t echnische u niversitÄt kaiserslautern k. bergmann lecture 6 lecture course - riga, fall 2013...
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TECHNISCHE UNIVERSITÄT
KAISERSLAUTERN
K. Bergmann
Lecture 6
Lecture course - Riga, fall 2013
Coherent light-matter interaction:
Optically driven adiabatic transfer processes
summary of 5th lecture
reconsidered Rabi oscillations from the perspective of adiabatic states: interference of the amplitudes of adiabatic states (accumulation of a phase difference due to AT-splitting)
time
0
= ½ o
Coherent Population Return (CPR)
|1>
|a->
initially: population of
and/or only
|1> |a->
at the end: population of
and/or only|2>
|a+>
DURING radiative interaction:
X % admixture of population of
but NO coupling to
|a+>
|a->
X decreases with increasing
summary of 5th lecture: CPR - facts
key conclusion:
detection during radiative interaction power broadening observed
detection after radiative interaction NO power broadening observed
|a+>
|1>
|2>
|1>
|2>
o
= ½ o
|1>,
|2>|a+>
|a->
|o>
all population
in |1> or |a->
no population
in |2> or |a+>
|1>,
|2>
|a->
|o>
all population
in |a-> when AF
less populationin |1>
some populationin |2>
summary of 5th lecture: CPR – with Gaussian pulse shape
|1>
|2>
o
adiabatic state vector |a->
rotates smoothly into newposition (new direction)
state vector |o> followsadiabatically
the larger , the smallerthe angle of rotation for given o
the larger o, thelarger the max.angle of rotation
for given
= ½ o
|1>,
|2>|a+>
|a->
|o>
all population
in |1> or |a->
no population
in |2> or |a+>
summary of 5th lecture: CPR – sudden switch on
|1>
|2>
o
adiabatic state vector |a->
rotates suddenly into newposition (new direction)
state vector |o> cannotfollow
states |a-> and |a+>populated
|1>,
|2>
|a->
|o>
sudden changeof direction of |a->
|a+>
sudden rotation back
|a+> and |a-> projectedon |1> and |2>
result depends on relative phase
|1> and |2> populated
the goals for this lecture
understanding the complex structure of spectra in a 2 + 1 level system
radiatively coupled 3-level system in the rate equation limit
understanding the phenomenon of electromagnetically induced transparency (EIT) – a qualitative approach
approaching the RWA Hamiltonian for the radiatively coupled 3-level system
7th lecture: the properties of the 3-level RWA Hamiltonian and the basics of the STIRAP process
outlook
Understanding the (complex) spectral properties in coherently driven 2 + 1 level systems
or
probing Autler-Townes structure
AT induced between a pair of levels WITH population
experiments by Aigars Ekers
2.4.4 spectral properties of coherently driven 2 + 1 level systems
strong
weak
Ref. 71
2.4.4 spectral properties of coherently driven 2 + 1 level systems
Na2
fluorescence from level f as a function of S-laser frequency for varies settings of P-laser frequency
what do we want to explained ?
?
detunings s and s are small, not exceeding the Rabi frequency by much.
2
13
SP
bare states
13
S
adiab. states
P= 0
13
S
adiab. states
P> 0
2´
3´
1´
S
P
bare states3´
S
adiab. states
P= 0
S
adiab. states
P> 0
3´
Lamba system, initially: level 1 populated, levels 2 and 3 empty
Ladder system, initially: level 1´ populated, levels 2´ and 3´ empty
2.4.4 spectral properties of coherently driven 2 + 1 level systems
coupling / excitation / population flow possible when adiabatic states are in resonance
this radiation obesrved
strong
weak
excitation to state f is possible at two locations (or two times)
look at population flow to level f followed by spont. emissionRef. 71
2.4.4 spectral properties of coherently driven 2 + 1 level systems
Na2
P = 0
S > Ef - Ee
P S
|f>
weak S, some excitation to level f, followed by spontaneous emission e
f
g
S
P
bare states
|a+> = + |g> + + |e>
|a-> = - |g> + - |e>
2.4.4 spectral properties of coherently driven 2 + 1 level systems
1 mm @ 1000 m/s : 1 µs
coupling
f fe
P S
|a+> = + |g> + + |e>
|a-> = - |g> + - |e>|f>
strong S, strong excitation to level f, followed by spontaneous emission e
f
g
S
P
bare states
2.4.4 spectral properties of coherently driven 2 + 1 level systems
P S
|f>
very strong S, all the population driven through level f,
followed by spontaneous emission
e
f
g
S
P
bare states
|a+> = + |g> + + |e>
|a-> = - |g> + - |e>
2.4.4 spectral properties of coherently driven 2 + 1 level systems
P S
|a+> = |g> + |e>
|a-> = |g> - |e>|f>
interference structure , reminiscent of Rabi oscillation (but of entirely different origin)
population may reach level f via two different paths
e
f
g
S
P
bare states
2.4.4 spectral properties of coherently driven 2 + 1 level systems
P S
|a+> = |g> + |e>
|a-> = |g> - |e>
increase detuning
no excitation, except ……..
e
f
g
S
P
bare states
2.4.4 spectral properties of coherently driven 2 + 1 level systems
coupling strength at crossingchanges, because changes
increase detuning
no excitation, except …….. when P is increased
P S
|a+> = |g> + |e>
|a-> = |g> - |e>
2´
3´
1´
S
P
bare states|f>
|a+> = + |g> + + |e>
|a-> = - |g> + - |e>
2.4.4 spectral properties of coherently driven 2 + 1 level systems
increase detuning
no excitation, except ……when P is increased ….. or P is increased
SP
|a+> = + |g> + + |e>
|a-> = - |g> + - |e>
e
f
g
S
P
bare states
2.4.4 spectral properties of coherently driven 2 + 1 level systems
e
f
g
S
P
bare states
laser induced fluorescence from level 3´, as a function of the S-laser frequency
for various P-laser detuningsS and P
kept constant
spectral propertiesdepend sensitivilyon all parameters:P, S, P, S
Ref. 71
2.4.4 spectral properties of coherently driven 2 + 1 level systems
Ref. 71
contribution of individual m-states, J = 7
sum over all m-states
sum over allm-states andaveraged overDoppler width
exp. data
theory
2.4.4 spectral properties of coherently driven 2 + 1 level systems
features are difficult to pre-dict in the bare state picturebut relatively easily under-stood in the adiabatic state approach
3 Coherent excitation in a 3-level system
3.1 Rate equations, optical pumping, preview of STIRAP features 3.2 Electromagnetically induced transparency 3.3 The 3-level Hamiltonian
3.1 Rate equation (incoherent radiation) and optical pumping,
coincident pulses
delayed pulses
50%
33%
maximum transfer: 33% reached without loss through spontaneous emission
maximum transfer: 25 % reached without loss through spontaneous emission
2
13
PS 4
loss to other levels
50%
33%
3.1 two sequential - pulses in a three level system
COMPLETE transfer from level 1 to level 3 via coupling through the (possibly rapidly decaying) state 2
File: Pi21
one problem: all populationreaches level 2 and much ofit is lost by spontaneous emission to other states.
1
2
3
SP
COMPLETE population transfer from
|1> → |3> via resonant coupling through
the (possibly rapidly decaying) state |2>
3.1 preview of STIRAP features
Stimulated Raman Adiabatic Passage
The interaction with the S–laser, coupling the two unpopulated levels,starts FIRST. Does this make sense ???
The interaction with the P–laser, coupling level 2 to the populated level 1 begins LATER – but a suitable overlap between S and P is needed.
The STIRAP puzzles
1
2
3
SP
Turn on the Stokes laser first ! - ??The initial population resides in state 1 !!
The population in state 3 not depleted (by S-laser optical pumping) ! - ??
No radiative loss from state 2 ! - ?? The S- and P-Laser are tuned to resonance, afterall !!
COMPLETE population transfer from
|1> → |3> via resonant coupling through
the (possibly rapidly decaying) state |2>
3.1 preview of STIRAP features
Stimulated Raman Adiabatic Passage
3.1 STIRAP
The “building blocks” of STIRAP are:
The Autler-Townes (AT) effect (splitting)
The adiabatic passage (AP) process
The phenomenon of electro-magnetically induced transparency (EIT)
AT – EIT – AP properly combined STIRAP
discussed
discussed
to bediscussed
Lorentzian profile
Intensity ≠ 0 ?
P – laser frequency
two transition dipole moments:
180o out of phase
adiabatic
fluo
resc
ence
bare
P
1
3
S
2 AT
3.2 Electromagnetically induced transparency
amplitude of transition dipole moment:
<1| |a> <1||3> <1||2> File: Lorentz0 …50_2xSUM needed
3.2 electromagnetically induced transparency (EIT)
spectral profile probed on |1> -- |2> transition
as coupling of
|2> -- |3> increases
probe laser frequency (|1> -- |2>)
inte
nsity
= decay rate of level |2>
start EIT/AT
kiki
ki
E ,,,
File: EIT_Final-1
3.2 electromagnetically induced transparency (EIT)
much smaller than : ( = natural line width)
interference structure(narrow) observed,
which is called: EIT
larger than :
two separate features (of width ≈ ) observed,
called AT-splitting
also zero (EIT) between AT-components
Experiment
0
200
400PP=6.2µW
Fl u
ores
cen c
e [ C
nts/
0.5s
]
=11mW
PS=55mW
0
200
400PP=4.0µW
-200 -100 0 100 200
PS=11mW
[MHz]P exactly zero
PSNe*
PS
adiabat. states
Ref. 24
3.2 Electromagnetically induced transparency
13
PS
bare states
2
3.2 Electromagnetically induced transparency
PS = 55 mW
PS = 35 mW
PS = 11 mW
PS = 1,4 mW
PP = 6,2 mW
PP = 3,4 mW
PP = 4,0 mW
PP = 6,9 mW
S = 7.4 rad/ns
S = 5,9 rad/ns
S = 3,3 rad/ns
S = 1,2 rad/ns
P = 0.02 rad/ns
Ref. 24
337.1 nm
570.3 nm
Sr
cell
detector
transmissionless than 10-6
3.2 Electromagnetically induced transparency
Ref. 76
WITHOUT 570 nm radiation
WITH 570 nm radiation
Questions related to the topics discussed in lecture 6
(6.2) What physical mechanism causes electromagnetically induced transparency (EIT) and what is the connection, if any, between EIT and the Autler-Townes splitting ?
(6.1) Draw the adiabatic state energies for a three-level system g, e, f with e,g = P , P-field detuning = P and e,f = S, S-field detuning = S
for the following conditions: (a) P = 0, S = 0, (b) P = 0, S > 0, (c) P > 0 , S < 0. Also assume that the S-field intensity is constant while the P-pulse is on and P is much larger S than .
end of 6th lecture
Coherent light-matter interaction:Optically driven adiabatic transfer processes