78 research outputs found
Topological characterization of chiral models through their long time dynamics
We study chiral models in one spatial dimension, both static and periodically
driven. We demonstrate that their topological properties may be read out
through the long time limit of a bulk observable, the mean chiral displacement.
The derivation of this result is done in terms of spectral projectors, allowing
for a detailed understanding of the physics. We show that the proposed
detection converges rapidly and it can be implemented in a wide class of chiral
systems. Furthermore, it can measure arbitrary winding numbers and topological
boundaries, it applies to all non-interacting systems, independently of their
quantum statistics, and it requires no additional elements, such as external
fields, nor filled bands
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.Comment: v1: 17 pages, 10 figures; v2: minor changes, reference added, SciPost
style, 26 pages, 10 figures; v3: published versio
Bulk detection of time-dependent topological transitions in quenched chiral models
The topology of one-dimensional chiral systems is captured by the winding
number of the Hamiltonian eigenstates. Here we show that this invariant can be
read-out by measuring the mean chiral displacement of a single-particle
wavefunction that is connected to a fully localized one via a unitary and
translational-invariant map. Remarkably, this implies that the mean chiral
displacement can detect the winding number even when the underlying Hamiltonian
is quenched between different topological phases. We confirm experimentally
these results in a quantum walk of structured light
Two-dimensional topological quantum walks in the momentum space of structured light
Quantum walks are powerful tools for quantum applications and for designing
topological systems. Although they are simulated in a variety of platforms,
genuine two-dimensional realizations are still challenging. Here we present an
innovative approach to the photonic simulation of a quantum walk in two
dimensions, where walker positions are encoded in the transverse wavevector
components of a single light beam. The desired dynamics is obtained by means of
a sequence of liquid-crystal devices, which apply polarization-dependent
transverse "kicks" to the photons in the beam. We engineer our quantum walk so
that it realizes a periodically-driven Chern insulator, and we probe its
topological features by detecting the anomalous displacement of the photonic
wavepacket under the effect of a constant force. Our compact, versatile
platform offers exciting prospects for the photonic simulation of
two-dimensional quantum dynamics and topological systems.Comment: Published version of the manuscrip
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