Topological matter with arrays of Rydberg atoms
Transcript of Topological matter with arrays of Rydberg atoms
Topological matter
with arrays of Rydberg atoms
Laboratoire Charles Fabry,Institut d’Optique, CNRS, Palaiseau, France
GdR COMPLEXEDecember 1st 2020
V. Lienhard, S. de Léséleuc, P. Scholl, D. Barredo,
K.N. Schymik, H. Williams, T. Lahaye and A. Browaeys
Open problems in condensed-matter physics 1/21
Quantum many-body systems, prominent effect of interactions
Quantum magnetism
Herbertsmithite
Nature 492, 406 (2012)
Superconductivity
Charles O'Rear Getty Images
Many-body localization
Science 352, 1547 (2016)
Open questions : effect of spin-statistics, emergence of exotic phases, out-of-
equilibrium dynamics…
Synthetic quantum matter
Ion trapsSuperconducting
qubits
Rydberg atoms
Optical tweezers
Quantum gas
microscopes
Well-controlled assemblies of interacting particles
Implement a many-body Hamiltonian to mimic condensed-matter problems
Cre
dit
: Hél
oïs
e C
ho
cho
is Georgescu et al., RMP 86, 153 (2014)
Quantum simulation
o Study of spin systems
o Study of transport phenomena
VL et al., PRX 8, 021070 (2018)
H. Labuhn et al., Nature 534, 667 (2016)
S. de Léséleuc et al., Science 365, 7757 (2019)
VL et al., PRX 10, 021031 (2020)
2/21
Our platform
Arrays of single atoms
10 µm
Interaction between Rydberg atoms
+
e-
+
e-
D. Barredo et al., Science 354, 1021 (2016)
A. Browaeys and T. Lahaye, Nat. Phys. 16, 132 (2020)
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Topological phases
Non-interacting
fermions
With interactions?Fractional Chern insulators
Exotic statistics
No demonstration
on artificial systemsBosons or fermions
Effect of spin-statistics
M. König et al., Science 318, 766 (2007)
Topological insulatorsBand structure
- Excitation gap
- Edge states
Conduction
band
Valence
band
Fermi
level
Edge
states
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Outline
Implementation
of the SSH model
Observation of
edge states
Towards 2D
edge states
Outline
Implementation
of the SSH model
Observation of
edge states
Towards 2D
edge states
The SSH model
Normal
Chain of dimers with or without weakly coupled edges: two configurations
No coupling between subchains: sub-lattice symmetry
Infinite 1D-chain
of dimers
Strong link Weak link
x
Finite-size chain cases:
Topological
Electronic transport
in polyacetylene
Reviews: Asboth, arXiv:1509.02295; Cooper, arXiv:1803.00249
Su, Schrieffer and HeegerPRL 42, 1698 (1979)
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The SSH model, single-particle spectrum
Normal Topological
Edge
states
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Exchange of a P excitation Hopping of a particle
Resonant dipole-dipole interaction
0 particle
1 particle
Mapping to a bosonic problem
Microwave field:o Adds/removes particles coherently in the chain
o Probe energy spectrum
Atom 1 Atom 2
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Spatial dependence 8/21
The SSH model, experimental realization
TopologicalNormal
θMθM
x x
14-atom chain 14-atom chain
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Outline
Implementation
of the SSH model
Observation of
edge states
Towards 2D
edge states
Mic
row
ave d
etu
nin
g (
MH
z)
Site
Lower band
Site
Edge
states
Band gap
Single-particle regime
Vacuum
Single-particle
spectrum
Normal Topological
Observation of edge states,
signature of topology
Microwave probe
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Hybridization of edge states
Prepare one excitation on left edge site
and
Coherent exchange between left and right
Chain length
Nearest-neighbour
Long-range
Time (µs)
Site
Site
Site
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Going to the many-body regime
S. de Léséleuc et al., Science 365, 775 (2019)
0 particle
1 particle
Mapping to a bosonic problem
2 particles
System of hard-core bosons
Adiabatic passage
Spectroscopy from
a half-filled bulk Observation of a
symmetry protected
topological (SPT) phase
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Outline
Implementation
of the SSH model
Observation of
edge states
Towards 2D
edge states
Peierls phases
Complex-valued hopping
(Peierls phase)
Topological band structure
(Haldane model)
Effective magnetic field for neutral particles
Artificial gauge fieldsN. R. Cooper et al., RMP 91, 015005 (2019)
J. Dalibard et al., RMP 83, 1523 (2011)
D. Jaksch et al., NJP 5, 56 (2003)
Laser-assisted
tunneling
M. Aidelsburger et al.,
PRL 107, 255301 (2011)
Driven lattices
J. Struck et al.,
PRL 108, 255304 (2012)
Superconducting
qubits
P. Roushan et al.,
Nat. Phys. 13, 146 (2017)
On our platform : engineer a Peierls phase using the intrinsic
spin-orbit coupling of the dipolar interaction
VL et al., PRX 10, 021031 (2020)
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Spin-orbit coupling and dipole-dipole interaction
Atom 1 Atom 2
Atomic plane
B
Intrinsic spin-orbit coupling
Perturbative regime Virtual spin-flip hopping to pick up a phase
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Perturbative approach
Atomic plane
B
1
2
3
Energy levels
Two ways to go from site 1 to site 3:
- Direct hopping
- Off-resonant hopping
Combination of the two processes
Implementation of a
complex hopping amplitudeArtificial gauge field
(Peierls phase) Cold atom platforms: Spielman, Bloch, Sengstock, Esslinger, Beugnon, Fallani,…
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Required flux for a chiral motion
Coupling P. Roushan et al., Nature Physics 13, 146 (2017)
Total flux1
2
3
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Chiral motion on a triangle
B
1
2
3 B
1
2
3
VL et al., PRX 10, 021031 (2020)
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Many-body regime?
1
2
3B
1
2
3B
Interacting hopping particles
Fourth-order process
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A density-dependent Peierls phase
1
2
3
Hopping amplitude
between 1 and 3
o If complex-valued
o If real
Mapping to an anyonic statistics (with an additional particle-hole transformation)
1 anyon = 1 hole = 2 particles
Single-anyon Hamiltonian has real hopping amplitudes
No chirality for the propagation of the hole
The Hamiltonian for two anyons has complex hopping amplitudes
due to their exchange statistics
Chirality for the propagation of one particle
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Summary and outlookSummary
A platform to build synthetic matter : arbitrary geometries and tunable interactions
Implementation of complex hopping amplitude using spin-orbit coupling
Observation of a 1D topological phase
20/21
Summary and outlook
Chiral edge states on
honeycomb lattices
Many-body regime?- Density-dependent Peierls phase
- Fractional bosonic Chern insulator?
Outlook
Summary
A platform to build synthetic matter : arbitrary geometries and tunable interactions
Observation of spin-ordered phases
Implementation of complex hopping amplitude using spin-orbit coupling
21/21
The Rydberg team in Palaiseau
Antoine
Browaeys
Sylvain de
Léséleuc
Thierry
Lahaye
Daniel
Barredo
Vincent
Lienhard
Florence
Nogrette
Pascal
Scholl
H.-P. Büchler N. Lang S. WeberTheory:
https://atom-tweezers-io.org/
Kai-Niklas
Schymik
Hannah
Williams
M. Fleischhauer