Marco Polo, Daniel Felinto and Sandra Vianna

Departamento de Física

Universidade Federal de Pernambuco

Modeling the coupling between cw lasers

and a frequency comb in atomic samples

Index

1 - Introduction

2 - Coherent accumulation and frequency comb

3 - Theoretical model

4 - Results

5 - Conclusions

Introduction

We use a cw laser to probe the interaction of a frequency comb in an

atomic vapor in regime of intense field.

We are interested in the situation where the repetition rate of fs laser is

greater than the atomic relaxation rate, coherent accumulation

processes.

Rb

vapor Ti:sapphire

Coherent accumulation and frequency comb

fs

Ni t0 R

fs fs

n 0 p

t nTE (t) E sech e c.c

T

Coherent accumulation and frequency comb

fs

Ni t0 R

fs fs

n 0 p

t nTE (t) E sech e c.c

T

Two-level sistem:

Doppler 400 MHz

22T 25 ns

fs /50

012fs fs

2E (t)dt

on resonance

atoms stopped

groups of atoms

with different

velocities

D. Felinto et al, Opt. Comm. (2003)

*

*

*

Theoretical model

0 i t

cw cwE (t) E e c.c

4

n

n 2

ˆH n n .E(t)

fs cwE(t) E (t) E (t)

pT 150 fs

RT 10 ns

33 44T T 26 ns

Model based on the energy levels

of Rb, in the transition

Rb and fs laser

parameters:

2 6.82 GHz

fs ~ 5 THz

1/ 2 3/ 25S 5P

Theoretical model

0 i t

cw cwE (t) E e c.c

4

n

n 2

ˆH n n .E(t)

fs cwE(t) E (t) E (t)

ˆ i ˆ ˆH,t

Equation of Liouville:

Approaches:

1 – slow envelope

fs ,cwi t

ij ij(t) (t)e

2 – rotating wave approximation

pT 150 fs

RT 10 ns

33 44T T 26 ns

Rb and fs laser

parameters:

Transmission of laser cw:

13ˆIm 1 3 Im

2 6.82 GHz

fs ~ 5 THz

1/ 2 3/ 25S 5PModel based on the energy levels

of Rb, in the transition

cw 14

* * 03311 4413 14 11 11

44 33

2i i c.c. 1

t T T 2

Bloch equations

24

* 03322 4424 11 22

44 33

2i c.c.

t T T 2

33 33cw 31 33

33

i c.c.t T

44 4414 41 24 42 44

44

i i c.c.t T

13cw 13 cw 33 11 14 43 13

13

1i i i i

t T

0 0

11 22 0.5

1, open transition

0,closed transition

time of flight

atoms

0

n,4 fs

n,4

E (t)(t)

0

13 cwcw

E

fs intensity dependence

fs,cw cw

13 13T Im Im

Change in the transmission of cw field

induced by the presence of the fs field:

fs intensity dependence

fs,cw cw

13 13T Im Im

Change in the transmission of cw field

induced by the presence of the fs field:

cw 0.006

fs pulses of the order of pi

Two-level sistem:

Bloch sphere

cw /100

fs pulses of the order of pi

Three-level sistem:

14 fs

2sin 2

8

For a single pulse:

periodic behavior with fs

cw /100

Open and closed transitions

open closed

fs / 25

cw / 4

Open and closed transitions

Theory Experiment

fs / 25

cw / 4

open closed

Summary

We presented theoretical results of the coupling between a cw

laser and a frequency comb in atomic vapor where TR < Tij.

We observe good agreement between theoretical and

experimental data.

Effects of coherence and population accumulation are observed

in the transmission variation of the cw laser induced by the fs

laser.

We intend to use the cw laser to study electromagnetic induced

transparency by the fs laser.

Dependence with:

Different atom group velocities

fs intensity

Open and closed transition – optical pumping process

Thank you!