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
โข Introduction of Rydberg atoms
โข Brief review of several typical types of field ionization
Background
โข Intense THz generation via optical rectification
โข THz streak
โข THz ionization of low-lying Rydberg atoms
โข THz ionization of Rydberg stark states
My work
โข Electron Scattering
Future Plan
Outline
n=6 n=15
0.38eV 0.06eV
0.13eV 0.008eV
54๐๐ 338๐๐
0.03ps 0.5ps
30THz 2THz
-0.02
-0.01
0
-2000 -1000 0 1000 2000
Z (๐๐)
En
ergy
(a.u
.)
n=6
n=15
Rydberg atoms
Hydrogen coulomb potential and energy diagram
โข Hydrogen-like atoms
โข Valance electron at highly excited orbit, with large principle quantum number n
โข 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
Examples of Field ionization
๐๐ญ๐๐๐๐ ~๐๐๐๐๐
Examples of Field ionization
๐ญ โ๐
๐๐~๐
๐
๐๐ญ>๐๐๐๐๐ Half Cycle Pulse:
โimpulsiveโ regime
Time
Fie
ld
R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 12361239 (1993)
Examples of Field ionization
๐ญ =๐
๐ช๐๐
๐๐ญ < ๐๐๐๐๐, static or quasi-static field.
Classical field ionization.
Time
Fie
ld
T. F. Gallagher, Rydberg Atoms, Cambridge University Press (1994)
Examples of Field ionization
๐ญ =๐
๐๐๐
๐๐ญ < ๐๐๐๐๐ , 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
โข Low-lying n levels (n=6-15), which require very high field for ionization
โข Oscillating field, but single cycle
โข Very fast pulsed field ๐~4๐๐ compared to ns or ฮผs scale pulsed field usually used. And very strong peak field strength ~500 ๐๐/๐๐
โข But still relatively slow (๐๐ญ < ๐๐๐๐๐) 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 (๐๐)
n=6
n=15
THz ionization of low-lying Rydberg atoms
๐น โ1
๐?
Time
Fie
ld
Relatively slow: ๐๐ญ < ๐๐๐๐๐
Absolutely fast: ps scale
THz generation
Characteristics of THz radiation
โข Frequency: ฮฝ = 1 THz = ๐๐๐๐ Hz
โข Period: ฯ = 1/ฮฝ = 1 ps = ๐๐โ๐๐ S
โข Wavelength: ฮป = c/ฮฝ = 0.3 mm = 300 ฮผm
โข Wavenumber: 1/ฮป = 33.3 ๐๐โ๐
โข Photon energy: ฤงฯ = 4.14 meV
โข Temperature: T = hฮฝ/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
โข Second order nonlinear effect
โข Difference-frequency mixing among the spectral components contained within the ultrashort pulse bandwidth
๐ ๐
Phase matching
โข Large nonlinear coefficient
โข 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 of low-lying Rydberg atoms
THz ionization: Experimental Setup
THz ionization of low-lying Rydberg atoms
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%
THz ionization of low-lying Rydberg atoms
New Scale Law: ๐ญ โ๐
๐๐ !!!
6 7 8 9 10 11 12 13 14 1510
100
T
Hz F
ield
(k
V/c
m)
n
50
200
300
โข Experimental
* CMC Simulation
๐ญ =๐
๐๐๐๐
THz ionization of low-lying Rydberg atoms
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
โข Experimental * CMC Simulation
๐ญ =๐
๐๐๐๐
Analyze electron energy distributions
Electron energy distributions at Max THz field (470 kV/cm)
Analyze electron energy distributions
ฮP
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
Analyze electron energy distributions
Time
Fie
ld
Analyze electron energy distributions
Up: The cycle averaged quiver energy of a free electron in an oscillating
electric field:
๐ผ๐ =๐๐๐ญ๐
๐๐๐๐ =๐ญ๐
๐๐๐ (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
Analyze electron energy distributions
F(t)=๐ญ๐sin(ฯt)
๐๐ท = โ ๐ญ ๐ ๐ ๐โ
๐๐
โ๐ฌ = (๐๐ท๐โ๐ท + (โ๐ท)๐)/2
100.2 eV
~0.25THz and ~322 kV/cm
๐ผ๐ =๐ญ๐
๐๐๐ โ ๐๐. ๐ ๐๐ฝ
Max energy~ ๐. ๐ ๐ผ๐ โผ!
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?
๐ญ =๐
๐ช๐๐
10d
THz ionization of Rydberg Stark states
elec. ion
+/โ
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
THz ionization of Rydberg Stark states
Simplest case: 2-level
H(F)=๐ฌ๐(๐ญ)
๐
๐โ๐ฌ
๐
๐โ๐ฌ ๐ฌ๐(๐ญ)
โ๐ฌ: coupling/quantum defect
๐ท๐ ๐๐=๐โ๐๐ ๐
๐=(๐
๐โ๐ฌ)๐
|๐ ๐ฌ๐
๐ ๐โ๐ ๐ฌ๐
๐ ๐| =
(๐
๐โ๐ฌ)๐
|๐ญ ๐ ๐ฌ๐
๐ ๐ญโ๐ ๐ฌ๐
๐ ๐ญ|
โ๐ธ ๐ธ2
๐ธ1
๐ธ+
๐ธโ
๐ธ1
๐ธ2
๐ธ+
๐ธโ
F
E
Landau-Zener Transition
THz ionization of Rydberg Stark states
๐ฌ+
๐ฌโ
๐ฌ+
๐ฌโ
F
E
๐น0
๐ฌ+
๐ฌโ
๐ฌ+
๐ฌโ
F
E
๐น0
t
THz field
THz ionization of Rydberg Stark states
โข Aptitude of static field โข Direction of static field (Relative to THz) โข Initial stark level โข Asymmetry of THz and THz slew rate
What may influence the result ?
THz ionization of Rydberg Stark states
Multi-level Landau-Zener Transitions
( )
( )( ) ( )
( ) ( ) ( ) niE t t
n n
n
ti H t t
t
t C t t e
Spherical basis |๐, ๐, ๐ > : ๐น๐ , ๐ธ๐
Parabolic/Diabatic basis |๐, ๐,๐ > : ๐น๐ , ๐ธ๐(๐ก)
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
๐น๐(๐ก) , ๐ธ๐(๐ก)
THz ionization of Rydberg Stark states
Still working on numerical simulation codes !
Future plan โฆ
Future plan
Electron Scattering โข Electron been โdragged backโ by THz to the nucleus
and โknocks offโ more electrons.
Conclusion
Conclusion
โข Can generate THz with peak field strength as high as 500 kV/cm
Intense THz generation via optical rectification
โข Can measure THz waveform inside the chamber.
โข Electrons from ionization of lower n states have higher energies
โข Electron energy distribution shows the asymmetry of the field
โข In THz streak, have electrons with energy exceed 2Up.
THz streak & Electron energy distributions
โข Ionization of low-lying Rydberg atoms: Scales as 1/n^3
โข 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!
Analyze electron energy distributions
Time
Fie
ld
THz ionization of Rydberg Stark states
Numerical Simulation: 2 -Level
โ๐ธ ๐ธ2
๐ธ1
๐ธ+
๐ธโ
๐ธ1
๐ธ2
๐ธ+
๐ธโ
F
E
๐
500๐
50๐
10๐
5๐
100โ๐ธ
10โ๐ธ
โ๐ธ
25โ๐ธ
50โ๐ธ
๐โโ ๐+โ
๐ท๐
๐ท๐
ฮ=(1
2โ๐ธ)2
|๐๐ธ1
๐๐กโ๐๐ธ2
๐๐ก| =
(1
2โ๐ธ)2
|๐น ๐๐ธ1
๐๐นโ๐๐ธ2
๐๐น|
Initially in state โโโ, with a linear ramp ๐น = ๐๐ก from very large negative time to very large
positive time. work in |1>,|2> basis
THz ionization of low-lying Rydberg atoms
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
Analyze electron energy distributions
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
๐ ๐
๐ ๐ ๐ ๐๐
-U (V)
T (ns)