Dipole-dipole interactions between atoms for many-body ... · Ultracold atoms in lattices Munich,...
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Dipole-dipole interactions between atoms
for many-body physics and
quantum information
Antoine Browaeys
Laboratoire Charles Fabry,Institut d’Optique, CNRS, FRANCE
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Rydberg interactions
R
+
A
+
B
Van der Waals resonantC3R3
C6R6
Ini_al
Final
Galleryofassembled2Darrays…(single-shotimages…)
Barredo,deLéséleuc,etal.,Science354,1021(2016)
10μm
ω0
E0, ω
Interactions betweenlight-induced dipoles
Dipole interactions for QIP and many-body physics
See: A. Asenjo-GarciaR. Kaiser
?
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Our Goal(as many groups…)
Héloïse Chochois, for LabexPALM
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Quantum metrologyMany-body physics
Transition quantum / classicalQuantum information
Message
Dura
tion
size L
Ln
Exp L
�⌫
⌫0/ 1p
N
�⌫
⌫0/ 1
N
qu. states
Quantum state engineering: create controlled quantum states
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Neutral atoms Trapped ions Photons
NV centers Quantum dots Superconducting qubits
Quantum state engineering with individual systems
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Neutral atoms Trapped ions Photons
NV centers Quantum dots Superconducting qubits
Ions
Two-level systems to encode a spin:
Addressable + controlled interactions
Quantum state engineering with individual systems
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# of ‘spins’1 102 104
Nearestneighbors
Ultracold atoms in lattices Munich, JQI, Harvard…
Jij ⇠1
r6ij
Rydberg atoms
Coupling range
See e.g. Hazzard et al., PRA 90, 063622 (2014)
Trapped ionsJQI, Innsbruck…
Polar moleculesMagnetic atoms
JILA, Stuttgart, Paris…
Platforms in AMO physics
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Lecture 1: Dipole-dipole interaction between atoms
Lecture 2: Basics of Rydberg physics. Arrays of cold atoms. Rydberg blockade & QIP
Lecture 3: Many-body physics with Rydberg atoms
Outline
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5 10 15 20 25 30 35R (au)
0
10000
20000
30000
ener
gy (c
m-1
)
Rb2+ Rb2+
5s+5s
5s+5p
5s+4d5s+6s
5s+6p
5s+6d5s+7s
singlet_sigma_g
singlet_sigma_u
singlet_sigma_u
triplet_sigma_u
singlet_pi_g
singlet_pi_u
triplet_pi_g
triplet_pi_u
singlet_delta_g
triplet_delta_g
singlet_delta_u
triplet_delta_u
5 10 15 20 25 30 35R (au)
0g+0g-0u+0u-1g1u2g2u
Molecular potentials Rb2
O. Dulieu, LAC
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On-line interaction calculator
https://arc-alkali-rydberg-calculator.readthedocs.io/en/latest/
N. Sibalic
S. Weber
https://pairinteraction.github.io/pairinteraction/sphinx/html/index.html
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A
B
r
Sub-radiantSub-radiant
Super-radiantSuper-radiant
q = 0
Sub- and super radiant states (linear dipoles)
0 2 4 6 8 10-4
-2
0
2
4
0 2 4 6 8 100.0
0.5
1.0
1.5
2.0
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A B
r
Super-radiant
Super-radiant Sub-radiant
Sub-radiant
q = p/2
Sub- and super radiant states (linear dipoles)
0 2 4 6 8 10-1.0
-0.5
0.0
0.5
1.0
0 2 4 6 8 100.0
0.5
1.0
1.5
2.0
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Þ “coherent” interaction
Rydbergstates
0
200
400
600
800
1000
Ener
gy [T
Hz]
l = 0 l = 1 l = 2
Optical transition
�opt2⇡
⇠ 100 nm
�µ2⇡
⇠ 1 cm
Microwave transition
kr ⌧ 1 kr & 1
Þ Dissipative spin models
Vdd ⇠~�kr
⇠ ~�
87Rb
Near-field vs. far-field = coherent vs. collective dissipation
Vdd = �d2egk
3
4⇡✏0eikr
✓1
(kr)3� i
(kr)2
◆(3 cos2 ✓ � 1) + sin
2 ✓
kr
�
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
Vdd ⇠d2egr3
� ~�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1. Far field (R = 2 λ): Modification of lifetime Ba+, 6S1/2 – 6P3/2
2. Near field (R = 0.02 λ): spectroscopy of 2 Terrylene molecules
super-rad
sub-rad
DeVoe, Brewer,PRL 76, 2049 (1996)
Hettich, Science 298, 385 (2002)
Resonant dipole interaction: observations of the eigenmodes
