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