Analysis of quantum properties of two-mode coupled Harmonic Oscillator based on the entangled state representation

Abstract

The quantum oscillator model plays a significant role in quantum optics and quantum information and has been one of the hot research topics in related fields. Inspired by the single-mode linear harmonic oscillator and the two-mode entangled state representation, this paper constructs a two-mode coupled harmonic oscillator. Different from the quantum transformation method used in previous literature, this paper directly uses the entangled state representation to solve its energy eigenvalues ​​and eigenfunctions easily. Compared with the one-mode harmonic oscillator, the energy eigenvalues ​​and eigenfunctions of this two-mode coupled harmonic oscillator are continuous.<br>Using the matrix theory of quantum operators, we derive the transformation and inverse transformation of the time evolution operator corresponding to the two-mode coupled harmonic oscillator. In addition, using the entangled state representation, the specific form of the time evolution of the two-mode vacuum state under the action of the oscillator is obtained. Through the analysis of quantum fidelity, it is found that the fidelity of the output quantum state decreases with the increase of the oscillator frequency, and the fidelity eventually tends to zero with the increase of time.<br>When analyzing the orthogonal squeezing properties of the output quantum state, this type of two-mode oscillator does not have the orthogonal squeezing effect, but instead has a strong quantum dissipation effect. This conclusion is further verified by the quasi-probability distribution Q function of the quantum state phase space. Therefore, the two-mode coupled harmonic oscillator has a major reference value in quantum control such as quantum decoherence and quantum information transmission.<br>Like the two-mode squeezed vacuum state, the photon distribution of the output quantum light field corresponding to the two-mode harmonic oscillator presents a super-Poisson distribution, and the photons exhibit a strong anti-bunching effect. Using the three-dimensional discrete plot of the photon number distribution, the super-Poisson distribution and quantum dissipation effect of the output quantum state are intuitively demonstrated.<br>Finally, the SV entanglement criterion is used to determine that the output quantum state has a high degree of entanglement. Further numerical analysis shows that the degree of entanglement increases with the action time and the oscillator frequency.<br>In summary, the two-mode coupled harmonic oscillator constructed in this paper can be used to prepare highly entangled quantum states through a complete quantum dissipation process. This provides theoretical support for the experimental preparation of quantum entangled states based on dissipative mechanisms.