Study on cross correlation function of vibrational modes of nonlinear trapped ions

WANG Zhongjie; FANG Xu

doi:10.7510/jgjs.issn.1001-3806.2015.01.022

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.

Study on cross correlation function of vibrational modes of nonlinear trapped ions

1. College of Physics and Electric Information, Anhui Normal University, Wuhu 241000, China

Received Date: 2014-01-12

Accepted Date: 2014-02-20

Available Online: 2015-01-25

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.

HTML

Reference (18)

[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 Schrdinger 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.

Study on cross correlation function of vibrational modes of nonlinear trapped ions

Abstract

References

Proportional views

通讯作者: 陈斌, bchen63@163.com

Proportional views