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

Jesus P. Lopez, Marcio H. G. de Miranda, Sandra S. ViannaDepartamento de Fısica, Universidade Federal de Pernambuco

Marco P. M. de SouzaDepart. de Fısica, Universidade Federal de Rondonia, Campus Ji-Parana

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 1 / 16

Introduction

The objective is to study the coherent blue light generated inrubidium vapor due to the combined action of an ultrashort pulsetrain and a cw diode laser.

Coherent blue beam

Rubidium vapor

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 2 / 16

Four-wave mixing

Four-wave mixing

Four-wave mixing is a nonlinear process that involves fourelectromagnetic waves.

In general, we have three incident beams and one generated beam.

In the weak interaction limit, it is a third-order process. We areinterested in the generated field that is the result from thepolarization that can be expressed as

P4 = ε0χ(3)E1E2E3

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 3 / 16

Four-wave mixing

Four-wave mixing

Four-wave mixing is a nonlinear process that involves fourelectromagnetic waves.

In general, we have three incident beams and one generated beam.

In the weak interaction limit, it is a third-order process. We areinterested in the generated field that is the result from thepolarization that can be expressed as

P4 = ε0χ(3)E1E2E3

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 3 / 16

Four-wave mixing

Four-wave mixing

Four-wave mixing is a nonlinear process that involves fourelectromagnetic waves.

In general, we have three incident beams and one generated beam.

In the weak interaction limit, it is a third-order process. We areinterested in the generated field that is the result from thepolarization that can be expressed as

P4 = ε0χ(3)E1E2E3

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 3 / 16

Correlated work

Correlated work

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 4 / 16

Correlated work

Correlated work

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 4 / 16

Setup

Setup

1/ 25S

3/ 25P

5/ 25D

6P

420 nm

5.2 mµ776 nm

780 nmDiode(generated)

(generated)

Ti:sapph

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 5 / 16

Experimental Results

Experimental Results

Icw = 1.9 W/cm2

Ifs = 1.0 mW/cm2

(each mode)

T = 85oC

Broad peaks:fluorescence induced byboth lasers

Flat Background:fluorescence induced byfemtosecond laser

-2 0 2 4 60.0

0.1

0.2

0.3

0.4

0.5

0.6

85Rb, Fg=2

85Rb, Fg=3

87Rb, Fg=2

Diode frequency (GHz)

Blu

e in

tens

ity (

arb.

uni

ts)

saturated absorption

87Rb, Fg=1

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 6 / 16

Experimental Results

Experimental Results

Icw = 1.9 W/cm2

Ifs = 1.0 mW/cm2

(each mode)

T = 85oC

Broad peaks:fluorescence induced byboth lasers

Flat Background:fluorescence induced byfemtosecond laser

-2 0 2 4 60.0

0.1

0.2

0.3

0.4

0.5

0.6

85Rb, Fg=2

85Rb, Fg=3

87Rb, Fg=2

Diode frequency (GHz)

Blu

e in

tens

ity (

arb.

uni

ts)

saturated absorption

87Rb, Fg=1

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 6 / 16

Experimental Results

Experimental Results

Icw = 1.9 W/cm2

Ifs = 1.0 mW/cm2

(each mode)

T = 85oC

Broad peaks:fluorescence induced byboth lasers

Flat Background:fluorescence induced byfemtosecond laser -2 0 2 4 6

0.0

0.1

0.2

0.3

0.4

0.5

0.6

85Rb, Fg=2

85Rb, Fg=3

87Rb, Fg=2

Diode frequency (GHz)

Blu

e in

tens

ity (

arb.

uni

ts)

saturated absorption

87Rb, Fg=1

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 6 / 16

Experimental Results

Polarization and density dependence

-3 -2 -1 0 1 20.0

0.1

0.2

0.3

0.4

0.5 Blue fluorescence at 90o

-2 -1 0 10.15

0.20

0.25

0.30

Blu

e in

tens

ity (a

rb. u

nits

)

Diode frequency (GHz)

parallelpolarization

perpendicular polarization

P

Rubidium vapor

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 7 / 16

Experimental Results

Polarization and density dependence

-3 -2 -1 0 1 20.0

0.1

0.2

0.3

0.4

0.5 Blue fluorescence at 90o

-2 -1 0 10.15

0.20

0.25

0.30

Blu

e in

tens

ity (a

rb. u

nits

)

Diode frequency (GHz)

parallelpolarization

perpendicular polarization

P

Rubidium vapor

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 7 / 16

Experimental Results

Polarization and density dependence

-3 -2 -1 0 1 20.0

0.1

0.2

0.3

0.4

0.5 Blue fluorescence at 90o

-2 -1 0 10.15

0.20

0.25

0.30

Blu

e in

tens

ity (a

rb. u

nits

)

Diode frequency (GHz)

parallelpolarization

perpendicular polarization

P

Rubidium vapor

0.00

0.05

0.10

0.00

0.05

0.10

0.0

0.2

0.4

-2 -1 0 10.0

0.2

0.4

87 Rb, 2gF =

Blu

e in

tens

ity (

arb.

uni

ts)

o82 C

o87 C

o73 C

( )d

85 Rb, 3gF =

( )c

( )b

( )a o72 C

Diode frequency (GHz)

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 7 / 16

Experimental Results

Experimental Results

T = 85oC

Slow scanning

Average of 10measurements

Peak linewidths: ≈ 55 MHz

Frequency differencebetween two adjacentpeaks: 78± 4 MHz

-600 -300 0 300 6000.00

0.05

0.10

0.15

0.20

0.25

Blu

e in

tens

ity (

arb.

uni

ts)

Diode frequency (MHz)

85Rb, Fg = 3

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 8 / 16

Experimental Results

Experimental Results

T = 85oC

Slow scanning

Average of 10measurements

Peak linewidths: ≈ 55 MHz

Frequency differencebetween two adjacentpeaks: 78± 4 MHz

-600 -300 0 300 6000.00

0.05

0.10

0.15

0.20

0.25

Blu

e in

tens

ity (

arb.

uni

ts)

Diode frequency (MHz)

85Rb, Fg = 3

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 8 / 16

Experimental Results

Experimental Results

T = 85oC

Slow scanning

Average of 10measurements

Peak linewidths: ≈ 55 MHz

Frequency differencebetween two adjacentpeaks: 78± 4 MHz -600 -300 0 300 600

0.00

0.05

0.10

0.15

0.20

0.25

Blu

e in

tens

ity (

arb.

uni

ts)

Diode frequency (MHz)

85Rb, Fg = 3

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 8 / 16

Experimental Results

Density dependence

Femtosecond and diodelasers in resonance withyour transitions

Exponential growth

“Threshold” shift as afunction of the diodeintensity

0 10 20 30 400.0

0.1

0.2

0.3

0.4

0.5

Icw

= 9.4 W/cm2

Atomic density (1012 cm-3)PF

WM

sig

nal a

mpl

itude

(ar

b. u

nits

)

Icw

= 1.9 W/cm2

0

1

2

3

PF

WM

sig

nal a

mpl

itude

(ar

b. u

nits

)

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 9 / 16

Experimental Results

Density dependence

Femtosecond and diodelasers in resonance withyour transitions

Exponential growth

“Threshold” shift as afunction of the diodeintensity

0 10 20 30 400.0

0.1

0.2

0.3

0.4

0.5

Icw

= 9.4 W/cm2

Atomic density (1012 cm-3)PF

WM

sig

nal a

mpl

itude

(ar

b. u

nits

)

Icw

= 1.9 W/cm2

0

1

2

3

PF

WM

sig

nal a

mpl

itude

(ar

b. u

nits

)

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 9 / 16

Experimental Results

Density dependence

Femtosecond and diodelasers in resonance withyour transitions

Exponential growth

“Threshold” shift as afunction of the diodeintensity

0 10 20 30 400.0

0.1

0.2

0.3

0.4

0.5

Icw

= 9.4 W/cm2

Atomic density (1012 cm-3)PF

WM

sig

nal a

mpl

itude

(ar

b. u

nits

)

Icw

= 1.9 W/cm2

0

1

2

3

PF

WM

sig

nal a

mpl

itude

(ar

b. u

nits

)

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 9 / 16

Theory

Theory

Diamond-type four-level systeminteracting with four cw lasers.

Ω1: diode laserΩ2: one mode of the femtosecond laserΩ3: seed fieldΩ4: blue beam generated

Hint = −µ · E

(Dipole electric approximation)

1

2

3

4

1Ω

2Ω3Ω

4Ω

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 10 / 16

Theory

Theory

Diamond-type four-level systeminteracting with four cw lasers.

Ω1: diode laserΩ2: one mode of the femtosecond laserΩ3: seed fieldΩ4: blue beam generated

Hint = −µ · E

(Dipole electric approximation) 1

2

3

4

1Ω

2Ω3Ω

4Ω

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 10 / 16

Theory

Maxwell-Bloch equations

∂ρ

∂t= − i

[H, ρ

](Liouville-Neumann)

∂2E

∂z2− 1

c2∂2E

∂t2= µ0

∂2P

∂t2(Wave equation)

P = N 〈µ〉 (Polarization)

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 11 / 16

Theory

Maxwell-Bloch equations

∂ρjk(z, t)

∂t= −(iωjk + γjk)ρjk(z, t)− i

〈j| [Hint, ρ] |k〉

∂Ωj(z, t)

∂z= −iαjkγjkσjk(z, t)

where

Ωj =µjkE

0j

(Rabi frequency)

αjk =µ2jkωj

2cε0γjkN

σjk = ρjke−iωjt

1

2

3

4

1Ω

2Ω3Ω

4Ω

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 12 / 16

Theory

Theoretical result

Numerical solution of the equations

All fields at resonance

Initial conditions:Ω1 = 0.7γ22, Ω2 = 2.4γ33, Ω3 = 2.4× 10−7γ33 and Ω4 = 0ρ11 = 1, ρij = 0 for (i, j) 6= (1, 1)

0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0 Diode Blue

α12

z

Ω1 (

norm

aliz

ed)

0

500

1000

1500

2000

2500

Ω4

(rad

/s)

0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

α12

z

ρ11

ρ22

ρ33

ρ44

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 13 / 16

Theory

Theoretical result

Numerical solution of the equations

All fields at resonance

Initial conditions:Ω1 = 0.7γ22, Ω2 = 2.4γ33, Ω3 = 2.4× 10−7γ33 and Ω4 = 0ρ11 = 1, ρij = 0 for (i, j) 6= (1, 1)

0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0 Diode Blue

α12

z

Ω1 (

norm

aliz

ed)

0

500

1000

1500

2000

2500

Ω4

(rad

/s)

0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

α12

z

ρ11

ρ22

ρ33

ρ44

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 13 / 16

Theory

Theoretical result

0 2 4 6 8 10

0

20

40

60

80

α12

z

Ω4 (

rad/

s)

0

500

1000

1500

2000

2500

Ω1 = 1.4γ

22

Ω1 = 0.7γ

22

Ω4 (

rad/

s)

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 14 / 16

Conclusions

Conclusions

We have investigated the coherent blue light generated in atomicvapor using a parametric four-wave mixing process due to thecombined 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 CUDAparallel programming (See poster P116 this afternoon).

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 15 / 16

Acknowledgments

Thank you very much!

Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 16 / 16