在這篇論文中, 我們主要討論電磁引發透明(EIT)系統的非古典螢光光譜之計算。 EIT介質是由三個能階組成Λ組態的原子系統, 並與外來兩道同方向入射的電磁波做交互作用, 此兩道電磁波分別為探測波與泵浦波; 藉由泵浦電磁波引發的量子干涉效應, 探測波可以穿透介質而不被介質中的原子所吸收, 如同此介質是為透明一般。

在一般的情況下, 入射的電磁波皆為一般的同調光(如雷射光), 然後主要去觀察探測波的螢光光譜。 然而在這裡我們考慮一個特別的情況 : 入射的探測波是為非古典光(量子壓縮態), 而泵浦波則維持一般的同調光, 然後我們分別去計算這兩道電磁波的螢光光譜。我們利用Mathematica程式去解一組對應原子與電磁場的Heisenberg-Langevin方程式, 我們發現探測波與泵浦波的量子態建立了相關聯的性質, 彼此間的量子特性相互轉換, 且在二者的強度相等時, 有最大的轉換效果。此性質說明了電磁場的量子特性在EIT介質中傳遞, 其量子特性發生改變, 完全不同於最初的量子性質, 因此暗示著EIT介質對於場的量子態不是透明的。

We mainly discuss the calculations of non-classical fluorescence spectrum of electromagnetically induced transparency (EIT) in the thesis. EIT medium is an atomic system of Λ configuration consisted of three energy levels, interacted with two external incident EM waves propagating in the same direction, which are called probe and pump wave, respectively. By the quantum interference effect due to the pump wave, the probe wave can transmit the medium without being absorbed by the atoms inside medium, just as the medium is transparent.

In general situation, the incident EM waves are ordinary coherent light (as laser light), and one mainly observe the fluorescence spectrum of probe wave. However, we consider a special case here: The incident probe wave is non-classical light (quantum squeezed state), and the pump wave is maintained an ordinary coherent light, and then we calculate the fluorescence spectrum of the two EM waves respectively. We utilize Mathematica program to solve the set of Heisenberg-Langevin equations corresponding to atom and EM fields. We find that the correlation between the quantum states of probe waves and pump wave are established. Their quantum properties mutually transfer, and the effect to be maxima when two fields approach equal intensities. This property presents that the quantum states of EM fields are changed, and completely different from initial quantum properties when propagating inside the EIT medium. Thus it implies that the EIT medium is not transparent for the quantum states of fields.

Reference

[1] S. Harris, Phys. Today 50, No. 7, 36 (1997)
[2] 陳應誠, 余怡德, “光速減漫至每秒600公尺—
原子的電磁波引發透明效應”, 物理雙月刊23卷5期,572- 578 (2001)
[3] M. O. Scully, M. S. Zubairy, QUANTUM OPTICS,
Cambridge University Press 1997
[4] D. F. Walls, Phys. Rev. Lett. 47, 709 (1981)
[5] A. Dantan, M. Pinard, Phys. Rev. A 69, 043810 (2004)
[6] M. Fleischhauer, M. D. Lukin, Phys. Rev.A 65,022314 (2002)
[7] M. Fleischhauer, M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000)
[8] B. R. Mollow, Phys. Rev 188 (1969)
[9] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod.
Phys. 77, 633 (2005)
[10] P. Barberis-Blostein, N. Zagury, Phys. Rev. A 70, 053827 (2004)
[11] M. Orszag, Quantum Optics, Springer-Verlag, Berlin, 2000
[12] M. J. Collett, D. F. Walls, and P. Zoller, Opt. Comm. 52 (1984)
[13] R. Loudon, The Quantum Theory of Light, 3rd ed, Oxford University Press,
New York (2000)
[14] P. Barberis-Blostein, M. Bienert, Phys. Rev. Lett. 98, 033602 (2007)
[15] P. Meystre, M. SargentⅢ, Elements of quantum optics, Springer-Verlag 1991
[16] A. Dantan, A. Bramati, and M. Pinard, Phys.Rev. A 71, 043801 (2005)
[17] M. Bajcsy, A. S. Zibrov, and M.D. Lukin, Nature(London) 426, 638 (2003)
[18] A. André, M.D. Lukin, Phys. Rev. Lett. 89, 143602 (2002)
[19] A. André, M. Bajcsy, A. S. Zibrov, and M.D. Lukin, Phys. Rev. Lett. 94, 063902 (2005)
[20] Claude Cohen-Tannoudji, Atom-Photon Interactions, Wiley 1998
[21] M. Fleischhauer, T. Richter, Phys. Rev. A 51, 2430 (1995)
[22] P. Barberis-Blostein, Phys. Rev. A 74, 013803 (2006)