Nonlinear Optics
High laser optical intensity
Defination : Wikipedia
|e GHz ~ THz
(n)

1 n
|e ~MHz
|g
|g
6 order difference (n=2)!
Nonlinear Optics in Single Photon Level
2012, Manipulating the quantum systems Serge Haroche, College of France, France Davie J.Wineland, NIST, Univ. of Colorado at Boulder, USA
How cold is the coldest?
2001, cold atoms: Bose-Einstein Condensation (BEC) Eric A. Cornell, JILA, Univ. of Colorado at Boulder, USA Carl E.Wieman , JILA, Univ. of Colorado at Boulder, USA Wolfgang Ketterle, MIT, USA
Optical Radiation Force
Absorption
Radiation
Force
Net effect
No refrigerator!
MOT
(Magnetic Optical Trap )
F

r

v
+
3D MOT: Atom number 108-109 Temperature: 10-100 K
t
L Forerunners Main signal
Travel with the speed of light in vacuum c
Pulse wave fronts give rise to the precursor fields, propagating faster than the whole bulk of light pulse, travel with the speed of light in vacuum c.
vp

(k)
k

c n(k)
vg

d
dk

c
n
dn
d
<<c Slow light
vg >c Fast light <0
Re()
dn/ d 0


Negative group velocity of light
The development of superluminal medium start up a stir.
2005, quantum optics & optical frequency comb Roy J. Glauber, Harvard Univ, USA John L. Hall , JILA, Univ. of Colorado at Boulder, USA Theodor W. Hänsch , Germany
M=+1 M=0 M=-1
-
M=0
x
Bose-Einstein Condensate
Thermal Atoms
BEC (ultra cold, 10-100nk)
2D 85Rb MOT
5P3/2
121 MHz
63 MHz 29 MHz
780 nm
Trapping
F'=4
F'=3 F'=2 F'=1
Repump
F=3
5S1/2
3036 MHz
F=2
2D 85Rb MOT
1.5 cm
Temperature: ~100 K Number of Atoms: ~108
Why Cold Atoms?
It provides a pure and ideal quantum system. Condensed Matter Physics quantum simulator (Optical
Implication: Effect happens before the cause.
Information Velocity c
No information 0? 1?
peak contains no (uncertainty) information about the future
(2) Electromagnetically-induced transparency (EIT):
create passage for main signal
Transmission
1.0
Quantum interference induced by two laser fields: high transmission at near 0.8
Observation of optical precursor
Use Cold atomic ensemble as medium:
greatly suppress Doppler broadening
absorption >>GHz

6MHz
absorption

Linewidth of Rb atomic energy level from natural broadening
As a fundamental physics research, AMO has a direct connection to Quantum Mechanics. Quantum Mechanics was born from AMO, and AMO is an expression of quantum mechanics.
refrigerator Heat pump:
mechanical, electronic, chemical
No refrigerator!
Use lasers and magnetic fields to cool and trap atoms!
MOT (magneto-optical trap)
M. Buttiker et al., Nature 422, 271 (2003)
L. J. Wang et. al. Nature 406, 277 (2000).
•D. J. Gauthier and R.W. Boyd, Photonics Spectra 82 (2007) •G. M. Gehring, et. al, Science 312, 895 (2006). •L. J. Wang et. al. Nature 406, 277 (2000).
(1) Two dimensional Magneto-optical Trap (MOT): High optical depth
Precursor signal is significant at 0L>>1
L=1.5cm
Optical depth
0L~40
High optical depth increase main field’s group delay time, and separate it with the precursor
Wide-bandwidth resonance: Transient signal duration: fs;
Narrow linewidth of resonance Duration: ~ ns
To observe optical precursors:
Medium with narrow bandwidth of resonance Near or on-resonance excitation
resonant frequency region
0.6
0.4
0.2
Slow light effect:
0.0
group velocity << c (speed of light in
-40
-20
0
20
40
2(MHz)
p
vacuum)
|3
c
p
|2
|1
In EIT system
g
L
Vg
0 L
S. E. Harris, Physics Today 50, No. 7, 36 (1997).
Optical Precursors with EIT
m
s
n
a
5P1/2 (F=3) |3
lattice) Matter wave optics Atom optics new sensor
technology ……… Quantum Optics and low light level nonlinear optics
Nonlinear Optics in Low Light Level
Nobel prize likes AMO very much!
Nobel Prize in the past 12 years
(cold atom and quantum optics)
1997, cold atoms: laser cooling and trapping Steven Chu, Stanford Univ., USA Claude Cohen-Tannoudji, France William D. Phillips, NIST, USA