我們討論不同類型的電磁誘發透明模型並提出一個新的全量子電磁誘發透明模型，其中針對單光子等級的探測光的情形做了改進。在這模型下討論了各種量子狀態的探測光與耦合光的行為，以及探測光的輸入與輸出的量子狀態演變。耦合光的量子特性對探測光造成的影響我們藉由探測光的穿透率與保真度來做討論。在我們的模型預測之下，電磁誘發透明作為一個量子記憶體即使在單光子等級的探測光且考量耦合光的量子特性之下在大多的情況下也是適當的。

We discuss different types of the electromagnetically induced transparency (EIT) model and propose one new quantum model for the EIT mechanism, which improves the ability for behavior prediction of single–photon cases of the probe photons. Different states of the probe photons and coupling fields are discussed under this quantum model, along with the state evolutions of the probe photons. The total influences from the quantum properties of the coupling field are discussed by studying the fidelities and the transmittances of the probe photons. Our model shows EIT to be a quantum memory is appropriate in most cases, including the single–photon condition of the probe photons and the influences from a quantized coupling field.

[1] S. E. Harris, “Electromagnetically induced transparency,” Physics Today, vol. 50, no. 7, pp. 36–42, 1997.
[2] G. S. Agarwal, “Inhibition of spontaneous emission noise in lasers without inversion,” Phys. Rev. Lett., vol. 67, pp. 980–982, Aug 1991.
[3] S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett., vol. 64, pp. 1107–1110, Mar 1990.
[4] U. D. Rapol and V. Natarajan, “Precise measurement of hyperfine intervals using avoided crossing of dressed states,” Europhysics Letters (EPL), vol. 60, pp. 195–200, oct 2002.
[5] D. Das and V. Natarajan, “Hyperfine spectroscopy on the 6 p 3/2 state of 133 cs using coherent control,” Europhysics Letters (EPL), vol. 72, pp. 740–746, dec 2005.
[6] A. Krishna, K. Pandey, A. Wasan, and V. Natarajan, “High-resolution hyperfine spectroscopy of excited states using electromagnetically induced transparency,” Europhysics Letters (EPL), vol. 72, pp. 221–227, oct 2005.
[7] 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.
[8] M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett., vol. 82, pp. 5229–5232, Jun 1999.
[9] D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, “Nonlinear magnetooptics and reduced group velocity of light in atomic vapor with slow ground state relaxation,” Phys. Rev. Lett., vol. 83, pp. 1767–1770, Aug 1999.
[10] M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: Dark-state polaritons,” Phys. Rev. A, vol. 65, p. 022314, Jan 2002.
[11] A. B. Matsko, Y. V. Rostovtsev, O. Kocharovskaya, A. S. Zibrov, and M. O. Scully, “Nonadiabatic approach to quantum optical information storage,” Phys. Rev. A, vol. 64, p. 043809, Sep 2001.
[12] M. D. Lukin, S. F. Yelin, and M. Fleischhauer, “Entanglement of atomic ensembles by trapping correlated photon states,” Phys. Rev. Lett., vol. 84, pp. 4232–4235, May 2000.
[13] C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature, vol. 409, pp. 490–493, Jan 2001.
[14] Y.-F. Chen, C.-Y. Wang, S.-H. Wang, and I. A. Yu, “Low-light-level cross-phasemodulation based on stored light pulses,” Phys. Rev. Lett., vol. 96, p. 043603, Feb 2006.
[15] Z.-Y. Liu, J.-T. Xiao, J.-K. Lin, J.-J. Wu, J.-Y. Juo, C.-Y. Cheng, and Y.-F. Chen, “Highefficiency backward four-wave mixing by quantum interference,” Scientific Reports, vol. 7, p. 15796, Nov 2017.
[16] G. Wang, Y. Xue, J.-H. Wu, Z.-H. Kang, Y. Jiang, S.-S. Liu, and J.-Y. Gao, “Efficient frequency conversion induced by quantum constructive interference,” Opt. Lett., vol. 35, pp. 3778–3780, Nov 2010.
[17] C.-K. Chiu, Y.-H. Chen, Y.-C. Chen, I. A. Yu, Y.-C. Chen, and Y.-F. Chen, “Low-lightlevel four-wave mixing by quantum interference,” Phys. Rev. A, vol. 89, p. 023839, Feb 2014.
[18] Z.-Y. Liu, Y.-H. Chen, Y.-C. Chen, H.-Y. Lo, P.-J. Tsai, I. A. Yu, Y.-C. Chen, and Y.- F. Chen, “Large cross-phase modulations at the few-photon level,” Phys. Rev. Lett., vol. 117, p. 203601, Nov 2016.
[19] H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.- F. Chen, Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A, vol. 83, p. 041804, Apr 2011.
[20] A. Feizpour, M. Hallaji, G. Dmochowski, and A. M. Steinberg, “Observation of the nonlinear phase shift due to single post-selected photons,” Nature Physics, vol. 11, pp. 905–909, Nov 2015.
[21] S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett., vol. 64, pp. 1107–1110, Mar 1990.
[22] M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett., vol. 84, pp. 5094–5097, May 2000.
[23] A. Joshi and M. Xiao, “Generalized dark-state polaritons for photon memory in multilevel atomic media,” Phys. Rev. A, vol. 71, p. 041801, Apr 2005.
[24] A. Peng, M. Johnsson, W. P. Bowen, P. K. Lam, H.-A. Bachor, and J. J. Hope, “Squeezing and entanglement delay using slow light,” Phys. Rev. A, vol. 71, p. 033809, Mar 2005.
[25] Y.-L. Chuang, I. A. Yu, and R.-K. Lee, “Quantum theory for pulse propagation in electromagnetically-induced-transparency media beyond the adiabatic approximation,” Phys. Rev. A, vol. 91, p. 063818, Jun 2015.
[26] Y.-L. Chuang, I. A. Yu, and R.-K. Lee, “Nonseparated states from squeezed dark-state polaritons in electromagnetically induced transparency media,” J. Opt. Soc. Am. B, vol. 32, pp. 1384–1391, Jul 2015.
[27] S. E. Harris, “Electromagnetically induced transparency with matched pulses,” Phys. Rev. Lett., vol. 70, pp. 552–555, Feb 1993.
[28] M. Fleischhauer and T. Richter, “Pulse matching and correlation of phase fluctuations in Λ systems,” Phys. Rev. A, vol. 51, pp. 2430–2442, Mar 1995.
[29] M. Fleischhauer, “Correlation of high-frequency phase fluctuations in electromagnetically induced transparency,” Phys. Rev. Lett., vol. 72, pp. 989–992, Feb 1994.
[30] X. Yang and M. Xiao, “Electromagnetically induced entanglement,” Scientific Reports, vol. 5, p. 13609, Aug 2015.
[31] Y.-L. Chuang, R.-K. Lee, and I. A. Yu, “Generation of quantum entanglement based on electromagnetically induced transparency media,” Opt. Express, vol. 29, pp. 3928–3942, Feb 2021.
[32] X. Yang, J. Sheng, U. Khadka, and M. Xiao, “Generation of correlated and anticorrelated multiple fields via atomic spin coherence,” Phys. Rev. A, vol. 85, p. 013824, Jan 2012.
[33] L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature, vol. 414, pp. 413–418, Nov 2001.
[34] M. O. Scully and M. S. Zubairy, Quantum Optics. Cambridge University Press, 1997.
[35] C.-Y. Cheng, J.-J. Lee, Z.-Y. Liu, J.-S. Shiu, and Y.-F. Chen, “Quantum frequency conversion based on resonant four-wave mixing,” Phys. Rev. A, vol. 103, p. 023711, Feb 2021.
[36] W. H. Louisell, Quantum statistical properties of radiation. Wiley New York, 1973.
[37] L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett., vol. 84, pp. 2722–2725, Mar 2000.
[38] L. Davidovich, “Sub-poissonian processes in quantum optics,” Rev. Mod. Phys., vol. 68, pp. 127–173, Jan 1996.
[39] D. Akamatsu, Y. Yokoi, M. Arikawa, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Ultraslow propagation of squeezed vacuum pulses with electromagnetically induced transparency,” Phys. Rev. Lett., vol. 99, p. 153602, Oct 2007.