Multimode quantum optics
Nicolas TrepsClaude Fabre
Gaëlle KellerVincent DelaubertBenoît ChalopinGiuseppe PateraVirginia d’Auria
Jean-François MorizurOlivier Pinel
Laurent Lopez
Thomas CoudreauAgnès Maître
En collaboration avec Hans Bachor, Canberra
Light : information
light beam
detector
intensity
photocurrent
Continuous variable regime : about 1016 photons/second
intensity
phase
Light : information
intensity
phasepolarization
Light : information
intensity
phase
polarization
position
Light : information
intensity
phase
polarization
position
imaging
traitement d’image
Light : information
intensity
phase
polarization
position
imagerietraiteme
nt d’image
time
Light : information
intensity
phase
polarization
position
imagingtraiteme
nt d’image
time
Light : information
Multimode light
Light beam
Monochromatic case :
All modes, even vacuum, have to be considered
polarization
space frequency
Electric field operator
Quantum description of multimode light
(n-1) non-classical state of zero mean value
1( )u r
( )nu r
vacuum
vacuum
Single mode “classically” : 0 0ˆ ( ) ( )E r u r
modes
0 ( )u rsingle mode beam
state of mean value 0 state of mean value 0
multimode beam
Single mode vs. multimode
Prospective : use of symplectic transformation to extract invariant quantities
Menu
Quantum optics with frequency combs
Position measurement and spatial entanglement
Noiseless image amplification
EPR states generation and characterization : see poster of Gaëlle Keller
Menu
Quantum optics with frequency combs
Position measurement and spatial entanglement
Noiseless image amplification
1er ordre (Taylor)
proportionnel à Pas de dépendanceen
d
= + x
For small displacement ( ) of a TEM00
Displacement of a gaussian beam
Small displacementIntensity measurement
light beamw0 light beamw0
+1
-1x
g xg
x
g
Detection mode : image x gain function
1i
2i
64% overlap
Standard Cramer Rao bound is reached
+PZT
incident TEM00 beam -
LO
x
Homodyne detection
Field measure
Multimode quantum light
+PZT
TEM00 incident -
LO
x
+Coherent squeezed vacuum
Experimental realization in Canberra : 2dB of spatial noise squeezing
position squeezed beam
Several bits on a focal point :
Application to optical read-out
+Coherent squeezed vacuum
+Coherent squeezed vacuum
Spatial entanglementConjugate variable ?
Multimode entanglement
Transverse displacement
d
Displacement and tilt of a gaussian beam
+
Tilt
+
Entanglement between position and momentum of a macroscopic beam !First results :inseparability « measure »
mesurécorrigé des pertes
critère EPR critère EPR
Other variables : angular momentum, rotationsQuantum information
Experiment at ANU
Menu
Quantum optics with frequency combs
Position measurement and spatial entanglement
Noiseless image amplification
Signal
PumpParametric generation
Idler
Parametric generation
Spatial and time correlations
pump
signal
idlerin
2out
pump2
Parametric amplification
IN
OUT
IN
OUT
Insensible à la phase Sensible à la phase
OPO in a dual cavity
Semi-confocal
Relative phase between pump and image
Injectionoutput
Setup
EOMintensitymodulation
spectrumanalyser
image generation
Noiseless amplification in Type II
Noise
fact
or
Gain
Amplified images
noiseless amplification regime
phase insensitive
phase sensitive
Relative phase (amplification/deamplification)Time (Locked traces)
Noiseless amplificationTwin images
Squeezing and entanglement
Squeezing and entanglement
OPA
Squeezed and entangled beams of various transverse shapes
OPA in a self imaging cavity
pumpAll images !Bellow threshold :
- local squeezing- multimode entanglement
Squeezing and entanglement
Réduction du bruit quantique et intrication
Menu
Quantum optics with frequency combs
Position measurement and spatial entanglement
Noiseless image amplification
Time and frequency
Mode locked femtosecond laser
synchronously pumped OPO
LaserOPO
Advantages
Act as a continuous laser with very high peak intensityVery low threshold cavity
High efficiency for generation of non classical light
…
Frequency domain
frequency comb
signal and idler
Time and frequency
Mode locked femtosecond laser
synchronously pumped OPO
LaserOPO
Temporal homodyne detection
LaserOPO
frequency doubling
pulse shaping
-
Application : scanning the temporal modes emitted by the OPOtime measurement by analogy with spatial measurementcorrelations / entanglement
Prospective : quantum noise in metrology quantum information and communication
spatiotemporal quantum effects
