Researching | Evolution Characteristics of Three-Qubit Quantum Entanglement Under External Field Effect

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 21 >Page 2127001 > Article

Laser & Optoelectronics Progress
Vol. 58, Issue 21, 2127001 (2021)

Evolution Characteristics of Three-Qubit Quantum Entanglement Under External Field Effect

Weidong Luo¹, Xuan Zhou^2、3, Xiaoqing Zhou^2、*, Yunwen Wu^1、**, and Shangjiang Huang¹

Author Affiliations

¹College of Physics, Mechanical and Electrical Engineering, Jishou University,Jishou, Hunan 416000, China

²College of Information Science and Engineering, Jishou University, Jishou, Hunan 416000, China

³Hunan Province Higher Education Key Laboratory of Modeling and Monitoring;on the Near-Earth Electromagnetic Environments, Changsha University of Science and;Technology, Changsha , Hunan 410015, China

show less

DOI: 10.3788/LOP202158.2127001 Cite this Article Set citation alerts

Weidong Luo, Xuan Zhou, Xiaoqing Zhou, Yunwen Wu, Shangjiang Huang. Evolution Characteristics of Three-Qubit Quantum Entanglement Under External Field Effect[J]. Laser & Optoelectronics Progress, 2021, 58(21): 2127001 Copy Citation Text

show less

Abstract

The coherent state orthogonalization expansion method is used to analyze and investigate the factors influencing the three-qubit entanglement degree. In addition, the three-qubit entanglement in the interaction process with the vacuum state as the initial state of the light field is investigated by numerical calculation combined with analytical solution. The relationship between the entanglement degree of three identical qubits and the light field frequency as well as the influence of light-field-qubit coupling strength on the three-qubit entanglement degree is analyzed. The research results show that the evolutions of the three-qubit intrinsic energy and the three-qubit co-occurrence entanglement degree with light field frequency and time

g_{0} t

are related to the coupling strength, while the evolutions with time gt have nothing to do with the coupling strength.

Keywords

GHZ model orthogonalization of coherent states quantum entanglement quantum optics vacuum state

H = g_{1} ω_{0} (a + a^{+}) δ_{x, 1} + g_{2} ω_{0} (a + a^{+}) δ_{x, 2} + g_{3} ω_{0} (a + a^{+}) δ_{x, 3} + a^{+} a ω_{0}

，（1）

H = g_{1} ω_{0} (a + a^{+}) δ_{z, 1} + g_{2} ω_{0} (a + a^{+}) δ_{z, 2} + g_{3} ω_{0} (a + a^{+}) δ_{z, 3} + a^{+} a ω_{0}

，（2）

|φ〉 = (ϕ_{1} |0_{1} 0_{2} 1_{3}〉 + ϕ_{2} |0_{1} 1_{2} 1_{3}〉 + ϕ_{3} |1_{1} 0_{2} 1_{3}〉 + ϕ_{4} |1_{1} 1_{2} 1_{3}〉) |0_{W}〉

，（3）

\{\begin{array}{l} A = \frac{1}{2} ω_{0} g a + \frac{g}{ω_{0}} \\ B = \frac{1}{2} ω_{0} g a - \frac{g_{0}}{ω_{0}} \\ C = \frac{1}{2} ω_{0} g a + \frac{g_{0}}{ω_{0}} \\ D = \frac{1}{2} ω_{0} g a - \frac{g}{ω_{0}} \\ A^{+} = \frac{1}{2} ω_{0} g a^{+} + \frac{g}{ω_{0}} \\ B^{+} = \frac{1}{2} ω_{0} g a^{+} - \frac{g_{0}}{ω_{0}} \\ C^{+} = \frac{1}{2} ω_{0} g a^{+} + \frac{g_{0}}{ω_{0}} \\ D^{+} = \frac{1}{2} ω_{0} g a^{+} - \frac{g}{ω_{0}} \end{array}

，（4）

\{\begin{array}{l} \frac{4}{ω_{0}^{2} g^{2}} [A^{+} A - {(\frac{g}{ω_{0}})}^{2} - \frac{g}{ω_{0}} A^{+} + \frac{2 g^{2}}{ω_{0}^{2}} - \frac{g}{ω_{0}} A] |φ_{1}〉 + \\ g ω_{0} [\frac{2}{ω_{0} g} (A + A^{+} - \frac{2 g}{ω_{0}})] |φ_{1}〉 δ_{z} = E_{1} |φ_{1}〉 \\ \frac{4}{ω_{0}^{2} g^{2}} [B^{+} B - {(\frac{g_{0}}{ω_{0}})}^{2} + \frac{g_{0}}{ω_{0}} B^{+} - \frac{2 g_{0}^{2}}{ω_{0}^{2}} + \frac{g_{0}}{ω_{0}} B] |φ_{2}〉 + \\ g ω_{0} [\frac{2}{ω_{0} g} (B + B^{+} - \frac{2 g}{ω_{0}})] |φ_{2}〉 δ_{z} = E_{2} |φ_{2}〉 \\ \frac{4}{ω_{0}^{2} g^{2}} [C^{+} C - {(\frac{g_{0}}{ω_{0}})}^{2} - \frac{g_{0}}{ω_{0}} C^{+} - \frac{2 g_{0}^{2}}{ω_{0}^{2}} + \frac{g_{0}}{ω_{0}} C] |φ_{3}〉 + \\ g ω_{0} [\frac{2}{ω_{0} g} (C + C^{+} - \frac{2 g}{ω_{0}})] |φ_{3}〉 δ_{z} = E_{3} |φ_{3}〉 \\ \frac{4}{ω_{0}^{2} g^{2}} [D^{+} D - {(\frac{g}{ω_{0}})}^{2} + \frac{g}{ω_{0}} D^{+} - \frac{2 g^{2}}{ω_{0}^{2}} + \frac{g}{ω_{0}} D] |φ_{4}〉 + \\ g ω_{0} [\frac{2}{ω_{0} g} (D + D^{+} - \frac{2 g}{ω_{0}})] |φ_{4}〉 δ_{z} = E_{4} |φ_{4}〉 \end{array}

，（5）

\{\begin{array}{l} |φ_{1}〉 = \sum_{n = 0}^{N} a_{n} {|n〉}_{A} \\ |φ_{2}〉 = \sum_{n = 0}^{N} b_{n} {|n〉}_{B} \\ |φ_{3}〉 = \sum_{n = 0}^{N} c_{n} {|n〉}_{C} \\ |φ_{4}〉 = \sum_{n = 0}^{N} d_{n} {|n〉}_{D} \end{array}

，（6）

\{\begin{array}{l} {|n〉}_{A} = \frac{1}{\sqrt[]{n!}} (A^{+})^{n} {|0〉}_{A} \\ {|n〉}_{B} = \frac{1}{\sqrt[]{n!}} (B^{+})^{n} {|0〉}_{B} \\ {|n〉}_{C} = \frac{1}{\sqrt[]{n!}} (C^{+})^{n} {|0〉}_{C} \\ {|n〉}_{D} = \frac{1}{\sqrt[]{n!}} (D^{+})^{n} {|0〉}_{D} \end{array}

，（7）

\{\begin{matrix} A^{+} A {|n〉}_{A} = n_{1} {|n〉}_{A} \\ B^{+} B {|n〉}_{B} = n_{2} {|n〉}_{B} \\ C^{+} C {|n〉}_{C} = n_{3} {|n〉}_{C} \\ D^{+} D {|n〉}_{D} = n_{4} {|n〉}_{D} \end{matrix}

，（8）

\{\begin{matrix} _{A} {〈m| n〉}_{A} = δ_{m n} \\ _{B} {〈m| n〉}_{B} = δ_{m n} \\ _{C} {〈m| n〉}_{C} = δ_{m n} \\ _{D} {〈m| n〉}_{D} = δ_{m n} \end{matrix}

，（9）

\{\begin{array}{l} \frac{4}{ω_{0}^{2} g^{2}} n_{1} - \frac{4}{ω_{0}^{4}} - \frac{4}{ω_{0}^{3} g} + \frac{8}{ω_{0}^{4}} + 1 - \frac{a_{1}}{a_{0}} + \frac{2 g^{2}}{ω_{0}} = E_{1, m} \\ \frac{4}{ω_{0}^{2} g^{2}} n_{2} - \frac{4 g_{0}^{2}}{ω_{0}^{4} g^{2}} + \frac{4 g_{0}}{ω_{0}^{3} g^{2}} - \frac{8 g_{0}^{2}}{ω_{0}^{4} g^{2}} + \frac{4 g_{0} b_{1}}{ω_{0}^{3} g^{2} b_{0}} + 1 - \frac{b_{1}}{b_{0}} + \frac{2 g^{2}}{ω_{0}} = E_{2, m} \\ \frac{4}{ω_{0}^{2} g^{2}} n_{3} - \frac{4 g_{0}^{2}}{ω_{0}^{4} g^{2}} - \frac{8 g_{0}^{2}}{ω_{0}^{4} g^{2}} + \frac{4 g_{0}}{ω_{0}^{3} g^{2}} + \frac{4 g_{0} c_{1}}{ω_{0}^{3} g^{2} c_{0}} + 1 - \frac{c_{1}}{c_{0}} + \frac{2 g^{2}}{ω_{0}} = E_{3, m} \\ \frac{4}{ω_{0}^{2} g^{2}} n_{4} - \frac{4}{ω_{0}^{4}} - \frac{8}{ω_{0}^{4}} + \frac{4}{ω_{0}^{3} g} + \frac{4 d_{1}}{ω_{0}^{3} g d_{0}} + 1 - \frac{d_{1}}{d_{0}} + \frac{2 g^{2}}{ω_{0}} = E_{4, m} \end{array}

，（10）

\begin{array}{l} E_{1, m}^{\pm} = \frac{4}{ω_{0}^{2} g^{2}} n_{1} - \frac{4}{ω_{0}^{4}} - \frac{4}{ω_{0}^{3} g} + \frac{8}{ω_{0}^{4}} + \\ 1 - \frac{a_{1}}{a_{0}} + \frac{2 g^{2}}{ω_{0}} \end{array}

，（11）

E_{2, m}^{\pm} = \frac{4}{ω_{0}^{2} g^{2}} n_{2} - \frac{4 g_{0}^{2}}{ω_{0}^{4} g^{2}} + \frac{4 g_{0}}{ω_{0}^{3} g^{2}} - \frac{8 g_{0}^{2}}{ω_{0}^{4} g^{2}} + \frac{4 g_{0} b_{1}}{ω_{0}^{3} g^{2} b_{0}} + 1 - \frac{b_{1}}{b_{0}} + \frac{2 g^{2}}{ω_{0}}

，（12）

E_{3, m}^{\pm} = \frac{4}{ω_{0}^{2} g^{2}} n_{3} - \frac{4 g_{0}^{2}}{ω_{0}^{4} g^{2}} - \frac{8 g_{0}^{2}}{ω_{0}^{4} g^{2}} + \frac{4 g_{0}}{ω_{0}^{3} g^{2}} + \frac{4 g_{0} c_{1}}{ω_{0}^{3} g^{2} c_{0}} + 1 - \frac{c_{1}}{c_{0}} + \frac{2 g^{2}}{ω_{0}}

，（13）

\begin{array}{l} E_{4, m}^{\pm} = \frac{4}{ω_{0}^{2} g^{2}} n_{4} - \frac{4}{ω_{0}^{4}} - \frac{8}{ω_{0}^{4}} + \frac{4}{ω_{0}^{3} g} + \frac{4 d_{1}}{ω_{0}^{3} g d_{0}} + \\ 1 - \frac{d_{1}}{d_{0}} + \frac{2 g^{2}}{ω_{0}} \end{array}

。（14）

C_{E} = m a x (0, λ_{1} - λ_{2} - λ_{3} - λ_{4})

，（15）

Get PDF(in Chinese)

Figures&Tables (10)

References (28)

Copy Citation Text

Weidong Luo, Xuan Zhou, Xiaoqing Zhou, Yunwen Wu, Shangjiang Huang. Evolution Characteristics of Three-Qubit Quantum Entanglement Under External Field Effect[J]. Laser & Optoelectronics Progress, 2021, 58(21): 2127001

Download Citation

Set citation alerts for the article

Set citation alerts for the article

Save the article for my favorites

Paper Information

Recommended Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology

Set citation alerts for the article

Please enter your email address