韓殿君 中正大學 物理系
DESCRIPTION
Probing Atoms with Light. 韓殿君 中正大學 物理系. NDHU, Dec. 28, 2009. Outline. In this talk,. 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!. - PowerPoint PPT PresentationTRANSCRIPT
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
0.2
0.4
0.6
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
0.4
0.6
0.8
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
0.4
0.6
0.8
1
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