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Nonlinear Thouless Pumping: Solitons and Transport Breakdown
Qidong Fu1, Peng Wang1, Yaroslav V Kartashov2
1School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
Physical Review Letters
|May 2, 2022
Summary
Attractive nonlinearity in topological pumping of matter waves can arrest atomic transfer above a threshold. Below this, quantized transport persists, with topology governing soliton dynamics even in nonlinear regimes.
Area of Science:
- Quantum physics
- Condensed matter physics
- Atomic physics
Background:
- Topological pumping offers precise control over matter-wave transport.
- Nonlinearity can significantly alter quantum transport phenomena.
- Optical lattices provide a tunable platform for simulating quantum systems.
Purpose of the Study:
- To investigate the impact of attractive nonlinearity on one-dimensional topological pumping of matter waves.
- To determine the conditions under which topological transport is preserved or broken down by nonlinearity.
- To explore the role of band topology in nonlinear matter-wave dynamics.
Main Methods:
- Theoretical analysis of matter-wave propagation in two overlaid optical lattices.
- Inclusion of attractive nonlinearity in the system's Hamiltonian.
- Calculation of dynamical Chern numbers for the lowest energy bands.
- Application of perturbation theory for soliton dynamics.
Main Results:
- A threshold nonlinearity level was identified, above which matter transfer is completely arrested.
- Below the threshold, matter transfer (of wave packets and solitons) is quantized and follows linear theory predictions.
- Nonlinearity-induced Rabi oscillations between bands can lead to transport breakdown.
- The topology of linear bands dictates soliton evolution even in the strongly nonlinear regime.
Conclusions:
- Topological pumping is robust below a critical nonlinearity, with quantized transport governed by band topology.
- Nonlinearity can induce novel transport regimes, including complete breakdown or quantized fractional transport.
- The interplay between topology and nonlinearity offers new avenues for controlling quantum matter transport.
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