Parametric four-wave mixing in atomic vapor induced by a frequency-comb and a cw laser

Transcription

1 Parametric four-wave mixing in atomic vapor induced by a frequency-comb and a cw laser Jesus P. Lopez, Marcio H. G. de Miranda, Sandra S. Vianna Universidade Federal de Pernambuco Marco P. M. de Souza Universidade Federal de Rondônia Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 1 / 25

2 Goal The objective is to study the coherent blue light generated in rubidium vapor by four wave mixing due to the combined action of an ultrashort pulse train and a cw diode laser. Coherent blue beam Rubidium vapor Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 2 / 25

3 Outline 1 Lasers 2 Atomic system 3 Four-wave mixing 4 Correlated work 5 Setup 6 Experimental Results 7 Theory 8 Conclusions Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 3 / 25

4 Lasers Diode laser arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 4 / 25

5 Lasers Diode laser Power = 30 mw Linewidth < 1 MHz λ = 780 nm Scan frequency = 10 GHz arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 4 / 25

6 Lasers Diode laser 80 Potência (mw) Corrente (ma) Power = 30 mw Linewidth < 1 MHz λ = 780 nm Scan frequency = 10 GHz E(t) = E 0 e iωcwt arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 4 / 25

7 Lasers Femtosecond laser arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 5 / 25

8 Lasers Femtosecond laser Average power = 500 mw Peak power = 50 kw Repetition rate = 76 MHz Temporal width = 150 fs arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 5 / 25

9 Lasers Femtosecond laser Average power = 500 mw Peak power = 50 kw Repetition rate = 76 MHz Temporal width = 150 fs N 1 [ ] 1.76(t ntr ) E(t) = E 0 sech e in(ω fst R φ)+iω fs t n=0 T p arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 5 / 25

10 Lasers Femtosecond laser ( a) ( b) Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 6 / 25

11 Atomic system Atomic system 85 Rb 5D 5/ 2 0,2 nm 5D 3/ nm 5P 3/ nm 5P 1/ nm 3 MHz 5 MHz 8 MHz 9 MHz 9 MHz 19 MHz 12 MHz 7 MHz F' = MHz F' = 3 63 MHz F' = 2 29 MHz F' = MHz F'' = MHz F'' = 0 F'' = 1 F'' = 2 F'' = 3 F'' = 4 F'' = MHz F' = 4 F'' = 3 F'' = 2 F'' = MHz F' = MHz 5S 1/ MHz F = 3 F = 2 Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 7 / 25

12 Atomic system Atomic system 85 Rb 5D 5/ 2 0,2 nm 5D 3/ nm 5P 3/ nm 5P 1/ nm 5S 1/ 2 3 MHz 5 MHz 8 MHz 9 MHz 9 MHz 19 MHz 12 MHz 7 MHz F' = MHz F' = 3 63 MHz F' = 2 29 MHz F' = MHz F'' = MHz 3036 MHz F'' = 0 F'' = 1 F'' = 2 F'' = 3 F'' = 4 F'' = MHz F' = 4 F'' = 3 F'' = 2 F'' = MHz F' = MHz F = 3 F = 2 Transmissão (V) 0,6 0,5 0,4 0,65 0,60 0,55 0,50 ( a) 85 Rb, F = ( b) Frequência (GHz) F' = 1 F' = Frequência (MHz) 87 F' = 3 87 Rb, F = Rb, F = 1 Rb, F = 2 Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 7 / Tensão (V)

13 Four-wave mixing Four-wave mixing Four-wave mixing is a nonlinear process that involves four electromagnetic waves. Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 8 / 25

14 Four-wave mixing Four-wave mixing Four-wave mixing is a nonlinear process that involves four electromagnetic waves. In general, we have three incident beams and one generated beam. Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 8 / 25

15 Four-wave mixing Four-wave mixing Four-wave mixing is a nonlinear process that involves four electromagnetic waves. In general, we have three incident beams and one generated beam. In the weak interaction limit, it is a third-order process, where the generated field can be expressed as P 4 = ɛ 0 χ (3) E 1 E 2 E 3 Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 8 / 25

16 Four-wave mixing Driven nonlinear oscillator: classical analysis m Fext ( t) Nonlinear spring: F el = kx k 2 x 2 F ext (t) = F 0 (cos ω 1 t + cos ω 2 t) arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 9 / 25

17 Four-wave mixing Driven nonlinear oscillator: classical analysis m Fext ( t) Nonlinear spring: F el = kx k 2 x 2 F ext (t) = F 0 (cos ω 1 t + cos ω 2 t) mẍ + γẋ + kx + k 2 x 2 = F ext (t) arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 9 / 25

18 Four-wave mixing Driven nonlinear oscillator: classical analysis m Fext ( t) Nonlinear spring: F el = kx k 2 x 2 F ext (t) = F 0 (cos ω 1 t + cos ω 2 t) mẍ + γẋ + kx + k 2 x 2 = F ext (t) 2 1 Amplitude Time arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 9 / 25

19 Four-wave mixing Driven nonlinear oscillator: classical analysis m Fext ( t) Nonlinear spring: F el = kx k 2 x 2 F ext (t) = F 0 (cos ω 1 t + cos ω 2 t) mẍ + γẋ + kx + k 2 x 2 = F ext (t) 2 1 ω 1 ω ω 1 ω 1 + ω 2 2ω 2 Amplitude 0-1 Amplitude 0.2 ω 1 - ω Time Frequency arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 9 / 25

20 Four-wave mixing Wave-mixing ω 1, ω 2 ω 1 ω 2 2ω 1 2ω 2 ω 1 + ω 2 ω 1 ω 2 Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 10 / 25

21 Four-wave mixing Wave-mixing General formula: ω 1, ω 2 ω 1 ω 2 2ω 1 2ω 2 ω 1 + ω 2 ω 1 ω 2 ω 1, ω 2, ω 3,... α 1 ω 1 ± α 2 ω 2 ± α 3 ω 3 ± Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 10 / 25

22 Four-wave mixing Wave-mixing General formula: Electromagnetism: ω 1, ω 2 ω 1 ω 2 2ω 1 2ω 2 ω 1 + ω 2 ω 1 ω 2 ω 1, ω 2, ω 3,... α 1 ω 1 ± α 2 ω 2 ± α 3 ω 3 ± P = ɛ 0 χ (1) E + ɛ 0 χ (2) E 2 + ɛ 0 χ (3) E 3 + χ (1) 1 χ (2) m/v χ (3) m 2 /V 2 Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 10 / 25

23 Correlated work Correlated work Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 11 / 25

24 Correlated work Correlated work Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 11 / 25

25 Setup Setup 5.2 µ m (generated) 6P 5D 5/ nm Ti:sapph 420 nm (generated) 5P 3/ nm Diode 5S 1/ 2 Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 12 / 25

26 Setup Mesa óptica Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 13 / 25

27 Experimental Results Experimental Results I cw = 1.9 W/cm 2 I fs = 1.0 mw/cm 2 (each mode) T = 85 o C Blue intensity (arb. units) Rb, F g =2 saturated absorption 87 Rb, F g =1 85 Rb, F 85 g =3 Rb, F g = Diode frequency (GHz) Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 14 / 25

28 Experimental Results Experimental Results I cw = 1.9 W/cm 2 I fs = 1.0 mw/cm 2 (each mode) T = 85 o C Broad peaks: fluorescence induced by both lasers Blue intensity (arb. units) Rb, F g =2 saturated absorption 87 Rb, F g =1 85 Rb, F 85 g =3 Rb, F g = Diode frequency (GHz) Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 14 / 25

29 Experimental Results Experimental Results I cw = 1.9 W/cm 2 I fs = 1.0 mw/cm 2 (each mode) T = 85 o C Broad peaks: fluorescence induced by both lasers Blue intensity (arb. units) Rb, F g =2 85 Rb, F g =3 saturated absorption 85 Rb, F g =2 Flat Background: 0.1 fluorescence induced by 0.0 femtosecond laser Diode frequency (GHz) 87 Rb, F g =1 Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 14 / 25

30 Experimental Results Polarization and density dependence Blue intensity (arb. units) 0.5 Blue fluorescence 0.30 at 90 o perpendicular polarization parallel polarization Diode frequency (GHz) P Rubidium vapor arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 15 / 25

31 Experimental Results Polarization and density dependence Blue intensity (arb. units) 0.5 Blue fluorescence 0.30 at 90 o perpendicular polarization parallel polarization Diode frequency (GHz) P Rubidium vapor arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 15 / 25

32 Experimental Results Polarization and density dependence Blue intensity (arb. units) 0.5 Blue fluorescence 0.30 at 90 o perpendicular polarization parallel polarization Diode frequency (GHz) P Rubidium vapor Blue intensity (arb. units) ( a) ( b) ( c) ( d) 87 Rb, F g = 2 85 Rb, F g = 3 o 72 C o 73 C o 82 C o 87 C Diode frequency (GHz) Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 15 / 25

33 Experimental Results Experimental Results T = 85 o C Slow scanning Average of 10 measurements Blue intensity (arb. units) Rb, F g = Diode frequency (MHz) arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 16 / 25

34 Experimental Results Experimental Results T = 85 o C Slow scanning Average of 10 measurements Peak linewidths: 55 MHz Blue intensity (arb. units) Rb, F g = Diode frequency (MHz) arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 16 / 25

35 Experimental Results Experimental Results T = 85 o C Slow scanning Average of 10 measurements Peak linewidths: 55 MHz Blue intensity (arb. units) Frequency difference between two adjacent 0.00 peaks: 78 ± 4 MHz Rb, F g = 3 Diode frequency (MHz) arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 16 / 25

36 Experimental Results Density dependence Femtosecond and diode lasers in resonance with your transitions PFWM signal amplitude (arb. units) 0.5 I cw = 1.9 W/cm I cw = 9.4 W/cm Atomic density (10 12 cm -3 ) PFWM signal amplitude (arb. units) Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 17 / 25

37 Experimental Results Density dependence Femtosecond and diode lasers in resonance with your transitions Exponential growth PFWM signal amplitude (arb. units) 0.5 I cw = 1.9 W/cm I cw = 9.4 W/cm Atomic density (10 12 cm -3 ) PFWM signal amplitude (arb. units) Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 17 / 25

38 Experimental Results Density dependence Femtosecond and diode lasers in resonance with your transitions Exponential growth Threshold shift as a functions of the diode intensity PFWM signal amplitude (arb. units) 0.5 I cw = 1.9 W/cm I cw = 9.4 W/cm Atomic density (10 12 cm -3 ) PFWM signal amplitude (arb. units) Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 17 / 25

39 Experimental Results Diode intensity dependence Blue intensity (arb. units) Diode power 0.5 mw 2 mw 4 mw 6 mw 8 mw 10 mw Diode frequency (MHz) Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 18 / 25

40 Theory Theory Diamond-type four-level system interacting with four cw lasers. Ω 1 : diode laser Ω 2 : one mode of the femtosecond laser Ω 3 : seed field Ω 4 : blue beam generated Ω 3 4 Ω Ω 4 Ω 1 1 arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 19 / 25

41 Theory Theory Diamond-type four-level system interacting with four cw lasers. Ω 1 : diode laser Ω 2 : one mode of the femtosecond laser Ω 3 : seed field Ω 4 : blue beam generated Ω 3 4 Ω Ĥ int = ˆµ E Ω 4 Ω 1 (Dipole electric approximation) 1 arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 19 / 25

42 Theory Maxwell-Bloch equations ˆρ t = i ] [Ĥ, ˆρ ħ (Liouville-Neumann) 2 E z E c 2 t 2 = µ 2 P 0 t 2 (Wave equation) P = N ˆµ (Polarization) Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 20 / 25

43 Theory Maxwell-Bloch equations ρ jk (z, t) t Ω j (z, t) z = (iω jk + γ jk )ρ jk (z, t) i ħ j [Ĥint, ˆρ] k = iα jk γ jk σ jk (z, t) Ω 3 3 where 4 Ω 2 Ω j = µ jkej 0 (Rabi frequency) ħ µ 2 jk α jk = ω j N 2ħcɛ 0 γ jk σ jk = ρ jk e iω jt Ω 4 Ω arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 21 / 25

44 Theory Theoretical result Numerical solution of the equations: Runge-Kutta method All field at resonance Initial conditions: Ω 2 = 2.4γ 33, Ω 3 = γ 33 and Ω 4 = 0. Ω 1 (normalized) 1.0 Diode Blue α 12 z Ω 4 (rad/s) Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 22 / 25

45 Theory Theoretical result Numerical solution of the equations: Runge-Kutta method All field at resonance Initial conditions: Ω 2 = 2.4γ 33, Ω 3 = γ 33 and Ω 4 = Diode Blue ρ ρ 22 ρ 33 Ω 1 (normalized) Ω 4 (rad/s) ρ α 12 z α 12 z Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 22 / 25

46 Theory Theoretical result Ω 4 (rad/s) Ω 1 = 0.7γ 22 Ω 1 = 1.4γ Ω 4 (rad/s) α 12 z Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 23 / 25

47 Conclusions Conclusions We have investigated the coherent blue light generated in atomic vapor using a parametric four-wave mixing process due to the combined action of a cw laser and a train of ultrashort pulses. Each individual mode is responsible for inducing the nonlinear process. Blue signal characterization: exponential growth with saturation. The density dependence was theoretically modeled. Next step: frequency dependence modeling (with CUDA!). Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 24 / 25

48 Acknowledgments Thank you very much! arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 25 / 25