Transcript Diapositive 1

Multimode quantum optics
Nicolas Treps
Claude Fabre
Thomas Coudreau
Agnès Maître
Gaëlle Keller
Vincent Delaubert
Benoît Chalopin
Giuseppe Patera
Virginia d’Auria
Jean-François Morizur
Olivier Pinel
Laurent Lopez
En collaboration avec Hans Bachor, Canberra
Light : information
intensity
light beam
photocurrent
detector
Continuous variable regime : about 1016 photons/second
Light : information
intensity
phase
Light : information
intensity
polarization
phase
Light : information
intensity
position
phase
polarization
Light : information
position
intensity
imaging
phase
polarization
traitement
d’image
Light : information
position
intensity
time
phase
imagerie
traitement
d’image
polarization
Light : information
intensity
position
phase
imaging
traitement
d’image
polarization
time
Multimode light
Light beam
Electric field operator
polarization
space
Monochromatic case :
All modes, even vacuum, have to be considered
frequency
Quantum description of multimode light
Single mode vs. multimode
Eˆ (r )   0u0 (r )
Single mode “classically” :
modes
u0 (r )
u1 (r )
un ( r )
single mode beam
state of mean value 0
multimode beam
state of mean value 0
vacuum
vacuum
(n-1) nonclassical state
of zero mean
value
Prospective : use of symplectic transformation to extract invariant quantities
Menu
Position measurement and spatial entanglement
Noiseless image amplification
Quantum optics with frequency combs
EPR states generation and characterization : see poster of
Gaëlle Keller
Menu
Position measurement and spatial entanglement
Noiseless image amplification
Quantum optics with frequency combs
Displacement of a gaussian beam
For small displacement (
) of a TEM00
1er ordre (Taylor)
Pas de dépendance
en
=
d
proportionnel à
+
x
Intensity
Small displacement
measurement
i1
w0 beam
light
w0 beam
light
i2
Detection mode : image x gain function
g   x
g
g
+1
x
x
-1
64% overlap
Field measure
Homodyne detection
incident TEM00
beam
PZT
+
-
x
LO
Standard Cramer Rao bound is reached
Multimode quantum light
squeezed vacuum
Coherent
TEM00
incident
+
PZT
-
+
x
LO
Experimental realization in Canberra : 2dB of spatial noise squeezing
position squeezed beam
Application to optical read-out
Several bits on a focal point :
Multimode entanglement
Spatial entanglement
Conjugate variable ?
squeezed vacuum
Coherent
+
squeezed vacuum
Coherent
+
Displacement and tilt of a gaussian beam
Transverse displacement
Tilt
q
d
+
+
Entanglement between position and momentum of a macroscopic beam !
critère EPR
mesuré
corrigé des pertes
Other variables : angular momentum, rotations
Quantum information
critère EPR
First results :
inseparability «
measure »
Experiment at ANU
Menu
Position measurement and spatial entanglement
Noiseless image amplification
Quantum optics with frequency combs
Parametric generation
Signal
Parametric generation
Pump
Spatial and time correlations
Idler
Parametric amplification

signal
Insensible à la phase
pump
in
pump

2
2
idler

Sensible à la phase
OUT
OUT
IN
IN
out
OPO in a dual cavity
Semi-confocal
Relative phase between
pump and image
Noiseless amplification in Type II
Setup
Injection
image
generation
EOM
intensity
modulation
output
spectrum
analyser
Noise factor
Amplified images
noiseless
amplification
regime
Gain
Squeezing and entanglement
Noiseless amplification
Twin images
Squeezing and
entanglement
Relative phase (amplification/deamplification)
Time (Locked traces)
Squeezing and entanglement
OPA
Squeezed and entangled beams of
various transverse shapes
OPA in a self imaging cavity
pump
All images !
Bellow threshold :
- local squeezing
- multimode entanglement
Réduction du bruit quantique et intrication
Menu
Position measurement and spatial entanglement
Noiseless image amplification
Quantum optics with frequency combs
Time and frequency
Mode locked femtosecond laser
Laser
synchronously pumped OPO
OPO
Advantages
Act as a continuous laser with very
high peak intensity
Very low threshold cavity
High efficiency for generation of
non classical light
Time and frequency
Mode locked femtosecond laser
Laser
synchronously pumped OPO
OPO
Frequency domain
signal and idler


frequency comb

…
Temporal homodyne detection
frequency
doubling
Laser
OPO
pulse
shaping
Application : scanning the temporal modes emitted by the OPO
time measurement by analogy with spatial measurement
correlations / entanglement
Prospective : quantum noise in metrology
quantum information and communication
spatiotemporal quantum effects