Download Trapping beam

Single atom manipulations
Benoît Darquié, Silvia Bergamini, Junxiang Zhang,
Antoine Browaeys and Philippe Grangier
Laboratoire Charles Fabry de l'Institut d'Optique Théorique
et Appliquée
UMR 8501 du CNRS
91 403 Orsay
http://www.iota.u-psud.fr/~grangier/Quantum_optics.html
Introduction
• Experience : study and manipulation of an optical dipole trap
for single atoms
• Context :
–
–
–
–
• Goals :
– entangle the atoms
– make a quantum gate
two neutral atoms
trapped in two different dipole traps
confinement :  mm3
a few microns away from one another
Principle of a dipole trap
Assumption : two-level atom, in a laserfield of frequency wL, with a red
detuning : d = wL - w0 < 0.
laser-induced non-dissipative
force associated with a potential

energy U (r )
For large detunings d :


 (r ) 1
U (r )    
<0
4 d
2
1

with : - 1 (r ) the Rabi frequency
-  the lightshift
two-level atom
|e
hw0
h
hwL
|g
atom in the
laser field
Atoms are trapped in the high intensity
regions
The transition frequency is shifted to the
blue
Dipole trap
Dipole force= non-dissipative force=> we previously have to cool atoms
We use a magneto-optical trap as a reservoir of cooled atoms :
- to trap and cool atoms
- to induce the fluorescence of the atoms (which will allow us to observe them)
Focussing of a Titanium-Sapphire laser beam
in the centre of this reservoir
Atoms are gathering at the
focussing spot => dipole trap
Dimensions of the trap
=
dimensions of the focussing spot
dipole trap
The microscope objective :
MIGOU
Characteristics of MIGOU :
~5 cm
– large numerical aperture : 0,7
Trapping beam
– diffraction limited spot
– large working distance
(~1cm)
Position
– ultra high vacuum
of the MOT
compatible
waist of the beam < 1 mm
Double use of MIGOU :
– to secure the focussing of the trapping beam in the center of the MOT
– to collect the fluorescence of trapped atoms with a large efficiency
Experimental
set-up
MOT & dipole trap
Vacuum chamber
Avalanche
Photodiode
Computers
y
x
z
CCD camera
780 nm filters
Filtering pinhole
Spatial filtering
Dipole
trap beam
Fluorescence
Pictures of the dipole trap
on the CCD camera
• Continuous observation of the fluorescence of the
dipole trap on the CCD caméra.
• One picture every 200 ms.
Y
Fluorescence
Fluorescence
(CCD)
10 000 counts
(200 ms)
Y
X
X
scaling of imaging system :
1 pixel = 1 mm
Single atom regime
Images on the
CCD camera
5 mm
Counting rate
(counts/10ms)
120
1 atom
80
40
Background
0
0
5
10
15
Time (s)
20
25
MOT & dipole trap
Double trap
What we observe on the CCD caméra
4 mm
second
trapping beam.
In single atom regime, there are
four likely configurations :
Temperature of the atoms
and trap frequencies
• Goals :
– entangle the atoms
– make a quantum gate
• Requirements : – atom in the Lambe-Dicke regime : h << 1
2
k BT
h  k  x 


mw 2
we have to measure the temperature of the atoms and
the trap frequencies
Oscillation frequencies :
principle of the measurement
• We trap one atom.
• We switch off and on the dipole trap during t1.
 If the atom is recaptured, it starts to oscillate in the trap.
• We wait for t and then, we switch off and on the dipole trap during t2.
 P(t) is the probability to recapture the atom after the whole sequence.
P(t)
Dipole trap
t1
t2
ON
t
OFF
 oscillate at 2fosc.
t
Probability of recapturing the atom
Probability of recapturing the atom
Oscillation frequencies :
experimental results
0.8
0.6
fosc=134 KHz
0.4
Ptrap = 1,9 mW
0.2
0.0
1.0
0.8
0.6
0.4
fosc = 108 Khz
0.2
Ptrap = 1,5 mW
0.0
0
2
4
6
8
Delay ( ms)
10
12
14
0
t1 = 1 ms
• w0 = 0.89 mm
• Ptrap = 2 mW
2
4
6
8
Retard
(ms)
Delay (ms)
10
12
t1 = 2.5 ms
}
fr = 140 kHz , fz = 29 kHz
14
Temperature of the atom :
time of flight experiments
MOT
• Time sequence:
1 : We trap one atom
Objective
Trapping
beam
Temperature of the atom :
time of flight experiments
• Time sequence:
1 : We trap one atom
2 : We switch off the MOT
Objective
Trapping
beam
Temperature of the atom :
time of flight experiments
MOT
• Time sequence:
1 : We trap one atom
2 : We switch off the MOT
3 : The trapping beam is
switched off during t
Objective
Trapping
beam
4 : We check if the atom
is still there
 We measure the probability of recapturing the atom
after t.
Temperature of the atom :
results
1.0
Probability of recapturing the atom
= 2 mW P = 2 mW
+PSimulation
with T = 140 mK
simulation with T = 140 mK
simulation with T = 35 mK
Simulation with T = 35 mK
0.8
0.6
0.4
T = 35 mK
0.2
0.0
0
10
20
30
t (seconds)
40
50x10
-6
Conclusion and outlooks
• We are now able to evaluate the trap frequencies and the temperature
of the atoms
Lamb-Dicke parameters : hr  0.5
hz  2.5
• We need :
– a better confinement
– a smaller temperature
• Better confinement  retro-reflexion of the trapping beam,
standing wave
• Smaller temperatures  Raman cooling
Single atom manipulations
Benoît Darquié, Silvia Bergamini, Junxiang Zhang,
Antoine Browaeys and Philippe Grangier
Laboratoire Charles Fabry de l'Institut d'Optique Théorique
et Appliquée
UMR 8501 du CNRS
91 403 Orsay
http://www.iota.u-psud.fr/~grangier/Quantum_optics.html
Entanglement of two atoms
probe
beam

|2>
probe
beam
s
|0>
|1>
|0>
Atome 1

|2>
s
|1>
Atome 2
beam splitter
detector of -polarized
light:
Entanglement of two atoms
probe
beam
|2>

s
|1>
|0>
Excitation by a photon of
the probe beam:
detection of s-polarized
ligt:
atoms behave as Young's slits
 interferences
00  00  bei1 02  bei2 20
detection of -polarized
light:
projection onto the state:
ei1 01  ei2 10
 entanglement
Plan of my talk
• Principle of the optical dipole trap
• Implementing a dipole trap
A microscope objective : MIGOU
Experimental set-up
Pictures of the dipole trap
Double dipole trap
• Temperature of the atoms
• Oscillation frequencies of the dipole trap
• Conclusion and outlooks