In Thouless pump, the charge transport in a one-dimensional insulator over an adiabatic cycle is topologically quantized. For nonequilibrium initial states, however, interband coherence will induce a previously unknown contribution to Thouless pumping. Though not geometric in nature, this contribution is independent of the time scale of the pumping protocol. In this work, we perform a detailed analysis of our previous finding [Phys. Rev. B 91, 085420 (2015)] in an already available cold-atom setup. We show that initial states with interband coherence can be obtained via a quench of the system's Hamiltonian. Adiabatic pumping in the post-quench system are then examined both theoretically and numerically, in which the interband coherence is shown to play an important role and can hence be observed experimentally. By choosing adiabatic protocols with different switching-on speeds, we also show that the contribution of interband coherence to adiabatic pumping can be tuned. It is further proposed that the interband coherence induced correction to Thouless pumping may be useful in capturing a topological phase transition point. All our results have direct experimental interests.
The adiabatic charge pumping of a non-equilibrium state of spinless fermions in a one-dimensional lattice is investigated, with an emphasis placed on its usefulness in revealing many-body interaction effects on interband coherence. For a non-interacting system, the pumped charge per adiabatic cycle depends not only on the topology of the occupied bands but also on the interband coherence in the initial state. This insight leads to an interesting opportunity for quantitatively observing how quantum coherence is affected by many-body interaction that is switched on for a varying duration prior t…
We propose a two-dimensional (2D) version of Thouless pumping that can be realized by using ultracold atoms in optical lattices. To be specific, we consider a 2D square lattice tight-binding model with an obliquely introduced superlattice. It is demonstrated that quantized particle transport occurs in this system, and that the transport is expressed as a solution of a Diophantine equation. This topological nature can be understood by mapping the Hamiltonian to a three-dimensional (3D) cubic lattice model with a homogeneous magnetic field. We also propose a continuum model with obliquely introd…
Thouless pumping provides one of the simplest manifestations of topology in quantum systems, and has attracted a lot of recent interest, both theoretically and experimentally. Since the seminal works by Thouless and Niu in 1983 and 1984, it is argued that the quantization of the pumped charge is robust against weak disorder, but a clear characterization of the localization properties of the relevant states, and the breakdown of quantized transport in the presence of interaction or out of the adiabatic approximation, has been long debated. Thouless pumping is also the first example of a topolog…
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, w…
We elucidate the mechanism for instability of topological Thouless pumping in strongly interacting systems from a viewpoint of symmetry-protected topological phases. If the protecting symmetries of the underlying topological phases change between noninteracting fermions and a bosonic system in the strong coupling limit, the symmetry protection argument enforces a gap closing and thereby predicts a breakdown of the topological pumping. We also demonstrate that, even in the weakly interacting regime where the bulk topological pumping is still robust, the interaction effects manifest themselves i…
Thouless pumping is a mechanism to perform topologically protected transport of particles by adiabatically modulating the Hamiltonian. The transported current is a topological invariant that is intimately related to the integer quantum Hall effect. Most of the previous works focus on topological pumping in linear and square lattices. In this work, we theoretically propose a mechanism to perform topological pumping in arrays of spin chains with complex geometries. To achieve this, we consider an array where the spin chains are coupled through their edges, which allows to split the populations t…
Non-abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands. To this end we consider a photonic Lieb lattice having two degenerate non-dispersive modes and we show that, when the lattice parameters are slowly modulated, the propagation of the photons bear the fingerprints of the underlying non-abelian gauge structure. The non-dispersive character of the bands enables a high degree of control on photon propagation. Our work paves th…
University of Maryland（马里兰大学）；Institute for Physical Science and Technology, University of Maryland（马里兰大学物理科学与技术研究院）；Condensed Matter Theory Center, Department of Physics, University of Maryland（马里兰大学物理系凝聚态理论中心）
We study topological features of interacting spin- 1 2 particles in one-dimensional state-dependent optical lattices. Due to the co-translational symmetry, we introduce the center-of-mass Zak phase with the help of center-of-mass momentum. There appear topological bound states composed by two particles in different spin states via tuning hopping and interaction strengths. Under symmetric open boundary conditions, topological edge bound-states appear as a result of the non-trivial center-ofmass Zak phase of bound-state band, which is protected by the center-of-mass inversion symmetry. The inter…
Periodic driving can create topological phases of matter absent in static systems. In terms of the displacement of the position expectation value of a time-evolving wavepacket in a closed system, a type of adiabatic dynamics in periodically driven systems is studied for general initial states possessing coherence between different Floquet bands. Under one symmetry assumption, the displacement of the wavepacket center over one adiabatic cycle is found to be comprised by two components independent of the time scale of the adiabatic cycle: a weighted integral of the Berry curvature summed over al…
We study nonequilibrium carriers (electrons and holes) in an intrinsic graphene at low temperatures under far- and mid-infrared (IR) radiation in a wide range of its intensities. The energy distributions of carriers are calculated using a quasiclassic kinetic equation which accounts for the energy relaxation due to acoustic phonons and the radiative generation-recombination processes associated with thermal radiation and the carrier photoexcitation by incident radiation. It is found that the nonequilibrium distributions are determined by an interplay between weak energy relaxation on acoustic …
Recent studies indicated that helical organic molecules, such as DNA and $α$-helical protein, can behave as Thouless quantum pumps when a rotating electric field is applied perpendicularly to their helical axes. Here we investigate the influence of long-range hoppings on this topological pumping of electrons in single-helical organic molecules. Under variation of the long-range hoppings governed by a decay exponent $μ$, we find an energy gap in the molecular band structure closes at a critical value $μ_c$ of the decay exponent and reopens for $μ$ deviating from $μ_c$. The relevant bulk bands i…
Nonlinear Thouless pumps for bosons exhibit quantized pumping via soliton motion, despite the lack of a meaningful notion of filled bands. However, the theoretical underpinning of this quantization, as well as its relationship to the Chern number, has thus far been lacking. Here we show that for low power solitons, transport is dictated by the Chern number of the band from which the soliton bifurcates. We do this by expanding the discrete nonlinear Schrödinger equation (equivalently, the Gross-Pitaevskii equation) in the basis of Wannier states, showing that the soliton's position is dictated …
Thouless pump is a one-dimensional dynamic topological effect that stems from the same topological mechanism as the renowned two-dimensional Chern insulators, with one momentum dimension replaced by a time variant evolution parameter. The underlying physics is abelian, concerning topologies of individual bands. By introducing multi-band non-abelian topology into pumping, much richer physics is expected that goes beyond the abelian counterpart. Here we report the observation of a non-abelian Thouless pump in an acoustic waveguide array with judiciously engineered coupling configurations. The ob…
We show how to implement topological or Thouless pumping of interacting photons in one dimensional nonlinear resonator arrays, by simply modulating the frequency of the resonators periodically in space and time. The interplay between interactions and the adiabatic modulations enables robust transport of Fock states with few photons per site. We analyze the transport mechanism via an effective analytic model and study its topological properties and its protection to noise. We conclude by a detailed study of an implementation with existing circuit QED architectures.
Thouless pumping is a fundamental instance of quantized transport, which is topologically protected. Although its theoretical importance, the adiabaticity condition is an obstacle for further practical applications. Here, focusing on the Rice-Mele model, we provide a family of finite-frequency examples that ensure both the absence of excitations and the perfect quantization of the pumped charge at the end of each cycle. This family, which contains an adiabatic protocol as a limiting case, is obtained through a mapping onto the zero curvature representation of the Euclidean sinh-Gordon equation…
Pumping of charge (Q) in a closed ring geometry is not quantized even in the strict adiabatic limit. The deviation form exact quantization can be related to the Thouless conductance. We use Kubo formalism as a starting point for the calculation of both the dissipative and the adiabatic contributions to Q. As an application we bring examples for classical dissipative pumping, classical adiabatic pumping, and in particular we make an explicit calculation for quantum pumping in case of the simplest pumping device, which is a 3 site lattice model.
We investigate adiabatic charge pumping in disordered system in one dimension with open and closed boundary conditions. In contrast to the Thouless charge pumping, the system has no gap even though all the states are localized, i.e., strong localization. Charge pumping can be achieved by making a loop adiabatically in the two-dimensional parameter space of the Hamiltonian. It is because there are many $δ$-function-like fluxes distributed over the parameter space with random strength, in sharp contrast to the single $δ$-function in the pure case. This provides a new and more efficient way of ch…
Quantum pumping in closed systems is considered. We explain that the Kubo formula contains all the physically relevant ingredients for the calculation of the pumped charge ($Q$) within the framework of linear response theory. The relation to the common formulations of adiabatic transport and ``geometric magnetism" is clarified. We distinguish between adiabatic and dissipative contributions to $Q$. On the one hand we observe that adiabatic pumping does not have to be quantized. On the other hand we define circumstances in which quantized adiabatic pumping holds as an approximation. The deviatio…
The transfer of conserved charges through insulating matter via smooth deformations of the Hamiltonian is known as quantum adiabatic, or Thouless, pumping. Central to this phenomenon are Hamiltonians whose insulating gap is controlled by a multi-dimensional (usually two-dimensional) parameter space in which paths can be defined for adiabatic changes in the Hamiltonian, i.e., without closing the gap. Here, we extend the concept of Thouless pumps of band insulators by considering a larger, three-dimensional parameter space. We show that the connectivity of this parameter space is crucial for def…
We have numerically studied a non-adiabatic charge transport in the quantum Hall system pumped by a magnetic flux, as one of the simplest theoretical realizations of non-adiabatic Thouless pumping. In the adiabatic limit, a pumped charge is quantized, known as Laughlin's argument in a cylindrical lattice. In a uniform electric field, we obtained a formula connecting quantized pumping in the adiabatic limit and no-pumping in the sudden limit. The intermediate region between the two limits is determined by the Landau gap. A randomness or impurity effect is also discussed.
The discovery of the quantization of particle transport in adiabatic pumping cycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linked the Chern number, a topological invariant characterizing the quantum Hall effect in two-dimensional electron gases, with the topology of dynamical periodic systems in one dimension. Here, we demonstrate its counterpart for higher-order topology. Specifically, we show that adiabatic cycles in two-dimensional crystals with vanishing dipole moments (and therefore zero overall particle transport) can nevertheless be topologically nontrivial. T…
