ZOOM Lecture live at 13:30 – light sources at the nanoscale TAs live at 15:30 [ photonic crystals ] Till 13:30 - Download slides www.koenderink.info/teaching - Q & A Next session - May 6 – minisymposion For input: talk to the TA’s. Ilan is your main contact On May 6: start at 13:00 sharp.
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ZOOM Lecture live at 13:30 – light sources at the nanoscaleTAs live at 15:30 [ photonic crystals ]
Till 13:30- Download slides www.koenderink.info/teaching- Q & A
Next session - May 6 – minisymposionFor input: talk to the TA’s. Ilan is your main contact
Suppose Alice has a secret message to communicate to Bob..
Quantum information in 1 photoncan not be eavesdropped
Also: suppose you have two localized qubits. How do you transfer a quantum state from A to B
Possible solution: spin A photon spin B
Single molecules [Moerner & Orrit, ’89]
100 micron
1018 molecules
Keep on diluting
1 molecule can emit about 107 photons per second (1 pW)Observable with a standard [6k€] CCD camera + NA=1.4 objective
Fluorescence from quantum sources
Space• Whereto does the photon go ?• With what polarization ?
Time• How long does it take for the photon to appear ?
Matter• Selection rules – what color comes out?
Light from electron transitions in a quantum object
Energy scale for light 1 to 3 eV
Compare: kBT ~ 25 meV
Vibrations in molecules: 0.1 eV
e- transitions in hydrogen: 13.6 eV [1/n12-1/n2
2]
Band gap in Si: 1.1 eV
Interaction of an atom with light
Consider two states of an atom, with energies and states
Suppose I shine light at frequency w on the system.This gives rise to a time-varying perturbation
Just the first term gives a potential energy
Transition dipole moment
Dipole approximation – a small object k.r<<1
potential
Perturbation theory: transitions are governed by
‘Transition dipole moment’
Matrix element means: selection rules
Typical moleculesLarge conjugated carbon chains
Rhodamines
Pentacene, perylene, teryllene
DBATT
Electronic levels explained by particle in a 1D boxN bond chain: about 2N electrons in a 1D box of length ~ NaGround state: first N levels are completely filledExcited state: one electron goes from level N to level N+1
Quantum dot nanocrystals
TEM/you see single atoms
CdSe (CdTe, PbS, PbSe, CdS)Semiconductor nano-crystalsElectron & hole confined as particlesin a box
II-VI quantum dots in solution: Bawendi & Norris (early ‘90s)
Molecules are not just electronic systems
Thermally populated vibrations, rotations ….
energy scales < electronic transition
Jablonski diagram
S0
S1
Electronic ground state
Electronic excited state
T1Triplet
1. Fluorescence is spin-allowed, nanosecond time scales2. Phosphorescence is spin-forbidden, so very slow
Jablonski diagram
S0
S1
Electronic excited state
Franck-Condon principleElectronic transition is instantaneous compared to the nucleiNuclei rearrange in picoseconds after the e- transitionTransition requires large vibrational wave function overlap
Franck Condon
Absorption & fluorescence probabilities are proportionalto vibrational overlap ‘Franck-Condon factor’
Expect mirror-symmetricemission vs absorptionspectra
Sharp peaks obscured by(1) Ensemble(2) Rotations & collisions
If this is all wavefunctions,.....
why care about nanophotonics?
A. A bare molecule radiates as a dipole
How do you create directivity
B. The rate of emission controls brightness
How do you control rate
Controlling brightness
Radiation resistance – environment sets power to current ratio
The work you need to do keep current j going depends on environment
Radiation resistance
1) Dipole antenna2) Ground plane
(Balanis Antenna Handbook)
RF antenna in front of a mirror
- +
-+
-
+
-
+
The same current radiates a different far field power“Method of image charge”’ - Interference with its mirror image
Single quantum emitter
20
• After one excitation, emits just one quantum of light
• Probabilistic timing of when emission occurs
Laser pulses
Hits ondetector
Hits onAPD 2
Time
S0
S1
Time (ns)
Lounis & Orrit, Single photon sources, Rep. Prog. Phys (2005)