arXiv subjects

André Eckardt

Publications and source records attributed to André Eckardt.

At least 55 records · Page 3Linked to original sources

arXiv2021

Robust and Ultrafast State Preparation by Ramping Artificial Gauge Potentials

The implementation of static artificial magnetic fields in ultracold atomic systems has become a powerful tool, e.g. for simulating quantum-Hall physics with charge-neutral atoms. Taking an interacting bosonic flux ladder as a minimal model, we investigate protocols for adiabatic state preparation via magnetic flux ramps. Considering the fact that it is actually the artificial vector potential (in the form of Peierls phases) that can be experimentally engineered in optical lattices, rather than the magnetic field, we find that the time required for adiabatic state preparation dramatically depends on which pattern of Peierls phases is used. This can be understood intuitively by noting that different patterns of time-dependent Peierls phases that all give rise to the same magnetic field ramp, generally lead to different artificial electric fields during the ramp. Remarkably, we find that an optimal choice allows for preparing the ground state almost instantaneously. We relate this observation to shortcuts to adiabaticity via counterdiabatic driving. Our findings open new possibilities for robust state preparation in atomic quantum simulators.

cond-mat.quant-gas↗

arXiv2020

Realization of an anomalous Floquet topological system with ultracold atoms

Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties. In particular, it has been employed to study topological phenomena in a variety of different platforms. In driven systems, the topological properties of the quasienergy bands can often be determined by standard topological invariants, such as Chern numbers, which are commonly used in static systems. However, due to the periodic nature of the quasienergy spectrum, this topological description is incomplete and new invariants are required to fully capture the topological properties of these driven settings. Most prominently, there exist two-dimensional anomalous Floquet systems that exhibit robust chiral edge modes, despite all Chern numbers are equal to zero. Here, we realize such a system with bosonic atoms in a periodically-driven honeycomb lattice and infer the complete set of topological invariants from energy gap measurements and local Hall deflections.

cond-mat.quant-gas↗

arXiv2020

Prethermal memory loss in interacting quantum systems coupled to thermal baths

We study the relaxation dynamics of an extended Fermi-Hubbard chain with a strong Wannier-Stark potential tilt coupled to a bath. When the system is subjected to dephasing noise, starting from a pure initial state the system's total von Neumann entropy is found to grow monotonously. The scenario becomes rather different when the system is coupled to a thermal bath of finite temperature. Here, for sufficiently large field gradients and initial energies, the entropy peaks in time and almost reaches its largest possible value (corresponding to the maximally mixed state), long before the system relaxes to thermal equilibrium. This entropy peak signals a prethermal memory loss and, relative to the time where it occurs, the system is found to exhibit a simple scaling behavior in space and time. By comparing the system's dynamics to that of a simplified model, the underlying mechanism is found to be related to the localization property of the Wannier-Stark system, which favors dissipative coupling between eigenstates that are close in energy.

cond-mat.dis-nn↗

arXiv2020

Design and characterization of a quantum heat pump in a driven quantum gas

We propose the implementation of a quantum heat pump with ultracold atoms. It is based on two periodically driven coherently coupled quantum dots using ultracold atoms. Each dot possesses two relevant quantum states and is coupled to a fermionic reservoir. The working principle is based on energy-selective driving-induced resonant tunneling processes, where a particle that tunnels from one dot to the other either absorbs or emits the energy quantum $\hbarω$ associated with the driving frequency, depending on its energy. We characterize the device using Floquet theory and compare simple analytical estimates to numerical simulations based on the Floquet-Born-Markov formalism. In particular, we show that driving-induced heating is directly linked to the micromotion of the Floquet states of the system.

cond-mat.quant-gas↗

arXiv2020

The optimal frequency window for Floquet engineering in optical lattices

The concept of Floquet engineering is to subject a quantum system to time-periodic driving in such a way that it acquires interesting novel properties. It has been employed, for instance, for the realization of artificial magnetic fluxes in optical lattices and, typically, it is based on two approximations. First, the driving frequency is assumed to be low enough to suppress resonant excitations to high-lying states above some energy gap separating a low energy subspace from excited states. Second, the driving frequency is still assumed to be large compared to the energy scales of the low-energy subspace, so that also resonant excitations within this space are negligible. Eventually, however, deviations from both approximations will lead to unwanted heating on a time scale $τ$. Using the example of a one-dimensional system of repulsively interacting bosons in a shaken optical lattice, we investigate the optimal frequency (window) that maximizes $τ$. As a main result, we find that, when increasing the lattice depth, $τ$ increases faster than the experimentally relevant time scale given by the tunneling time $\hbar/J$, so that Floquet heating becomes suppressed.

cond-mat.quant-gas↗

arXiv2019

Phasonic Spectroscopy of a Quantum Gas in a Quasicrystalline Lattice

Phasonic degrees of freedom are unique to quasiperiodic structures, and play a central role in poorly-understood properties of quasicrystals from excitation spectra to wavefunction statistics to electronic transport. However, phasons are challenging to access dynamically in the solid state due to their complex long-range character and the effects of disorder and strain. We report phasonic spectroscopy of a quantum gas in a one-dimensional quasicrystalline optical lattice. We observe that strong phasonic driving produces a nonperturbative high-harmonic plateau strikingly different from the effects of standard dipolar driving. Tuning the potential from crystalline to quasicrystalline, we identify spectroscopic signatures of quasiperiodicity and interactions and map the emergence of a multifractal energy spectrum, opening a path to direct imaging of the Hofstadter butterfly.

cond-mat.quant-gas↗

arXiv2019

Is there a Floquet Lindbladian?

The stroboscopic evolution of a time-periodically driven isolated quantum system can always be described by an effective time-independent Hamiltonian. Whether this concept can be generalized to open Floquet systems, described by a Markovian master equation with time-periodic Lindbladian generator, remains an open question. By using a two level system as a model, we explicitly show the existence of two well-defined parameter regions. In one region the stroboscopic evolution can be described by a Markovian master equation with a time-independent Floquet Lindbladian. In the other it cannot; but here the one-cycle evolution operator can be reproduced with an effective non-Markovian master equation that is homogeneous but non-local in time. Interestingly, we find that the boundary between the phases depends on when the evolution is stroboscopically monitored. This reveals the non-trivial role played by the micromotion in the dynamics of open Floquet systems.

quant-ph↗

arXiv2019

Hopf characterization of two-dimensional Floquet topological insulators

We present a topological characterization of time-periodically driven two-band models in 2+1 dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect to both time and the underlying two-dimensional momentum space constitutes a map from a three dimensional torus to the Bloch sphere. As a result, we find that the driven system can be understood by appealing to a Hopf map that is directly constructed from the micromotion of the drive. Previously found winding numbers are shown to correspond to Hopf invariants, which are associated with linking numbers describing the topology of knots in three dimensions. Moreover, after being cast as a Hopf insulator, not only the Chern numbers, but also the winding numbers of the Floquet topological insulator become accessible in experiments as linking numbers. We exploit this description to propose a feasible scheme for measuring the complete set of their Floquet topological invariants in optical lattices.

cond-mat.quant-gas↗

arXiv2019

Quantifying and controlling prethermal nonergodicity in interacting Floquet matter

The use of periodic driving for synthesizing many-body quantum states depends crucially on the existence of a prethermal regime, which exhibits drive-tunable properties while forestalling the effects of heating. This motivates the search for direct experimental probes of the underlying localized nonergodic nature of the wave function in this metastable regime. We report experiments on a many-body Floquet system consisting of atoms in an optical lattice subjected to ultrastrong sign-changing amplitude modulation. Using a double-quench protocol we measure an inverse participation ratio quantifying the degree of prethermal localization as a function of tunable drive parameters and interactions. We obtain a complete prethermal map of the drive-dependent properties of Floquet matter spanning four square decades of parameter space. Following the full time evolution, we observe sequential formation of two prethermal plateaux, interaction-driven ergodicity, and strongly frequency-dependent dynamics of long-time thermalization. The quantitative characterization of the prethermal Floquet matter realized in these experiments, along with the demonstration of control of its properties by variation of drive parameters and interactions, opens a new frontier for probing far-from-equilibrium quantum statistical mechanics and new possibilities for dynamical quantum engineering.

quant-ph↗

arXiv2019

How to Directly Measure Floquet Topological Invariants in Optical Lattices

The classification of topological Floquet systems with time-periodic Hamiltonians transcends that of static systems. For example, spinless fermions in periodically driven two-dimensional lattices are not completely characterized by the Chern numbers of the quasienergy bands, but rather by a set of winding numbers associated with the quasienergy gaps. We propose a scheme for measuring these winding numbers in a system of fermionic cold atoms in a periodically driven optical lattice efficiently and directly. It is based on the construction of a one-parameter family of experimentally feasible drives, continuously connecting the Floquet system of interest to a trivial reference system. The winding numbers are then determined by the identification and the tomography of the band-touching singularities occurring on the way. As a byproduct, we also propose a method for probing spectral properties of time evolution operators via a time analog of crystallography.

cond-mat.quant-gas↗

arXiv2019

Bath-induced decay of Stark many-body localization

We investigate the relaxation dynamics of an interacting Stark-localized system coupled to a dephasing bath, and compare its behavior to the conventional disorder-induced many body localized system. Specifically, we study the dynamics of population imbalance between even and odd sites, and the growth of the von Neumann entropy. For a large potential gradient, the imbalance is found to decay on a time scale that grows quadratically with the Wannier-Stark tilt. For the non-interacting system, it shows an exponential decay, which becomes a stretched exponential decay in the presence of finite interactions. This is different from a system with disorder-induced localization, where the imbalance exhibits a stretched exponential decay also for vanishing interactions. As another clear qualitative difference, we do not find a logarithmically slow growth of the von-Neumann entropy as it is found for the disordered system. Our findings can immediately be tested experimentally with ultracold atoms in optical lattices.

cond-mat.dis-nn↗

arXiv2019

Measuring topology by dynamics: Chern number from linking number

Integer-valued topological indices, characterizing nonlocal properties of quantum states of matter, are known to directly predict robust physical properties of equilibrium systems. The Chern number, e.g., determines the quantized Hall conductivity of an insulator. Using fermionic atoms in a periodically driven optical lattice, here we demonstrate experimentally that the Chern number determines also the far-from-equilibrium dynamics of a quantum system. Following the proposal of ref. [Wang et al., Phys. Rev. Lett. 118, 185701 (2017)] and extending it to Floquet systems, we measure the linking number that characterizes the trajectories of momentum-space vortices emerging after a strong quench. We observe that it directly corresponds to the ground-state Chern number. This one-to-one relation between a dynamical and a static topological index allows us to experimentally map out the phase diagram of our system. Furthermore, we measure the instantaneous Chern number and show that it remains zero under the unitary dynamics.

cond-mat.quant-gas↗

arXiv2019

Measuring the single-particle density matrix for fermions and hard-core bosons in an optical lattice

Ultracold atoms in optical lattices provide clean, tunable, and well-isolated realizations of paradigmatic quantum lattice models. With the recent advent of quantum-gas microscopes, they now also offer the possibility to measure the occupations of individual lattice sites. What, however, has not yet been achieved is to measure those elements of the single-particle density matrix, which are off-diagonal in the occupation basis. Here, we propose a scheme to access these basic quantities both for fermions as well as hard-core bosons and investigate its accuracy and feasibility. The scheme relies on the engineering of a large effective tunnel coupling between distant lattice sites and a protocol that is based on measuring site occupations after two subsequent quenches.

cond-mat.quant-gas↗

arXiv2019

Creating, probing, and manipulating fractionally charged excitations of fractional Chern insulators in optical lattices

We propose a set of schemes to create and probe fractionally charged excitations of a fractional Chern insulator state in an optical lattice. This includes the creation of localized quasiparticles and quasiholes using both static local defects and the dynamical local insertion of synthetic flux quanta. Simulations of repulsively interacting bosons on a finite square lattice with experimentally relevant open boundary conditions show that already a four-particle system exhibits signatures of charge fractionalization in the quantum-Hall-like state at the filling fraction of $1/2$ particle per flux quantum. This result is favorable for the prospects of adiabatic preparation of fractional Chern insulators. Our work is inspired by recent experimental breakthroughs in atomic quantum gases: the realization of strong artificial magnetic fields in optical lattices, the ability of single-site addressing in quantum gas microscopes, and the preparation of low-entropy insulating states by engineering an entropy-absorbing metallic reservoir.

cond-mat.quant-gas↗

arXiv2018

Describing many-body localized systems in thermal environments

In this work we formulate an efficient method for the description of many-body localized systems in weak contact with thermal environments at temperature $T$. For this purpose we exploit the representation of the system in terms of quasi-local integrals of motion ($l$-bits) to derive a quantum master equation using Born-Markov approximations. We show how this equation can be treated by using quantum-jump Monte-Carlo techniques as well as by deriving approximate kinetic equations of motion. As an example, we consider the one-dimensional Anderson model for spinless fermions including also nearest-neighbor interactions, which we diagonalize approximately by employing a recently proposed method valid in the limit of strong disorder and weak interactions. Coupling the system to a global thermal bath, we study the transport between two leads with different chemical potentials at both of its ends. We find that the temperature-dependent current is captured by an interaction-dependent version of Mott's law for variable range hopping, where transport is enhanced/lowered depending on whether the interactions are attractive or repulsive, respectively. We interpret these results in terms of spatio-energetic correlations between the $l$-bits.

cond-mat.dis-nn↗

arXiv2018

Charge density wave and charge pump of interacting fermions in circularly shaken hexagonal optical lattices

We analyze strong correlation effects and topological properties of interacting fermions with a Falicov-Kimball type interaction in circularly shaken hexagonal optical lattices, which can be effectively described by the Haldane-Falicov-Kimball model, using the real-space Floquet dynamical mean-field theory (DMFT). The Haldane model, a paradigmatic model of the Chern insulator, is experimentally relevant, because it has been realized using circularly shaken hexagonal optical lattices. We show that in the presence of staggering a charge density wave emerges, which is affected by interactions and resonant tunneling. We demonstrate that interactions smear out the edge states by introducing a finite life time of quasiparticles. Even though a general method for calculating the topological invariant of a nonequilibrium steady state is lacking, we extract the topological invariant using a Laughlin charge pump set-up. We find and attribute to the dissipations into the bath connected to every lattice site, which is intrinsic to real-space Floquet DMFT methods, that the pumped charge is not an integer even for the non-interacting case at very low reservoir temperatures. Furthermore, using the rate equation based on the Floquet-Born-Markov approximation, we calculate the charge pump from the rate equations for the non-interacting case to identify the role of the spectral properties of the bath. Starting from this approach we propose an experimental protocol for measuring quantized charge pumping.

cond-mat.quant-gas↗

arXiv2018

Floquet engineering of optical solenoids and quantized charge pumping along tailored paths in two-dimensional Chern insulators

The insertion of a local magnetic flux, as the one created by a thin solenoid, plays an important role in gedanken experiments of quantum Hall physics. By combining Floquet engineering of artificial magnetic fields with the ability of single-site addressing in quantum-gas microscopes, we propose a scheme for the realization of such local solenoid-type magnetic fields in optical lattices. We show that it can be employed to manipulate and probe elementary excitations of a topological Chern insulator. This includes quantized adiabatic charge pumping along tailored paths inside the bulk, as well as the controlled population of edge modes.

cond-mat.quant-gas↗

arXiv2018

On the number of Bose-selected modes in driven-dissipative ideal Bose gases

In an ideal Bose gas that is driven into a steady state far from thermal equilibrium, a generalized form of Bose condensation can occur. Namely, the single-particle states unambiguously separate into two groups: the group of Bose-selected states, whose occupations increase linearly with the total particle number, and the group of all other states whose occupations saturate [Phys. Rev. Lett. 111, 240405 (2013)]. However, so far very little is known about how the number of Bose-selected states depends on the properties of the system and its coupling to the environment. The answer to this question is crucial since systems hosting a single, a few, or an extensive number of Bose-selected states will show rather different behavior. While in the former two scenarios each selected mode acquires a macroscopic occupation, corresponding to (fragmented) Bose condensation, the latter case rather bears resemblance to a high-temperature state of matter. In this paper, we systematically investigate the number of Bose-selected states, considering different classes of the rate matrices that characterize the driven-dissipative ideal Bose gases in the limit of weak system-bath coupling. These include rate matrices with continuum limit, rate matrices of chaotic driven systems, random rate matrices, and rate matrices resulting from thermal baths that couple to a few observables only.

cond-mat.quant-gas↗