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