DAY 5 FRIDAY reload 80thequautizedfiehd.FI Katt te field hint a la Hint at d E K T nowhere quantized field EC att are Hint at I E K dI dTE dt du le C 21 t d z 12 Cat E t t Eq GE Fiz AL t ge ah ran Notations Tig Ii j I go 8elez t what happened to the other 2 terms RWA we want to remove the quickly oscillating terms the energy non consering terms
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80thequautizedfiehd · 2018. 10. 15. · DAY 5 FRIDAY reload 80thequautizedfiehd.FI Katt te field hint a la Hint at d E K T nowhere quantized field ECatt are Hint at I E K dI dTE
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DAY 5 FRIDAY
reload
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