Transcript PowerPoint 簡報

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!
Introduction: Why need probe atoms?
 Temperature Measurement
 Monitoring the C.M. motion!
 Watching the time evolution of cold clouds!
I will com back
to this later!
g
Evaporative cooling
process!
BEC formation!
1 ms
20 ms
Studying the dynamics and many more …
 Condensate Excitation (m=0 mode)
 Cold Collisions
axial z
radial r 5 ms
55 ms
55
axial size
Cloud Width (A.U.)
50
~ 2.5 mm
43.77Hz
45
excitation frequency
e ~ 43.2 Hz
40
42.61Hz
http://www.iop.org/EJ/mmedia/1367-2630/6/1/146/movie2.avi
35
radial size
30
0
10
20
30
40
50
60
Niels Kjærgaard et al., New J. Phys. 6, 146
(2004).
Time (ms)
Fluorescence and absorption!
All the measurements are based on atom-light interactions!
However, they are mostly destructive and harmful to the
atoms!
Light focusing and defocusing
by a small ball (linear optics)
n0: linear refractive index
R: radius
: light detuning (to the
resonance frequency!)
A small uniform ball:
“weak” incident light
f
Effective focal length: f 
if R > 0,
f < 0,
f > 0,
f  ,
n0 > 1,  < 0
n0 < 1,  > 0
n0 = 1,  = 0
R
2(n0 1)
Could be tens of microns!
n0 is independent of light intensity,
but depends on ball parameters !
Optical lensing effect (1)
A small ball made by cold atoms in high density!
n >1013 atoms/cm3!!
Absorption imaging:
n0 > 1 for red-detuned probe light
probe laser
f
Imaging lens
CCD
di
do
z=0
zc
Optical lensing effect (2)
1.5
1.5
1
1.2
1
0.5
0.5
0
0
-0.5
-0.2
-0.5
-0.2
1
Optical density
2
optical density
2
Opticall density
Optical density
false-color absorption images
0.8
0.6
0.4
0.2
0
-0.15
-0.1
-0.05
0
0.05
0.1
Vertical position (mm)
zc < di
vertical cut profiles
0.15
0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Vertical position (mm)
zc = di
0.2
-0.2
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
Vertical position (mm)
zc > di
0.15
0.2
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)
z
n(I)
I(x, y)
“intense” incident light
nonlinear coefficient of
refractive index
Alkaline gas:
n(I)=n0+n2I
Clear measurements on detuning
and polarization are still not
well established!
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.
cold atom Calorimetry!?
Optical lensing effect (3)
saturation intensity
Gaussian beam: I >> Is
CCD
Rb MOT
defocusing!
(ultracold atoms!)
Measure the nonlinear lensing effect:
Z-scan method
iris
Stryland et al., IEEE J. of Quantum Electronics 26, 760 (1990)
z0
lens
sample
detector
laser
laser intensity: I
-z
laser detuning: 
0
+z
d
For a saturable Kerr medium (3rd order nonlinearity), the refractive
index n(I) and absorption coefficient (I) are
n( I )  n n( I )
0
 (I ) 
0
1
I
,
and
I
s
n( I ) 
 Is (1 
Is
Is : saturation intensity
0: linear absorption coefficient
n2 : Kerr index,
: spontaneous decay rate
Na atoms
Rb atoms
Cs MOT
4 2
2
n I
2
1
I
Is
)
Sinha et al., Opt. Comm. 203, 427 (2002)
Chiao et al., JOSA 20, 2480 (2003).
Saffman et al., PRA 70, 013801 (2004).
Positive Lensing
positive lensing: sample works as a positive
lens! sample position: z, beam waist position: z = 0!
lens
sample
z>0
detector
laser
r
0
z
size

signal

lens
detector
sample
laser
z<0
r
0
z
A Gaussian beam produces an r-dependent refractive
index at each position z!
size

signal

Z-scan measurement in hot atoms
(heated Rb cell)
+/– 480 MHz to 85Rb F=3  F’=4 transition
I ~ 0.2 Is cw measurement
measured by photodiode!
0.25
0.8
0.6
Transmission
Transmission
0.2
0.4
0.2
negative lensing
0.15
0.1
0.05
positive lensing
0
-100
-50
0
50
Cell Position (mm)
open aperture
T~ 80 C
100
0
-100
-50
0
50
100
Cell Position (mm)
closed aperture
significant Doppler broadening!
Z-scan measurement in cold atoms
+/– 30 MHz to 87Rb F=2  F’=3 transition
15
Measured by CCD
at 70 s after MOT
turned off!
Compared the beam
size with and without
MOT atoms!
Size Deviation (%)
10
positive lensing
negative lensing
5
0
-5
-10
-15
-10
-5
0
5
MOT Position ( cm )
I ~ 10 Is , 3 s duration
3 * 10
+30MHz n0~1.1
MOT density ~ 1.11010 atoms/cm
MOT temperature ~ 300 K
10
-3
cm
10
10
-3
-30MHz n0 ~ 1.6 * 10 cm
no Doppler broadening!
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 …
CCD
probe beam 
Cs MOT
d
3
3
N

i  2 / 
n  n  i  1 
0
0
8 2 1 (2 /  ) 2
Stable intensity is
required!
.
N ~ 1010 atoms/cm3
 = 0.5 
Strauch et al., Opt. Commun. 145, 57 (1998)
Far-field diffraction pattern through
a cold atom cloud (2)
Rb clouds
probe beam:
size (1/e2 radius): 710 m
detuning: -50 MHz
red: d= 3 cm, N=5×106 atoms
n=1012 atoms/cm3
blue: d= 10 cm, N=5×106 atoms
n=1012 atoms/cm3
Simulation
25
green: d= 3 cm, N=4×105 atoms
n=1013 atoms/cm3
Residual Intensity (%)
20
15
10
5
0
-5
-10
-15
0
100
200
300
400
500
600
Raidial Position (micron)
700
800
Optical Diffraction from a 2D lattice
Lattice with periodicity in the two transverse
dimensions x and y!
Far-field diffraction pattern!
photorefractive crystal
Schwartz et al., Nature 446, 52 (2007)
Dynamics of optical lattice loading?
OL beam
patterned profile from
many mini-lenses while
atoms are trapped into
each 1D lattice potential?
probe beam
1. Switching on OL beams
in a MOT
2. Waiting for 
3. Probe on and detect
4. Possible to see patterned
profiles?
5. Allows to trace the density
distribution with ?
Rb MOT
OL beam
The second part was initially motivated by simply
making an interferometer for phase stabilization
in 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
n
n
y
x
U  Uo  [cos2 (kx x)  cos2 (ky y)  2cos(kx x)  cos(ky y)cos( )],
   x   y  phase difference.
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!
Top View
 = 0°
 = 90°
 =180°
Previous work on atomic tunneling in
1D optical lattice
1D optical lattice
+
gravity g
matter wave
interference
due to tunneling!
OL beam
Rb BEC
Tunneling probability
per oscillation:
P=exp(-2/82g),
: energy gap between
the ground state band
and the continuum
states!
OL beam
Anderson et al., Science 282, 1686 (1998)
Possibly applied to 2D optical lattice?
1D tube array!
2D optical lattice
+
gravity
“top view”
OL beam
Rb BEC
“3D view”
1. Matter wave Interference Atom Grating?
while tunneling out?
2. Matter wave interference under different ?
OL beam
Simulation Results
Yes! In theory!
g
g
g
g
 = 90°
 = 0°
Waiting for experiment to confirm!
Probe atoms by optical Interference!
(nondestructive and more sensitive)
Another application:
Spatial heterodyne imaging of cold atoms
I ( x)  I r  I p  2
Ir
Ip
Rb MOT
• two-beam detection
• possibly nondestructive
• high S/N ratio
I r I p cos[  2k x   ( x )]

 = 1-2

=phase difference
between the two beams!
position-dependent
phase shift: phase image
( x )
Kadlecek et al.,
Opt. Lett. 26, 137 (2001)
even better than the
phase contrast imaging!
In general, it requires a little complicated algorithm for phase-shift retrieval!
However, direct phase shift imaging is possible if   0, and  is stabilized
to /2!
We can do this as seen in the next page!
Adjustable Phase difference using a
Mach-Zehnder Interferometer (1)
 = 1-2 =phase difference
PD2
Block
1st-order
PZT
Mirror
I 2, 2
Brewster Plates
Laser
0th-order
Window
AO Modulator
PD3
BS I1,
1
Mirror
CCD
Brewster Plate
Controller
BS
PD1
VT
PZT
Controller
Driver
VR
 I T  I1  I 2  2
I1I 2 cos()
Tunable while with high phase stability!
Adjustable Phase difference using a
Mach-Zehnder Interferometer (2)
Phase stability of 0.2°(rms) is achieved!
L
2
(b)
VR
1
1
VT
0.8
L
 (degree)
Interference Signal (V)
1.2
180
0.6
0
0.4
-1
0.2
Interference Signal (V)
-180
Phase Difference (degree)
-120
-60
0
60
120
1.2
V
1
V
T
0.8
-63
63
0.6
0.4
 = -121
0.2
-2
0
(b)
R
121
0
0
100
200
300
400
Time (ms)
500
600
continuous sweep
0
500
1000
Time (ms)
1500
step-wise sweep
2000
One another application:
Phase-shifting Interferometry (PSI)
sample
I2
BS
Mirror
I1
light source
interferogram
I
T
( x, y) I1  I 2  2

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
moving for phase adjustment
I1I 2 cos [  ( x, y)]
Phase image
(x, y)
λ tan1( C-B )
optical phase difference (x, y) =
2π
A-B
Useful for 2D surface cold atoms imaging?
(Michelson type)
Li MOT with 108 atoms!
Conventional PSI
Silicone chip
GaAs substrate
top view
Iwai et al., Opt. Lett. 29, 2399 (2004)
fluorescence!
destructive!
possible for PSI?
Less destructive!
Folman et al., PRL 84, 4749 (2000)
Trap can leave on!
Direct diagnosis of wiring!
Phase-shifting Interferometry on cold atoms
(Mach-Zehnder type)
PD
BS
Mirror
CCD
Laser
BS
Mirror
BS
lens to image
the position right
after the cloud
atom cloud
Similar to the heterodyne method!
However, possible to mapping out other phase disturbances
other than pure density distribution, such as magnetic field
distribution …
Phase-shifting Interferometry on cold atoms
(Mach-Zehnder type)
Simulation:
Rb cloud
false color images
N ~ 5× 106 atoms
density ~1012
atoms/cm3
(a) =0
(b) =45
(c) =90
(d) =135
The probe laser has a radius of 710 m and –50 MHz detuning.
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