韓殿君中正大學 物理系

NDHU, Dec. 28, 2009

Probing Atoms with Light

Outline

• I will start by showing you the optical lensing effects in systems from cold to hot gases!• Some of the related topics, including the ongoing works and proposed ideas will be discussed subsequently!

In this talk,

Introduction: Why need probe atoms?

Watching the time evolution of cold clouds!

Temperature Measurement Monitoring the C.M. motion!

BEC formation!Evaporative cooling process!

1 ms 20 ms

g

I will com back to this later!

Studying the dynamics and many more … Condensate Excitation (m=0 mode)

30

35

40

45

50

55

0 10 20 30 40 50 60

Clo

ud W

idth

(A.U

.)

Time (ms)

42.61Hz

43.77Hz

5 ms 55 ms

radial size

axial size

excitation frequencye ~ 43.2 Hz

radial r

axial z Cold Collisions

~ 2.5 mm

http://www.iop.org/EJ/mmedia/1367-2630/6/1/146/movie2.avi

Niels Kjærgaard et al., New J. Phys. 6, 146 (2004).

All the measurements are based on atom-light interactions!However, they are mostly destructive and harmful to the atoms!

Fluorescence and absorption!

Light focusing and defocusing by a small ball (linear optics)

f

02( 1)R

nf

A small uniform ball:

Effective focal length:

n0: linear refractive indexR: radius: light detuning (to the resonance frequency!)

if R > 0, f < 0, n0 > 1, < 0 f > 0, n0 < 1, > 0 f , n0 = 1, = 0

“weak” incident light

n0 is independent of light intensity, but depends on ball parameters !

Could be tens of microns!

Optical lensing effect (1)A small ball made by cold atoms in high density!

Imaging lensCCD

Absorption imaging:

dodi

f

z = 0 zc

n0 > 1 for red-detuned probe lightn >1013 atoms/cm3!!

probe laser

Optical lensing effect (2)

-0.5

0

0.5

1

1.5

2

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Optic

all de

nsity

Vertical position (mm)

zc = di

-0.5

0

0.5

1

1.5

2

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Optic

al de

nsity

Vertical position (mm)

zc < di

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2Vertical position (mm)

optic

al d

ensi

ty

Opt

ical

den

sity

zc > divertical cut profiles

false-color absorption images

The first part of the following works shown here began by a coincident conversation with my colleague Prof. T.H. Wei . . .

Light focusing and defocusing by uniform medium (nonlinear

optics)

“intense” incident light

n(I)I(x, y)

z

Alkaline gas:

n(I)=n0+n2I

nonlinear coefficient of refractive index

We are interested in the two mechanisms:

1. Saturated atomic absorption: response time 10-8 sec, n2 ~ 10-

7 cm2/W,

2. Thermal effects: response time 10-3 sec, n2 ~ 10-6 cm2/W.

Clear measurements on detuningand polarization are still not well established!

cold atom Calorimetry!?

Optical lensing effect (3)

CCD

Rb MOT(ultracold atoms!)

Gaussian beam: I >> Issaturation intensity

defocusing!

Measure the nonlinear lensing effect:Z-scan methodStryland et al., IEEE J. of Quantum Electronics 26, 760 (1990)

Na atoms Sinha et al., Opt. Comm. 203, 427 (2002).Rb atoms Chiao et al., JOSA 20, 2480 (2003). Cs MOT Saffman et al., PRA 70, 013801 (2004).

For a saturable Kerr medium (3rd order nonlinearity), the refractive index n(I) and absorption coefficient (I) are

Is : saturation intensity0: linear absorption coefficientn2 : Kerr index, : spontaneous decay rate

sample

z0

-z d+z0

detectorlens

laser

laser intensity: Ilaser detuning:

2( )1

s

n In I

II

0( ) ,1

s

II

I

0( ) ( )n I n n I and

24(1 )

2sI Is

iris

sample

z0

detectorlens

laser

sample

z0

detectorlens

laser

positive lensing: sample works as a positive lens!z > 0

z < 0

size signal

size signal

Positive Lensingsample position: z, beam waist position: z = 0!

A Gaussian beam produces an r-dependent refractive index at each position z!

r

r

Z-scan measurement in hot atoms(heated Rb cell)

closed aperture

0

0.05

0.1

0.15

0.2

0.25

-100 -50 0 50 100Tr

ansm

issi

on

Cell Position (mm)

0

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0.8

-100 -50 0 50 100

Tran

smis

sion

Cell Position (mm)

+/– 480 MHz to 85Rb F=3 F’=4 transitionI ~ 0.2 Is cw measurement

open aperture

measured by photodiode!

T~ 80 C significant Doppler broadening!

negative lensing

positive lensing

Z-scan measurement in cold atoms

-15

-10

-5

0

5

10

15

-10 -5 0 5 10

+30MHz n0~1.1 * 1010cm-3-30MHz n0 ~ 1.6 * 1010cm-3

Siz

e D

evia

tion

(%)

MOT Position ( cm )

I ~ 10 Is , 3 s durationMOT density ~ 1.11010 atoms/cm3

MOT temperature ~ 300 K

+/– 30 MHz to 87Rb F=2 F’=3 transition

Measured by CCDat 70 s after MOT turned off!

no Doppler broadening!

negative lensingpositive lensing

Compared the beamsize with and withoutMOT atoms!

Probe atoms by optical diffraction!(depending on refraction! less destructive!)

Far-field diffraction pattern through a cold atom cloud (1)

• Single beam detection• Probe beam size larger than cloud size• Allows to measure the cloud parameters, such as density distribution …

Strauch et al., Opt. Commun. 145, 57 (1998)

3

0 0 2 23 2 /1 .8 1 (2 / )N in n i

N ~ 1010 atoms/cm3

= 0.5

Cs MOTprobe beam

CCD

Stable intensity is required!

d

-15

-10

-5

0

5

10

15

20

25

0 100 200 300 400 500 600 700 800

Res

idua

l Int

ensi

ty (%

)

Raidial Position (micron)

probe beam: size (1/e2 radius): 710 m detuning: -50 MHz

red: d= 3 cm, N=5×106 atoms n=1012 atoms/cm3

Far-field diffraction pattern through a cold atom cloud (2)

blue: d= 10 cm, N=5×106 atoms n=1012 atoms/cm3

green: d= 3 cm, N=4×105 atoms n=1013 atoms/cm3

Simulation

Rb clouds

Optical Diffraction from a 2D lattice

Lattice with periodicity in the two transverse dimensions x and y!

Schwartz et al., Nature 446, 52 (2007)

Far-field diffraction pattern!photorefractive crystal

Dynamics of optical lattice loading?

Rb MOT

OL beam

OL beam

1. Switching on OL beams in a MOT2. Waiting for 3. Probe on and detect4. Possible to see patterned profiles?5. Allows to trace the density distribution with ?

probe beam

patterned profile from many mini-lenses while atoms are trapped into each 1D lattice potential?

The second part was initially motivated by simply making an interferometer for phase stabilizationin order to construct a 2D/3D optical lattice.

It seems we can do more and do better and do more . . .

2D optical lattice: two dimensional optical standing

wave

x y x y2 2 [cos ( ) cos ( ) 2cos( ) cos( )cos( )],oU U k x k y k x k y

phase difference.x y

xy

The phase difference locking scheme shown above can be directly applied to the 2D OL by injecting the locking beam into the OL!

2D optical lattice configuration

Lattice configuration changes while varies!

= 90° =180° = 0°

Top View

Previous work on atomic tunneling in 1D optical lattice

Rb BEC

OL beam

OL beam

1D optical lattice + gravity g

matter wave interferencedue to tunneling!

Anderson et al., Science 282, 1686 (1998)

Tunneling probabilityper oscillation:

P=exp(-2/82g),: energy gap between the ground state band and the continuum states!

Possibly applied to 2D optical lattice?

Rb BEC

OL beam

OL beam

2D optical lattice + gravity

1. Matter wave Interference while tunneling out?2. Matter wave interference under different ?

1D tube array!

Atom Grating?

“top view”“3D view”

Simulation ResultsYes! In theory!

= 90° = 0°

g

gg

g

Waiting for experiment to confirm!

Probe atoms by optical Interference! (nondestructive and more sensitive)

Another application:Spatial heterodyne imaging of cold

atoms

• two-beam detection• possibly nondestructive• high S/N ratio

( ) 2 cos[ 2 ( )]r p r pxI x I I I I k x

( )x

position-dependent phase shift: phase image

In general, it requires a little complicated algorithm for phase-shift retrieval!

Ir

Ip

Rb MOT

We can do this as seen in the next page!

= 1-2 =phase difference between the two beams!

even better than the phase contrast imaging!

However, direct phase shift imaging is possible if 0, and is stabilized to /2!

Kadlecek et al., Opt. Lett. 26, 137 (2001)

Adjustable Phase difference using a Mach-Zehnder Interferometer (1)PZT

PD1

Brewster Plates

BS BS

Laser

Mirror

MirrorBrewster Plate Controller

PZT Controller

AO Modulator

PD2

PD3

Block

Window

CCD0th-order

1st-order

VR

Driver

Tunable while with high phase stability!

2 cos( )T 1 2 1 2I I I I I

VT

I2, 2

I1, 1

= 1-2 =phase difference

Adjustable Phase difference using a Mach-Zehnder Interferometer (2)

0

0.2

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1

1.2

-2

-1

0

1

2

0 100 200 300 400 500 600

-180 -120 -60 0 60 120 180

Time (ms)

Phase Difference (degree)

L (degree)

Inte

rfere

nce

Sig

nal (

V)

L

VR

VT

(b)

0

0.2

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1.2

0 500 1000 1500 2000

Inte

rfere

nce

Sig

nal (

V)

Time (ms)

VR

VT

(b)

= -121

-63 63

121

continuous sweep step-wise sweep

Phase stability of 0.2°(rms) is achieved!

One another application:Phase-shifting Interferometry (PSI)

BS Mirror

light source

sample

interferogram moving for phase adjustment

optical phase difference (x, y) =

TI ( , ) 2 cos [ ( , )]1 2 1 2x y I I I I x y

C-B1λ tan ( )2π A-B

I1

I2

Phase image(x, y)

minimum 3 frames required!

• Fast measurement allowed• High longitudinal accuracy• Offset effects from the detected signal are cancelled out by subtraction• Gain effects are eliminated by taking the ratio

Useful for 2D surface cold atoms imaging?

(Michelson type)

Folman et al., PRL 84, 4749 (2000)

fluorescence! destructive!

Iwai et al., Opt. Lett. 29, 2399 (2004)

Silicone chip

Li MOT with 108 atoms!Conventional PSI

possible for PSI? Less destructive! Trap can leave on! Direct diagnosis of wiring!

GaAs substrate

top view

Phase-shifting Interferometry on cold atoms(Mach-Zehnder type)

CCD

PD

BS

BS

Laser

Mirror

Mirror

BS

atom cloud

lens to image the position rightafter the cloud

Similar to the heterodyne method!However, possible to mapping out other phase disturbances other than pure density distribution, such as magnetic field distribution …

(a) =0

Phase-shifting Interferometry on cold atoms(Mach-Zehnder type)density ~1012 atoms/cm3

N ~ 5× 106 atoms

The probe laser has a radius of 710 m and –50 MHz detuning.

(d) =135 (c) =90

(b) =45

Rb cloudSimulation:false color images

Acknowledgements

nonlinear optical refraction and absorption of atoms 林志杰 (Rb cell) 康振方 (Rb cell) 吳旭昇 (Rb cell) 陳致融 (Rb MOT) 黃上瑜 (numerical simulation) 黃智遠 (Cs cell) 魏台輝 (collaborator)phase difference adjustment, stabilization, and imaging 蕭博文 顧子平atom tunneling 吳欣澤 丁威志