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Quantum entanglement degrees of a two-level atom in the photonic crystals heat reservoir

Siqi Zhang, Hong Li, Meixuan Li, Ming Hui Guo, Li-Jun Song

Published Dec 18, 2019• 0 citations
Publisher

Abstract

In this paper, we have calculated the entanglement degrees of a two-level atom in the one-dimensional photonic crystals heat reservoir, researched the effect of parameter q on the quantum entanglement degrees, and given the quantum entanglement degrees curves with time evolution. We have taken the parameter q=1, 2, 3.5 and 8.5. Our results show when the parameter q=2, keep the time of entanglement degrees near E=1 longest, it is helpful to quantum communication. Furthermore, we have designed the one-dimensional photonic crystals heat reservoir, which meet the parameter q=1, 2, 3.5 and 8.5. These can guide the fabrication of quantum devices based on photonic crystals.

DOI
10.1117/12.2543443

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In this paper, we have calculated the entanglement degrees of a two-level atom in the one-dimensional photonic crystals heat reservoir, researched the effect of parameter q on the quantum entanglement degrees, and given the quantum entanglement degrees curves with time evolution. We have taken the parameter q=1, 2, 3.5 and 8.5. Our results show when the parameter q=2, keep the time of entanglement degrees near E=1 longest, it is helpful to quantum communication. Furthermore, we have designed the one-dimensional photonic crystals heat reservoir, which meet the parameter q=1, 2, 3.5 and 8.5. These can guide the fabrication of quantum devices based on photonic crystals.
The time evolutions of the entanglement between a two-level atom and its spontaneous emission field in free space, cavity, isotropic and anisotropic photonic crystal are studied by using quantum entropy. It is found that the evolution properties of the atom-field entanglement are directly related to the nature of the structured reservoir,specifically, to the distribution of the density of modes. In free space and cavity, as the density of the modes varies smoothly with frequency, the atom-field entanglement decays to zero in a finite time. However in an isotropic and anisotropic photonic crystal, the atom-field entanglement can keep steady due to the existence of a photonic band gap in the density of the modes. Thus, we can control the time evolution of the entanglement between the atom and its spontaneous emission field by changing the density of the modes of the structured reservoirs.
The quantum entangled degrees of entangled states become smaller with the transmission distance increasing, how to keep the purity of quantum entangled states is the puzzle in quantum communication. In the paper, we have designed a new type entanglement degrees amplifier by one-dimensional photonic crystal, which is similar as the relay station of classical electromagnetic communication. We find when the entangled states of two-photon and three-photon pass through photonic crystal, their entanglement degrees can be magnified, which make the entanglement states can be long range propagation and the quantum communication can be really realized.
By means of Von Neumann entropy and Schmidt number K, we study the time evolution properties of the entanglement between a two-level atom and spontaneous emission field in anisotropic photonic crystal. The evolution properties of the atom-field entanglement are directly related to the relative position of the upper level from the band edge. The atom-field entanglement can keep steady when the atomic upper level is within the band gap. The atom-field entanglement increases to the maximum value firstly and then decay to zero when the atomic upper level is within the transmitting band. The atom-field entanglement also depends on the initial state of the atom. We can control the time evolution properties of the atom-field entanglement by choosing special atomic initial state and the relative position of the upper level from the band edge.
The statistic properties of photon in the system of a two-mode entangled coherent state interacting with a Ξ-type three-level atom are investigated by solving Schrdinger equation and using numerical calculations. The effects on the statistic properties of photon induced by the degree of entanglement of the two-mode entangled coherent state, the ground state probability amplitude of the atomic initial state, the detuning, the atom-field coupling constant and the mean photon number are analyzed. The results indicate that the influence of the degree of entanglement of the two-mode entangled coherent state on the statistic properties of photon is small. The increasing of the ground state probability amplitude of the atomic initial state causes the center of the time evolution curve to move up distinctly. The increasing of the detuning results in the decrease of the oscillating frequency of the time evolution curve. The influences of the atom-field coupling constant and the mean photon number on the statistic properties of photon are noticeable. The correlation of the two modes of light is non-classical all the time.
By means of the quantum theory and numerical calculations method,the entanglement time evolution of the two identical two-level atoms in Bell states interacting with the two-mode odd-even entangled coherent field is investigated by using Negativity.The effects of the atoms initial state,mean photon numbers of field,the degree of the entanglement for the entangled coherent fields,and the coupling strength of interaction between atoms on the Negativity are discussed.The results show that the two-atom entanglement state will forever stay in the maximum entangled state when the initial state is |β_(11)〉,while the Bell state |β_(00)〉atoms appear disentanglement most of the scaled time.For the state |β_(10)〉,mean photon numbers of field can be a great help,and in the state |β_(01)〉the coupling strength of interaction between atoms plays a major role in the two-atom entanglement.
In this article, the quantum properties of light field of the two identical two-level entangled atoms interacting with the binomial optical field were studied by means of time evolution operator and numerical calculations. The results show that the time evolution of the squeezing and coherence properties of the light field depends on the entanglement degree of the initial two identical two-level entangled atoms and the parameters of the binomial optical field. The optical field fluctuation can be completely squeezed via choosing appropriate parameters.