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Haruka Maeda
Department of Phys. & Math.,
Aoyama Gakuin University
Coherent control of
Rydberg atoms
Why Rydberg atom?
What can we study with Rydberg atom?
Microwave multiphoton ionization of multilevel system
Population control of quantum ladder system
Multilevel ladder system
Dynamic autoresonance and multiphoton adiabatic rapid passage
Excellent testing ground for coherent control of nonlinear system
72
71
73
74
70
75
69
76
77
78
Resonance ~17.3GHz
Multilevel coupling n
68
resonance frequencies microwave (RF) region
A+ e-
Large orbital radius r n2
n = 1 r 0.05 nm (Bohr radius)
n =100 r 0.5 m
Interesting properties (simple n-scaling law)
etc.
), (
,/1
/1
3
3
2
llown
nE
nE
n
n
n
En
erg
y
simple multilevel ladder system
Rydberg atom (H-like atom)
Why Rydberg atom?
Why Rydberg atom?
What can we study with Rydberg atom?
Microwave multiphoton ionization of multilevel system
Population control of quantum ladder system
Multilevel ladder system
Dynamic autoresonance and multiphoton adiabatic rapid passage
MCP
Atomic beam
Signal out
e-
Pair of field plates
MW
horn
Dye laser
pulses
WR-62 Wave guide
Dye laser
pulses
MCP
e-
Septum
Atomic beam
MW
Signal out (a)
Dye laser
pulses
Atomic beam
e-
Signal
MCP
Field
ramp
MW
MW
-Typical experiment-
Negative field
pulse
t
Dye laser
pulses
Timing diagram
MW
pulse
20ns
5snd Rydberg state
Sr I 5s2
5s5p 1P1
Sr II 5s
l1 = 460.9 nm
l2 = 412 ~ 416 nm
E (eV)
0
5.7
Excitation scheme of Sr
MW
pulse
H.M. and T.F. Gallagher, PRL 93, 193002 (2004)
0
MW
amplitude
F (V/cm)
5.1
7.7
9.4
11.0
Experimental results
-Typical experimental method and results-
-Scaled frequency -
3 n= : microwave frequency
in atomic units (a.u.) 1/n3 :Kepler frequency
H+ e-
1=
n
n+1
1 Resonance 1 Principal
resonance
see, for example, P.M. Koch and K.A.H. van Leeuwen,
Phys. Rep. 255, 289 (1995)
Low frequency regime
(classical dynamics) 1
1
Chaotic
ionization
Quantum chaos study
1n21 Photoelectric
effect
DC field ionization
1Tunnel ionization
1
-MW ionization at several frequency regimes-
High frequency regime
(Quantum mechanical) 1
Localization
1
∆2
∆3
∆4 Random
detuning
Rich physics
10
10
021
0 nphotoelectric
effect
10
10
2
02
1
n
0
3
002
1nn =
ω ≈17 GHz Li
-MW ionization at photoelectric effect regime-
J.H. Gurina, K.R. Overstreet, H. Maeda, T.F. Gallagher,
PPA 82, 043415 (2010)
High frequency regime
(Quantum mechanical) 1
Localization
1
1 Resonance 1 Principal
resonance
see, for example, P.M. Koch and K.A.H. van Leeuwen,
Phys. Rep. 255, 289 (1995)
Low frequency regime
(classical dynamics) 1
1
Chaotic
ionization Quantum chaos study
1n21 Photoelectric
effect
DC field ionization
1Tunnel ionization
1
-MW ionization at several frequency regimes-
18.83
18.05
17.31
n=70
n=80
13.63
13.12 (GHz)
14.17 ~ ~
71
72
73
77
78
79
r
local potential well
(bucket)
nonlinear interaction electron motion is phase locked to the MW field (NDWP)
~ 57 ps
Kepler orbital period of 72p state Kep 58 ps
Li 72p Rydberg atom
Li+ 1s2 e-
Nondispersing wave packets (NDWP)
En
erg
y
Li : 1s22s
・Extremely long lifetime
・Electron motion can be
detected with fs laser pulse
F(t)
F = 1 V/cm, 17.5 GHz, linearly polarized MW pulse +
near resonant
0 50 100 0.0
0.2
0.4
0.6
0.8
1.0
HC
P i
on
izati
on
pro
bab
ilit
y
Relative time delay (ps)
+HCP polarity
Li n=72, MW 17.5 GHz,
F ~ 3 V/cm
~ 57 ps
GaAs
High
voltage
THz HCP
~0.5 ps
THz half cycle field pulse (HCP) D. You, R.R. Jones, P.H. Bucksbaum, and D.R. Dykaar,
Opt. Lett. 18, 290 (1993)
HCP ( ~ 0.5 ps ) Kep (~ 57 ps @ n =72)
Ionization of phase-locked electron by
impulsive momentum kick
HCP
x +
100 fs, 800 nm
Ti:sapphire laser
pulse (< ~40J/cm2)
0.1 ps
large ionization probability
microwave is phase locked
to the harmonics of
80 MHz fs pulse train
57 ps
Delay
stage
How to detect NDWP with fs laser pulse?
HC
P i
on
izati
on
pro
ba
bil
ity
Relative time delay (ps)
NDWP!! 57 ps
small ionization probability
Periodically driven quantum system Floquet (dressed-atom) state
1D Rydberg atom in a linearly polarized microwave (MW) field
0 1 2 3 4 5-20
-15
-10
-5
0
5
10
7669
7570
74
71
73
Ene
rgy
(GH
z)
MW amplitude F (V/cm)
72
Floquet-state energy vs.
MW amplitude FMW
MW
(a) Bluest state=Trojan wave packet
(b) Red state
= Anti-Trojan WP
Phase
reversed
NDWP consists of a few states
Spatially well defined
)cos(1
2
1 2 txFx
H = Rotating frame ()&
Rotating-wave approximation
(a.u.)
QM representation of NDWP
0 50 100 150
0 1 2 3 4 5-20
-15
-10
-5
0
5
10
7669
75707471
73
En
erg
y (
GH
z)
MW amplitude F (V/cm)
72
n
65
66
67
68
69
70
71
72
73
74
75
76
77
78
Relative time delay (ps)
HC
P io
niz
ati
on
sig
nal
(arb
. u
nit
s)
@17.5GHz MW
Typical ionization signal of NDWP
Energies of two coupled states by a resonant coherent field
En
erg
y
-
+
electric dipole aligned
opposite to a static field
-
+
dipole aligned to the field
corresponding
classical picture
Ene
rgy
Rabi frequency
2
2
plotted in a rotating frame (with angular freq. )
dressed-atom or
Floquet picture
oscillating dipole
Y-HCP
X-HCP
Dye-laser pulses
Li beam
(a)
e-
Signal
MCP
Y-microwave
X-microwave
Field ramp
(c)
x
y
Li+ e-
(1) (2) (3) (4)
(b)
t
Y-MW pulse X-MW pulse Dye-laser
pulses
Field-ionization ramp (1) (2) (3) (4)
(b)
MW cavity
0 50 100 1500.0
0.5
1.0
Ion
izati
on
pro
bab
ilit
y
t (ps)
(c)
0 50 100 1500.0
0.5
1.0
Ion
izati
on
pro
bab
ilit
y
t (ps)
(d)
Circular polarization
0 50 100 1500.0
0.5
1.0
Ion
iza
tio
n p
rob
ab
ilit
y
t (ps)
(e)
0 50 100 1500.0
0.5
1.0
Ion
iza
tio
n p
rob
ab
ilit
y
t (ps)
(f)
Linear polarization along X
0 50 100 1500.0
0.5
1.0
Ion
iza
tio
n p
rob
ab
ilit
y
t (ps)
0 50 100 1500.0
0.5
1.0
Ion
iza
tio
n p
rob
ab
ilit
y
t (ps)
(a)
Linear polarization along Y
Y direction X direction Excitation of circular NDWP
HM, J.H. Gurian, T.F. Gallagher, PRL 102, 103001 (2009).
0.9
1.0
1.1
1.2
65
70
75
80
85
I
Classical interpretation of NDWP
Nonlinear phase locking
n
0 p 2p
q
Motion of principal resonance island
t = 0 t = p/2
t = p t = 3p/2
+ q x
units) atomic(in )cos(1
2
2
txFx
pH =1D atom :
x p
0.9
1.0
1.1
1.2
65
70
75
80
85
I
n
0 p 2p
q q x
t
Larger F
-Resonance islands and chaotic sea in Poincaré surface of sections -
txFHH cos0 =x
pH
1
2
2
0 =1D atom:
global chaos=ionization
0.9
1.0
1.1
1.2
1.3
65
70
75
80
85
90
95
I
0 p 2p
q
n
stable against
ionization
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
60
65
70
75
80
85
90
95
100
I
n
q
0 p 2p
V/cm76.3 GHz92.47
V/cm88.1 GHz96.23
22
11
==
==
F
F
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
60
65
70
75
80
85
90
95
100
I
n
(c) MW2
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
60
65
70
75
80
85
90
95
100
I
q
0 p 2p
(d)
n
MW1
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
60
65
70
75
80
85
90
95
100
I
n
(b)
nCR=70
MW1&2
)cos()cos(1
22211
2
txFtxFx
pH =
-Common resonances (CR) in bichromatic field-
0=12 2 =
What is Rydberg atom?
What can we study with Rydberg atom?
Microwave multiphoton ionization of multilevel system
Population control of quantum ladder system
Dynamic autoresonance and multiphoton adiabatic rapid passage
Multilevel ladder system
f
i
g
g
i
f
(c)
A B
C
wavelength
2-photon
avoided
crossing
Intuitive and counterintuitive population transfer :
Multiphoton adiabatic rapid passage(MARP)
g
i
f
Three-level ladder
g
i
f
f
i
g
(a)
A B
C
Dressed-state energy vs.
wavelength
f|
i|
g|
ladder climbing (g to f)
Positive chirp pulse
CIPT
Energ
y
f
i
g
g
i
f
(b)
A B
C
one-photon
avoided
crossings
t
Negative chirp pulse
Intuitive population
transfer (IPT)
Population
transfer
Multi-level Rydberg ladder system in dressed-atom picture
( , |n=74 + 1 , |n=75 + 0 ( = 0 ), |n=76 - 1 , )
Multiphoton ARP
zero coupling
13141516171819
-15
-10
-5
0
5
10
79
76
75
74
8081
69 70
71
0V/cm
En
erg
y (
GH
z)
n (GHz) 13141516171819
-15
-10
-5
0
5
10
76
75
n (GHz)
En
erg
y (
GH
z)
Two- level zero coupling
13141516171819
0
5 73
74
75
77
78
72
76
75
80
79
70710.05V/cm
n (GHz)
MW field FMW=0.05 V/cm E
ner
gy
(G
Hz)
Ladder climbing/
climbing down
13141516171819
-15
-10
-5
0
5
10
79
76
75
74
8081
69 70
71
1V/cm
MW field FMW=1 V/cm
En
erg
y (
GH
z)
n (GHz)
Ladder climbing
(dynamic
autoresonance)
18.82
18.05
17.31
n=70
n=80
13.64
13.13 (GHz)
14.17
~ ~
n=71
n=72
n=73
n=79
n=78
n=77
Phase-locking of the electron motion throughout the chirp
0.00 3.14 6.28
0.9
1.0
1.1
1.2
65
70
75
80
I
q
n
19GHz
13GHz
19 18 17 16 15 14 13
68
70
72
74
76
78
80
n
Frequency (GHz)
n=68
n=71
n=70
F = 0.2 V/cm
+
+
t
EMW
+ +
Z
Phase-locking
throughout the chirp
19GHz
13GHz
0.00 3.14 6.28
0.9
1.0
1.1
65
70
75
I
q
F= 0.2V/cm, /2p =19.0GHz
n
Dynamic autoresonance B. Meerson and L. Friedland, PRA 41, 5233 (1990)
t
State-selective field
ionization
4 F ~ 1/16n (a.u.)
n
Li 2s 2p 3s 70p
Laser pulses
Li 70p
Field ramp
19GHz 13GHz
~ 500 ns
Chirped MW pulse
F70
F80
Time-resolved electron signal
t
n = 70 80
FMW
Ladder-climbing experiment (ex.) n=70 to n=80 population transfer
t (ns)
(a)
n
90 80 70
0.1
1.0
10
MW
fie
ld F
MW
(V
/cm
)
400 600 800 1000
n=70 n=80
Contour plot
darker area : larger population
100-% MW ionization
threshold
70
80
n
Energy levels
Resonance
frequency 1/n3
~13 GHz
~19 GHz
19GHz 13GHz (Voltage
controlled
oscillator)
t
Li 70p
pulsed field
raw data
0 1000 2000 3000 4000
Laser shots
S(
)
A
HCP
t
Boxcar gate
Ionization signal
#3 HCP ionization signal
n
MW Phase retrieval
sorted data
The electron remain phase-locked as the frequency is chirped !! ( robust )
#1 Instantaneous MW field
#2 Its derivative
Fast sampling scope
Detecting nondispersing wave packets during the chirp (Experiment)
-p p 0 S
( )
13.5GHz 15.5GHz 17.5GHz
-p p 0 -p p 0
13141516171819-1
0
1
2
3
4
5
6
7
8
9
71
70
80
73
74
75
77
78
72
76 75
79
En
erg
y (
GH
z)
n (GHz)
t (ns)
(a)
Final Rydberg-state population (n)
90 80 70
0.1
1.0
10
MW
fie
ld F
MW
(V
/cm
)
400 600 800 1000
n=70 n=80
Population transfer by a sequence of one-photon adiabatic rapid
passages (ARP)
18.83
18.05
17.31
n=70
n=80
13.63
13.12 (GHz)
14.17
~ ~
71
72
73
77
78
79
Radiation frequency must cover the entire internal
frequencies of the ladder system
(19 to 13 GHz for n = 70 to 80 Rydberg atom)
large chirp is required !!
n=70
n=80
Atomic internal frequency adiabatically follows
the radiation frequency (phase-locked)
Energy-level structures of Li and Na
(n-1)p
(n-1) l ns
np
(n+1)s n l
(n-2) l
(l 2)
Quantum defect : ds ~ 1.35
dp ~ 0.85
dd ~ 0.016
Na Li
(n-1) l
ns
(n+1)s
n l
(n-2) l
(l 1)
Quantum defect : ds ~ 0.4
dp ~ 0.05
dd ~ 0.002
(n-1)s (n-1)s
1314151617
0
5
10
15
20
25
30
60p
58p
59p
61s
60s
59s
Frequency (GHz)
0.5 V/cm
58s
Dressed Na s & p states and a series of ARP’s
16.517.017.518.0
-2
-1
0
1
2
3
58s
60s59p
59s
57p
58p
Frequency (GHz)
0.06 V/cm
58s
16.517.017.518.0
-2
-1
0
1
2
3
60s59p
59s
57p
58p
Frequency (GHz)
0.0 V/cm
58s
Dynamic
Autoresonace
(Non-dispersing
wave packet)
No p-state population !?
(a)
(b)
(c)
0.1
1
10
0.1
1
10
0.1
1
10
58s
~65s
~63s
~62s
(d)
(e)
t(ns)
400 600 800
0.1
1
10
0.1
1
10
~61s
~60s
Mic
row
ave
fiel
d (
V/c
m)
t(ns)
400 600 800
Experimental results of Na population transfer through sp ladder
1314151617
0
5
10
15
20
25
30
60p
58p
59p
61s
60s
59s En
erg
y (
GH
z)
Frequency (GHz)
(c) 0.5 V/cm
58s
Population transfer via a single multiphoton ARP
13141516171819
-20
-15
-10
-5
0
5
1V/cm
n (GHz)
En
erg
y (
GH
z)
We want to know if this is true..
74
80
77
71
75
70
13141516171819
-20
-15
-10
-5
0
5
1.9V/cm
80
72
74
80
n (GHz)
Li 2s 2p 3s np
19GHz 13GHz
> 500 ns
t
Laser pulses
State-selective field
ionization
Li np
4 F ~ 1/16n (a.u.)
n
Time-resolved electron signal
Field ramp Fi
Chirped MW pulse
Fj
t n = i j
FMW
t
gate (Gaussian/
Square )
Frequency n, pulse width t, shape, chirp (width n, rate, direction), and FMW of
the MW pulse are cotrollable (MW pulse shaping is easy...)
Multiphoton ARP experiment (ex.) n=70 to n=80 population transfer
Population transfer a single multiphoton ARP (MARP)
n=70
n=80
~ ~
71
72
73
77
78
79
-595
-594
-593
-592
n=70
n=80
10
n (GHz)
En
erg
y (
GH
z)
16.6 16.5 16.4 16.3 16.2
~16.4
~16.4
~16.4
~16.4
~16.4
~16.4
~16.4 (GHz)
~16.4
~16.4
Selective excitation of the target avoided
crossing !!
Only a small frequency chirp is required !!
Good for optical pulse shaping
16.4GHz
Final Rydberg-state population (n)
85 80 75 70
0.1
1.0
10
MW
am
pli
tud
e F
MW
(V
/cm
)
t (ns)
600 700 800 900
n=70 n=80
Li 2s 2p 3s np
8 13 13 19 (GHz)
t
Laser pulses
Li np Field ramp
Two Chirped MW pulses
t
Doble-pulse experiment : transition via a sequential drive of two MARPs
Two gates
13141516171819
-20
-15
-10
-5
0
5
1V/cm
82
76
76
71
For example, 8276 71
Can we transfer the population largely with a
sequence of multiphton ARPs?
200 300
10
20
30
40
50 2 :79->scanned
14.8 GHz
200 300
10
20
30
40
50 1 :85->78->scanned
14.8 GHz
Double-pulse experiments (n=85 ~78 ~ 74)
n=79
n=85
~78
?
Summary
Population control of Rydberg ladder system has been demonstrated
both by means of dynamic autoresonance and by driving MARP
NDWP plays an important role in MW ionization around =1 region
acknowledgement
T.F. Gallagher@UVa