advanced experimental techniques ultracold atoms and...
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Advanced Experimental Techniques
Ultracold atoms and molecules Steven Knoop
VU, June 2014
1
Ultracold atoms
atom trap: magnetic trap or
optical dipole trap
BEC
Bose-Einstein condensation
laser cooling
evaporative cooling
Temperature: nK – mK Atom number: up to 108
Density: up to 1014 cm-3 (air 1019 cm-3) 2
LevT lab, Innsbruck 3
Overview of lectures
• Lecture 1:
– Laser cooling of neutral atoms
– Trapping of neutral atoms
• Lecture 2:
– Evaporative cooling
– Bose-Einstein condensation (BEC)
• Lecture 3:
– (Ultra)cold molecules
– Laser cooling of molecules
4 + labtour
http://arxiv.org/abs/1212.4108
5
Lecture 1
Laser cooling of neutral atoms
Trapping of neutral atoms
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Atomic level structure Group I, alkali-metal atoms
ground state: (closed shells)+ns first excited state: (closed shells)+np
n2S1/2
n2P1/2
n2P3/2
D2 D1
S=1/2 L=0
J=1/2 F=I-1/2, I+1/2
I
n2S+1LJ
S=1/2 L=1
J=1/2, 3/2 F=|I-3/2|, ..., I+3/2 F=I-1/2, I+1/2 I
fine-splitting hyperfine-splitting
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fine-structure hyperfine-structure
Zeeman effect:
Paschen-Bach
BmgE BFF m
MHz/G 4.1hBm
87Rb
Zeeman
D2
8
Light-atom interaction
g
e
1
3sat3
hcI
E 2
c
Inz
I
d
d
2
3 2
m -1 0 1
+ -
Frequency, wavelength, linewidth and lifetime
polarization
Saturation intensity Optical cross section
Beer’s law 9
Laser cooling and trapping
magneto-optical trap (MOT)
Zeeman slower
atomic beam source
Chu Cohen-Tannoudji Phillips
Nobelprize 1997
Raab et al, PRL 1987 Phillips et al, PRL 1982
Doppler effect
g
e
Zeeman effect
g
e
B
10
Radiation pressure atomic beam
source
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Radiation pressure atomic beam
source
rate) g(scatterinmomentum)(photon scatt F
3sat3
hcI
2scattscatt kkRF
2
maxmax
M
k
M
Fa
0
12
2412 22
sat
satscatt
II
IIR
1
Zeeman slower az2vv 22
0
Zeeman slower
atomic beam source
max
2
00
2
v
aL
2/1
0
0 1vv
L
zz
v)(B
0 kzB
m
bias
21
0
0 1 BL
zBzB
/
B
hB
m0
0
v
0bias m BB
Zeeman effect
g
e
B
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Zeeman slower
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He* lab, Amsterdam
Optical molasses
Doppler effect
g
e
vv2vv scatt0scatt0scattmolasses
-k
FkFkFF
22sat
2scatt
21
242
I
Ik
Fk
00
friction force-> molasses
15 red-detuned
Doppler cooling limit
2
21
4
2
TkB
2
DBTk2
spontspontabsabs FFFFF
Doppler temperature
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Example: Na MHz 102 K 240 mDT
randow walk
Magneto-optical trap
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Magneto-optical trap
zk
zF
kF
βzωkFβzωkωFF
v2v2
vv
0
scattscatt
0scatt0scattMOT
z
BB
d
d
m
friction force-> molasses
restoring force -> trap 18
Loading schemes
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• background gas • vapor cell (Monroe et al PRL 1990) • very simple • “high” background pressure
(limited lifetime and atom number)
• slow beam
• Zeeman slower • 2D-MOT • another MOT Zeeman slower
MOT
Fluoresence imaging
22
sat
satscatt
412
II
IINR
NaLi lab, Heidelberg
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NL
dt
N
d
3D-MOT loading from 2D-MOT
Camera Atom Cloud
Absorption imaging
Inz
I
d
d
2
3 2
zzyxnyxn d),,(),(
),(log
1),( 0
yxI
Iyxn
),(exp),( 0 yxnIyxI
21 light without atoms
I0
light with atoms
I(x,y)
Beer’s law
n(x,y)
Temperature
22
22
0)( tm
Tkt B
time-of-flight
Absorption imaging for variable expansion time
n(x,y)
MOT‘s
NaLi lab, Heidelberg
MOT
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first: sodium, Na (1987) latest: holmium, Ho (2014)
Laser cooling of alkali-metal elements
example: rubidium (87Rb)
• cycling transistion • F=2 -> F’=3
• need repumper • F=1 -> F’=2
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Rb vapour cell
photodetector
/2 /4
Wedge
Locking the laser on atomic transition
Saturated absorption spectroscopy
85Rb
87Rb
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Lasers
optical dipole trap
laser cooling Near-resonant laser light, wavelength atom specific
• Dye laser (visible, tunable) • Ti:Sapphire (NIR, tunable) • Diode laser (visible-NIR)
Far off-resonant laser light (IR, NIR, FIR) • Nd:YAG (1064nm) • Ytterbium fiber laser (1064nm) • Erbium Fiber Lasers (1550nm) • CO2 laser (10.6mm) 26
Light frequency and power control: AOM
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Acousto-Optical Modulator
RFif nvvv
• tunable frequency • tunable output power • fast switch on/off (<ms)
RF Bragg diffraction
• Limitation of laser cooling
– temperature
• (sub)-Doppler
• (sub)-recoil
– density
• light-assisted collisions
• reabsorption
• Magnetic trap and/or optical dipole trap – loaded from MOT (+cMOT+optical molasses+optical pumping)
– evaporative cooling 28
Trapping of neutral atoms
NaLi lab, Heidelberg
Vacuum requirements
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Collisions with “hot” background atoms and molecules lead to trap loss
tNtN exp)( 0i
i
in v1
loss
cross section
πm
TkB8v H2@300K: v=1.8*103 m/s
velocity
density
~ 10-14 cm2, very crude guess (R1+R2)2
Tk
Pn
B
1 mbar = 100 Pa = 0.75 Torr
s 10for mbar 102 9 P
We need Ultra-High Vacuum (UHV) conditions!
-37 cm 105 n
Magnetic trapping
)()(mag rBμr U
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BMgU FBF mmag
z
B
y
B
x
B zyx
d
d
2
1
d
d
d
d
222 4zyx B Quadrupole magnetic trap
Quadrupole magnetic trap
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QMT
Only low-field seeking states are trappable!
(asymmetry due to gravity)
Optical pumping
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spin
-po
lari
zin
g
mF -2 -1 0 1 2
F=2
F=1
F’=2
dark state
+
QMT limitation: Majorana loss
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Solutions: • harmonic potential with magnetic field offset -> Ioffe-Pritchard type magnetic trap • plugged QMT (with blue detuned laserbeam) • hybrid QMT + optical dipole trap
nonadiabatic spin flips to untrapped states at the magnetic field zero at the center of the QMT
tMeNtN
0)(
tTtT M 2
0)(
2
2
Tkm B
M
m
loss:
heating:
2
2
9
8
B
Mkm
m
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Optical dipole trap
)(2
)Re()()(
0
rrEdr Ic
Udip
)()Im(
)(0
scatt rr Ic
Chu et al, PRL 1986
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Optical dipole trap: 2-level system
0
D<0 red-detuned
D>0 blue-detuned
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Optical dipole trap: Rb
0,1
0,2
D2-line 780nm; D1-line 795nm
Typical wavelengths ODT Rb: 1064 nm, 1550 nm
5W 50mm
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Optical dipole trap: exp. realization
z
r
waist Rayleigh length
Rb 1557nm
5W 50mm
Crossed dipole trap
2
0
0w
PU
iw
fw
0
• Advantages – All Zeeman states (lowest spin-state)
– Mixture of Zeeman states (spinor BEC)
– Add homogeneous magnetic field (Feshbach resonances)
• Disadvantages – Shallow (<1 mK)
– Small (<1 mm)
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Optical dipole trap
MOT -> Magnetic trap -> Optical dipole trap
Plugged QMT
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Optical-plug beam prevent atoms from the center of the QMT
Blue-detuned (shorter wavelength than
optical transition)
Hybrid QMT+optical dipole trap
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Add single optical dipole beam to QMT, misaligned from QMT center
Levitated optical dipole trap
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Rb 1557nm
50mm 1W
0.5W
0.2W
Ugrav=mgz add quadrupole and bias field
to compensate gravity
dz
dBmg m
magnetic field gradient needed:
Example 87Rb (F=1, mF=1): m=mB/2
G/cm 5.302
B
Rb gm
dz
dB
m