Quantum Ideas Notes Week 1

7/27/2019 Quantum Ideas Notes Week 1

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Quantum Ideas

Syllabus:

The success of classical physics, measurements in classical physics. The nature of light,the ultraviolet catastrophe, the photoelectric effect and the quantisation of radiation. Atomicspectral lines and the discrete energy levels of electrons in atoms, the Frank-Hertz ex-periment and the Bohr model of an atom.

Magnetic dipoles in homogeneous and inhomogeneous magnetic fields and the Stern-Gerlach experiment showing the quantisation of the magnetic moment. The Uncertaintyprinciple by considering a microscope and the momentum of photons, zero point energy,stability and size of atoms. Measurements in quantum physics, the impossibility of measur-ing two orthogonal components of magnetic moments. The EPR paradox, entanglement,hidden variables, non-locality and Aspect's experiment, quantum cryptography and theBB84 protocol. Schrdinger's cat and the many-world interpretation of quantum mechan-ics. Interferometry with atoms and large molecules. Amplitudes, phases and wavefunc-tions. Interference of atomic beams, discussion of two-slit interference, Bragg diffraction ofatoms, quantum eraser experiments. A glimpse of quantum engineering and quantumcomputing. Schrdinger's equation and boundary conditions. Solution for a particle in an

infinite potential well, to obtain discrete energy levels and wavefunctions.

Quantum Ideas 2007 Axel Kuhn


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Quantum

Physics

Failureof

ClassicalPhysics

Photoelectric

Effect

Blackbody

Radiation

Uncertainty

Principle

Plancks

Hypothesis

W

ave-Particle

D

uality

Paradoxainearly

Gedanken-experiments

Entanglement

Superposition

Probabilities

Roleoftheobserver

Break-downof

the

Wavefunction

Many-worldinterpretation

ModernApplications

Quantum

Cryptography

Quantum

Computing

Stru

ctureofMatter

Ato

mmodel(Bohr)

Molecules,Solidstate,etc.

Schrdingers

Equation

Interferenceof

massiveparticles

Quantised

energylevels

Q

uantisation

o

fradiation

DeBrogie

Wavelength

Spectrallines



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Classical Physics:

classical mechanics (Newton; F = m a)

electricity and magnetism (Coulomb, Faraday, Maxwell)

electromagnetic waves (rf ... light ... x-ray ... gamma)

thermodynamics (energy conservation, equilibration, statistical mechanics)

accurate measurement of all observables (position x(t)and momentum p(t) )

Quantum Physics:

probabilistic - not deterministic (Einstein: Good does not play dice)

probability wave function (x,t) to describe a particle

superposition and entanglement

non-local behaviour (Spooky interaction at a distance that bothered Einstein)

uncertainty principle: x p /2 and E t /2



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illumination with a mercury lamp, filtering a single spectral line.

Cathode metal with a binding energy (or work function) of Ebind = 2.02 eV

yellow, 578nm, 5.19E+14 Hz, Ekin = 0.13 eV

green, 546nm, 5.50E+14 Hz, Ekin = 0.27 eV

blue, 436nm, 6.88E+14 Hz, Ekin = 0.81 eV

violet, 405nm, 7.41E+14 Hz, Ekin = 1.02 eV

Plancks constant is obtained from the slope of the kinetic energy, Ekin()



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Hints for quantisation:

a) threshold (minimum frequency required):

resonance phenomenon quantised medium or light

b) linear in the intensity (for =const).

electron number proportional to photon number

c) photo current insensitive to (provided h > Ebind)

no change of the electron current if photon flux constant albeit the intensity is increasing: Iphoto

d) no delay direct evidence!

it lasts seconds until a single atom accumulates enough energy, so the radiation cannot be continuous



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Blackbody = Cavity?

- Multiple reflections -> absorption of incident light

- Thermal equilibrium -> Walls Cavity modes

- Spectral energy density ()d

R()d (Radiance through whole)

- Boundary conditions: Nodes on the walls

- Standing waves along x,y,z

Consider a 2D problem and decompose into

x = / cos() y = / sin()

with nxx = 2L etc... ==> nx = (2L/) cos() and ny = (2L/) sin()

square and add these conditions (generalise into 3D):

(2L/)2 = nx2 + ny2 + nz2



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Number of Modes in the cavity with frequencies smaller than :

- sphere of radius R =(nx2 + ny2 + nz2) = 2L/ = 2L/c - mode number N() = 4/3R3 2/8 = ...

- same for N(+d) = ...

Mode number in the interval ...+d

N = N(+d) - N() = 82 L3 / c3 d

Spectral density per unit volume

()d = /L3 = 82 / c3 d



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1/t*1.* "{&ZD Lutb- *,id7

\"= )'/-x\7 =Vi*xLou- ,

L#

L

f-)r,.n-L h n-,"l lL fzL '- tL ,*tt

h" \, - ZLI h,o', ), --zLI h)r''rt = *"

7L.,\

ZLJ.qL;LJ

-' hr' *

-D 6 Lo f*,*C'J l" 3? ,

R



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Sil*'L i. lL h - slpaa svJ;u, IZ ,

//,-Lu o( ,--L = l,/o/,* ,l lL 70.,81,'hor==\rll (fry..))= ( ts' 7'trLt .r3o3L64I

8try" t,= a.'dytiJ',t=

r?,t# ,l --,,Ln

6N 0t)do=

(ot:l:.t ryn{r.^+7'.,{u*( 9.-.9, Jrt

,({,t,Ju1-//u)#'(y')'-'=8o4u1,

v 3Y'Jt'+ "(*L fu u--:L e'sb*,-I

Z g'l.,-:,J'-'



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Blackbody Radiation

Average energy per frequency mode, using the Boltzmann distribution P(E)

E =

En P(E)n=0

P(E)n=0

=

h ne

nhkT

n=0

enh

kT

n=0

= h

A

B

with B Bexp hkT( ) = 1

and A Aexp h kT( )= Bexp h kT( )

A

B=

1

exp hkT( ) 1

and E =h

exp hkT( ) 1



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Plancks law

Spectral energy density (energy per unit volume in the frequency range...+d):

()d=82

c3

h

exp hkT( ) 1

=8h3

c3

1

exp hkT( ) 1

total energy density:

= ()d= 85

k

4

15(hc)3 T

4= T4



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Ao^*'l a,- ola q- Pt L-= h?^tt^J/ c = hg

E;-,h,- ! = ,,o' PctIIl-]o' \

= t*t ClL(*" ( s tttt

De--Lnjt. ,"*(*rlL\ =%'7*" I iI.,"),o,ouin",u\"::f_ ?],+k tuL/...*Lo[u,*,eJ L k",J,

14'"'r'*iltLt=?x-t glno u).t/.' i

(G,t) = uflz(w-ailIv;lLa. ?rt)



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s&t?ro {_r"/-D d,.rk.- trLL* tJ,l-tU" +-J"{'-.6'ao'.gh|-, - "/.J** to.(-7;C.'->un-hn*"A!Jp-

u:lLL"l-- rt "kn

[n}ux{ut-

?os;"q?.*6 Ar 'I

of =r^P,9^l

CO',otte*{i*

)'s;"o(tL-%*o\t.7, 2fi,*'a

J*,J*r /Y

s Zh(t.*re)

z c)"(aL' er -

n*T fair,'tq,.t.k,a-[=hf,=b= blt\t?^'=":h.-zutLc'< t I e^: ^1

1i1t'+ 'aLn

.* (I{- ,)2,o"L i-*)- rt^*a



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I rrr '^ Vqu!/(e.-C(l"^:J

\ / t= Ao L l-a-e), . ' tt . . . r14v"rolo-lQ Ao- 7"., / _ _-,ov

c9

a-/F0/t>' I

- t2= Z.?3 - t0'- nelq



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Hanbury-Brown and Twiss:

Intensity correlation measurements

- dead time of the detectors

- beam splitter

- pair of photon counters

- cross correlation

Single-photon emitters:

- single atoms or ions

- crystal defects (Quantum dots)



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Quantum Ideas Notes Week 1

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