AAM

OP

2011

-201

2 2

012-

01-1

81

Ion

tra

ps

•Tr

app

ing

of c

har

ged

par

ticle

s in

ele

ctro

mag

net

ic

field

s•

Dyn

amic

s o

f tra

pp

ed io

ns

•A

pp

licat

ion

s to

nu

clea

r p

hys

ics

and

QED

•Th

e Pa

ul t

rap

•La

ser

coo

ling

, sym

pat

het

ic c

oo

ling

, op

tical

clo

cks

•C

ou

lom

b c

ryst

als

and

mo

lecu

lar

ion

s

AAM

OP

2011

-201

2 2

012-

01-1

82

The

Pen

nin

g t

rap

AAM

OP

2011

-201

2 2

012-

01-1

83

The

Pen

nin

g t

rap

AAM

OP

2011

-201

2 2

012-

01-1

84

Cyc

lotr

on

osc

illat

ion

:2

4 M

Hz

Axi

al o

scill

atio

n:

360

kH

zM

agn

etro

n o

scill

atio

n:

2.5

kH

z

•C

har

ged

par

ticle

s st

ore

d w

ith a

su

per

po

sitio

n o

f a m

agn

etic

fiel

d a

nd

a

stat

ic e

lect

ric

field

. •

B fi

eld

forc

es th

e p

artic

le in

to a

cyc

lotr

on

mo

tion

•C

on

finem

ent

in t

he

B-fi

eld

dir

ectio

n b

y el

ectr

od

es c

reat

ing

a e

lect

rost

atic

p

ote

ntia

l min

imu

m

•Io

n m

otio

n in

thre

e d

egre

es o

f fre

edo

m: t

hre

e u

nco

up

led

har

mo

nic

osc

illat

ion

s (r

edu

ced

cyc

lotr

on

, axi

al, a

nd

mag

net

ron

osc

illat

ion

The

Pen

nin

g t

rap

AAM

OP

2011

-201

2 2

012-

01-1

85

Tim

e-o

f-flig

ht

sig

nal

fro

m a

Pen

nin

g t

rap

AAM

OP

2011

-201

2 2

012-

01-1

86

Imag

e ch

arg

e in

du

ced

cu

rren

t

In g

ener

al th

e re

sist

or

R is

rep

lace

d b

y a

freq

uen

cy

reso

nan

t RL

C-c

ircu

it w

ith a

hig

h Q

AAM

OP

2011

-201

2 2

012-

01-1

87

Co

re o

f a P

enn

ing

tra

p

AAM

OP

2011

-201

2 2

012-

01-1

88

g-F

acto

r m

easu

rem

ents

in a

ser

ies

of e

lem

ents

up

to

U9

1+

low

-Z→

elec

tro

n m

ass

me

med

ium

-Z→

fine-

stru

ctu

re c

on

stan

t a

hig

h-Z

→te

st o

f bo

un

d-s

tate

QED

Bo

un

d-s

tate

QED

an

d fu

nd

amen

tal

con

stan

ts:

AAM

OP

2011

-201

2 2

012-

01-1

89

Mas

s m

easu

rem

ents

det

erm

ine

the

bin

din

g e

ner

gy

of a

sys

tem

AAM

OP

2011

-201

2 2

012-

01-1

810

Ever

y fie

ld r

equ

ires

diff

eren

t ac

cura

cy

AAM

OP

2011

-201

2 2

012-

01-1

811

Dev

elo

pm

ent

of a

ccu

racy

in m

ass

spec

tro

sco

py

AAM

OP

2011

-201

2 2

012-

01-1

812

The

g fa

cto

r o

f a b

ou

nd

par

ticle

Ener

gy

split

ting

bet

wee

n le

vels

Co

rrec

tion

s d

ue

to Q

ED

AAM

OP

2011

-201

2 2

012-

01-1

813

Co

ntr

ibu

tion

s to

th

e g

fact

or

AAM

OP

2011

-201

2 2

012-

01-1

814

Larm

or

and

cyc

lotr

on

freq

uen

cyLa

rmo

rfr

equ

ency

: sp

in fl

ip fr

equ

ency

AAM

OP

2011

-201

2 2

012-

01-1

815B

MQ ion

c=

ωB eQ

Mmg

ione

cLJ

⋅⋅

=ωω

2

Bme

ge

JL

2=

ωLarm

orpr

eces

sion

freq

uenc

yof

the

boun

del

ectr

onC

yclo

tron

freq

uenc

yof

th

etr

appe

dio

n

mea

sure

-m

ent

mea

sure

-m

ent

exte

rnal

inpu

tpa

ram

eter

exte

rnal

inpu

tpa

ram

eter

g-F

acto

r o

f th

e b

ou

nd

ele

ctro

n in

HC

I

g J(12C

5+) =

2.0

01 0

41 5

90 1

8 (3

) th

eore

tical

valu

eg J(12

C5+

) = 2

.001

041

596

4 (1

0)(4

4) m

easu

rem

ent

Erro

r bud

get:

δg/g

= 5

·10-1

0 ex

p. sy

stem

atic

sand

stat

istic

sδg

/g =

2·1

0-9 k

now

ledg

eof

ele

ctro

nm

ass(

Van

Dyc

k19

95)

g J(12C

5+) =

2.0

01 0

41 5

90 1

8 (3

) th

eore

tical

valu

eg J(12

C5+

) = 2

.001

041

596

4 (1

0)(4

4) m

easu

rem

ent

Erro

r bud

get:

δg/g

= 5

·10-1

0 ex

p. sy

stem

atic

sand

stat

istic

sδg

/g =

2·1

0-9 k

now

ledg

eof

ele

ctro

nm

ass(

Van

Dyc

k19

95)

AAM

OP

2011

-201

2 2

012-

01-1

816

Do

ub

le P

enn

ing

tra

ps

for

g fa

cto

r

AAM

OP

2011

-201

2 2

012-

01-1

817

Spin

flip

s o

f sin

gle

ele

ctro

ns

AAM

OP

2011

-201

2 2

012-

01-1

818

Spin

flip

pro

bab

ility

an

d a

nal

ysis

AAM

OP

2011

-201

2 2

012-

01-1

819

ge=

2.0

0231

9304

3737

(82)

g

C=

2.00

1041

596

(1)(

1)(4

)g

0 =

2.00

0047

0254

(15)

(44)

Fro

m g

Can

d g

Ofa

cto

r th

e cu

rren

tly m

ost

pre

cise

val

ue

of t

he

elec

tro

n’s

mas

s w

as d

eriv

ed:

me=

0.00

0549

5799

096(

4) u

(to

be

com

par

ed t

o t

he

fou

r-tim

es le

ss p

reci

se C

OD

ATA

val

ue)

me=

0.00

0549

5799

110(

12) u

Inve

stig

atin

g io

ns

with

hig

h n

ucl

ear

char

ge

Z w

ou

ld a

llow

for

anal

tern

ativ

e d

eter

min

atio

n o

f th

e fin

e-st

ruct

ure

co

nst

ant

sin

ce t

he

g fa

cto

r o

f th

e g

rou

nd

sta

te o

f a h

ydro

gen

-like

ion

to

lo

wes

t o

rder

s is

giv

en b

y

Nu

clea

r g

rou

nd

-sta

te p

rop

ertie

s su

ch a

s ra

diu

s, n

ucl

ear

po

lari

zatio

n, o

r (in

cas

e o

f nu

clei

with

sp

in) n

ucl

ear

mag

net

ic m

om

ents

can

be

det

erm

ined

for

stab

le a

nd

lon

g-li

ved

nu

clei

.

An

acc

ura

cy o

f δM

/M=

10-1

0fo

r an

ion

with

mas

s A

= 2

00 c

orr

esp

on

ds

to a

mea

sure

men

t o

f its

ele

ctro

nic

bin

din

g e

ner

gy

to δ

E=

20

eV.

AAM

OP

2011

-201

2 2

012-

01-1

820

Rece

nt

resu

lts w

ith 2

8Si

13

+

AAM

OP

2011

-201

2 2

012-

01-1

821

The

g fa

cto

r o

f a fr

ee p

roto

n

Mag

net

ic m

om

ent

invo

lved

is t

hre

e o

rder

s o

f m

agn

itud

e sm

alle

r: F

req

uen

cy s

hift

har

d t

o m

easu

re

AAM

OP

2011

-201

2 2

012-

01-1

822

Hig

h g

rad

ien

t an

alys

is t

rap

•A

larg

e m

agn

etic

fiel

d a

nis

otr

op

y m

agn

ifies

th

e en

erg

y sp

littin

g•

Phas

e-se

nsi

tive

det

ectio

n o

f cyc

lotr

on

mo

tion

en

han

ces

accu

racy

AAM

OP

2011

-201

2 2

012-

01-1

823

S. U

lmer

et a

l., P

hys.

Rev

. Let

t. 10

6, 2

5300

1 (2

011)

Spin

flip

pro

bab

ility

Co

mp

are

g-fa

cto

rs o

f pro

ton

an

d a

ntip

roto

n:

Test

of m

atte

r-an

timat

ter

sym

met

ry

AAM

OP

2011

-201

2 2

012-

01-1

824

Exp

erim

ent:

46

0.2

±4.6

eVTh

eory

:

46

4.2

6±0

.5 e

V

2005

2000

1996

1991

SE

VP

nuclear

size

hig

her-

ord

er

1020

4060

8010

0

10-4

10-3

10-2

10-1

1s Lamb Shift , ΔE / Z4 [meV]

nucl

ear c

harg

e nu

mbe

r, Z

The

HIT

RAP

pro

ject

AAM

OP

2011

-201

2 2

012-

01-1

825

Co

olin

g s

chem

e fo

r H

CI i

n H

ITRA

P

AAM

OP

2011

-201

2 2

012-

01-1

826

Co

olin

g s

chem

e fo

r H

CI i

n H

ITRA

P

AAM

OP

2011

-201

2 2

012-

01-1

827

•Li

gh

t fo

rce

isd

ue

to m

ulti

ple

ph

oto

nsc

atte

rin

g

•In

tera

ctio

n w

itha

dir

ecte

dla

ser

bea

mtr

ansf

ers

a m

om

entu

mh k

for

each

abso

rbed

ph

oto

n

•Sp

on

tan

eou

sem

issi

on

isis

otr

op

ic: z

ero

net

mo

men

tum

tran

sfer

•Sp

on

tan

teo

us

forc

e is

limite

db

ysa

tura

tion

Lase

r co

olin

g

AAM

OP

2011

-201

2 2

012-

01-1

828

v

F+F-

2 co

unte

rpro

paga

ting

beam

s, t

uned

belo

wre

sona

nce

(δ<0

).

Dop

pler

shi

ftδ v

=kv

brin

gs1

beam

clos

erto

res

onan

ce:

Capt

ure

in v

eloc

ity

spac

e.

Lith

ium

: vc=

4m/s

; 13.

3mK

Mag

net

o-o

ptic

altr

ap(M

OT)

1D-t

oy m

odel

of a

(J=0→

J‘=1

)-M

OT

Zeem

an-s

hift

δby

B-fi

eld

grad

ient

adds

posi

tion

depe

nden

tde

tuni

ng: R

esto

ring

forc

e

Cool

ing

and

trap

ping

in p

osit

ion

spac

e

Net

for

ce: (

)(

)z

vF

zv

Fz

vF

κη

δδ

−−

≈→

+−

−+

+)

,(

),

(

Cooling

limit:

phot

onmom

entu

mhk

futh

erco

olin

gto

ward

sBE

C: e

vapo

rati

on

AAM

OP

2011

-201

2 2

012-

01-1

829

Lin

ear

Pau

l tra

p

2r0

2re

RF is

app

lied

to a

ll el

ectr

od

es→

con

finem

enti

n r

adia

l dir

ectio

nD

C is

app

lied

to e

nd

cap

elec

tro

des

→co

nfin

emen

tin

z-d

irec

tion

AAM

OP

2011

-201

2 2

012-

01-1

830

Lin

ear

Pau

l tra

p

AAM

OP

2011

-201

2 2

012-

01-1

831

Lin

ear

Pau

l tra

p

AAM

OP

2011

-201

2 2

012-

01-1

832

The

rota

ting

po

ten

tial i

n t

he

Pau

l tra

p

AAM

OP

2011

-201

2 2

012-

01-1

833

Mo

tion

in t

he

pse

ud

op

ote

ntia

l

AAM

OP

2011

-201

2 2

012-

01-1

834

Slo

win

g d

ow

n a

tom

s w

ith li

gh

tLi

gh

t fo

rce

du

eto

ph

oto

nsc

atte

rin

g

•In

tera

ctio

n w

itha

lase

rb

eam

tran

sfer

sa

mo

men

tumh k

for

each

abso

rbed

ph

oto

n

•Sp

on

tan

eou

sem

issi

on

isis

otr

op

ic→

zero

net

mo

men

tum

tran

sfer

•Sp

on

tan

teo

us

forc

e is

limite

db

ysa

tura

tion

(max

imu

mra

te d

ue

to

lifet

ime)

iso

tro

pic

em

issi

on

of

n p

ho

ton

s

lase

rb

eam

mo

men

tum

tran

sfer

n·hk

AAM

OP

2011

-201

2 2

012-

01-1

835

Op

tical

mo

lass

esre

d d

etu

nin

gvelo

city

of

ato

m

•A

tom

s m

ovi

ng

tow

ard

the

lase

rex

per

ien

cea

forc

e ro

ug

hly

pro

po

rtio

nal

to th

eir

velo

city

: fri

ctio

n•

Seve

rall

aser

bea

ms

gen

erat

ea

den

se, v

isco

us

ato

mcl

ou

d

AAM

OP

2011

-201

2 2

012-

01-1

836

v

F+F-

2 co

un

terp

rop

agat

ing

bea

ms,

tun

edb

elo

wre

son

ance

(δ<0

).

Do

pp

ler

shiftδ v

=kv

bri

ng

s1

bea

mcl

ose

rto

re

son

ance

:

Cap

ture

in v

elo

city

spac

e.

Lith

ium

: vc=

4m

/s; 1

3.3

mK

Mag

net

o-o

ptic

altr

ap(M

OT)

Zee

man

-sh

iftδ

by

B-fi

eld

gra

die

nt

add

sp

osi

tion

dep

end

entd

etu

nin

g: R

esto

rin

gfo

rce

Co

olin

gan

d tr

app

ing

in p

osi

tion

spac

e

Net

forc

e:

()

()

zv

Fz

vF

zv

Fκ

ηδ

δ−

−≈

→+

−−

++

),

()

,(

Co

olin

glim

it: p

ho

ton

mo

men

tumhk

futh

erco

olin

gto

war

ds

BEC

: eva

po

ratio

n