Title

電磁誘發透明現象的偶極-偶極交互作用效應

Translated Titles

Electromagnetically Induced Transparency of Two Lambda-type Atoms with Dipole-dipole Interaction

DOI

10.6342/NTU201902602

Authors

詹資莘

Key Words

電磁波誘發透明現象 ; 偶極-偶極交互作用 ; 史塔克效應 ; 暗態 ; 綴飾態 ; EIT ; Dipole-dipole interaction ; AC Stark shift ; Dark state ; Dressed state

PublicationName

臺灣大學物理學研究所學位論文

Volume or Term/Year and Month of Publication

2019年

Academic Degree Category

碩士

Advisor

林俊達

Content Language

繁體中文

Chinese Abstract

本篇論文探討了兩顆受到電磁波誘發透明效應的Lambda原子間的偶極-偶極交互作用。利用引進了等效哈密頓函數的薛丁格方程式,我們可以得出系統的穩定態解。我們探討了探測雷射光的吸收譜、穿透譜和螢光強度。在狄基模型的案例中,六個對稱態形成了一個包含三個Lambda系統的塔狀組態,而另外三個非對稱態形成了一個V型組態,且這兩個組態間無任何關聯。從綴飾態的觀點出發,藉由狀態的衰變率,我們可以理解當驅動雷射光遠離共振時的探測光吸收譜特徵。當驅動雷射光為共振時,雙原子系統的探測光吸收譜和單原子系統相比有較小的最大值和較寬的半峰值寬。我們同時也推導出此系統的暗態。在非狄基模型案例中,我們探討了原子間距對探測光穿透譜的影響。當間距等於1/8倍的波長時,此穿透譜在非共振區有四個低谷,且在共振處有一最大值,此極值即為電磁波誘發透明現象。藉由一微擾參數逐漸調大此系統的偶極-偶極間交互作用,我們可以清楚觀測出此 穿透譜逐漸由對稱的兩低谷變成四個非對稱低谷。從綴飾態的觀點出發,並且考慮偶極-偶極交互作用所造成的對稱態與非對稱態間的能階分裂,我們可以找出這四個低谷的來源。原子間的偶極-偶極間交互作用除了受到原子間距的影響,也會因不同的探測光照射方向而改變。我們探討了不同照射光方向對穿透譜的影響,並將此結果與對稱態和非對稱態間的能階分裂做出連結。我們同時也探討了在不同探測器位置上量測的探測光穿透譜及螢光強度。

English Abstract

In this thesis, we want to investigate the dipole-dipole interaction between two lambda-type atoms with a probe and a control laser. We use the Schrodinger equation approach with the effective Hamiltonian to get the steady-state solution. We are interested in the absorption, transmission, fluorescence intensity of the probe field. In the Dicke model case, we find that the symmetric states form a “Poker Tower” configuration, which contains three Lambda systems, decoupled from the V-type configuration formed by the other three anti-symmetric states. In the far-detuned control laser case, the feature of the absorption spectrum can be interpreted by jumping into the dressed-state picture and finding the decay rates of the participated states. In the resonant control laser case, the absorption maximum is smaller but with broader peak comparing to it in the single-atom case. We also investigate the dark states of our system in the Dicke model case. In the non-Dicke case, we find that how the spacing of the atoms affects the transmission spectrum. In r=1/8 case, the spectrum has four dips in the non-resonance regime and a maximum at resonance. By adding a perturbative term of the dipole-dipole interaction, we can clearly see that the spectrum gradually splits to four dips along with the growing dipole-dipole interaction in this case. In order to realize the origin of the four dips, we further analyze our system in the dressed-state picture. Dipole-dipole interaction is also differed by the probe light incident direction. We find the relation between the probe light incident direction and the dips locations of the transmission spectrum. The probe light transmission and fluorescence intensity measurement of different detector locations are also mentioned.

Topic Category 基礎與應用科學 > 物理
理學院 > 物理學研究所
Reference
  1. [1] R. H. Lehmberg, “Radiation from an n-atom system. i. general formalism,” Phys. Rev. A, vol. 2, pp. 883–888, Sep 1970.
  2. [2] B. Zhu, J. Cooper, J. Ye, and A. M. Rey, “Light scattering from dense cold atomic media,” Phys. Rev. A, vol. 94, p. 023612, Aug 2016.
  3. [3] O. A. Kocharovskaya and Y. I. Khanin, “Population trapping and coherent bleaching of a three-level medium by a periodic train of ultrashort pulses,” Sov.Phys.JETP, 1986.
  4. [4] S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett., vol. 64, pp. 1107–1110, Mar 1990.
  5. [5] K.J. Boller, A. Imamoglu, and S. E. Harris, "Observation of electromagnetically induced transparency,” Phys. Rev. Lett., vol. 66, pp. 2593–2596, May 1991.
  6. [6] 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.
  7. [7] U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically induced transparency and light storage in an atomic mott insulator,” Phys. Rev. Lett., vol. 103, p. 033003, Jul 2009.
  8. [8] S. E. Harris, “Lasers without inversion: Interference of lifetime-broadened resonances,” Phys. Rev. Lett., vol. 62, pp. 1033–1036, Feb 1989.
  9. [9] G. Z. Zhang, M. Katsuragawa, K. Hakuta, R. I. Thompson, and B. P. Stoicheff, “Sum-frequency generation using strong-field coupling and induced transparency in atomic hydrogen,” Phys. Rev. A, vol. 52, pp. 1584–1593, Aug 1995.
  10. [10] M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nature Physics, vol. 2, p. 849, Nov. 2006.
  11. [11] M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with rydberg atoms,” Rev. Mod. Phys., vol. 82, pp. 2313–2363, Aug 2010.
  12. [12] J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Cooperative atom-light interaction in a blockaded rydberg ensemble, Phys. Rev. Lett., vol. 105, p. 193603, Nov 2010.
  13. [13] R. Röhlsberger, H.-C. Wille, K. Schlage, and B. Sahoo, “Electromagnetically induced transparency with resonant nuclei in a cavity,” Nature, vol. 482, p. 199, Feb. 2012.
  14. [14] M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature, vol. 465, p. 755, May 2010.
  15. [15] Y. Guo, K. Li, W. Nie, and Y. Li, Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system,” Phys. Rev. A, vol. 90, p. 053841, Nov 2014.
  16. [16] A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature, vol. 472, p. 69, Mar. 2011.
  17. [17] M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys., vol. 75, pp. 457–472, Apr 2003.
  18. [18] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys., vol. 77, pp. 633–673, Jul 2005.
  19. [19] 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.
  20. [20] O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys. Rev. Lett., vol. 86, pp. 628–631, Jan 2001.
  21. [21] M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency, Phys. Rev. Lett., vol. 84, pp. 5094–5097, May 2000.
  22. [22] M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: Dark-state polaritons,” Phys. Rev. A, vol. 65, p. 022314, Jan 2002.
  23. [23] M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, “Efficient nonlinear frequency conversion with maximal atomic coherence,” Phys. Rev. Lett., vol. 77, pp. 4326–4329, Nov 1996.
  24. [24] S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett., vol. 82, pp. 4611–4614, Jun 1999.
  25. [25] R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev., vol. 93, pp. 99–110, Jan 1954.
  26. [26] M. Gross and S. Haroche, “Superradiance: An essay on the theory of collective spontaneous emission,” Physics Reports, vol. 93, no. 5, pp. 301 – 396, 1982.
  27. [27] M. A. Macovei and J. Evers, “Phase dependence of collective fluorescence via interferences from incoherent pumping,” Optics Communications, vol. 240, no. 4, pp. 379 – 384, 2004.
  28. [28] T. J. Carroll, K. Claringbould, A. Goodsell, M. J. Lim, and M. W. Noel, “Angular dependence of the dipole-dipole interaction in a nearly one-dimensional sample of rydberg atoms,” Phys. Rev. Lett., vol. 93, p. 153001, Oct 2004.
  29. [29] S. L. Bromley, B. Zhu, M. Bishof, X. Zhang, T. Bothwell, J. Schachenmayer, T. L. Nicholson, R. Kaiser, S. F. Yelin, M. D. Lukin, A. M. Rey, and J. Ye, “Collective atomic scattering and motional effects in a dense coherent medium,” Nature Communications, vol. 7, p. 11039, Mar. 2016.
  30. [30] J. Eschner, C. Raab, F. Schmidt-Kaler, and R. Blatt, “Light interference from single atoms and their mirror images,” Nature, vol. 413, pp. 495–498, Oct. 2001.
  31. [31] G.-x. Li, K. Allaart, and D. Lenstra, “Entanglement between two atoms in an overdamped cavity injected with squeezed vacuum,” Phys. Rev. A, vol. 69, p. 055802, May 2004.
  32. [32] T. G. Rudolph, Z. Ficek, and B. J. Dalton, “Two-atom resonance fluorescence in running- and standing-wave laser fields,” Phys. Rev. A, vol. 52, pp. 636–656, Jul 1995.
  33. [33] G. S. Agarwal, Quantum statistical theories of spontaneous emission and their relation to other approaches, pp. 1–128. Berlin, Heidelberg: Springer Berlin Heidelberg, 1974.
  34. [34] M. Macovei and C. H. Keitel, “Laser control of collective spontaneous emission,” Phys. Rev. Lett., vol. 91, p. 123601, Sep 2003.
  35. [35] D. F. V. James, “Frequency shifts in spontaneous emission from two interacting atoms,” Phys. Rev. A, vol. 47, pp. 1336–1346, Feb 1993.
  36. [36] M. Lewenstein and J. Javanainen, “Cooperative quantum jumps with two atoms,” Phys. Rev. Lett., vol. 59, pp. 1289–1292, Sep 1987.
  37. [37] I. V. Bargatin, B. A. Grishanin, and V. N. Zadkov, “Analysis of radiatively stable entanglement in a system of two dipole-interacting three-level atoms,” Phys. Rev. A, vol. 61, p. 052305, Apr 2000.
  38. [38] M. D. Lukin and P. R. Hemmer, “Quantum entanglement via optical control of atom atom interactions,” Phys. Rev. Lett., vol. 84, pp. 2818–2821, Mar 2000.
  39. [39] G. S. Agarwal and A. K. Patnaik, “Vacuum-induced coherences in radiatively coupled multilevel systems,” Phys. Rev. A, vol. 63, p. 043805, Mar 2001.
  40. [40] J. Evers, M. Kiffner, M. Macovei, and C. H. Keitel, “Geometry-dependent dynamics of two l-type atoms via vacuum-induced coherences,” Phys. Rev. A, vol. 73, p. 023804, Feb 2006.
  41. [41] Y. Wu and X. Yang, “Electromagnetically induced transparency in v-, lambda- , and cascade-type schemes beyond steady-state analysis,” Phys. Rev. A, vol. 71, p. 053806, May 2005.
  42. [42] C. Cohen-Tannoudji and S. Reynaud, “Dressed-atom description of resonance fluorescence and absorption spectra of a multi-level atom in an intense laser beam, Journal of Physics B: Atomic and Molecular Physics, vol. 10, pp. 345–363, feb 1977.
  43. [43] C. Cohen-Tannoudji and S. Reynaud, “Modification of resonance raman scattering in very intense laser fields,” Journal of Physics B: Atomic and Molecular Physics, vol. 10, pp. 365–383, feb 1977.
  44. [44] S. Khan, V. Bharti, and V. Natarajan, “Role of dressed-state interference in electromagnetically induced transparency,” Physics Letters A, vol. 380, no. 48, pp. 4100 – 4104, 2016.
  45. [45] S. E. Harris, J. E. Field, and A. Kasapi, “Dispersive properties of electromagnetically induced transparency,” Phys. Rev. A, vol. 46, pp. R29–R32, Jul 1992.
  46. [46] R. H. Lehmberg, “Radiation from an n-atom system. ii. spontaneous emission from a pair of atoms,” Phys. Rev. A, vol. 2, pp. 889–896, Sep 1970.
  47. [47] A. Muthukrishnan, G. S. Agarwal, and M. O. Scully, “Inducing disallowed two-atom transitions with temporally entangled photons,” Phys. Rev. Lett., vol. 93, p. 093002, Aug 2004.
  48. [48] D. Petrosyan and G. Kurizki, “Scalable solid-state quantum processor using subradiant two-atom states,” Phys. Rev. Lett., vol. 89, p. 207902, Oct 2002.
  49. [49] A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the rydberg blockade regime,” Nature Physics, vol. 5, p. 115, Jan. 2009.
  50. [50] C. Hettich, C. Schmitt, J. Zitzmann, S. Kühn, I. Gerhardt, and V. Sandoghdar, “Nanometer resolution and coherent optical dipole coupling of two individual molecules,” Science, vol. 298, no. 5592, pp. 385–389, 2002.
  51. [51] B. H. McGuyer, M. McDonald, G. Z. Iwata, M. G. arallo, W. Skomorowski, R. Moszynski, and T. Zelevinsky, “Precise study of asymptotic physics with subradiant ultracold molecules,” Nature Physics, vol. 11, p. 32, Dec. 2014.
  52. [52] P. Grangier, A. Aspect, and J. Vigue, “Quantum interference effect for two atoms radiating a single photon,” Phys. Rev. Lett., vol. 54, pp. 418–421, Feb 1985.
  53. [53] R. G. DeVoe and R. G. Brewer, “Observation of superradiant and subradiant spontaneous emission of two trapped ions,” Phys. Rev. Lett., vol. 76, pp. 2049–2052, Mar 1996.
  54. [54] L. Slodiˇcka, G. Hétet, S. Gerber, M. Hennrich, and R. Blatt, “Electromagnetically induced transparency from a single atom in free space,” Phys. Rev. Lett., vol. 105, p. 153604, Oct 2010.
  55. [55] A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Electromagnetically induced transparency on a single artificial atom,” Phys. Rev. Lett., vol. 104, p. 193601, May 2010.
  56. [56] O. Astafiev, A. M. Zagoskin, A. A. Abdumalikov, Y. A. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. S. Tsai, “Resonance fluorescence of a single artificial atom,” Science, vol. 327, no. 5967, pp. 840–843, 2010.
  57. [57] P. Kochan and H. J. Carmichael, “Photon-statistics dependence of single-atom absorption,” Phys. Rev. A, vol. 50, pp. 1700–1709, Aug 1994.
  58. [58] D.-w. Wang, Z.-h. Li, H. Zheng, and S.-y. Zhu, “Time evolution, lamb shift, and emission spectra of spontaneous emission of two identical atoms,” Phys. Rev. A, vol. 81, p. 043819, Apr 2010.
  59. [59] M. Fleischhauer and A. S. Manka, “Propagation of laser pulses and coherent population transfer in dissipative three-level systems: An adiabatic dressed-state picture,” Phys. Rev. A, vol. 54, pp. 794–803, Jul 1996.
  60. [60] F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the dicke-model quantum phase transition in an optical cavity qed system,” Phys. Rev. A, vol. 75, p. 013804, Jan 2007.