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Modeling the coupling between cw lasers and a frequency comb in atomic samples

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We use a cw laser to probe the interaction of a frequency comb in an atomic vapor in regime of intense field.

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Modeling the coupling between cw lasers and a frequency comb in atomic samples

1. 1. Modeling the coupling between cw lasersand a frequency comb in atomic samples Marco Polo, Daniel Felinto and Sandra Vianna Departamento de Física Universidade Federal de Pernambuco
2. 2. Index 1 - Introduction 2 - Coherent accumulation and frequency comb 3 - Theoretical model 4 - Results 5 - Conclusions
3. 3. Introduction We use a cw laser to probe the interaction of a frequency comb in an atomic vapor in regime of intense field. Ti:sapphire Rb vapor We are interested in the situation where the repetition rate of fs laser is greater than the atomic relaxation rate, coherent accumulation processes.
4. 4. Coherent accumulation and frequency comb N  t  nTR  i tE fs (t)  E  sec h  0 e fs  c.c fs  Tp  n 0  
5. 5. Coherent accumulation and frequency comb Two-level sistem: T22  25 ns fs   / 50 on resonance atoms stopped * * groups of atoms with different velocities N  t  nTR  i tE fs (t)  E  sec h  0 e fs  c.c fs   212   n 0  Tp  fs  0 E fs (t)dt * D. Felinto et al, Opt. Comm. (2003) Doppler  400 MHz
6. 6. Theoretical model Model based on the energy levels of Rb, in the transition 5S1/ 2  5P3/ 2 4 H   n n n  .E(t) ˆ ˆ n2 E(t)  Efs (t)  E cw (t) Ecw (t)  E0 eit  c.c cw 2  6.82 GHz fs ~ 5 THzRb and fs laserparameters: Tp  150 fs TR  10 ns T33  T44  26 ns
7. 7. Theoretical model Model based on the energy levels of Rb, in the transition 5S1/ 2  5P3/ 2 Equation of Liouville:  ˆ i ˆ    H,   ˆ  t 4 H   n n n  .E(t) ˆ ˆ Transmission of laser cw: n2 E(t)  Efs (t)  E cw (t)  Im 1  3  Im 13 ˆ Ecw (t)  E0 eit  c.c cw Approaches: 2  6.82 GHz 1 – slow envelope fs ~ 5 THz ifs ,cw tRb and fs laserparameters: Tp  150 fs ij (t)  ij (t)e TR  10 ns T33  T44  26 ns 2 – rotating wave approximation
8. 8. Bloch equations 11 2    t  cw 14  T44 T33  2   i* 13  i* 14  c.c.  44  33  1     11  11 0  22 2   t  24   i* 24  c.c.  44  33   11  0 T44 T33 2 22    1, open transition   0,closed transition 33    icw 31  c.c.  33  33 t T33 44  time of flight   i1441  i2442  c.c.  44  44 atoms t T44 13  1   icw 13  icw  33  11   i14 43  i     13 t  T13  13E cw 0  n,4 E fs (t) 0 cw  n,4 (t)  11  0  0.5 0 22
9. 9. fs intensity dependence Change in the transmission of cw field induced by the presence of the fs field: T  Im 13  Im 13 fs,cw cw
10. 10. fs intensity dependence Change in the transmission of cw field induced by the presence of the fs field: cw  0.006 T  Im 13  Im 13 fs,cw cw
11. 11. fs pulses of the order of pi cw   /100 Two-level sistem: Bloch sphere
12. 12. fs pulses of the order of pi cw   /100 Three-level sistem: For a single pulse: 14  8 2 sin  2fs  periodic behavior with fs
13. 13. Open and closed transitions open closed fs   / 25 cw   / 4
14. 14. Open and closed transitions open closed fs   / 25 cw   / 4 Theory Experiment
15. 15. Summary We presented theoretical results of the coupling between a cw laser and a frequency comb in atomic vapor where TR < Tij. Effects of coherence and population accumulation are observed in the transmission variation of the cw laser induced by the fs laser. Dependence with: Different atom group velocities fs intensity Open and closed transition – optical pumping process We observe good agreement between theoretical and experimental data. We intend to use the cw laser to study electromagnetic induced transparency by the fs laser.
16. 16. Thank you!