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Fotonica ed elettronica quantistica
http://www.dsf.unica.it/~fotonica/teaching/fotonica.html
Fotonica ed elettronica quantistica
Quantum optics - Quantization of electromagnetic field - Statistics of light, photon counting and noise; - HBT and correlation; g1 e g2 coherence; antibunching; single photons - Squeezing - Quantum cryptography - Quantum computer, entanglement and teleportation
Light-matter Interaction - Two-level atom - Laser physics - Spectroscopy - Electronics and photonics at the nanometer scale - Cold atoms - Photodetectors - Solar cells
http://www.dsf.unica.it/~fotonica/teaching/fotonica.html
TeV
GeV
MeV
eV
keV
meV
µeV
neV
peV
1012K
109K
106K
10-3K
1K
10-6K
10-9K
10-12K
103K
1015K
Liquid He, superconductors, space
room temperature Sun surface
dilution refrigerators, quantum Hall
Bose-Einstein condensates
low T record 480 picokelvin
laser-cooled atoms
electron rest mass / gamma rays
Nuclear Fusion, x rays, Sun center
Atoms ionize - visible light
proton rest mass - quarks
LHC at CERN, Higgs, SUSY, ???
particle accelerators
Temperature fu
ndam
enta
l co
mponen
ts
com
ple
xity
, org
aniz
atio
n
q q
q
Energy
Nobel Prizes in Physics
2010 - Andre Geims, Konstantin Novoselov 2009 - Charles K. Kao, Willard S. Boyle, George E. Smith 2007 - Albert Fert, Peter Gruenberg 2005 - Roy J. Glauber, John L. Hall, Theodor W. Hänsch 2001 - Eric A. Cornell, Wolfgang Ketterle, Carl E. Wieman 1997 - Steven Chu, Claude Cohen-Tannoudji, William D. Phillips 1989 - Norman F. Ramsey, Hans G. Dehmelt, Wolfgang Paul 1981 - Nicolaas Bloembergen, Arthur L. Schawlow, Kai M. Siegbahn 1966 - Alfred Kastler 1964 - Charles H. Townes, Nicolay G. Basov, Aleksandr M. Prokhorov 1944 - Isidor Isaac Rabi 1930 - Venkata Raman 1921 - Albert Einstein 1907 - Albert A. Michelson
Textbook
Quantum Optics An Introduction (Oxford Master Series in Physics No. 15) di: Mark Fox Editore: Oxford University Press
Other books: B.A. Saleh, M.C. Teich - Fundamentals of Photonics - 1991, John Wiley & Sons, Inc Scully, Zubairy – Quantum Optics - Cambridge University Press Meystre, Sargent – Elements of Quantum Optics – Springer Verlag Walls, Milburn – Quantum Optics - Springer Verlag Gerry, Knight – Introductory Quantum Optics – Cambrdidge University Press Yamamoto, Imamoglu – Mesoscopic quantum optics - Wiley
Come passare l’esame
3 CFU = 24 ore di lezione
Esercizi a casa
Seminario finale (o interrogazione)
Quantization of the e.m. field
Classical harmonic oscillators
€
EHO =px2
2m+12mω 2x 2 =
mω 2x02
2cos2ωt + sin2ωt( )
Mass attached to spring
€
F = m˙ ̇ x = −kx
€
⇒ ˙ ̇ x = −ω 2x, ω =km
€
x t( ) = x0 sinωt; px t( ) = mωx0 cosωt
Light waves as classical harmonic oscillators I
EM standing wave in cavity
€
By z,t( ) =ε0µ0ε0ω
kcoskzcosωt =
ε0ccoskzcosωt = B0 coskzcosωt
€
∇ ⋅ε =ρε0
∇ ⋅ B = 0
∇ ×ε = −∂B∂t
∇ × B = µ0 j + ε0∂ε∂t
⎛
⎝ ⎜
⎞
⎠ ⎟
Maxwell, mon amour
€
εx z,t( ) =ε0 sinkzsinωt
€
−∂By
∂z= ε0µ0
∂εx
∂t= ε0µ0ε0ω sinkzcosωt c =
ωk
=1ε0µ0
⎡
⎣ ⎢
⎤
⎦ ⎥
Light waves as classical harmonic oscillators II
Energy of EM standing wave in cavity
€
Emag =14µ0
VB02 cos2ωt
Local energy density – to be integrated in space across cavity volume
€
U =12ε0ε 2 +
B2
µ0
⎛
⎝ ⎜
⎞
⎠ ⎟
€
Eel =12ε0A ε02 sin2 kzsin2ωtdz
0
L
∫ =14ε0Vε02 sin2ωt
€
Eem =V4ε0ε02 sin2ωt +
B02
µ0cos2ωt
⎛
⎝ ⎜
⎞
⎠ ⎟ =
V4ε0ε02 sin2ωt + cos2ωt( )
Light waves as classical harmonic oscillators III
New coordinates
€
q t( ) =ε0V2ω 2ε0 sinωt
p t( ) =V2µ0
B0 cosωt =V2µ0ε0ccosωt =
ε0V2ε0 cosωt
€
p = ˙ q ˙ ̇ q = ˙ p = −ω 2q
Eem =12
p2 +ω 2q( )
Light as a quantum harmonic oscillator
Vacuum field
Casimir force
Numerical examples:
For A = 1 m2 and L = 10-3 m, F = 1.3 10-15 N. For A = 10-4 m2 and L = 10-6 m, F = 1.3 10-7 N.
Between parallel perfect mirrors
Exercises
1. Calculate the volume required to make the vacuum field magnitude equal to 1V/m for a wavelength of (a) 1 µm and (b) 100 nm.
2. Show that the time-averaged energy in the electric and magnetic fields of an electromagnetic wave are identical.
3. Calculate the Casimir force between two conducting plates of area 1 cm2 separated by (a) 1mm and (b) 1µm.
Photodetection
Classes of photodetectors
Thermal detectors: photon energy converted into heat
Photoelectric detectors: photon energy converted into mobile charge carries to yield electric current
External photoeffect: photoelectric emission
Photoelectric emission from (a) a metal and (b) a semiconductor
(a) (b)
Photodetectors based on photoelectric emission
Phototube Photomultiplier tube (PMT)
Microchannel plate
Photomultiplier tubes (PMTs)
Internal photoeffect: photoconductivity
electron-hole photogeneration in a semiconductor
Photoconductor detectors
each carrier pair generates in the external circuit an electric pulse of area e
biased photoconductor detector
E
Φ = photocurrent (A)
= photon flux (photons/s)
The p-n photodiode
i-V characteristics
reverse biUͿԤԥԦԧԨԩԪԫԬԭԮԯՠֈ֍֎֏ࢪࢩࢨࢧࢦࢥࢤࢣࢢࢡࢠࡪࡩࡨࡧࡦࡥࡤࡣࡢࡡࡠ࡞࡛࡚࡙ࡘࡗࡖࡕࡔࡓࡒࡑࡐࡏࡎࡍࡌࡋࡊࡉࡈࡇࡆࡅࡄࡃࡂࡁࡀ࠾࠽࠼࠻࠺࠹࠸࠷࠶࠵࠴࠳࠲࠱࠰࠭ࠬࠫࠪࠩࠨࠧࠦࠥࠤࠣࠢࠡࠠࠟࠞࠝࠜࠛࠚ࠙࠘ࠗࠖࠕࠔࠓࠒࠑࠐࠏࠎࠍࠌࠋࠊࠉࠈࠇࠆࠅࠄࠃࠂࠁࠀ߿߾߽ٟؠׯ forward bias
Electron-hole pair generation in a p-n photodiode
Operation of a p-n photodiode
(ii) short-circuit operation (iii) reverse-bias (photoconductive) operation
(i) open-circuit (photovoltaic) operation
The p-i-n photodiode
Intrinsic (lightly doped) layer sandwitched between the n and p layers
Heterostructure devices: AlGaAs/GaAs, InGaAs/InP, HgCdTe/CdTe …
Avalanche photodiodes (APDs) An avalanche photodiode (APD) converts each detected photon into a cascade of moving carrier pairs by impact ionization
Properties of semiconductor photodetectors
• Quantum efficiency • Responsivity • Gain • Response time
Quantum efficiency
Probability that a single photon incident on the device generates a photocarrier pair that contribute to the detector current
= optical reflectance at the surface
= e-h fraction contributing to the detector current
= absorption coefficient of the material
= photodetector depth
Quantum efficiency vs. wavelength for various photodiodes
Responsivity
Relates the electric current (ip) flowing in the device to the incident optical power (P)
= incident optical power
= photon energy
Device with gain
Each carrier pair produces in the external circuit a current pulse of charge q >e:
PMT (G: 102÷108) APD (G: 1÷1000)
Response time
Charge delivered to the external circuit by carrier motion occupies an extended time
Impulse-response function determined by convolving i(t) with time-constant spread function f(t):
transit time
Ultrafast Si photodiode