Study on cross correlation function of vibrational modes of nonlinear trapped ions
-
摘要: 为了研究非线性对囚禁离子沿两个正交方向的振动模式之间的互相关函数的影响,采用理论分析和数值计算相结合的方法,对单个2维三能级囚禁离子与两个经典驻波激光相互作用的非线性双光子Jaynes-Cummings模型进行了严格求解,并对囚禁离子沿两个正交方向的振动模式之间的互相关函数进行了数值分析。结果表明,当初始平均量子数较小时,反关联效应随Lamb-Dicke参量的增大先是增强然后减弱,但是关联效应却随Lamb-Dicke参量的增大一直增强。随着初始平均量子数的增大,反关联效应会减弱直至消失;表征非线性效应的Lamb-Dicke参量和初始振动运动平均量子数对交叉关联有明显的影响。
-
关键词:
- 量子光学 /
- 交叉关联函数 /
- 囚禁离子 /
- 非线性Jaynes-Cummings模型
Abstract: In order to study the influence of nonlinear parameters on the cross-correlation function of two vibrational modes of the trapped ions along mutually orthogonal directions, the exact solution of the nonlinear double-photon Jaynes-Cummings model which describes the interaction between a single two-dimension three-level trapped ion and two classical standing wave lasers was obtained by theoretical analysis and numerical computation. The cross-correlation function of two vibrational modes of the trapped ion was analyzed numerically. The results show that the anticorrelation effect is strengthened at first and then weakened with the increasing of the Lamb-Dicke parameters when initial average quantum number is small. But the correlated effect is always strengthened with the increase of the Lamb-Dicke parameters. The anticorrelation effect will be weakened and then disappear with the increasing of initial average quantum number. The initial average quantum number and Lamb-Dicke parameters characterized by nonlinear effects have obvious influence on cross correlation. -
-
[1] LEIBFRIED D, BLATT R, MONROE C, et al. Quantum dynamics of single trapped ions[J].Reviews of Modern Physics, 2003, 75(1): 281-354.
[2] ROOS C, ZEIGER T, ROHDE H, et al. Quantum state engineering on an optical transition and decoherence in a Paul trap[J].Physics Review Letters, 1999, 83(23): 4713.
[3] BARRETT M D, CHIAVERINI J, SCHAETZ T, et al.Deterministic quantum teleportation of atomic qubits[J].Nature, 2004,429(6993):737-739.
[4] GARCIA-RIPOLL J J, ZOLLER P, CIRAC J I. Speed optimized two-qubit gates with laser coherent control techniques for ion trap quantum computing[J].Physics Review Letters,2003,91(15):157901-157904.
[5] DUAN L M. Scaling ion trap quantum computation through fast quantum gates[J]. Physics Review Letters, 2004,93(10): 100502-100505.
[6] CIRAC J I, BLATT R, ZOLLER P. Nonclassical states of motion in a three-dimensional ion trap by adiabatic passage[J].Physics Review, 1994,A49(5): R3174.
[7] KIRCHMAIR G, BENHELM J, ZAHRINGER F, et al. Deterministic entanglement of ions in thermal states of motion[J].New Journal of Physics, 2009, 11(2): 023002-023022.
[8] WANG Zh J. Preparation of squeezed state and entanglement state between vibrational motion of trapped ion and light[J]. Communications in Theoretical Physics,2010, 54(6): 1109-1110.
[9] ZHENG Sh B. Genereation of multi-mode excited coherent states for N trapped ions in strong-excitation regime[J]. Communications in Theoretical Physics, 2005,43(3):523.
[10] WANG Zh J, ZHANG X D, LI C. Properties and generation of photon-added Schrdinger cat states[J]. Communications in Theoretical Physics, 2012, 57(3): 459-462.
[11] WUNDERLICH H, WUNDERLICH C, SINGER K,et al. Two-dimensional cluster-state preparation with linear ion traps[J].Physics Review, 2009,A79(5):052324-052334.
[12] de MATOS FILHO R L, VOGEL W. Nonlinear coherent states[J]. Physics Review, 1996,A54(5):4560-4563.
[13] WANG Zh Q, DUAN Ch K, AN G L, Nonlinear jaynes-cummings model of a trapped ion and the evolution of the ion population inversion[J].Acat Physica Sinica, 2006, 55(7):3438-3442(in Chinese).
[14] YU W J, WANG J S, LIANG B L. Quantum properties of two-level atoms interacting with nonlinear coherent states[J].Acta Physica Sinica,2012, 61(6):060301(in Chinese).
[15] LI C, WANG Zh J. Amplitude-squeezed effects in nonlinear trapped model[J].Journal of Atomic and Molecular Physics, 2013,30(3):435-440(in Chinese).
[16] HAFFNER H, GULDE S, RIEBE M, et al. Precision measurement and compensation of optical stark shifts for an ion-trap quantum processor[J]. Physics Review Letters, 2003, 90(14): 143602-143607.
[17] GUO G C. Quantum optics[M].Beijing:Higher Education Press, 1990:76-87(in Chinese).
[18] WALTHER H. Spectroscopy of single trapped ions and applications to frequency standards and cavity quantum electrodynamics.Laser Physics, 1999, 9(1):225-233.
计量
- 文章访问数: 4
- HTML全文浏览量: 0
- PDF下载量: 8
下载: