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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 :
• Context :
• Goals :
– two neutral atoms– trapped in two different dipole traps– confinement : m3
– a few microns away from one another
– entangle the atoms– make a quantum gate
study and manipulation of an optical dipole trap for single atoms
Principle of a dipole trap
Assumption : two-level atom, in a laser-field of frequency L, with a red detuning : = L - .
Atoms are trapped in the high intensityregionsThe transition frequency is shifted to theblue
01
4
)()(
21
r
rU
laser-induced non-dissipative force associated with a potential energy )(rU
with : - the Rabi frequency- the lightshift
)(1 r
For large detunings
h
|e
|g
atom in the laser field
hLh
two-level atom
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)
Dipole trapDipole force= non-dissipative force=> we previously have to cool atoms
Focussing of a Titanium-Sapphire laser beamin the centre of this reservoir
dipole trap
Atoms are gathering at the focussing spot => dipole trap
Dimensions of the trap=
dimensions of the focussing spot
The microscope objective :MIGOU
Positionof the MOT
Trapping beam
Characteristics of MIGOU :– large numerical aperture : 0,7– diffraction limited spot– large working distance (~1cm)– ultra high vacuum compatible
waist of the beam < 1 m
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
~5 cm
Experimentalset-up
Vacuum chamber
MOT & dipole trap
x
y
z
Dipoletrap beam
Fluorescence
CCD camera
780 nm filters
Spatial filtering
Computers
Filtering pinhole
AvalanchePhotodiode
Pictures of the dipole trap on the CCD camera
scaling of imaging system :1 pixel = 1 m
• Continuous observation of the fluorescence of thedipole trap on the CCD caméra.• One picture every 200 ms. Y
X
Fluorescence(CCD)
X
Y
Fluorescence
10 000 counts(200 ms)
Images on theCCD camera
5 m
Single atom regime
120
80
40
0
2520151050Time (s)
Counting rate (counts/10ms)
1 atom
Background
Double trapMOT & dipole trap
secondtrapping beam.
4 m
What we observe on the CCD caméra
In single atom regime, there arefour likely configurations :
Temperature of the atoms and trap frequencies
• Goals :
• Requirements : – atom in the Lambe-Dicke regime : << 1
we have to measure the temperature of the atoms and the trap frequencies
– entangle the atoms– make a quantum gate
2
2
m
Tkxk B
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.
Dipole trapON
OFFt
t
P(t)
oscillate at 2fosc.
t1 t2
Oscillation frequencies : experimental results
0.8
0.6
0.4
0.2
0.0
Prob
abili
ty o
f re
capt
urin
g th
e at
om
14121086420Delay (s)
fosc=134 KHz
• w0 = 0.89 m • Ptrap = 2 mW
fr = 140 kHz , fz = 29 kHz}
Ptrap = 1,9 mW
1.0
0.8
0.6
0.4
0.2
0.0
Prob
abili
ty o
f re
capt
urin
g th
e at
om
14121086420Retard (s)
fosc = 108 Khz
Delay (s)
t1 = 2.5 st1 = 1 s
Ptrap = 1,5 mW
Temperature of the atom : time of flight experiments
• Time sequence:
Objective
MOT
1 : We trap one atom
Trappingbeam
Temperature of the atom : time of flight experiments
• Time sequence:
Objective
1 : We trap one atom
Trappingbeam
2 : We switch off the MOT
Temperature of the atom : time of flight experiments
• Time sequence:
1 : We trap one atom
2 : We switch off the MOT
3 : The trapping beam is switched off during t
ObjectiveTrapping
beam
MOT
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
0.8
0.6
0.4
0.2
0.0
Pro
babi
lity
of
reca
ptur
ing
the
atom
50x10-6
403020100t (seconds)
P = 2 mW Simulation with T = 140 K Simulation with T = 35 K
T = 35 K
P = 2 mWsimulation with T = 140 Ksimulation with T = 35 K
+
Conclusion and outlooks
• We are now able to evaluate the trap frequencies and the temperature of the atoms
• We need :– a better confinement– a smaller temperature
• Better confinement retro-reflexion of the trapping beam, standing wave
• Smaller temperatures Raman cooling
Lamb-Dicke parameters : r 0.5 z 2.5
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
|>|>
probebeam
|>
|>|>
probebeam
|>
Atome 1 Atome 2
beam splitter
detector of -polarizedlight:
Entanglement of two atoms
Excitation by a photon of the probe beam: 20020000 21 ii bebe
detection of -polarizedligt:
|>|>
probebeam
|>
detection of -polarizedlight:
atoms behave as Young's slits
interferences
projection onto the state: 1001 21 ii ee
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