-
量子谐振子模型在量子光学和量子信息具有十分重要作用，一直以来是相关领域研究的热点问题之一.在单模谐振子和双模纠缠态表象的基础上，构造了一种新的双模耦合谐振子模型.与以往文献中的双模耦合谐振子不同，本文提出的模型不仅仅是具有新耦合系数的坐标和动量两个耦合项，而且其能量本征值和波函数不需要消除耦合项便可直接求解，这大大简化了有关的量子计算.此外，进一步分析了双模真空态在此谐振子作用下，输出量子态的非经典特性，如正交压缩性质、相空间Q函数、粒子数空间分布和量子纠缠等.研究表明，此双模耦合谐振子对输入真空态具有很强的耗散作用.输出光场不仅呈现超泊松分布和强关联的特性，而且光子较高的量子纠缠度.因此，这种双模耦合谐振子是成为实现连续变量量子纠缠态的典型方案之一。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.
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.
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.
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.
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.
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.-
Keywords:
- Quantum oscillator /
- Quantum dissipation /
- Super-Poisson distribution /
- Quantum entanglement
-
[1] Xu X W, Ren T Q, Liu S Y, Dong Y M, Zhao J D 2006 Acta Phys Sin-Ch Ed 55 535(in Chinese) [徐秀玮，任廷琦，刘姝延，董永绵，赵继德2005物理学报55 535]
[2] Qu L C, Chen J, Liu Y X 2022 Phys Rev D 105 126015
[3] Hou B P, Wang S J, Yu W L, Sun W L, Wang G 2004 Chinese Phys Lett 21 2334
[4] Mechler M, Man'ko M A, Man'ko V I, Adam P 2024 J Russ Laser Res 45 1
[5] Schrödinger E 1926 Physical Review 28 1049
[6] Zhang X L, Liu H, Yu H J, Zhang W H 2011 Acta Phys Sin 60040303(in Chinese) [张秀兰，刘恒，余海军，张文海2011物理学报60040303]
[7] Zhong Z R, Sheng J Q, Lin L H, Zheng S B 2019 Opt Lett 44 1726
[8] Glauber R J 1963 Physical Review 130 2529
[9] Cardoso F R, Rossatto D Z, Fernandes G, Higgins G, Villas-Boas C J 2021 Phys Rev A 103 062405
[10] Lu H L, Fan H Y 2007 Commun Theor Phys 47 1024
[11] De Castro A S M, Dodonov V V 2001 J Opt B-Quantum S O 3 228
[12] Jiang L, Lai L, Yu T, Luo M K 2021 Acta Phys Sin-Ch Ed 70 130501(in Chinese)[姜磊，赖莉，蔚涛，罗懋康2021物理学报70 130501]
[13] Einstein A, Podolsky B, Rosen N 1935 Physical Review 47 777
[14] Fan H Y 2002 Chinese Phys Lett 19 897
[15] Zhang J-D, Wang S 2024 Phys Lett A 502 129400
[16] Caldeira A O, Leggett A J 1981Phys Rev Lett 46211
[17] Wang X B, Yu S X, Zhang Y D 1994 J Phys a-Math Gen 27 6563
[18] Ghiu I, Marian P, Marian T A 2013 Phys Scripta T153014028
[19] Tian L J, Zhu C Q, Zhang H B, Qin L G 2011 Chinese Phys B 20040302
[20] He H, Lou Y, Xu X, Liu S, Jing J 2023 Opt Lett 48 1375
[21] Bose S 2021 Phys Rev A 104 042419
[22] Harrington P M, Mueller E J, Murch K W 2022Nat. Rev. Phys. 4 660
[23] Chen Y H, Shi Z C, Song J, Xia Y, Zheng S B 2017Phys Rev A 96043853
[24] Sauer S, Gneiting C, Buchleitner A 2013Phys Rev Lett111 030405
[25] Krauter H, Muschik C A, Jensen K, Wasilewski W, Petersen J M, Cirac J I, Polzik E S 2011Phys Rev Lett 107 080503
[26] Choi T, Lee H J 2007Phys Rev A 76 012308
[27] Mandel L 1979 Opt Lett 4 205
[28] Xu X F, Wang S, Tang B 2014 Chinese Phys B 23024206
[29] Zhang H L, Jia F, Xu X X, Guo Q, Tao X Y, Hu L Y 2013 Acta Phys Sin 62014208(in Chinese) [张浩亮，贾芳，徐学翔，郭琴，陶向阳，胡利云2013物理学报62014208]
[30] Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev Mod Phys 81 865
[31] Shchukin E V, Vogel W 2005 Phys Rev A 72043808
计量
- 文章访问数: 97
- PDF下载量: 3
- 被引次数: 0
下载:
