American Journal of Modern Physics
Volume 7, Issue 5, September 2018, Pages: 180-184
Received: Oct. 1, 2018;
Accepted: Oct. 25, 2018;
Published: Nov. 26, 2018
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Jiu-Ming Li, School of Science, Tianjin Polytechnic University, Tianjin, China
Bo-Ying Zhang, School of Science, Tianjin Polytechnic University, Tianjin, China
Xue-Qun Yan, School of Science, Tianjin Polytechnic University, Tianjin, China
Quantum Zeno effect can be applied to quantum information processing，and can reveal the nature of quantum measurement. In addition, it has also many potential applications. This suggests that studying the quantum Zeno effect has great theoretical and experimental significance. In this work, the system of a two-level atom interacting with a single mode field is considered and the dynamics of the system subjected to successive projection measurements is studied, and the quantum Zeno effect is presented. Moreover, the influence of the quantum Zeno effect on atomic population inversion is discussed. Based on Schrödinger equation, the survival probability of the initial state of the two-level atom subjected to frequently repeated measurements can be obtained. The survival probability depends on the time interval between measurements. It is seen that the exponential decay of the system under slowly frequent measurements is presented instead of the naturally oscillatory process. For slowly repeated measurements the atomic population inversion and the survival probability of initial state decline rapidly at the early time and then both of them become unchanged. As the time intervals of the measurements are sufficiently short, the quantum Zeno effect occurs. These results have also shown how the measurement can inhibit the atomic population inversion.
Quantum Zeno Effect and Atomic Population Inversion, American Journal of Modern Physics.
Vol. 7, No. 5,
2018, pp. 180-184.
F. Francica, F. Plastina, and S. Maniscalco, “Quantum Zeno and anti-Zeno on quantum and classical correlations” , Phys. Rev. A, 82, 052118(1-9), November 2010.
A. Z. Chaudhry and J.-B. Gong, “ Zeno and anti-Zeno effects on dephasing”, Phys. Rev. A, 90, 012101(1-11), July 2014.
M. A. Porras, A. Luis, and I. Gonzalo, “Quantum Zeno effect for a free-moving particle”, Phys. Rev. A, 90, 062131(1-6), December 2014.
D. Layden, E. Martín-Martínez, and A. Kempf, “Perfect Zeno-like effect through imperfect measurements at a finite frequency”, Phys. Rev. A, 91, 022106(1-6), Febru ary 2015.
B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory”, J. Math. Phys. , 18, pp.756-763, February 1977.
W. M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, “Quantum Zeno effect”, Phys. Rev. A, 41, 2295-2300, March 1990.
M. C. Fischer, B. Gutiérrez-Medina, and M. G. Raizen, “ Observation of the quantum Zeno and anti-Zeno effects in an unstable system”, Phys. Rev. Lett. , 87, 040402(1-4), July 2001.
A. Peres, A. Ron, “Incomplete collapse and partial quantum Zeno effect”, Phys. Rev. A, 42, pp.5720-5722, November 1990.
H. Fearn, and W. E. Lamb, “Computational approaches to the quantum Zeno effect: Position measurements”, Phys. Rev. A, 46, 1199-1205, August 1992.
A. Lusi, “Zeno and anti-Zeno effects in two-level systems”, Phys. Rev. A, 67, 062113(1-4), June 2003.
N. Erez, G. Gordon, M. Nest, and G. Kurizki, “Thermodynamical control by frequent quantum measurements”, Nature, 452, pp.724-727, April 2008.
J. Peise, B. Lücke, L. Pezzé, F. Deuretzbacher, W. Ertmer, J. Arlt, A. Smerzi, L. Santos, and C. Klempt, “Interaction-free measurements by quantum Zeno stabilization of ultra-cold atoms”, Nature Commun. , 6, 6811(1-6), April 2015.
S. Maniscalco, F. Francica, R. L. Zaffino, N. L. Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect”, Phys. Rev. Lett. , 100, 090503(1-4), March 2008.
W. Q. Zheng, D. Z. Xu, X. H. Peng, X. Y. Zhou, J. F. Du, and C. P. Sun, “Experimental demonstration of the quantum Zeno effect in NMR with entanglement-based measurements”, Phys. Rev. A, 87, 032112(1-6), March 2013.
W.-A. Li and L. F. Wei, “Controllable entanglement preparation atoms in spatially-separated cavities via quantum Zeno dynamics”, Opt. Express, 20, pp.13440-13450, May 2012.
K. T. McCusker, Y.-P. Huang, A. S. Kowligy, and P. Kumar, “Experimental demonstration of interaction-free all-optical switching via the quantum Zeno effect”, Phys. Rev. Lett. , 110, 240403(1-5), June 2013.
S. Krishnamurthy, Y. Wang, Y. Tu, S. Tseng, and M. S. Shahriar, “High efficiency optical modulation at a telecom wavelength using the quantum Zeno effect in a ladder transition in Rb atoms”, Opt. Express, 20, pp.13798-13809, June 2012.
M. P. Telenkov, Y. A. Mityagin, A. A. Kutsevol, V. V. Agafonov, K. K. Nagaraja, “Intersubband population inversion in Landau level system in resonant tunneling quantum well structures with asymmetric double quantum well period”, JETP Lett., 100, pp.644-647, Januray 2015.
F. Jia, S.-Y. Xie, Y.-P. Yang, “Interaction of an atom with a field with varying frequency without rotating-wave approximation”, Acta Phys. Sin. , 55, pp.5835 -5841, November 2006.
X. Liao, H.-L. Cong, D.-L. Jiang, X.-Z. Ren, “Influence of the field with varying frequency modulation on atomic population inversion in non-rotating-wave approximation”, Acta Phys. Sin., 59, pp.5508-5513, August 2010.
R. Manson, K. Roy-Choudhury, and S. Hughes, “Polaron master equation theory of pulse driven phonon-assisted population inversion and single photon emission from quantum dot excitons”, Phys. Rev. B, 93, 155423(1-13), April 2016.
M. Macovei, M. Mishra, and C. H. Keitel, “Population inversion in two-level systems possessing permanent dipoles”, Phys. Rev. A, 92, 013846(1-6), July 2015.
E. T. Jaynes, F. W. Cummings, “ Comparison of quantum and semiclassical radiation theories with application to the beam maser”, Proc. IEEE, 51, pp.89-109, January 1963.