TWO-PHOTON ABSORPTION
IN SEMICONDUCTORS
Fabien BOITIER, Antoine GODARD, Emmanuel ROSENCHER
Claude FABRE
ONERA Palaiseau Laboratoire Kastler Brossel Paris
Measuring intensity correlations :
Hanbury-Brown Twiss experiment
g (t ) =
(2)
i (t ) i (t +t )
i (t )
2
g (2) (0) = 2
Photon Bunching effect
Understanding Photon bunching
- simple explanation in terms of fluctuating waves
- more difficult to understand in terms of photons as particles
1 for shot noise, even present when the intensity is constant,
1 due to extreme fluctuations of the mean intensity in chaotic light
Fano’s explanation in terms of
constructive interference between undistinguishable paths
E2
E1
D2
D1
E2
E1
D2
D1
Full quantum treatment given by Glauber
bunching
2
1
chaotic
tc =1 D
Coherent (single-mode laser)
anti-bunching
Non-classical
g(2)<1 : no classical explanation possible
g(2)>1 : classical explanation possible…
… but full quantum explanation still possible and interesting
Detectors response time limits observation
of narrow features in time
or broad in frequency
Experiments usually done with
« pseudothermal » light sources
laser
How to study broadband sources with ultra-short correlation times ?
Use fast nonlinear effects
I. Abram et al 1986, Silberberg et al
Use Hong Ou Mandel interferometer
parametric
fluorescence
Lame semi-réfléchissante
Another possibility :
two-photon absorption in semi-conductors
transient state
C
B
V
B
- Broadband
- No phase matching


Two photon characterization of a GaAs phototube
P2
N2  GaAs   
S  z 
Two photon absorption coefficient:
 ≈ 10 cm/GW @1.55 µm
 Quadratic response between 0.1 and 100 µW
Low efficiency: not yet a two-photon counter
Photocount histograms and detection operator
 
N
2 2
 
 N2
What is the two-photon counter observable ?
Nˆ = aˆ+ aˆ + aˆaˆ ?
1 2 a
1
N
=
Njj
N = Nj for perfect quantum efficiency
classical approach
2
1+ a Nj
2
1
1
Nˆ = aˆ + aˆ + aˆaˆ = Nˆ j Nˆ j -1
2
2
(
)
acceptable for photon numbers <3


 1 « click »
ˆ 0 0 -1 1
Nˆ = 1-
limited efficiency accounted by attenuator in front
exact quantum theory of two photon counter remains to be done
Two-photon absorption Intensity correlation apparatus
High pass filter
Pulse
counter
ASE
12500
S2()
10000
G(2)()
5000
2500
10
10
Resolution < fs :
7500
0
-1500 -1000 -500
Time delay
Counts (Arb. Units)
Counts (/s)
Asph.
Lens
0
 (fs)
500 1000 1500
-2
-1
0
 (fs)
1
2
Interferometric recorded signal
S2 ( )  1  2G(2) ( )  4Re F1( )e i   Re F2 ( )e 2i 
G(2)
F2
F1
G(2) ( ) 
F2 ( ) 
F1( ) 
-1500 -1000
-500
0
 (fs)
Source: cw ASE @ 1.55µm , 4dBm
Detector: Hamamatsu PMT GaAs
500
1000
1500
E (t )E (t   )E * (t   )E * (t )
I02 (t )
E (t )2 E *2 (t   )
I02 (t )

2
E (t )  E (t   )
2
 E(t )E (t   )
*
2 I02 (t )
Intensity correlation function
obtained by low pass filtering
TPA measurement of g(2)()
(1): laser, amplified spontaneous
emission, blackbody
Boitier et al., Nature phys. 5, 267(2009)
 Summary table of the main properties
g(2)(0)
c (fs)
λ0 (nm)
λ (nm)
Laser
1.01 ±0.03

1560
small
ASE
1.97 ±0.05
534
1530
6
Blackbody
1.8 ±0.1
37
1130
155
Bunching of unfiltered blackbody!
TPA measurement of g(2)()
(2): high gain parametric
fluorescence
with N. Dubreuil, P. Delaye
CW source ↔
14 / 23
Second order correlation function g(2)()
2,4
without dispersion compensation
signal alone
signal + idler
2,2
(2)
g ()
2,0
1,8
1,6
1,4
1,2
with dispersion compensation
1,0
-0,4
-0,2
0,0
0,2
0,4
 (ps)
far from degeneracy
near degeneracy
Evidence of an extrabunching effect
g(2) (0) = 3
Photon correlations in parametric fluorescence
(1) : full quantum calculation
quantum state produced by parametric fluorescence of gain G
n/2
æ 1ö
1
Y =
ç1- ÷
å
nè
Gø
G
ns = n, ni = n
quantum calculation of g(2)(0)
ˆ (-) Eˆ (-) Eˆ (+) Eˆ (+) Y
Y
E
1
g(2) (0) =
=
3+
2
G -1
Y Eˆ (-) Eˆ (+) Y
(in the experiment G>106)
nothing prevents g(2)(0) to be very large in weak sources with large noise
( value of 28 observed on squeezed vacuum (Ping Koy Lam)
Photon correlations in parametric fluorescence
(2) : fluctuating field approach
- The signal and idler fields are classical fields
taken as a sum of wavepackets with random phases fs
and fi.
the classical equations of parametric mixing imply:
fs+ fifpump
g (0) = 2 +
(2)
E s Ei
2
I s Ii
vacuum fluctuations are needed
to trigger the spontaneous parametric fluorescence
Photon correlations in parametric fluorescence
(3) : corpuscular approach
three kinds of photon coincidences:
- accidental
- pairs due to the twin photon source
- linked to the chaotic distribution of pairs
in a dispersive medium :
 Ideal case without dispersion
 Increase of chromatic dispersion
dispersion compensation needed !
CONCLUSION
TPA : efficient technique to measure g(2)() down to femtosecond range
not yet a two-photon counter : efficiency can be improved
no measurement so far in the full quantum regime g(2)() <1
in ideal tool for high flux isolated photon sources
classical and/or quantum effects ?
-many competing physical pictures
- even classical pictures have some quantum flavour
- quantum approach often provides more physical insight
and simple calculations than semi-classical ones