Dissipation assisted Thouless pumping in the Rice–Mele model

Abstract

We investigate the effect of dissipation from a thermal environment on topological pumping in the periodically-driven Rice-Mele model. We report that dissipation can improve the robustness of pumping quantisation in a regime of finite driving frequencies. Specifically, in this regime, a low-temperature dissipative dynamics can lead to a pumped charge that is much closer to the Thouless quantised value, compared to a coherent evolution. We understand this effect in the Floquet framework: dissipation increases the population of a Floquet band which shows a topological winding, where pumping is essentially quantised. This finding is a step towards understanding a potentially very useful resource to exploit in experiments, where dissipation effects are unavoidable. We consider small couplings with the environment and we use a Bloch-Redfield quantum master equation approach for our numerics: Comparing these results with an exact MPS numerical treatment we find that the quantum master equation works very well also at low temperature, a quite remarkable fact. arXiv:1905.08808v3 [cond-mat.quant-gas]

An ideal rapid-cycle Thouless pump

“…The existence of a lower bound (24) on the spectral gap of the operator ĥγ α (τ) in a small vicinity of α = 0 implies that the eigenvalues ε α (k) and the projectors P α ± (0, k) admit for uniform perturbative estimates [37]…”

“…Recently, attention has started to turn to ways of mitigating the non-adiabatic effects in finite-frequency protocols. Among the proposed strategies are the dissipation assisted pumping [24], non-Hermitean Floquet engineering [25,26] and adiabatic shortcuts by external control [27,28]. In this work we take a complementary route and look into the optimization of the driving path in the pump's parameter space.…”

Rapid-cycle Thouless pumping in a one-dimensional optical lattice

“…More details and properties of this transformation are given in Appendix A. This Weyl transform can be applied to our system containing the Rice-Mele Hamiltonian (1) and the added harmonic potential (21), such that the Weyl transform of the Hamiltonian is given by which is the sum of the Rice-Mele Hamiltonian in reciprocal space (11) and a scalar matrix associated with the harmonic potential, translated such that the center of the lattice lies at n = 0. The Weyl tansform therefore simplifies to a two dimensional problem, in which we consider the Weyl transformed Liouvile-von Neumann equation…”

“…When we consider the unperturbed Rice-Mele chain, so when ξ = 0, this density matrix is just the sum over the outer-products of the Bloch-states of the lower band. The addition of a weak harmonic potential (21) with ξ ≪ 1 will then result in small corrections to the density matrix. In particular, it will result in corrections to the Weyl transform of the density matrix.…”

“…For special cases of Thouless pumping, such as parametric pumps [11][12][13][14][15], these non-adiabatic effects were studied [9,10,[16][17][18][19][20]. In order to minimise corrections, strategies such as dissipation assisted pumping [21], non-Hermitian Floquet engineering [22,23] and adiabatic shortcuts by external control [24,25] were proposed. Recently however, a family of finite-frequency protocols on the Rice-Mele insulator have been constructed, in which all the quasi-excitations disappear altogether at the end of a rapid-cycle, resulting in a perfectly quantized and noise-free particle transport outside of the adiabatic limit [26].…”