Ionization of Rydberg atoms in Intense, Single-cycle …€¢THz ionization of low-lying Rydberg...

Ionization of Rydberg atoms in

Intense, Single-cycle THz field

April. 15th, 2013

4th year seminar of Sha Li

Advisor: Bob Jones

Dept. of Physics, Univ. of Virginia, Charlottesville, VA, 22904

Outline

• Introduction of Rydberg atoms

• Brief review of several typical types of field ionization

Background

• Intense THz generation via optical rectification

• THz streak

• THz ionization of low-lying Rydberg atoms

• THz ionization of Rydberg stark states

My work

• Electron Scattering

Future Plan

Outline

n=6 n=15

0.38eV 0.06eV

0.13eV 0.008eV

54𝒂𝟎 338𝒂𝟎

0.03ps 0.5ps

30THz 2THz

-0.02

-0.01

0

-2000 -1000 0 1000 2000

Z (𝒂𝟎)

En

ergy

(a.u

.)

n=6

n=15

Rydberg atoms

Hydrogen coulomb potential and energy diagram

• Hydrogen-like atoms

• Valance electron at highly excited orbit, with large principle quantum number n

• Experience effectively +1 net charge, can be considered as one electron system, but due to finite core size, QUANTUM DEFECT

Rydberg atoms

Sketch of a Kepler orbit with low angular momentum

2

,

1

2( )n

n l

En

1 3

1n n

E En

23

2r n

32T n

3

1

n

Examples of Field ionization


𝝎𝑭𝒊𝒆𝒍𝒅~𝝎𝒂𝒕𝒐𝒎


𝑭 ∝𝟏

𝒏𝟐~𝟏

𝒏

𝝎𝑭>𝝎𝒂𝒕𝒐𝒎 Half Cycle Pulse:

“impulsive” regime

Time

Fie

ld

R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 12361239 (1993)


𝑭 =𝟏

𝑪𝒏𝟒

𝝎𝑭 < 𝝎𝒂𝒕𝒐𝒎, static or quasi-static field.

Classical field ionization.

Time

Fie

ld

T. F. Gallagher, Rydberg Atoms, Cambridge University Press (1994)


𝑭 =𝟏

𝟑𝒏𝟓

𝝎𝑭 < 𝝎𝒂𝒕𝒐𝒎 , Multi-cycle Microwave ionization.

Energy

Classical Ionization

Limit

Field (V/cm)

0 1000 -2000 -1000 2000

n=20

n=29

n=22

n=24

n=21

n=28

n=27

n=26

n=25

n=23

Time

Fie

ld

P. Pillet, T. F. Gallagher, et.al Phys. Rev. A 30, 280294 (1984)

THz ionization of low-lying Rydberg atoms

• Low-lying n levels (n=6-15), which require very high field for ionization

• Oscillating field, but single cycle

• Very fast pulsed field 𝑇~4𝑝𝑠 compared to ns or μs scale pulsed field usually used. And very strong peak field strength ~500 𝑘𝑉/𝑐𝑚

• But still relatively slow (𝝎𝑭 < 𝝎𝒂𝒕𝒐𝒎) compared to the Kepler period of the Rydberg atoms studied: T (n=6-15) range from 0.03ps~0.5ps

Our Experiment

Time F

ield

-0.02

-0.01

0

-2000 -1000 0 1000 2000

Z (𝒂𝟎)

n=6

n=15


𝐹 ∝1

𝑛?

Time

Fie

ld

Relatively slow: 𝝎𝑭 < 𝝎𝒂𝒕𝒐𝒎

Absolutely fast: ps scale

THz generation

Characteristics of THz radiation

• Frequency: ν = 1 THz = 𝟏𝟎𝟏𝟐 Hz

• Period: τ = 1/ν = 1 ps = 𝟏𝟎−𝟏𝟐 S

• Wavelength: λ = c/ν = 0.3 mm = 300 μm

• Wavenumber: 1/λ = 33.3 𝒄𝒎−𝟏

• Photon energy: ħω = 4.14 meV

• Temperature: T = hν/kB = 48 K

Xi-Cheng Zhang, Jingzhou Xu, Introduction to THz Wave Photonics, Springer (2009)

Yun-Shik Lee, Principles of Terahertz Science and Technology, Springer (2008)

THz generation

THz generation via Optical Rectification

• Second order nonlinear effect

• Difference-frequency mixing among the spectral components contained within the ultrashort pulse bandwidth

𝝌 𝟐

Phase matching

• Large nonlinear coefficient

• Less THz absorption LiNbO3

g phase

pump THzv v

THz generation

Tilted-Pulse-Front Pumping

J. Hebling, Keith A. Nelson, et.al JOSA B, Vol. 25, Issue 7, pp. B6-B19 (2008)

THz generation

-40

-30

-20

-10

0

10

20

30

40

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Fie

ld s

tren

gth

(arb

. u

nit

)

time(ps)

3

0 411 0

3

0 412 0

3 0

1 2 Hz

2

2

( )

THz

THz

T

n En n

n En n

n n

dn n E

c

2 1/ 2{1, 1, 2}n

3 1/ 2{ 2, 2,0}n

1 1/ 2{ 1,1, 2}n

Electro-Optic Sampling

THz Streak

( )t

p F t dt

e-

e-

e-

THz Streak

390nm 150fs blue

589.8 nm

Na beam

LiNbO3

Polarizers

Pump

390nm 150fs

blue

3s

3p

Na+ & e-

589.8nm

390nm 150fs blue

589.8

nm

Time

THz

THz

THz Streak: Experimental setup

THz Streak: Experimental setup

Delay

THz Streak: Result

THz Streak: Result


THz ionization: Experimental Setup


Ion yield curve

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400 500

Ion

izati

on

Pro

bab

ilit

y

THz field (kV/cm)

n=6

n=7

n=8

n=9

n=10

n=11

n=12

n=13

n=14

n=1510%


New Scale Law: 𝑭 ∝𝟏

𝒏𝟑 !!!

6 7 8 9 10 11 12 13 14 1510

100

T

Hz F

ield

(k

V/c

m)

n

50

200

300

• Experimental

* CMC Simulation

𝑭 =𝟏

𝟏𝟔𝒏𝟒


n=15

n=6

6 7 8 9 10 11 12 13 14 1510

100

TH

z F

ield

(k

V/c

m)

n

50

200

300

• Experimental * CMC Simulation

𝑭 =𝟏

𝟏𝟔𝒏𝟒

Analyze electron energy distributions

Electron energy distributions at Max THz field (470 kV/cm)


ΔP

Time

( )t

p F t dt

Qualitative analysis

20 40 601E-4

1E-3

0.01

0.1

1

Pro

ba

bil

ity

Energy (eV)

6d10d

1

0 100 200 300 400 5000.0

0.2

0.4

0.6

0.8

1.0

Ion

iza

tio

n P

ro

ba

bil

ity

THz Field (kV/cm)

6d

10d


Time

Fie

ld


Up: The cycle averaged quiver energy of a free electron in an oscillating

electric field:

𝑼𝒑 =𝒆𝟐𝑭𝟐

𝟒𝒎𝝎𝟐 =𝑭𝟐

𝟒𝝎𝟐 (a.u.)

2Up: The max energy a free electron can get from a oscillating electric field

that slowly decreases in aptitude:

Max energy=2Up

What if the field have only a few cycles, or even one single cycle?

Ponderomotive Energy


F(t)=𝑭𝟎sin(ωt)

𝜟𝑷 = − 𝑭 𝒕 𝒅𝒕∞

𝒕𝟎

∆𝑬 = (𝟐𝑷𝟎∆𝑷 + (∆𝑷)𝟐)/2

100.2 eV

~0.25THz and ~322 kV/cm

𝑼𝒑 =𝑭𝟐

𝟒𝝎𝟐 ≈ 𝟏𝟖. 𝟓 𝒆𝑽

Max energy~ 𝟓. 𝟒 𝑼𝒑 ‼!

THz ionization of Rydberg Stark states

Field (kV/cm)

En

ergy

(a.u

.)

Na n=10, m=0 Stark manifold

11s

11p

What if the Rydberg atoms are initially prepared in Stark states?

𝑭 =𝟏

𝑪𝒏𝟒

10d


elec. ion

+/—

Na+/e-

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0 1 2 3 4 5 6 7 8 9

Fie

ld (

arb

. un

it)

nth stark level

elec.

ion


Simplest case: 2-level

H(F)=𝑬𝟏(𝑭)

𝟏

𝟐∆𝑬

𝟏

𝟐∆𝑬 𝑬𝟐(𝑭)

∆𝑬: coupling/quantum defect

𝑷𝒅𝒊𝒂=𝒆−𝟐𝝅𝜞

𝜞=(𝟏

𝟐∆𝑬)𝟐

|𝒅𝑬𝟏

𝒅𝒕−𝒅𝑬𝟐

𝒅𝒕| =

(𝟏

𝟐∆𝑬)𝟐

|𝑭 𝒅𝑬𝟏

𝒅𝑭−𝒅𝑬𝟐

𝒅𝑭|

∆𝐸 𝐸2

𝐸1

𝐸+

𝐸−

𝐸1

𝐸2

𝐸+

𝐸−

F

E

Landau-Zener Transition


𝑬+

𝑬−

𝑬+

𝑬−

F

E

𝐹0

𝑬+

𝑬−

𝑬+

𝑬−

F

E

𝐹0

t

THz field


• Aptitude of static field • Direction of static field (Relative to THz) • Initial stark level • Asymmetry of THz and THz slew rate

What may influence the result ?


Multi-level Landau-Zener Transitions

( )

( )( ) ( )

( ) ( ) ( ) niE t t

n n

n

ti H t t

t

t C t t e

Spherical basis |𝑛, 𝑙, 𝑚 > : 𝛹𝑛 , 𝐸𝑛

Parabolic/Diabatic basis |𝑛, 𝑘,𝑚 > : 𝛹𝑛 , 𝐸𝑛(𝑡)

Adiabatic/Local basis :

(no good quantum #)

( ) ( ) ( ) fni E t

f n fn

n

i C t C t H t e

0( )

( ) ( ) ( )

t

fni E t dt

f n fn

n

i C t C t H t e

𝛹𝑛(𝑡) , 𝐸𝑛(𝑡)


Still working on numerical simulation codes !

Future plan …

Future plan

Electron Scattering • Electron been “dragged back” by THz to the nucleus

and “knocks off” more electrons.

Conclusion

Conclusion

• Can generate THz with peak field strength as high as 500 kV/cm

Intense THz generation via optical rectification

• Can measure THz waveform inside the chamber.

• Electrons from ionization of lower n states have higher energies

• Electron energy distribution shows the asymmetry of the field

• In THz streak, have electrons with energy exceed 2Up.

THz streak & Electron energy distributions

• Ionization of low-lying Rydberg atoms: Scales as 1/n^3

• Ionization of Rydberg stark states: Shows the asymmetry and fast property of THz field.

THz ionization of low-lying Rydberg atoms and Rydberg stark states

Thank you!


Time

Fie

ld


Numerical Simulation: 2 -Level

∆𝐸 𝐸2

𝐸1

𝐸+

𝐸−

𝐸1

𝐸2

𝐸+

𝐸−

F

E

𝑘

500𝑘

50𝑘

10𝑘

5𝑘

100∆𝐸

10∆𝐸

∆𝐸

25∆𝐸

50∆𝐸

𝒕−∞ 𝒕+∞

𝑷𝟏

𝑷𝟏

Γ=(1

2∆𝐸)2

|𝑑𝐸1

𝑑𝑡−𝑑𝐸2

𝑑𝑡| =

(1

2∆𝐸)2

|𝐹 𝑑𝐸1

𝑑𝐹−𝑑𝐸2

𝑑𝐹|

Initially in state “—”, with a linear ramp 𝐹 = 𝑘𝑡 from very large negative time to very large

positive time. work in |1>,|2> basis


3

3

3 33

3

. e i s

e

e s s

i

i

sig P PN

EP

n

sig EP N N

P n

sig E

P n

3s-nd excitation prob. curves

0.0E+00

1.0E-06

2.0E-06

3.0E-06

4.0E-06

5.0E-06

6.0E-06

7.0E-06

8.0E-06

0 100 200 300 400 500 600

sign

al/P

i (ar

b.

u.)

Energy/n^3 arb. u.

6d/0.3846

7d/0.6631

8d/0.7692

9d/0.9077

10d/1


Time of Flight (ToF) spectrometer

2 1 2

0 0 0

2 10

2( )

2

d eU dmdt t v v

eU md d eUv

md

MCP

U

𝒅𝟐

𝒅𝟏 𝒅 𝒗𝟎

-U (V)

T (ns)

Ionization of Rydberg atoms in Intense, Single-cycle …€¢THz ionization of low-lying Rydberg...

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