas A. Garrity

Cambridge University Press eBooksJan 19, 20150 citations

Coupled oscillators, entangled oscillators, and Lorentz-covariant harmonic oscillators

Y S Kim, Marilyn E. Noz

Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of two-by-two matrices commonly called $SL(2,c)$ . Thus the coupled harmonic oscillators can play the role of combining quantum mechanics with special relativity. It is therefore possible to relate the current issues of physics to the Lorentz-covariant formulation of quantum mechanics.Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of two-by-two matrices commonly called $SL(2,c)$. Thus the coupled harmonic oscillators can play the role of combining quantum mechanics with special relativity. It is therefore possible to relate the current issues of physics to the Lorentz-covariant formulation of quantum mechanics.

arXiv:quant-ph/0502096Journal of Optics B Quantum and Semiclassical OpticsNov 4, 200522 citations

Harmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman

Y. S. Kim, Marilyn E. Noz

Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement, decoherence, and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called $SL(2,c)$ . Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement, decoherence, and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called $SL(2,c)$. Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.

arXiv:quant-ph/0411017Nov 2, 20040 citations

SL(2,c)

. Thus the coupled harmonic oscillators can play the role of combining quantum mechanics with special relativity. It is therefore possible to relate the current issues of physics to the Lorentz-covariant formulation of quantum mechanics.

SL(2,c)

. Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.