DAY 5 FRIDAY

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80thequautizedfiehd.FIKatt tefield hint

a laHint at d E K

T nowhere quantized fieldEC att are

Hint at I E K dI dTE dt

du le C21 t d z 12 Cat E

tt Eq GE Fiz AL tge ah ran

Notations Tig Ii j I

go8elez

t

what happened to the other 2 terms

RWA we want to remove the quicklyoscillating terms the energy non consering

terms

The 4 terms z

Lfl l is m f NoIn 221 a n

Z

j M YESin 21 at az

Z L N A MI YES Zz CM at 9 no No

We write the totalHamiltonian.coXruvsH 2 lineateage c I twerz t

th zgecaaqer.azJaynes Cummings

tea cuiltonian

NotationsOz 127221 HK 11

it 12h11r

aid

day

we start with a simple calculation

considering 9 field mode

H Kw ata t lztwrz tgco atr.at

te Hint

keep trade nowsimultaneously of

atone state les or 123

of photons

work in interaction picture

f tg rtaetatheist

D WL Wo

ih DI tryIt

for a 4 of the formyphoty

Ht Z Cain t 12 t Cantt IfTstate ofatom

according to energy conserv we allow onlyI 2 n 7 It htt

coupled equations

dem og ont e't cnn.caEnna ig Fee e can

solve this

I can test probability to find at time Cthe atom in state 2 and u

photons in the fieldIce u E I e Staheli nphotons

want to knowjust about field

pal I can G l't ke ult 12

only population

E d can tell't I G ult T 1

Population inversion

Wct Z I lean G f KunCHP

solving the equations we obtain

with II Sunco DI 49IY as rut

initial auditionsIF 15 14g httCz n o Cn o

fun o Cn o 12 Ginellprobability for photons at tweet

check thisEven for fun o on only n o photons

we still have

wttIgeRt4g2cnd ftJ

Oscillations even in vacuum

WH

Taint for n I

i becauseof superposition of cosinewaves

This looks completely different than theRabi oscillations in the teurielassical theory

ryDoes this make sense

A 2 level system left alone starts oscillatinglike crazy and experiences collapse revival

Even starting in vacuum from the excited stale

No where is our spontaneous decaySolution to this dilemma

the vacuum contains all field minders Asingle mode is not the true story

Weiskopf Wigner theoryof spontaneous emission

interaction Hamiltonian formany modes

v k zfg.pe ri r a e Mike teeEE Fo

gotCreo gieTo location of atom

Situation of interest for spontaneous decay

Czf D 111atom in excited stoletried in vacuum Iii P

wavelet T field4Ct Catt 12,0 t TE 9 I 11 he

pa 41 photon

atom hi one ofthe modes

it we

Edt iz g7 Cri ew wilt

c t

q.ec ig.cr seiwo

w4tactimwomauiqdfmtral eye

dates E lgecr.TT ouieicwo w4k t'facet.ee

Now some approximationsa go from Tz to fd3E a closely spaced

modes

o2 p dree Jdkle L E

O

get E I daces20 o is 4 d EkZIEV

Ect Yadj Idarewas dt'e 4 44

wk two

of II dareso that we can use

to

f dem eWo Wh t t

2 get Ea

4w3d2i II with P Ez fgu late f e

texponentialdecay

we have found our spontaneous decay

HERE Applet Rabi otaillationsRabi fn loss of population in the system

Maxwell Bloch equations

we turn back to the term classical theory

Block equations quantify the excitationin the atom

Can we describe the pulse propagation1271ns

a medium with

my t.FI many2 leveesystems

2

laser field response of the medium upstreampropagate together

Scatraft t z 221

d El as space and

time dependent

field creates polarization of the mediumP EXE N Sd Nth Cfd

N fu d

Polarization creates re emission new field

wave equation

EEE EEE weslowly varying amplitudes we approximate

neglect the secondderivative

dot to i.gg Nd Sza fmrr

EEE terk

Oz iz Se

y NILI NII opticalthickness

this is solved self consistently togetherwl Luations

few 8922 tier f iz fu

l i

The Maxwell Bloch eg

Discussion during lecture this condensedsketch of derivation is not at all convincingPlease check Section 5.4 of Quantum optics byM Scully and M Zubairy

In addition you can also

check our derivation forthe particular case ofnuclear forward scatteringNFS see followingslides ice

NewJournal of Physics

Please check also New Phys 16 013049 2074

Ex des

super radiancenuclear forward scatteringthick samplestheir samplesstorage of photonsEr'T

mimicking strongcoupling

summary slide summary of lecture

THANK YOU FOR YOURATTENTION