Thouless's quantum adiabatic pumping is of fundamental interest to condensed-matter physics. It originally considered a zero-temperature equilibrium state uniformly occupying all the bands below a Fermi surface. In light of recent direct simulations of Thouless's concept in cold-atom systems, this paper investigates the dynamics of quantum adiabatic pumping subject to dephasing for rather general initial states with nonuniform populations and possibly interband coherence. Using a theory based on pure-dephasing Lindblad evolution, we find that the pumping is contributed by two parts of different nature: a dephasing-modified geometric part weighted by initial Bloch state populations and an interband-coherence-induced part compromised by dephasing, both of them being independent of the pumping time scale. The overall pumping reflects an interplay of the band topology, initial state populations, initial state coherence, and dephasing. Theoretical results are carefully checked in a Chern insulator model coupled to a pure-dephasing environment, providing a useful starting point to understand and coherently control quantum adiabatic pumping in general situations.
Thouless's quantum adiabatic pumping is of fundamental interest to condensed-matter physics. It originally considered a zero-temperature equilibrium state uniformly occupying all the bands below a Fermi surface. In light of recent direct simulations of Thouless's concept in cold-atom systems, this paper investigates the dynamics of quantum adiabatic pumping subject to dephasing for rather general initial states with nonuniform populations and possibly interband coherence. Using a theory based on pure-dephasing Lindblad evolution, we find that the pumping is contributed by two parts of different nature: a dephasing-modified geometric part weighted by initial Bloch state populations and an interband-coherence-induced part compromised by dephasing, both of them being independent of the pumping time scale. The overall pumping reflects an interplay of the band topology, initial state populations, initial state coherence, and dephasing. Theoretical results are carefully checked in a Chern insulator model coupled to a pure-dephasing environment, providing a useful starting point to understand and coherently control quantum adiabatic pumping in general situations.
The adiabatic charge pumping of a nonequilibrium 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 noninteracting 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 to adiabatic pumping. In particular, interband coherence effects can be clearly observed by adjusting the switch-on rates with different adiabatic pumping protocols and by scanning the duration of many-body interaction prior to adiabatic pumping. The time dependence of single-particle interband coherence in the presence of many-body interaction can then be examined in detail. As an interesting side result, for relatively weak interaction strength, it is found that the difference in the pumped charges between different pumping protocols vanishes if a coherence measure defined by the single-particle density matrix in the sublattice representation reaches its local minima. Our results hence provide an interesting means to quantitatively probe the dynamics of quantum coherence in the presence of many-body interaction (e.g., in a thermalization process).
The manifestations of topology are ubiquitous in condensed matter physics. One of the most striking examples is the integer quantum Hall effect, which served as a theoretical basis for developing many classes of new materials in the last years such as topological insulators. It has been realized that topology can manifest itself also in time-dependent quantum systems. The question that we try to address in this thesis is how much of these topological structures can be harnessed in the realistic dynamics of a periodically driven closed quantum system. We investigate two kinds of topological periodically driven systems Thouless pumping and Floquet Chern insulators. Our analysis shows that the nonequilibrium occupations of the eigenvalues of the Floquet Hamiltonian, the so called quasienergies, play a crucial role. In the case of Thouless pumping we analysed the pumped charge averaged over many cycles and discovered that the corrections to perfect quantization of the pumped charge are actually quadratic in the frequency of the driving for a suddenly switched-on driving. In the case of Floquet Chern insulators, we studied fermions on the honeycomb lattice subjected to a circularly polarised field. We found that while the quasienergy bulk states can be populated in a controlled way, edge states get unavoidable excitations due to exponentially small gaps preventing adiabaticity. These defects reflect in nonequilibrium currents flowing at the edges, that can be manipulated by tailoring the parameters of the periodic driving. Nevertheless, the nonequilibrium state undergoes a generalized form of topological transition, thanks to the controlled population of bulk states. We describe it with a generalized version of the Chern marker of Bianco and Resta
We describe the effect of pure dephasing upon the time-dependent dynamics of two-state quantum systems in the framework of a Lindblad equation for the time evolution of the density matrix. A uniform approximate formula is derived, which modifies the corresponding lossless transition probability by an exponential factor containing the dephasing rate and the interaction parameters. This formula is asymptotically exact in both the diabatic and adiabatic limits; comparison with numerical results shows that it is highly accurate also in the intermediate range. Several two-state models are considered in more detail, including the Landau-Zener, Rosen-Zener, Allen-Eberly, and Demkov-Kunike models, along with several other models, such as a Gaussian model and a Landau-Zener model with a pulsed coupling.
We consider theoretically the nonlinear quantized Thouless pumping of a Bose-Einstein condensate loaded in two-dimensional dynamical optical lattices. We encountered three different scenarios of the pumping: a quasilinear one occurring for gradually dispersing wave packets, transport carried by a single two-dimensional soliton, and a multisoliton regime when the initial wave packet splits into several solitons. The scenario to be realized depends on the number of atoms in the initial wave packet and on the strength of the two-body interactions. The magnitude and direction of the displacement of a wave packet are determined by Chern numbers of the populated energy bands and by the interband transitions induced by two-body interactions. As a case example we explore a separable potential created by optical lattices whose constitutive sublattices undergo relative motion in the orthogonal directions. For such potentials, obeying parity-time symmetry, fractional Chern numbers, computed over half period of the evolution, acquire relevance. We focus mainly on solitonic scenarios, showing that one-soliton pumping occurs at relatively small as well as at sufficiently large amplitudes of the initial wave packet, while at intermediate amplitudes the transport is multisolitonic. We also describe peculiarities of the pumping characterized by two different commensurate periods of the modulations of the lattices in the orthogonal directions.
A topological “Thouless” pump represents the quantized motion of particles in response to a slow, cyclic modulation of external control parameters. The Thouless pump, like the quantum Hall effect, is of fundamental interest in physics, because it links physically measurable quantities, such as particle currents, to geometric properties of the experimental system, which can be robust against perturbations and, thus, technologically useful. So far, experiments probing the interplay between topology and interparticle interactions have remained relatively scarce. Here, we observe a Thouless-type charge pump in which the particle current and its directionality inherently rely on the presence of strong interactions. Experimentally, we utilize a two-component Fermi gas in a dynamical superlattice which does not exhibit a sliding motion and remains trivial in the single-particle regime. However, when tuning interparticle interactions from zero to positive values, the system undergoes a transition from being stationary to drifting in one direction, consistent with quantized pumping in the first cycle. Remarkably, the topology of the interacting pump trajectory cannot be adiabatically connected to a noninteracting limit, highlighted by the fact that only one atom is transferred per cycle. Our experiments suggest that Thouless charge pumps are promising platforms to gain insights into interaction-driven topological transitions and topological quantum matter. Published by the American Physical Society 2024
We develop a theory of adiabatic response for open systems governed by Lindblad evolutions. The theory determines the dependence of the response coefficients on the dephasing rates and allows for residual dissipation even when the ground state is protected by a spectral gap . We give the quantum response a geometric interpretation in terms of Hilbert space projections: for a two-level system and, more generally, for systems with a suitable functional form of the dephasing, the dissipative and non-dissipative parts of the response are linked to a metric and to a symplectic form. The metric is the Fubini–Study metric and the symplectic form is the adiabatic curvature. When the metric and symplectic structures are compatible , the non-dissipative part of the inverse matrix of response coefficients turns out to be immune to dephasing . We give three examples of physical systems whose quantum states induce compatible metric and symplectic structures on control space: qubit, coherent states and a model of the integer quantum Hall effect.