ionization of rydberg atoms in intense, single-cycle thz field
TRANSCRIPT
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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
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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
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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
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Examples of Field ionization
Examples of Field ionization
𝝎𝑭𝒊𝒆𝒍𝒅~𝝎𝒂𝒕𝒐𝒎
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Examples of Field ionization
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)
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Examples of Field ionization
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)
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Examples of Field ionization
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)
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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
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THz ionization of low-lying Rydberg atoms
𝐹 ∝1
𝑛?
Time
Fie
ld
Relatively slow: 𝝎𝑭 < 𝝎𝒂𝒕𝒐𝒎
Absolutely fast: ps scale
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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)
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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
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THz generation
Tilted-Pulse-Front Pumping
J. Hebling, Keith A. Nelson, et.al JOSA B, Vol. 25, Issue 7, pp. B6-B19 (2008)
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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
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THz Streak
( )t
p F t dt
e-
e-
e-
THz Streak
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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
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THz Streak: Result
THz Streak: Result
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THz ionization of low-lying Rydberg atoms
THz ionization: Experimental Setup
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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%
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THz ionization of low-lying Rydberg atoms
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
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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
• Experimental * CMC Simulation
𝑭 =𝟏
𝟏𝟔𝒏𝟒
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Analyze electron energy distributions
Electron energy distributions at Max THz field (470 kV/cm)
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Analyze electron energy distributions
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
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Analyze electron energy distributions
Time
Fie
ld
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Analyze electron energy distributions
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
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Analyze electron energy distributions
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 ‼!
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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
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THz ionization of Rydberg Stark states
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
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THz ionization of Rydberg Stark states
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
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THz ionization of Rydberg Stark states
𝑬+
𝑬−
𝑬+
𝑬−
F
E
𝐹0
𝑬+
𝑬−
𝑬+
𝑬−
F
E
𝐹0
t
THz field
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THz ionization of Rydberg Stark states
• 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 ?
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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 |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)
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THz ionization of Rydberg Stark states
Still working on numerical simulation codes !
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Future plan …
Future plan
Electron Scattering • Electron been “dragged back” by THz to the nucleus
and “knocks off” more electrons.
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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
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Thank you!
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Analyze electron energy distributions
Time
Fie
ld
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THz ionization of Rydberg Stark states
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
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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
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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
𝒅𝟐
𝒅𝟏 𝒅 𝒗𝟎
-U (V)
T (ns)