1. Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National Taiwan Normal University 2011.12.19@NTHU

2. Outline Introduction to Electromagnetically Induced Transparency (EIT) and time-dependent simulation approach. Single atom response with intense, ultra-short pulses 1D atomic array response with intense, ultra- short pulses with pulse turn-off and turn-on Metamaterials and EIT

3. Electromagnetically Induced Transparency

4. Simulation model 1.8 GHz Na atom Probe field =589 nm Coupling field 1-D EM wave and 1-D atomic array

5. Numerical simulation methods The electromagnetic fields are solved by discretizing Maxwell equation and propagating the electromagnetic waves by finite-difference method. With one-directional radiation boundary condition

6. Numerical simulation methods The atomic states and atomic polarization P is simulated by solving time-dependent Schrödinger equation by Runge-Kutta 4 th -order method. Using simple c j or density-matrix approach Without rotating wave approximation. No spontaneous emission yet! explicit or implicit method

7. At Resonance - Absorption Position (x/λ) Amplitude -- Probe Field No coupling field

8. EIT – Transparency Position (x/λ) Amplitude -- Probe Field with coupling field

9. EIT from purterbation theory K.-J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).

10. Energy level shift from simulations Total wave Probe field Scattering field Frequency( ω /ω 31 ) coupling field power = 3×10 4 mW cm -2

11. Energy level shift from simulations Total wave Probe field Scattering field Frequency( ω /ω 31 ) Ω c /2 coupling field power = 3×10 7 mW cm -2

12. Total wave Probe field Scattering field Frequency( ω /ω 31 ) Large Energy level shift - Transparency coupling field power = 1.2×10 8 mW cm -2

13. Mode coupling and energy level shift in EIT Ec » Ep

14. Single atom in intense, ultra-short pulses E 12 = 1 a.u. E 13 = 0.95 a.u. Decay rate = 2 π / 1000 Density-matrix simulation

15. Polarization with various coupling filed intensity coupling field FWHM=256 T/2π probe field FWHM=16 T/2π Ωp=0.01

16. Polarization with various coupling filed intensity coupling field FWHM=256 T/2π probe field FWHM=16 T/2π Ωc=0.1

17. Polarization with various coupling filed intensity coupling field FWHM=256 T/2π probe field FWHM=16 T/2π Ωp=1.0

18. Polarization with various coupling filed intensity coupling field FWHM=256 T/2π probe field FWHM=16 T/2π Ωp=10.0

19. Time-dependent polarization behavior coupling field FWHM =256 T/2π Ωp=10.0 probe field FWHM =16 T/2π Ωc=0.0

20. Time-dependent polarization behavior coupling field FWHM =256 T/2π Ωp=10.0 probe field FWHM =16 T/2π Ωc=10.0

21. Time-dependent polarization behavior coupling field FWHM =256 T/2π Ωp=10.0 probe field FWHM =16 T/2π Ωc=100.0

22. Time-dependent polarization behavior coupling field FWHM =256 T/2π Ωp=10.0 probe field FWHM =16 T/2π Ωc=400.0

23. Interaction between light and polarization wave Coupling field turned off by a Gaussian profile

24. Coupling field turn-off –  = 50 fs Position (x/λ) Amplitude -- Probe Field-- Polarization between 1-2 level

25. Position (x/λ) Amplitude -- Polarization between 1-2 level Coupling field turn-off –  = 20 fs -- Probe Field

26. Position (x/λ) Amplitude -- Polarization between 1-2 level Coupling field turn-off –  = 10 fs -- Probe Field

27. Position (x/λ) Amplitude -- Polarization between 1-2 level Coupling field turn-off –  = 5 fs -- Probe Field

28. Coupling field turn-off –  = 1 fs Position (x/λ) Amplitude -- Polarization between 1-2 level-- Probe Field

29. Coupling field turn-off –  = 1 fs (zoom in) Position (x/λ) Amplitude -- Polarization between 1-2 level-- Probe Field

30. Analyze polarization wave from one atom in the array The polarization between |1> and |2> of one atom in the atomic array under constant coupling field is analyzed.The polarization becomes similar to the envelope of the probe field, while the intensity of the coupling field is large enough

31. Atomic Dynamics - Coupling field = 3×10 7 mW cm -2 Time (t/T) Amplitude -- Polarization between 1-2 level-- Probe Field

32. Atomic Dynamics - Coupling field = 6×10 7 mW cm -2 Time (t/T) Amplitude -- Polarization between 1-2 level-- Probe Field

33. Atomic Dynamics - Coupling field = 1.2×10 8 mW cm -2 Time (t/T) Amplitude -- Polarization between 1-2 level-- Probe Field

34. C 1 * C 2 e -i  12 t component with different coupling light turn-off rate perturbation theory, single atom without atom-atom interaction with atom-atom interaction

35. Coupling field turn-off and on  off = 25 period Position (x/λ) Amplitude － Probe Field -- Polarization between 1-2 level

36. Coupling field turn-off and on  off = 50 period Position (x/λ) Amplitude － Probe Field -- Polarization between 1-2 level

37. Coupling field turn-off and on  off = 75 period Position (x/λ) Amplitude － Probe Field -- Polarization between 1-2 level

38. Coupling field turn-off and on  off = 100 period Position (x/λ) Amplitude － Probe Field -- Polarization between 1-2 level

39. Probe pulse reading efficiency vs coupling light turn-off duration atomic density 1×10 18 cm -3 decay rate Γ 3 =ω 31 /20π ratio

40. Probe pulse reading efficiency vs atomic density coupling light turn-off duration τ c =τ p decay rate Γ 3 =ω 31 /20π ratio

41. Probe pulse reading efficiency vs decay rate coupling light turn-off duration τ c =τ p atomic density 4×10 17 cm -3 ratio

42. Metamaterial Metamaterials are artificially structured materials that can have profoundly unique electromagnetic or optical properties. - D. R. Smith Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior. - Wikipedia

43. Epsilon-negative (ENG) medium Classification of Metamaterials DPS DNG ENG MNG Regular Dielectrics DPS Double positive (DPS) medium Mu-negative (MNG) medium Double-negative (DNG) medium

44. Realization of DNG Metamaterials 44 R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001). 2001

45. Subwavelength Focusing Perfect lens (Pendry, 2000) 45 n=1 n=-1 y = 2d y = -2d

46. Cloaking and Transformation Optics Is it possible to smoothly bend light around an object? No backscatter, no shadow = effectively invisible. Can there really be such an interesting solution still lurking in classical electromagnetics? Pendry et al. [Science, 2006] showed how it can be done. Key realization: coordinate transformations on electromagnetic fields are completely equivalent to a nonuniform permittivity and permeability.

47. Induced transparency in metamaterials by symmetry breaking Papasimakis and Zheludev, Optics & Photonics News, p22 (Oct 2009)

48. Active metamaterial for loss- compensated pulse delays Loss-compensated slow-light device: metamaterial array with EIT-like dispersion placed on a gain substrate (  =9.5+035i). At the wavelength of 1.7 µm, it shows single-pass amplification and simultaneously sharp normal dispersion.

49. Metamaterial mimicking EIT N. Papasimakis, et al. Appl. Phys. Lett. 94, 211902 (2009)

50. Acknowledgements Dar-Yeong Ju ( 朱達勇 )at NIU and NTNU Meng-Chang Wu ( 吳孟昌 ) (currently at IAMS, AS) Supported by NSC