Refractive Index Enhancement in Atomic Vapors

Deniz Yavuz, Nick Proite, Brett Unks, Tyler Green, Dan Sikes

Department of Physics, University of Wisconsin Madison, WI

Key Question

How much can we increase the refractive index, n, of an atomic medium while maintaining vanishing absorption?

When an electromagnetic wave is in a medium with refractive index n, the wavelength of the wave is /n. As a result the resolution is increased.

Two-level scheme

g

e

Ep

e2

max0

1

2 e

N

A laser beam tuned close to a two level resonance can experience a large refractive index.

In a gas with a pressure of 1 torr, can get values as large as 100. However, thiseffect is not useful since, is just as large.

Two two-level scheme

g

1

pE

g

2

+

g

e

1

pE1cE+

g

e

2

pE 2cEpE

The interference between an absorptive resonance and an amplifying resonancecan result in a large refractive index with vanishing absorption.

M. Fleischhauer et. al. Phys. Rev. A 46, 1468 (1992).

Numerical calculation in Rbsu

scep

tibili

ty

10-2

p (MHz) p (MHz)

10-2 10-2

p (MHz)

-4

-2

0

2

4

-1 0 1 2 3 4-4

-2

0

2

4

-1 0 1 2 3-4

-2

0

2

4

-1 0 1 2

1F

2F

pE1cE

2F 3F

pE 2cE87Rb 85Rb

N=1015 /cm3

Ic1 Ic2 100 W/cm2

Detuning=30 GHz

Maximum susceptibility

1 10 102 103 104

10-2

10-1

1

10

Ic1, Ic2 (W/cm2)

real

par

t of

susc

eptib

ility

10-3

How much can one increase the real part of the susceptibility while maintainingvanishing imaginary part?

2

max0

1

2 e

N

D. D. Yavuz, Phys. Rev. Lett. 95, 223601 (2005)

First experiments

F=0, 1, 2, 3

Ep Ec

optical pumpinglaser

F=1

F=287Rb vapor cell

Ep

Ecoptical pumpinglaser

85 GHz

beam detectionand diagnostics

87Rb energy level diagram

B. E. Unks, N. A. Proite, and D. D. Yavuz, Rev. Sci. Inst. 78, 083108 (2007).

N=1.71013 /cm3

Raman self-focusing and self-defocusing

/ 2π (MHz)

norm

aliz

ed tr

ansm

issi

on

0.8

1

1.2

1.4

-8 -4 0 4 8

The refractive index increases and decreases on either side of the resonance causesself-focusing and self-defocusing.

>0, self-focusing

<0, self-defocusing

Self-focused and defocused profilesIn

tens

ity

x (mm)

0

0.5

1

1.5

2

-1 -0.5 0 0.5 10

0.5

1

1.5

2

-1 -0.5 0 0.5 1

x (mm)

>0, self-focusing <0, self-defocusing

Inte

nsity

Future work

Cold atomic clouds offer key advantages over vapor cells:

Narrow Raman linewidths

Tighter focusing

Orthogonal geometries

Spatial Raman Solitons

Combine an absorptive resonance with an amplifying resonance

All-optical devices

Ep

atomic cloud

Ec1 Ec2

Intensity pattern

refractive index pattern

I(x)

n(x)

Since the refractive index enhancement is proportional to the intensity of the control lasers, an intensity pattern is transferred to a refractive index pattern.

Conclusions

Far-off resonant Raman systems offer a new approach for achieving largerefractive index with vanishing absorption.

As a first step, we have observed Raman self-focusing and self-defocusing in an alkali vapor cell.

Adiabatic vs non-adiabatic evolution

before the cell after the cell

0 2 4 6

inte

nsit

y (a

. u.)

inte

nsit

y (a

. u.)

time (s) time (s)0 2 4 6

time (s)

inte

nsit

y (a

. u.)

0 4 8 0 4 8time (s)

inte

nsit

y (a

. u.)

adiabatic evolution

non-adiabatic evolution