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