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Measuring Chern numbers in Hofstadter strips

Measuring Chern numbers in Hofstadter strips
Measuring Chern numbers in Hofstadter strips
Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems with open boundary conditions and limited spatial extension. Here, we consider transport in Hofstadter strips, that is, two-dimensional lattices pierced by a uniform magnetic flux which extend over few sites in one of the spatial dimensions. As we show, an atomic wavepacket exhibits a transverse displacement under the action of a weak constant force. After one Bloch oscillation, this displacement approaches the quantized Chern number of the periodic system in the limit of vanishing tunneling along the transverse direction. We further demonstrate that this scheme is able to map out the Chern number of ground and excited bands, and we investigate the robustness of the method in presence of both disorder and harmonic trapping. Our results prove that topological invariants can be measured in Hofstadter strips with open boundary conditions and as few as three sites along one direction.
2542-4653
Mugel, S.
22d0e4d2-9f1f-4d04-a091-38c70279da38
Dauphin, A.
ea82e6c7-ff30-4740-96eb-bd4c63201c70
Massignan, P.
b30b697f-1848-41bb-90f5-0704235aedd9
Tarruell, L.
5c1f4fc9-2c8c-4b70-a115-8d6fd93c3bd9
Lewenstein, M.
c75d2e82-4f4c-4402-8491-b93d91e91563
Lobo, C.
cde7843a-c00b-4242-a8cd-1abb2dfe0703
Celi, A.
59d56f87-a6a8-41ba-9946-4fd42d8254e8
Mugel, S.
22d0e4d2-9f1f-4d04-a091-38c70279da38
Dauphin, A.
ea82e6c7-ff30-4740-96eb-bd4c63201c70
Massignan, P.
b30b697f-1848-41bb-90f5-0704235aedd9
Tarruell, L.
5c1f4fc9-2c8c-4b70-a115-8d6fd93c3bd9
Lewenstein, M.
c75d2e82-4f4c-4402-8491-b93d91e91563
Lobo, C.
cde7843a-c00b-4242-a8cd-1abb2dfe0703
Celi, A.
59d56f87-a6a8-41ba-9946-4fd42d8254e8

Mugel, S., Dauphin, A., Massignan, P., Tarruell, L., Lewenstein, M., Lobo, C. and Celi, A. (2017) Measuring Chern numbers in Hofstadter strips. Scipost Physics, 3 (12). (doi:10.21468/SciPostPhys.3.2.012).

Record type: Article

Abstract

Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems with open boundary conditions and limited spatial extension. Here, we consider transport in Hofstadter strips, that is, two-dimensional lattices pierced by a uniform magnetic flux which extend over few sites in one of the spatial dimensions. As we show, an atomic wavepacket exhibits a transverse displacement under the action of a weak constant force. After one Bloch oscillation, this displacement approaches the quantized Chern number of the periodic system in the limit of vanishing tunneling along the transverse direction. We further demonstrate that this scheme is able to map out the Chern number of ground and excited bands, and we investigate the robustness of the method in presence of both disorder and harmonic trapping. Our results prove that topological invariants can be measured in Hofstadter strips with open boundary conditions and as few as three sites along one direction.

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More information

Accepted/In Press date: 2 August 2017
e-pub ahead of print date: 15 August 2017

Identifiers

Local EPrints ID: 412969
URI: http://eprints.soton.ac.uk/id/eprint/412969
ISSN: 2542-4653
PURE UUID: b3967478-7bc1-4346-aa57-969462dd0f47
ORCID for C. Lobo: ORCID iD orcid.org/0000-0001-7060-3905

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Date deposited: 10 Aug 2017 16:30
Last modified: 08 Feb 2020 01:30

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