Refractive Index Enhancement without Absorption
N. A. Proite, J. P. Sheehan, J. T. Green, D. E. Sikes, B. E. Unks, and D. D. Yavuz
University of Wisconsin, Madison
Proof-of-principle experiment and results
Control Beam 1 and
Control Beam 2
peak intensity
1.25
Weak probe
is absorbed
probe
1
0.75
0
0.25
0.5
Probe Frequency (MHz)
Control 2
1N.
|F=3›
Weak probe
1.2
2
1
1.1
0
1
0.9
0
Absorptive
resonance
Suppressed Index2
1.2
1
1
0.8
0
0.3
0.6
Probe Frequency (MHz)
1.1
0
1
-1
0.9
2Preliminary
Results
In the time since the published results (above), we have made several changes that have
resulted in a dramatic 100-fold improvement in our measured index of refraction.
2-photon0
detuning
10
Real
Imag
Enhanced Refractive Index
(c’ adds constructively)
0
-1
2-photon
detuning
-10
0
10
Zero absorption
(c’’ cancels to zero)
1.4
1.31.3
Improvements include:
•We showed 40% gain and 40% loss simultaneously in a 1mm
vapor cell
•We demonstrated that two opposite Raman resonances can be
constructed in a single isotope of rubidium
•Our next step is to perform this experiment in a magneto-optical
trap, and to understand mechanisms that are limiting the
magnitude of the achieved refractive index.
p
1.2
1.1
1.0
1
0.9
0.8
0.70.72x 10
33
-5
2.5
3
3.5
4
4.5
2
1
00
pumping vs. density when locked to
85
Rb F=3
100
85
Rb pumping
90
87
p
Rb pumping
80
70
1
60
-3
-3
2
0
3.5
13
24
Two-photon detuning (MHz)
2.5
4.5
We thank the Air Force Office of Scientific Research and Wisconsin Alumni Research Foundation for funding.
0.7
0.6
0.5
6.8 GHz
0.4
Density: 1014 cm-3
0.3
3.035 GHz
0.1
0
1
50
-4
-2
0
2
4
Relative Frequency (GHz)
6
8
The peaks in the red circle
(87Rb F=1 and 85Rb F=2)
are optically pumped with
70% efficiency.
0.9
40
30
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
20
0
-4
0
-1
Dn = 3 × 10-5
0.8
0.2
10
-2
Absorption profile of a
dense rubidium vapor
in a thin vapor cell.
0.9
Transmission (normalized to 1)
Susceptibility (c)
1
-1
-10
1.5
Transmission
-1 2-photon detuning
-10
0
10
1.6
1.6
1017
In order to achieve a refractive index of Dn=0.1 in a gas, we first need to
efficiently optical pump vapor densities as high as 1015 cm-3. The plot
demonstrates our optical pumping in a simple pump-probe experiment in 85Rb.
Enhanced Index (Dn > 0)
1.7
Absorptive
resonance
1013
1015
Density (atoms/cm3)
Optical pumping
high-density vapor cells
% of atoms pumped
0
0
2008
P. Anisimov and O. Kocharovskaya, 38th Winter Colloquium on Physics of Quantum Electronics,
Snowbird, Utah, 2008
100-fold improvement
Real
Imag
2009
10-4
1011
0.3
0.6
Frequency
(MHz)
Probe
Frequency
(MHz)
A. Proite, et. al., Phys. Rev. Lett., 101, 147401 (2008)
Refractive Index (10-5)
Real
Imag
Susceptibility (c)
Susceptibility (c)
Amplifying
resonance
1
ultracold cloud
hot vapor
10-6
|F=2›
1
10-2
-2
0.8
0
0.25
0.5
Frequency
(MHz)
Probe
Frequency
(MHz)
A key advantage of our scheme is that the laser
beams are tuned far from any excited state lines.
This means that the scheme is relatively insensitive
to excited-state dephasing mechanisms. We can
use exceptionally high vapor densities, along with
buffer gases for spatial confinement and radiation
dampening.
Dn (10-7)
probe
Amplifying
resonance
Dn (10-7)
Control 1
The maximum achievable n is equal to the atom’s
maximum two-level refractive index. We plot this
curve below.
Susceptibility c’
Enhanced Index1
10 GHz detuned
The same probe
is used in two
different Raman
resonances
1mm cell, 130°C
Control Beam 1 and
Control Beam 2
An amplifying and an absorbing Raman resonance are set up using strong (100 mW) control
beams detuned 10 GHz from the excited rubidium D2 line. The experiment is conducted in
magnetically shielded hot rubidium vapor.
pinhole transmission
D2 line of
Triple shielded
m-metal
Weak probe
When the probe frequency is tuned to exactly between the
amplifying and absorptive resonances, it travels through
the vapor with perfect transmission. The steep dispersion
curve produces an enhanced index of refraction.
85Rb
PBS
peak intensity
We use strong control beams to induce Raman (2-photon)
resonances in the vapor. One resonance amplifies the weak
probe, while the other resonance absorbs the probe. All
three beams are tuned far outside the excited D2 line of
Rubidium-85.
Weak probe
is amplified
PBS
pinhole transmission
We report a proof-of-principle experiment where the
refractive index of an atomic vapor is enhanced while
maintaining vanishing absorption on a weak probe beam.
Transmission (normalized to 1)
Theory
How high of a refractive
index is possible?
0
0
0.5
1
1.5
2
2.5
density
3
3.5
4
4.5
5
14
x 10
-2
0
2
4
Relative Frequency (GHz)
4
8
Frequency (GHz)
6
8
12