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