"Photon Switching by Quantum Interference" which was proposed by Harris and Yamamoto in 1998[1] introduced a
four-state atomic system that an additional light field besides the three-state EIT[2] system was added to destroy the quantum interference of EIT system. The scheme and theoretical study were introduced in it. And in this thesis, we go a step further to theoretically study this optical switches utilizing storage and retrieval light pulses[3]. We found that the theoretical prediction did not match the experimental results properly, hence the study of how to revise it was developed. The required theoretical analysis equation and simulation results are all involved in this thesis.

[1] S. E. Harris and Y. Yamamoto, "Photon switching by quantum interference,"
Phys. Rev. Lett., vol. 81, pp. 3611{3614, Oct 1998.
[2] S. E. Harris, "Electromagnetically induced transparency," Physics Today, vol. 50,
pp. 36{42, 1997.
[3] D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin,
"Storage of light in atomic vapor," Phys. Rev. Lett., vol. 86, pp. 783{786, Jan
2001.
[4] C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, "Observation of coherent opti-
cal information storage in an atomic medium using halted light pulses," Nature,
vol. 409, pp. 490{493, Jan. 2001.
[5] L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, "Light speed reduction to
17 metres per second in an ultracold atomic gas," Nature, vol. 397, pp. 594{598,
Feb. 1999.
[6] M. Fleischhauer and M. D. Lukin, "Dark-state polaritons in electromagnetically
induced transparency," Phys. Rev. Lett., vol. 84, pp. 5094{5097, May 2000.
[7] C. Y. Wang, Y. F. Chen, S. C. Lin, W. H. Lin, P. C. Kuan, and I. A. Yu,
"Low-light-level all-optical switching," Opt. Lett., vol. 31, pp. 2350{2352, 2006.
[8] M. S. Scully, M. O. & Zubairy, Quantum Optics. Cambridge Univ. Press, 1997.
[9] R. W. Boyd, Nonlinear Optics. Academic Press, 1992.
[10] Y.-F. Chen, C.-Y. Wang, S.-H. Wang, and I. A. Yu, "Low-light-level cross-phase-
modulation based on stored light pulses," Phys. Rev. Lett., vol. 96, p. 043603,
Feb 2006.
[11] Y. F. Chen, Z. H. Tsai, Y. C. Liu, and I. A. Yu, "Low-light-level photon switching
by quantum interference," Opt. Lett., vol. 30, pp. 3207{3209, 2005.
[12] D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, "Frequency mixing
using electromagnetically induced transparency in cold atoms," Physical Review
Letters, vol. 93, no. 18, p. 183601, 2004.
[13] V. Balic, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, "Generation of
paired photons with controllable waveforms," Physical Review Letters, vol. 94,
no. 18, p. 183601, 2005.
[14] S.-H. Wang, "Study of the double-species magneto-optical trap," Master's thesis,
National Tsing-Hua University, 2005.
[15] S. E. Harris and L. V. Hau, "Nonlinear optics at low light levels," Phys. Rev.
Lett., vol. 82, pp. 4611{4614, Jun 1999.