, Volume 13, Issue 4, pp 1243–1253 | Cite as

Gain-Assisted Magneto-Optical Rotation in a Four-Level Quantum System Near a Plasmonic Nanostructure

  • Hamid Talkhabi
  • Ali MortezapourEmail author


We propose and theoretically demonstrate a mechanism to achieve a gain-assisted magneto optical rotation (MOR) of a linearly polarized probe beam in a double V–type closed-loop atomic system. The quantum system is considered to be placed in the proximity of a plasmonic nanostructure which can produce quantum interference between decay channels of the quantum system. We also apply a linearly polarized control beam and a microwave beam to the system. It is shown that manipulating the intensity of the microwave beam and relative phase of the applied beams results in well-optimizing optical properties of the system where by proper choice of these parameters the atomic medium becomes birefringent gain media. Induced birefringence can be reinforced by increasing the intensity of the magnetic field and quantum interference coefficient. It is found, compared with the absence of the plasmonic nanostructure, the presence of the plasmonic nanostructure causes the gain-assisted MOR to occur at much smaller magnetic field. Hence, we propose that such a gain-assisted MOR can have potential application in detecting quantum interference effect.


Magneto optical rotation ‌Birefringence Gain Plasmonic nanostructure 


  1. 1.
    Huard S (1997) Polarization of Light. Wiley, New YorkGoogle Scholar
  2. 2.
    Klyshko DN (1997) Polarization of light: Fourth-order effects and polarization-squeezed states. J Exp Theor Phys 84:1065CrossRefGoogle Scholar
  3. 3.
    Damask JN (2005) Polarization Optics in Telecommunications. Springer, New YorkGoogle Scholar
  4. 4.
    Klimov AB, Sánchez-Soto LL, Yustas EC, Söderholm J, Björk G (2005) Distance-based degrees of polarization for a quantum field. Phys Rev A 72:033813CrossRefGoogle Scholar
  5. 5.
    Kumar A, Ghatak A (2011) Polarization of Light with Applications in Optical Fibers. SPIE-International Society for Optical Engineering, BellinghamCrossRefGoogle Scholar
  6. 6.
    Zhao Y, Alù A (2011) Manipulating light polarization with ultrathin plasmonic metasurfaces. Phys Rev B 84:205428CrossRefGoogle Scholar
  7. 7.
    Iskhakov TS, Agafonov IN, Chekhova MV, Leuchs G (2012) Polarization-Entangled Light Pulses of 105 Photons. Phys Rev Lett 109:150502CrossRefPubMedGoogle Scholar
  8. 8.
    Ginzburg P, Rodríguez-Fortuño FJ, Wurtz G, Zayats AV (2013) Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials. Optics Express 21(12):14907–14917CrossRefPubMedGoogle Scholar
  9. 9.
    Li W, Coppens ZJ, Besteiro LV, Wang W, Govorov AO, Valentine J (2015) Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials. Nature Communications 6:8379CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Connerade JP (1998) Highly Excited Atoms. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  11. 11.
    Budker D, Jackson Kimball DF (2013) Optical Magnetometry. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  12. 12.
    Bouchiat MA, Bouchiat C (1997) Parity violation in atoms. Rep Prog Phys 60:1351–1396CrossRefGoogle Scholar
  13. 13.
    Zvezdin AK, Kotov VA (1997) Modern Magnetooptics and Magnetooptical Materials. Taylor and Francis Group, New YorkCrossRefGoogle Scholar
  14. 14.
    Sugano S, Kojima N (eds) (2000) Magneto-Optics. Springer-Verlag, BerlinGoogle Scholar
  15. 15.
    Budker D, Gawlik W, Kimball DF, Rochester SM, Yashchuk VV, Weis A (2002) Resonant nonlinear magnetooptical effects in atoms. Rev Mod Phys 74:1153–1201CrossRefGoogle Scholar
  16. 16.
    Faraday M (1855) Experimental Research in Electricity. Taylor & Francis 3:1–26Google Scholar
  17. 17.
    Voigt W (1901) Über das elektrische Analogon des Zeemaneffektes. Ann. Phys 309:197–208CrossRefGoogle Scholar
  18. 18.
    Cotton A, Mouton H (1911) Sur la biréfringence magnétique des liquides purs. Comparaison avec le phénomène électro-optique de Kerr. J Phys Theory Appl 1:5–52CrossRefGoogle Scholar
  19. 19.
    Macaluso D, Corbino OM (1898) Sopra una nuova azione che la luce subisce attraversando alcuni vapori metallici in un campo magnetico. Nuovo Cimento 8:257–258CrossRefGoogle Scholar
  20. 20.
    Macaluso D, Corbino OM (1898) Sulla relazione tra il fenomeno di Zeeman e la rotazione magnetica anomala del piano di polarizzazione della luce. Nuovo Cimento 9:384–389CrossRefGoogle Scholar
  21. 21.
    Patnaik AK, Agarwal GS (2000) Laser field induced birefringence and enhancement of magneto-optical rotation. Opt Commun 179:97CrossRefGoogle Scholar
  22. 22.
    Patnaik AK, Agarwal GS (2001) Coherent control of magneto-optical rotation in inhomogeneous broadened medium. Opt Commun 199:127CrossRefGoogle Scholar
  23. 23.
    Petrosyan D, Malakyan YP (2004) Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration. Phys Rev A 70:023822CrossRefGoogle Scholar
  24. 24.
    Wang B, Li S, Ma J, Wang H, Peng KC, Xiao M (2006) Controlling the polarization rotation of an optical field via asymmetry in electromagnetically induced transparency. Phys Rev A 73:051801RCrossRefGoogle Scholar
  25. 25.
    Li S, Wang B, Yang X, Han Y, Wang H, Xiao M, Peng KC (2006) Controlled polarization rotation of an optical field in multi-Zeeman sublevel atoms. Phys Rev A 74:033821CrossRefGoogle Scholar
  26. 26.
    Chen SJ, Mei HH, Ni WT (2007) Q & A Experiment to Search for Vacuum Dichroism, Pseudoscalar-Photon Interaction and Millicharged Fermions. Mod Phys Lett A 22:2815CrossRefGoogle Scholar
  27. 27.
    Pandey K, Wasan A, Natarajan V (2008) Coherent control of magneto-optic rotation. J Phys B At Mol Opt Phys 41:225503CrossRefGoogle Scholar
  28. 28.
    Zavattini E, Zavattini G, Ruoso G, Raiteri G, Polacco E, Milotti E, Lozza V, Karuza M, Gastaldi U, Di Domenico G, Della Valle F, Cimino R, Carusotto S, Cantatore G, Bregant M (2008) New PVLAS results and limits on magnetically induced optical rotation and ellipticity in vacuum. Phys Rev D 77:032006CrossRefGoogle Scholar
  29. 29.
    Zigdon T, Wilson-Gordon AD, Guttikonda S, Bahr EJ, Neitzke O, Rochester SM, Budker D (2010) Nonlinear magneto-optical rotation in the presence of a radio-frequency field. OPTICS EXPRESS 18(25):25494–25508CrossRefPubMedGoogle Scholar
  30. 30.
    Khanbekyan A, Novikova I, Welch GR (2012) Thermodynamic and transport properties in equilibrium air plasmas in a wide pressure and temperature range. Eur Phys J D 66:278CrossRefGoogle Scholar
  31. 31.
    Hombo N, Taniguchi S, Sugimura S, Fujita K, Mitsunaga M (2012) Electromagnetically induced polarization rotation in Na vapor. J Opt Soc Am B 29:1717CrossRefGoogle Scholar
  32. 32.
    Mortezapour A, Saleh A, Mahmoudi M (2013) Birefringence enhancement via quantum interference in the presence of a static magnetic field. Laser Phys 23:065201CrossRefGoogle Scholar
  33. 33.
    Zhang W, Qi Q, Zhou J, Chen L (2014) Mimicking Faraday rotation to sort the orbital angular momentum of light. Phys Rev Lett 112:153601CrossRefPubMedGoogle Scholar
  34. 34.
    Shi S, Ding D-S, Zhou ZY, Li Y, Zhang W, Shi BS (2015) Magnetic-field-induced rotation of light with orbital angular momentum. Applied Physics Letters 106:261110CrossRefGoogle Scholar
  35. 35.
    Kumar P, Deb B, Dasgupta S (2016) Probing vacuum-induced coherence via magneto-optical rotation in molecular systems. Phys Rev A 93:063826CrossRefGoogle Scholar
  36. 36.
    Matsubara M, Schmehl A, Mannhart J, Schlom DG, Fiebig M (2012) Giant third-order magneto-optical rotation in ferromagnetic EuO. Phys Rev B 86:195127CrossRefGoogle Scholar
  37. 37.
    Martinez JC, Jalil MBA, Tan SG (2013) Optical Faraday rotation with graphene. Journal of Applied Physics 113:17B529CrossRefGoogle Scholar
  38. 38.
    Mortezapour A, Ghaderi Goran Abad M, Mahmoudi (2015) Magneto-optical rotation in a GaAs quantum well waveguide. J Opt Soc Am B 32:1338CrossRefGoogle Scholar
  39. 39.
    Yao X, Tokman M, Belyanin A (2015) Strong magneto-optical effects due to surface states in threedimensional topological insulators. OPTICS EXPRESS 23:795CrossRefPubMedGoogle Scholar
  40. 40.
    Mortezapour A, Ghaderi Goran Abad M, Ahmadi Borji M (2016) M Magneto-optical rotation in the diamond nitrogen-vacancy center. Laser Phys Lett 13:055202CrossRefGoogle Scholar
  41. 41.
    Raether H (1988) Surface Plasmons on Smooth and Rough Surfaces and on Gratings. Springer-Verlag, BerlinCrossRefGoogle Scholar
  42. 42.
    Barnes WL, Dereux A, Ebbesen TW (2003) Surface plasmon subwavelength optics. Nature 424:824CrossRefPubMedGoogle Scholar
  43. 43.
    Maier SA, Brongersma ML, Kik PG, Meltzer S, Requicha AAG, Atwater HA (2001) Adv Mater 13:1501CrossRefGoogle Scholar
  44. 44.
    Ozbay E (2006) Plasmonics: merging photonics and electronics at nanoscale dimensions. Science 311:189CrossRefPubMedGoogle Scholar
  45. 45.
    Pendry JB (2000) Negative Refraction Makes a Perfect Lens. Phys Rev Lett 85:3966CrossRefPubMedGoogle Scholar
  46. 46.
    Ebbesen TW, Lezec HJ, Ghaemi HF, Thio T, Wolff PA (1998) Extraordinary optical transmission through hole arrays in metallic films. Nature 391:667CrossRefGoogle Scholar
  47. 47.
    Gu Y, Wang L, Ren P, Zhang J, Zhang T, Xu JP, Zhu SY, Gong Q (2012) Intrinsic Quantum Beats of Atomic Populations and Their Nanoscale Realization Through Resonant Plasmonic Antenna. Plasmonics 7:33–38CrossRefGoogle Scholar
  48. 48.
    Wang L, Gu Y, Chen H, Zhang JY, Cui Y, Gerardot BD, Gong Q (2013) Polarized linewidth-controllable doubletrapping electromagnetically induced transparency spectra in a resonant plasmon nanocavity. Sci Rep 3:2879CrossRefPubMedPubMedCentralGoogle Scholar
  49. 49.
    Chen H, Ren J, Gu Y, Zhao D, Zhang J, Gong Q (2015) Nanoscale Kerr Nonlinearity Enhancement Using Spontaneously Generated Coherence in Plasmonic Nanocavity. Sci. Rep 5:18315CrossRefPubMedPubMedCentralGoogle Scholar
  50. 50.
    Tang B, Wang J, Xia X, Liang X, Ci S, Qu S (2015) Plasmonic-induced transparency and unidirectional control based on the waveguide structure with quadrant ring resonators. Applied Physics Express 8:032202CrossRefGoogle Scholar
  51. 51.
    Shang XJ, Zhai X, Li XF, Wang LL, Wang BX, Liu GD (2016) Realization of Graphene-Based Tunable Plasmon-Induced Transparency by the Dipole-Dipole Coupling. Plasmonics 11:419–423CrossRefGoogle Scholar
  52. 52.
    Chang DE, Sorensen AS, Hemmer PR, Lukin MD (2006) Quantum Optics with Surface Plasmons. Phys Rev Lett 97:053002CrossRefPubMedGoogle Scholar
  53. 53.
    Govorov AO, Bryant GW, Zhang W, Skeini T, Lee J, Kotov NA, Slocik JM, Naik RR (2006) Exciton−Plasmon Interaction and Hybrid Excitons in Semiconductor−Metal Nanoparticle Assemblies. Nano Lett 6:984CrossRefGoogle Scholar
  54. 54.
    Chang DE et al (2007) A single-photon transistor using nanoscale surface plasmons. Nature Phys 3:807–812CrossRefGoogle Scholar
  55. 55.
    Yannopapas V, Vitanov NV (2007) Spontaneous emission of a two-level atom placed within clusters of metallic nanoparticles. J Phys Condens Matter 19:096210CrossRefGoogle Scholar
  56. 56.
    Colas des Francs G, Girard C, Laroche T, Leveque G, Martin OJF (2007) Theory of molecular excitation and relaxation near a plasmonic device. J Chem Phys 127:034701CrossRefPubMedGoogle Scholar
  57. 57.
    Chen GY, Chen YN, Chuu DS (2008) Spontaneous emission of quantum dot excitons into surface plasmons in a nanowire. Opt Lett 33:2212CrossRefPubMedGoogle Scholar
  58. 58.
    Chen YN, Chen GY, Chuu DS, Brandes T (2009) Quantum-dot exciton dynamics with a surface plasmon: Band-edge quantum optics. Phys Rev A 79:033815CrossRefGoogle Scholar
  59. 59.
    Trügler A, Hohenester U (2008) Strong coupling between a metallic nanoparticle and a single molecule. Phys Rev B 77:115403CrossRefGoogle Scholar
  60. 60.
    Yannopapas V, Paspalakis E, Vitanov NV (2009) Plasmon-Induced Enhancement of Quantum Interference near Metallic Nanostructures. Phys Rev Lett 103:063602CrossRefPubMedGoogle Scholar
  61. 61.
    Gu Y, Huang L, Martin OJF, Gong Q (2010) Resonance fluorescence of single molecules assisted by a plasmonic structure. Phys Rev B 81:193103CrossRefGoogle Scholar
  62. 62.
    Marty R, Arbouet A, Paillard V, Girard C, Colas des Francs G (2010) Photon antibunching in the optical near field. Phys Rev B 82:081403(R)CrossRefGoogle Scholar
  63. 63.
    Gonzalez-Tudela A, Rodriguez FJ, Quiroga L, Tejedor C (2010) Dissipative dynamics of a solid-state qubit coupled to surface plasmons: From non-Markov to Markov regimes. Phys Rev B 82:115334CrossRefGoogle Scholar
  64. 64.
    Dzsotjan D, Sorensen AS, Fleischhauer M (2010) Quantum emitters coupled to surface plasmons of a nanowire: A Green's function approach. Phys Rev B 82:075427CrossRefGoogle Scholar
  65. 65.
    Gu Y et al (2012) Surface-plasmon-induced modification on the spontaneous emission spectrum via subwavelengthconfined anisotropic Purcell factor. Nano Lett 12:2488–2493CrossRefPubMedGoogle Scholar
  66. 66.
    Anger P, Bharadwaj P, Novotny L (2006) Enhancement and quenching of single-molecule fluorescence. Phys Rev Lett 96:113002CrossRefPubMedGoogle Scholar
  67. 67.
    Fedutik Y, Temnov VV, Schöps O, Woggon U, Artemyev MV (2007) Exciton-plasmon-photon conversion in plasmonic nanostructures. Phys Rev Lett 99:136802CrossRefPubMedGoogle Scholar
  68. 68.
    Kühn S, Mori G, Agio M, Sandoghdar V (2008) Modification of single molecule fluorescence close to a nanostructure: radiation pattern, spontaneous emission and quenching. Mol Phys 106:893CrossRefGoogle Scholar
  69. 69.
    Vasa P et al (2008) Coherent Exciton–Surface-Plasmon-Polariton Interaction in Hybrid Metal-Semiconductor Nanostructures. Phys Rev Lett 101:116801CrossRefPubMedGoogle Scholar
  70. 70.
    Ringler M, Schwemer A, Wunderlich M, Nichtl A, Kürzinger K, Klar TA, Feldmann J (2008) Shaping Emission Spectra of Fluorescent Molecules with Single Plasmonic Nanoresonators. Phys Rev Lett 100:203002CrossRefPubMedGoogle Scholar
  71. 71.
    Wang Y, Yang T, Tuominen MT, Achermann M (2009) Radiative Rate Enhancements in Ensembles of Hybrid Metal-Semiconductor Nanostructures. Phys Rev Lett 102:163001CrossRefPubMedGoogle Scholar
  72. 72.
    Hakala TK, Toppari JJ, Kuzyk A, Pettersson M, Tikkanen H, Kunttu H, Torma P (2009) Vacuum Rabi Splitting and Strong-Coupling Dynamics for Surface-Plasmon Polaritons and Rhodamine 6G Molecules. Phys Rev Lett 103:053602CrossRefPubMedGoogle Scholar
  73. 73.
    Salomon A, Genet C, Ebbesen TW (2009) Molecule-light complex: dynamics of hybrid molecule-surface plasmon states. Angew Chem Int Ed 48:8748CrossRefGoogle Scholar
  74. 74.
    Gomez DE, Vernon KC, Mulvaney P, Davis TJ (2010) Nano Lett 10:274CrossRefPubMedGoogle Scholar
  75. 75.
    Evangelou S, Yannopapas V, Paspalakis E (2011) Simulating quantum interference in spontaneous decay near plasmonic nanostructures: Population dynamics. Phys Rev A 83:055805CrossRefGoogle Scholar
  76. 76.
    Evangelou S, Yannopapas V, Paspalakis E (2011) Modifying free-space spontaneous emission near a plasmonic nanostructure. Phys Rev A 83:023819CrossRefGoogle Scholar
  77. 77.
    Evangelou S, Yannopapas V, Paspalakis E (2012) Transparency and slow light in a four-level quantum system near a plasmonic nanostructure. Phys Rev A 86:053811CrossRefGoogle Scholar
  78. 78.
    Paspalakis E, Evangelou S, Yannopapas V, Terzis AF (2013) Phase-dependent optical effects in a four-level quantum system near a plasmonic nanostructure. Phys Rev A 88:053832CrossRefGoogle Scholar
  79. 79.
    Evangelou S, Yannopapas V, Paspalakis E (2014) Transient properties of transparency of a quantum system near a plasmonic nanostructure. Opt Commun 314:36CrossRefGoogle Scholar
  80. 80.
    Evangelou S, Yannopapas V, Paspalakis E (2014) Modification of Kerr nonlinearity in a four-level quantum system near a plasmonic nanostructure. J Mod Opt 61:1458CrossRefGoogle Scholar
  81. 81.
    Wang H, Kundu J, Halas NJ (2007) Plasmonic Nanoshell Arrays Combine Surface-Enhanced Vibrational Spectroscopies on a Single Substrate. Angewandte Chemie 46:9040CrossRefPubMedGoogle Scholar
  82. 82.
    Zhang S, Ni W, Kou X, Yeung MH, Sun L, Wang J, Yan C (2007) Advanced Functional Materials 17:3258CrossRefGoogle Scholar
  83. 83.
    Liu JB, Dong H, Li YM, Zhan P, Zhu MW, Wang ZL (2006) A Facile Route to Synthesis of Ordered Arrays of Metal Nanoshells with a Controllable Morphology. Japanese Journal of Applied Physics 45:L582CrossRefGoogle Scholar
  84. 84.
    Yang S, Cai W, Kong L, Lei Y (2010) Surface Nanometer-Scale Patterning in Realizing Large-Scale Ordered Arrays of Metallic Nanoshells with Well-Defined Structures and Controllable Properties. Advanced Functional Materials 20:2527CrossRefGoogle Scholar
  85. 85.
    Sainidou R, Stefanou N, Modinos A (2004) Green’s function formalism for phononic crystals. Phys Rev B 69:064301CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of PhysicsUniversity of GuilanRashtIran

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