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

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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 Departamento de Física, Universidade Federal de Pernambuco Marco P. M. de Souza Depart. de Física, Universidade Federal de Rondônia, Campus Ji-Paraná Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 1 / 16

2 Introduction The objective is to study the coherent blue light generated in rubidium vapor 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 / 16

3 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 3 / 16

4 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 3 / 16

5 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. We are interested in the generated field that is the result from the polarization that 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 3 / 16

6 Correlated work Correlated work Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 4 / 16

7 Correlated work Correlated work Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 4 / 16

8 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 5 / 16

9 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 6 / 16

10 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 6 / 16

11 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 6 / 16

12 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 7 / 16

13 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 7 / 16

14 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 7 / 16

15 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 8 / 16

16 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 8 / 16

17 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 8 / 16

18 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 9 / 16

19 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 9 / 16

20 Experimental Results Density dependence Femtosecond and diode lasers in resonance with your transitions Exponential growth Threshold shift as a function 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 9 / 16

21 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 10 / 16

22 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 10 / 16

23 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 11 / 16

24 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 12 / 16

25 Theory Theoretical result Numerical solution of the equations All fields at resonance Initial conditions: Ω 1 = 0.7γ 22, Ω 2 = 2.4γ 33, Ω 3 = γ 33 and Ω 4 = 0 ρ 11 = 1, ρ ij = 0 for (i, j) (1, 1) 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 13 / 16

26 Theory Theoretical result Numerical solution of the equations All fields at resonance Initial conditions: Ω 1 = 0.7γ 22, Ω 2 = 2.4γ 33, Ω 3 = γ 33 and Ω 4 = 0 ρ 11 = 1, ρ ij = 0 for (i, j) (1, 1) 1.0 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 13 / 16

27 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 14 / 16

28 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. Many modes can be responsible for inducing the nonlinear process. Blue signal characterization: exponential growth with saturation. The density dependence was theoretically modeled. Next step: frequency diode dependence modeling with CUDA parallel programming (See poster P116 this afternoon). Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 15 / 16

29 Acknowledgments Thank you very much! arco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminário de grupo 16 / 16

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

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