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 Energy Temperature LHC at CERN, Higgs, SUSY, ??? TeV 15 q q particle accelerators 10 K q GeV proton rest mass - quarks 1012K MeV electron rest mass / gamma rays 109K keV Nuclear Fusion, x rays, Sun center 106K Atoms ionize - visible light eV Sun surface fundamental components components fundamental room temperature 103K meV Liquid He, superconductors, space 1K dilution refrigerators, quantum Hall µeV laser-cooled atoms 10-3K neV Bose-Einstein condensates 10-6K peV low T record 480 picokelvin 10-9K

-12 complexity, organization organization complexity, 10 K 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

Mass attached to spring

k F = mx˙˙ = −kx ⇒ x˙˙ = −ω 2 x, ω = m

x t = x sinωt; p t = mωx cosωt € ( ) 0 x ( ) 0 € p2 1 mω 2 x 2 E = x + mω 2 x 2 = 0 cos2 ωt + sin2 ωt € HO 2m 2 2 ( )

€ Light waves as classical harmonic oscillators I Maxwell, mon amour ρ ∇ ⋅ε = ε0 ∇ ⋅ B = 0 ∂B ∇ ×ε = − ∂t ⎛ ∂ε⎞ EM standing wave in cavity ∇ × B = µ ⎜ j + ε ⎟ 0⎝ 0 ∂t ⎠

εx (z,t) =ε0 sinkzsinωt

€ ⎡ ⎤ ∂By ∂εx ω 1 − = ε0µ0 = ε0µ0ε0ω sinkzcosωt ⎢c = = ⎥ ∂z ∂t k € ⎣ ε0µ0 ⎦

ε0µ0ε0ω ε0 By (z,t) = coskzcosωt = coskzcosωt = B0 coskzcosωt k c €

€ Light waves as classical harmonic oscillators II

Energy of EM standing wave in cavity

2 1⎛ 2 B ⎞ Local energy density U = ⎜ε 0ε + ⎟ – to be integrated in space across cavity volume 2⎝ µ0 ⎠

L 1 2 2 2 1 2 2 E el = ε0 A ∫ε0 sin kzsin ωtdz = ε0Vε0 sin ωt 2 0 4 €

1 2 2 E mag = VB0 cos ωt 4µ0 € ⎛ 2 ⎞ V 2 2 B0 2 V 2 2 2 E em = ⎜ε 0ε0 sin ωt + cos ωt⎟ = ε0ε0 (sin ωt + cos ωt) 4 ⎝ µ0 ⎠ 4 €

€ Light waves as classical harmonic oscillators III

New coordinates

ε0V q(t) = ε0 sinωt 2ω 2

V V ε0 ε0V p(t) = B0 cosωt = cosωt = ε0 cosωt 2µ0 2µ0 c 2 p = q˙ q˙˙ = p˙ = −ω 2q € 1 E = p2 + ω 2q em 2 ( )

€ Light as a quantum harmonic oscillator Vacuum field Casimir force

Between parallel perfect mirrors

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.

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

(a) (b)

Photoelectric emission from (a) a metal and (b) a semiconductor 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

biased photoconductor detector

= photon flux (photons/s)

Φ = photocurrent (A)

E

each carrier pair generates in the external circuit an electric pulse of area e The p-n photodiode

Electron-hole pair generation in a p-n photodiode

i-V characteristics

reverse biU͸ forward bias Operation of a p-n photodiode

(i) open-circuit (photovoltaic) operation

(ii) short-circuit operation (iii) reverse-bias (photoconductive) 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

Quantum efficiency vs. wavelength for various photodiodes

= optical reflectance at the surface = e-h fraction contributing to the detector current

= absorption coefficient of the material

= photodetector depth 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

transit time

Impulse-response function determined Ultrafast Si photodiode by convolving i(t) with time-constant spread function f(t):