Post on 23-Jul-2020
Dipole-dipole interactions between atoms
for many-body physics and
quantum information
Antoine Browaeys
Laboratoire Charles Fabry,Institut d’Optique, CNRS, FRANCE
Rydberg interactions
R
+
A
+
B
Van der Waals resonantC3
R3
C6
R6
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
?
Our Goal(as many groups…)
Héloïse Chochois, for LabexPALM
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
Neutral atoms Trapped ions Photons
NV centers Quantum dots Superconducting qubits
Quantum state engineering with individual systems
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
# 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
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
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
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
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
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
Þ “coherent” interaction
Rydbergstates
0
200
400
600
800
1000
Ener
gy [T
Hz]
l = 0 l = 1 l = 2
Optical transition
�opt
2⇡⇠ 100 nm
�µ
2⇡⇠ 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) +
sin2 ✓
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