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.
We provide provide a detailed study of biasless coherent transport of singlet electron pairs in one-dimensional (1D) channels induced by electron-electron interactions that are time-varying in certain spatially localized regions of the channel. When the time variation is cyclic, the mechanism is analogous to the adiabatic quantum pumping of charge and spin previously studied. However, the presence of interactions that vary only in localized regions of space requires an intrinsically two-body description which is irreducible to the 1D single particle scattering matrix elements that are sufficient to describe quantum pumping of charge and spin. Here we derive a generalized theory for the pumping of such interacting pairs starting from first principles. We show that the standard description of charge pumping is contained within our more broadly applicable expressions. We then apply our general results to a concrete lattice model and obtain an exact analytical expression for the pumped singlet current. We further demonstrate that such a model can be implemented with a chain of currently available quantum dots with certain minor modifications that we suggest; we present a detailed numerical feasibility analysis of the characteristics of such experimentally realizable quantum dots, showing that the requirements for a measurable pumped singlet current are within experimental range.
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
Ultracold atoms in optical lattices constitute a versatile many-body platform with highly tunable parameters, allowing us to emulate a multitude of complex quantum systems, in the laboratory, even those eluding analytical treatment. In particular, the nonequilibrium dynamics of strongly correlated many-body systems represents one of the most challenging problems of modern quantum physics, with applications ranging from thermalization dynamics and transport properties to the management of correlations and the control of the dynamics. Understanding nonequilibrium phenomena of strongly correlated systems is a formidable task. A very promising route to gain insight into such systems is to examine few-body setups which contain only a few relevant degrees of freedom, yet incorporating the quantum correlations between the particles.
The present dissertation contributes to the understanding of the nonequilibrium dynamics of strongly-correlated quantum many-body systems by exploring systems of few-bosons
− of one or two species
− trapped in optical lattices. The systems are driven out-of-equilibrium either by performing a quench of a Hamiltonian parameter or by considering a time-periodic modulation of the external confinement. In the course of several consecutive works, we showcase different ways to couple the nonequilibrium modes, while unveiling their correlated nature and microscopic origin. To simulate the nonequilibrium dynamics, a sophisticated, highly flexible ab-initio method for numerically solving the time-dependent many-body Schrodinger equation is utilized, namely the Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Atomic Mixtures (ML-MCTDHX).
Within the first part we study in six consecutive works the correlated nonequilibrium dynamics of few-boson systems in one-dimensional finite lattices. Starting from weak interactions, it is shown that a sudden increase of the interaction strength generates a global density-wave tunneling dynamics as well as intrawell breathing and cradle-like excited-band processes. The cradle process is a dipole-like process generated by the quench-induced over-barrier transport and it is one of the central results of the present thesis. Remarkably enough, the interaction quenches couple the density-wave and cradle modes, inducing resonance phenomena between the inter and intrawell dynamics. We further show that the cradle mode is inherently related to the initial delocalization and, following a quench from strong-to-weak interactions, can be excited only for incommensurate setups with filling larger than unity. Alternatively, a sudden ramping down of the lattice depth which favors the spatial delocalization is employed to access the cradle mode for setups with filling smaller than unity. Following a multiple interaction quench protocol, we observe the rise of several lowest-band tunneling modes as well as the cradle and the breathing mode. Besides the cradle mode, all other excited modes are highly tunable possessing different frequencies during and in between the quenches. In the excitation dynamics a monotonic behavior with increasing quench amplitude and a non-linear dependence on the duration of the application of the quenched interaction strength is revealed. Additionally, a periodic population transfer between momenta for quenches of increasing interaction is observed, with a power-law frequency dependence on the quench amplitude. Linear interaction quenches from a superfluid to a Mott-insulator state excite various inter- and intraband tunneling modes. The competition between the quench rate and the interparticle repulsion leads to a resonant dynamical response, at moderate ramp times, being related to avoided-crossings in the many-body eigenspectrum.
The resultant higher-band excitation dynamics is shown to obey an exponential decay possessing two distinct time scales with varying ramp time. Inspecting the crossover from shallow to deep lattices we find that for a diabatic quench the excited-band fraction decreases, while approaching the adiabatic limit it exhibits a nonlinear behavior for increasing height of the potential barrier. Quenching from strong-to-weak interactions leads to a melting of the Mott-insulator and negligible higher-band excitations.
Performing quenches either on the wavevector or the phase of a spatially dependent interaction profile triggers various tunneling channels and a rich excitation dynamics which is amplified for increasing inhomogeneity amplitude. Most importantly, the phase quench is shown to induce a directional transport enabling us to discern, otherwise, energetically degenerate tunneling pathways.
Finally, a periodic population transfer between distinct momenta for quenches of increasing wavevector and a directed occupation of higher momenta following a phase quench is observed. Employing a quench of an additional harmonic trap from strong-to-weak confinement, we find that the competition between the initial localization and the repulsive interaction leads to a resonant response of the system related to avoided-crossings in the many-body eigenspectrum with varying final trap frequency. Furthermore, we show that these avoided-crossings can be utilized to prepare the system in a desired state.
The second part comprises two efforts and is devoted to the study of the nonequilibrium dynamics of finite ultracold bosonic ensembles in periodically driven one-dimensional optical lattices. For a shaken lattice, a wide range of driving frequencies is covered and a resonant behavior of the intrawell dynamics is revealed and found to be related to a rich intraband excitation spectrum.
Moreover, it is shown that for increasing repulsion a strong suppression of the interwell tunneling and an enhanced excitation dynamics occurs. For a vibrating lattice, an additional interaction quench gives rise to admixtures of different excitations in the outer wells, an enhanced breathing in the center and an amplification of the emerging tunneling dynamics. The occurence of multiple resonances between the inter- and intrawell dynamics at different quench amplitudes is revealed, with the position of the resonances being tunable via the driving frequency and thus allowing for further control of the mode coupling in optical lattices.
In the third and final part of this thesis we unravel the quench dynamics of a Bose-Bose and a Bose-Fermi mixture. Utilizing an interspecies interaction quench we cross the miscibility-immiscibility threshold in a harmonically confined Bose-Bose mixture. We show that increasing the interspecies repulsion coefficient results in a filamentation of the density of each species, with the spontaneously generated filaments being strongly correlated and exhibiting domain-wall structures. Strikingly, by following the reverse quench protocol, i.e., upon decreasing the interspecies interaction strength, the formation of multiple dark-antidark solitary waves is observed. These solitary wave structures are found to decay into the many-body environment, soon after their generation in sharp contrast to the predictions of the mean-field approximation. To relate our findings with possible experimental realizations, we simulate, for the first time for binary mixtures, single-shot images showcasing that the growth rate of the variance of a sample of single-shots probes the degree of entanglement inherent in the system. As a next step we investigate the expansion dynamics of a mass balanced Bose-Fermi mixture confined in a one-dimensional optical lattice upon quenching an imposed harmonic trap from strong-to-weak confinement. Tuning the interspecies interaction strength we realize the immiscible and miscible correlated ground state phases. We further show that the system's dynamical response crucially depends on the initial phase and consists of an expansion of each cloud and an interwell tunneling dynamics. Varying the quench amplitude and referring to a fixed phase a multitude of response regimes is unveiled, being richer within the immiscible phase, which are described by distinct expansion strengths and tunneling channels. Finally, in the expansion dynamics a two-body anti-correlated behavior between the predominantly occupied wells is unveiled.
As the basis for generating multi-particle quantum correlations, inter-particle interaction plays a crucial role in collective quantum phenomena, quantum phase transitions, and quantum information processing. It can profoundly alter the band structure of quantum many-body systems and give rise to exotic topological phenomena. Conventional topological pumping, which has been well demonstrated in driven linear or noninteracting systems, may break down in the presence of strong interaction. However, the interplay between band topology and interaction could also induce emergent topological pumping of interacting particles, but its experimental realization has proven challenging. Here we demonstrate interaction-induced topological pumping in a solid-state quantum system comprising an array of 36 superconducting qubits. With strong interaction inherent in the qubits and site-resolved controllability of the lattice potential and hopping strength, we realize the topological Thouless pumping of single and two bounded particles. Beyond these topological phenomena with linear or noninteracting counterparts, we also observe topologically resonant tunneling and asymmetric edge-state transport of interacting particles. Our work creates a paradigm for multi-particle topological effects, and provides a new pathway to the study of exotic topological phenomena, many-body quantum transport, and quantum information transfer.
Motivated by experimental realizations of integer quantized charge pumping in one-dimensional superlattices [Nat. Phys. 12, 350 (2016); Nat. Phys. 12, 296 (2016)], we generalize and propose the adiabatic pumping of a fractionalized charge in interacting bosonic systems. This is achieved by dynamically sweeping the modulated potential in a class of one-dimensional interacting systems. As concrete examples, we show the charge pumping of interacting bosons at certain fractionally occupied fillings. We find that, for a given ground state, the charge pumping in a complete potential cycle is quantized to the fractional value related to the corresponding Chern number, characterized by the motion of the charge polarization per site. Moreover, the difference between charge polarizations of two ground states is quantized to an intrinsic constant revealing the fractional elementary charge of quasiparticle.