Topics in steady-state MRI sequences and RF pulse optimization
Optimal Pulse sequences for efficient population transfer in lower (n
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Optimal Pulse sequences for efficient population transfer in lower (n<10) Rydberg states Mudessar Shah How Camp Marc Trachy Supervisor: Brett DePaola
description
Optimal Pulse sequences for efficient population transfer in lower (n
Transcript of Optimal Pulse sequences for efficient population transfer in lower (n
Optimal Pulse sequences for efficient population
transfer in lower (n<10) Rydberg states
Mudessar ShahHow Camp
Marc Trachy
Supervisor:Brett DePaola
Application
Need for a system to be in a specified quantum state
o Laser control of chemical reactions
o Atom optics
o Quantum information
0.0
0.5
1.0
Exc
i. p
opu
lati
on
time
incoh. exc.
coh. exc.adiab.
Two level system
k Absorp.
E=ћωP=ћKJ= ћ
E=0P=0J= 0
E=ћωP=ћKJ= ћ
Pe(t)=1/2[1-e-F(T)]F(T)= I(t)dt
Pe(t)=1/2[1-cosΩt]
when radiation varies in amplitude cosine argument is
replaced by so-called pulse area
Advantages
Excitation between state of same parity can be produced, for which single photon transition are forbidden for electric dipole radiation, or between magnetic sublevels. (for 3 and higher)
Excitation efficiency can be made insensitive to many of experimental details (pulse area, Shape etc).
100% population transfer between same parity state is possible
-50 0 50 100 150 200
0.0
0.2
0.4
0.6
0.8
1.0
-50 0 50 100 150 200
0
2
4
6
8
10
12 |1> |2> |3>
Po
pu
latio
n
Time (ns)
1,2
(GH
z)
I1 = 250 mW/cm2
w1 = 33 ns
I2 = 250 mW/cm2
w2 = 33 ns
t = 20 ns = 44 MHz
1
2
Theoratical prediction For three level systems
|1>
2
|3>
Ladder
|2>
1
4d
5p
5s
Adiabatic population transfer using sequential pulses (Three photon transition)
Delay1Delay2
L3 L1L2
|4>3
Ladder
|2>
|1>
1
|3>
2
1
2
5s
5p
4d
9f
iikkk
ijjkikk
ijij
ijijij
AAA
ii
)(2
1
,
Equation of motion
Delay1 Vs %f population
Delay1Delay2
L3 L1L2
Delay2 Vs %f population
Delay1Delay2
L3 L1L2
L1 vs %f
|4>3
Ladder
|2>
|1>
1
|3>
2
1
2
L3 vs %9f
|4>3
Ladder
|2>
|1>
1
|3>
2
1
2
L2 vs %f
|4>3
Ladder
|2>
|1>
1
|3>
2
1
2
Detuning1 vs %f
|4>3
Ladder
|2>
|1>
1
|3>
2
1
2
Detuning2 vs %f
|4>3
Ladder
|2>
|1>
1
|3>
2
1
2
General Apparatus Design
Q-Value SpectraQ-Value Spectra
50 75 100 125 150
0
500
1000
1500
2000
2500
3000
3500
Co
un
ts
Q-Value (Channel)
5s-3p
4d-3d5s-3s
-5
-4
-3
-2
-1
0
4d 2D5/2
, 4d2D3/2
4f 2F7/2
, 4f2F5/2
4s 2S1/2
4p 2P1/2
, 4p 2P3/2
23Na
4s 2S1/2
3d 2D5/2
, 3d2D3/2
3p 2P
1/2, 3p
2P
3/2
3s 2S
1/2
12f
4d 2D3/2,5/2
5p 2P
3/2
5s 2S
1/2
87Rb
Pote
ntia
l Ene
rgy
(eV)
2D Spectrum2D Spectrum
Q-Value (Channel)
Tim
e (s
)
50 100 150
0.5
1.0
1.5
2.0
2.5
0.0
5s-3p 5p-3p 5s-3s
4d-3d4d-3s
5p-3p
Time Evolution of Population
TAC spectra for 9f
Thanks!
%5p vs %9f
|4>3
Ladder
|2>
|1>
1
|3>
2
1
2
%5s vs %9f
|4>3
Ladder
|2>
|1>
1
|3>
2
1
2
%4d vs %9f
|4>3
Ladder
|2>
|1>
1
|3>
2
1
2
