Quantized Nonlinear Thouless Pumping
- URL: http://arxiv.org/abs/2106.14128v1
- Date: Sun, 27 Jun 2021 03:02:39 GMT
- Title: Quantized Nonlinear Thouless Pumping
- Authors: Marius J\"urgensen, Sebabrata Mukherjee and Mikael C. Rechtsman
- Abstract summary: We show that nonlinearity acts to quantize transport via soliton formation and spontaneous symmetry breaking bifurcations.
Our result shows that nonlinearity and interparticle interactions can induce quantized transport and topological behavior even where the linear limit does not.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The sharply quantized transport observed in the integer quantum Hall effect
can be explained via a simple one-dimensional model with a time-periodic,
adiabatically varying potential in which electronic charge is pumped from one
side of the system to the other. This so-called `Thouless pump' captures the
topological physics of the quantum Hall effect using the notion of dimensional
reduction: The time-varying potential mathematically maps onto a momentum
coordinate in a conceptual second dimension. Importantly, this assumes an
electronic system in equilibrium and in its ground state, that is, with
uniformly filled bands below a Fermi energy. Here, we theoretically propose and
experimentally demonstrate quantized nonlinear Thouless pumping of photons with
a band that is decidedly not uniformly occupied. In our system, nonlinearity
acts to quantize transport via soliton formation and spontaneous symmetry
breaking bifurcations. Quantization follows from the fact that the
instantaneous soliton solutions centered upon a given unit cell are identical
after each pump cycle, up to translation invariance; this is an entirely
different mechanism from traditional Thouless pumping of fermions in
equilibrium. Our result shows that nonlinearity and interparticle interactions
can induce quantized transport and topological behavior even where the linear
limit does not.
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