C' Fabre

1
Quantum metrology and information
processing with frequency combs

• C. Fabre
• B. Lamine, N. Treps, B. Chalopin, G. Patera, O.
  Pinel

2
Need of highly multimode quantum light in the
continuous variable regime
- to generate multi-partite entanglement
needed in quantum computing
- to increase information capacity in quantum
information
- to improve information processing techniques
beyond the standard quantum limit
3
A highly multimode system The optical frequency
comb
Mode-locked laser
time
frequency
100 fs pulses 100,000 longitudinal modes
4
Quantum frequency combs
Nobel prize 2005
5
The Synchronously Pumped Optical Parametric
Oscillator (SPOPO)
Parametric crystal
Mode-locked laser
Twin photon generation with 105 different pump
photons !
6
Quantum description of highly multimode
parametric interaction
pump
G. de Valcarcel et al. PRA 74 061801 (2006)
Crystal phase matching coefficient
pump spectral amplitude
Symmetrical matrix
7
Diagonalization of the parametric interaction
Eigenstates  supermodes 
Eigenvalues
System generates Nm -mode squeezed state
8
Eigenvalues and eigenmodes
Degenerate collinear type I phase-matched BIBO
at 0.4µm with tp100fs and l5mm
150 non zero eigenvalues
9
From a highly multimode situation (100,000
frequency modes)
it is in general possible to extract a smaller
Hilbert space (1 100) In which the quantum
effects are concentrated and maximized (entanglem
ent and/or squeezing)
10
Link with Schmidt modes
Part 1 modes
Case of the bipartite system
Part 2 modes
Couples of Schmidt modes, defined in parts 1 and 2
 supermodes  extension of Schmidt modes
to general multimode
systems
11
Experiment in progress in Paris
-very low SPOPO oscillation threshold
(30mW) -phase sensitive amplification and vacuum
squeezing observed
12
What to do with quantum frequency combs ?
1) tailoring quantum hamiltonians
2) improving clock synchronization
13
1) Tailoring quantum hamiltonians
By changing pump and/or nonlinear medium shape It
is possible to tailor at will the number and the
spectrum of eigenvalues
 coherent control  of frequency combs
quantum states
14
Example
eigenvalues
matrix
A possible way to produce at will cluster states ?
15
B. Lamine, C. Fabre, N. Treps, Phys. Rev. Letters
101 123601 (2008)
2) clock synchronization
Homodyne detection with optimized shape of local
oscillator
Cramer Rao limit reached No other shot noise
limited measurement technique can do better
Limit passed using non-classical supermodes
emitted by SPOPO
Expected synchronization accuracy 20
yoctoseconds (10 fs pulses, integration time 1s)
16
Conclusion
It is possible to produce non-classical multimode
trains of pulses in a completely controlled way
-tailor multipartite quantum entanglement
A way to produce CV cluster states ?
-optimize noise reduction for temporal
measurements
Measurement of ultra-small time delays
how to simply separate the squeezed or entangled
supermodes ?
17
O Pinel
G De Valcarcel G Patera B Lamine
N Treps
B Chalopin
CF