TY - JOUR
T1 - Bloch oscillations, Landau–Zener transition, and topological phase evolution in an array of coupled pendula
AU - Neder, Izhar
AU - Sirote-Katz, Chaviva
AU - Geva, Meital
AU - Lahini, Yoav
AU - Ilan, Roni
AU - Shokef, Yair
N1 - Publisher Copyright:
© 2024 the Author(s). Published by PNAS.
PY - 2024/2/27
Y1 - 2024/2/27
N2 - We experimentally and theoretically study the dynamics of a one-dimensional array of pendula with a mild spatial gradient in their self-frequency and where neighboring pendula are connected with weak and alternating coupling. We map their dynamics to the topological Su–Schrieffer–Heeger model of charged quantum particles on a lattice with alternating hopping rates in an external electric field. By directly tracking the dynamics of a wave-packet in the bulk of the lattice, we observe Bloch oscillations, Landau–Zener transitions, and coupling between the isospin (i.e., the inner wave function distribution within the unit cell) and the spatial degrees of freedom (the distribution between unit cells). We then use Bloch oscillations in the bulk to directly measure the nontrivial global topological phase winding and local geometric phase of the band. We measure an overall evolution of 3.1 ± 0.2 radians for the geometrical phase during the Bloch period, consistent with the expected Zak phase of p. Our results demonstrate the power of classical analogs of quantum models to directly observe the topological properties of the band structure and shed light on the similarities and the differences between quantum and classical topological effects.
AB - We experimentally and theoretically study the dynamics of a one-dimensional array of pendula with a mild spatial gradient in their self-frequency and where neighboring pendula are connected with weak and alternating coupling. We map their dynamics to the topological Su–Schrieffer–Heeger model of charged quantum particles on a lattice with alternating hopping rates in an external electric field. By directly tracking the dynamics of a wave-packet in the bulk of the lattice, we observe Bloch oscillations, Landau–Zener transitions, and coupling between the isospin (i.e., the inner wave function distribution within the unit cell) and the spatial degrees of freedom (the distribution between unit cells). We then use Bloch oscillations in the bulk to directly measure the nontrivial global topological phase winding and local geometric phase of the band. We measure an overall evolution of 3.1 ± 0.2 radians for the geometrical phase during the Bloch period, consistent with the expected Zak phase of p. Our results demonstrate the power of classical analogs of quantum models to directly observe the topological properties of the band structure and shed light on the similarities and the differences between quantum and classical topological effects.
KW - Bloch oscillations
KW - Landau–Zener transition
KW - metamaterials
KW - topological phase
UR - http://www.scopus.com/inward/record.url?scp=85185862463&partnerID=8YFLogxK
U2 - 10.1073/pnas.2310715121
DO - 10.1073/pnas.2310715121
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C2 - 38394241
AN - SCOPUS:85185862463
SN - 0027-8424
VL - 121
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 9
M1 - e2310715121
ER -