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We discuss impurities in a trapped one-dimensional Bose gas with arbitrary boson-boson and boson-impurity interactions. To fully account for quantum effects, in particular in the regime of strong boson-boson interactions, we employ numerical simulations based on the density-matrix renormalization group (DMRG) and analytic approximations exploiting the mapping to weakly interacting fermions. Mobile impurities in a box potential undergo a phase transition between a delocalized state and a solution localized at one of the potential edges upon increasing the impurity-boson interaction. While a mean-field ansatz based on coupled Gross-Pitaevski -- Schr\"odinger equations gives reasonable predictions of this transition, it also predicts the existence of a self-localized polaron solution, which we show to be an artifact of the underlying decoupling approximation. This demonstrates that impurity-boson correlations are important even in the limit of weak boson-boson interactions, where mean-field approaches are expected to work well. Furthermore we calculate the energy of a single polaron formed by a heavy impurity for arbitrary interaction strengths and give analytical approximations for large but finite boson-boson couplings. Finally we numerically determine the polaron-polaron interaction potential in Born-Oppenheimer approximation, which in the Tonks gas limit is oscillatory due to Friedel oscillations in the Bose gas.

In recent experiments, a novel type of cascaded quantum system has been realized using nanofiber-coupled cold atomic ensembles. This setup has enabled the study of superradiant decay of highly excited collective spin states of up to a thousand atoms, featuring unidirectional coupling mediated by the waveguide mode. The complexity arising from the large, multi-excited ensemble and the cascaded interactions between atoms makes conventional simulation methods unsuitable for predicting the correlations of superradiant emission beyond the first order. To address this challenge, we developed a new simulation technique based on the truncated Wigner approximation for spins. Our stochastic simulation tool can predict the second-order quantum coherence function, $g^{(2)}$, along with other correlators of the light field emitted by a strongly excited cascaded system of two-level emitters. This approach thus provides an effective and scalable method for analyzing cascaded quantum systems with large numbers of particles.

The facilitation of Rydberg excitations in a gas of atoms provides an ideal model system to study epidemic evolution on (dynamic) networks and self organization of complex systems to the critical point of a non-equilibrium phase transition. Using Monte-Carlo simulations and a machine learning algorithm we show that the universality class of this phase transition can be tuned. The classes include directed percolation (DP), the most common class in short-range spreading models, and mean-field (MF) behavior, but also different types of anomalous directed percolation (ADP), characterized by rare long-range excitation processes. In a frozen gas, ground state atoms that can facilitate each other form a static network, for which we predict DP universality. Atomic motion then turns the network into a dynamic one with long-range (Levy-flight type) excitations. This leads to continuously varying critical exponents corresponding to the ADP universality class, eventually reaching MF behavior. These findings also explain the recently observed critical exponent of Rydberg facilitation in an ultra-cold gas experiment [Helmrich et al., Nature 577, 481 (2020)], which was in between DP and MF values.

We exploit controlled breaking of time-reversal symmetry to realize coherent routing of quantum information in spin networks. The key component of our scheme is a spin triangle whose chirality is determined by the quantum state of a control qubit which thus defines the propagation direction, or a superposition thereof, of the quantum information. We then consider a particular realization of a coherent router using Rydberg atoms. Our results can facilitate scalable quantum information processing and communication in large arrays of Rydberg atoms., Comment: 12 pages, 8 figures

We propose a mechanism for engineering chiral interactions in Rydberg atoms via a directional antiblockade condition, where an atom can change its state only if an atom to its right (or left) is excited. The scalability of our scheme enables us to explore the many-body dynamics of kinetically constrained models with unidirectional character. We observe non-ergodic behavior via either scars, confinement, or localization, upon simply tuning the strength of two driving fields acting on the atoms. We discuss how our mechanism persists in the presence of classical noise and how the degree of chirality in the interactions can be tuned, opening towards the frontier of directional, strongly correlated, quantum mechanics using neutral atoms arrays., Comment: 5+5 pages, 3+3 figures; close to published version

The excitation spread caused by Rydberg facilitation in a gas of laser driven atoms is an interesting model system for studying epidemic dynamics. We derive a mean-field approach to describe this facilitation process in the limits of high and low temperatures, which takes into account Rydberg blockade and the network character of excitation spreading in a low-temperature gas. As opposed to previous mean-field models, our approach accurately predicts all stages of the facilitation dynamics from the initial fast epidemic growth, an extended saturation period, to the final relaxation phase., Comment: arXiv admin note: text overlap with arXiv:2302.14145

Interfaces of light and matter serve as a platform for exciting many-body physics and photonic quantum technologies. Due to the recent experimental realization of atomic arrays at sub-wavelength spacings, collective interaction effects such as superradiance have regained substantial interest. Their analytical and numerical treatment is however quite challenging. Here we develop a semiclassical approach to this problem that allows to describe the coherent and dissipative many-body dynamics of interacting spins while taking into account lowest-order quantum fluctuations. For this purpose we extend the discrete truncated Wigner approximation, originally developed for unitarily coupled spins, to include collective, dissipative spin processes by means of truncated correspondence rules. This maps the dynamics of the atomic ensemble onto a set of semiclassical, numerically inexpensive stochastic differential equations. We benchmark our method with exact results for the case of Dicke decay, which shows excellent agreement. For small arrays we compare to exact simulations and a second order cumulant expansion, again showing good agreement at early times and at moderate to strong driving. We conclude by studying the radiative properties of a spatially extended three-dimensional, coherently driven gas and compare the coherence of the emitted light to experimental results., Comment: 25 pages, 5 figures

We discuss the dynamics of the formation of a Bose polaron when an impurity is injected into a weakly interacting one-dimensional Bose condensate. While for small impurity-boson couplings this process can be described within the Froehlich model as generation, emission and binding of Bogoliubov phonons, this is no longer adequate if the coupling becomes strong. To treat this regime we consider a mean-field approach beyond the Froehlich model which accounts for the backaction to the condensate, complemented with Truncated Wigner simulations to include quantum fluctuation. For the stationary polaron we find an energy-momentum relation that displays a smooth crossover from a convex to a concave dependence associated with a non-monotonous relation between impurity velocity and polaron momentum. For larger momenta the energy is a periodic function including regions of negative impurity velocity. Studying the polaron formation after turning on the impurity-boson coupling quasi adiabatically and in a sudden quench, we find a very rich scenario of dynamical regimes. Due to the build-up of an effective mass, the impurity is slowed down even if its initial velocity is below the Landau critical value. For larger initial velocities we find deceleration and even backscattering caused by emission of density waves or grey solitons and subsequent formation of stationary polaron states in different momentum sectors. In order to analyze the effect of quantum fluctuations we consider a trapped condensate to avoid 1D infrared divergencies. Using Truncated Wigner simulations in this case we show under what conditions the influence of quantum fluctuations is small., Comment: 25 pages, 13 figures

Robust states emerging at the boundary of a system constitute a hallmark for topological band structures. Other than in closed systems, topologically protected states can occur even in systems with a trivial band structure, if exposed to suitably modulated losses. Here, we study the dissipation-induced emergence of a topological band structure in a non-Hermitian one-dimensional lattice system, realized by arrays of plasmonic waveguides with tailored loss. We obtain direct evidence for a topological edge state that resides in the center of the band gap. By tuning dissipation and hopping, the formation and breakdown of an interface state between topologically distinct regions is demonstrated., Comment: 9 pages, 6 figures

The spread of excitations by Rydberg facilitation bears many similarities to epidemics. Such systems can be modeled with Monte-Carlo simulations of classical rate equations to great accuracy as a result of high dephasing. In this paper, we analyze the dynamics of a Rydberg many-body system in the facilitation regime in the limits of high and low temperatures. While in the high-temperature limit a homogeneous mean-field behaviour is recovered, characteristic effects of heterogeneity can be seen in a frozen gas. At large temperatures the system displays an absorbing-state phase transition and, in the presence of an additional loss channel, self-organized criticality. In a frozen or low-temperature gas, excitations are constrained to a network resembling an Erd\"os-Renyi graph. We show that the absorbing-state phase transition is replaced with an extended Griffiths phase, which we accurately describe by a susceptible-infected-susceptible model on the Erd\"os-Renyi network taking into account Rydberg blockade. Furthermore, we expand upon an existing macroscopic Langevin equation to more accurately describe the density of Rydberg atoms in the frozen and finite temperature regimes., Comment: 14 pages, 11 figures

The Born-Fock theorem is one of the most fundamental theorems of quantum mechanics and forms the basis for reliable and efficient navigation in the Hilbert space of a quantum system with a time-dependent Hamiltonian by adiabatic evolution. In the absence of level crossings, i.e. without degeneracies, and under adiabatic time evolution all eigenstates of the Hamiltonian keep their energetic order, labelled by a conserved integer quantum number. Thus controlling the eigenstates of the Hamiltonian and their energetic order in asymptotic limits allows to engineer a perfect adiabatic transfer between a large number of initial and target states. The fidelity of the state transfer is only limited by adiabaticity and the selection of target states is controlled by the integer invariant labelling the order of eigenstates. We here show for the example of a finite superlattice Wannier-Stark ladder, i.e. a one-dimensional lattice with alternating hopping amplitudes and constant potential gradient, that such an adiabatic control of eigenstates can be used to induce perfectly quantized single-particle transport across a pre-determined number of lattice sites. We dedicate this paper to the memory of our late friend and colleague Bruce Shore, who was an expert in adiabatic processes and taught us much about this field.

We propose and analyze a protocol to create and control the superfluid flow in a one dimensional, weakly interacting Bose gas by noisy point contacts coupled to the density of the bosons. Considering first a single contact in a static or moving condensate, we identify three different dynamical phases: I. a linear response regime, where the noise induces a coherent flow in proportion to the strength of the noise accompanied by a counterflow of the normal component of the gas, II. a Zeno regime with suppressed currents and negative differential current to noise characteristics, and III. for a non-vanishing relative velocity, a regime of continuous soliton emission. The velocity of the condensate at the dissipative impurity determines the threshold for Zeno suppression of the current through the point contact, and the onset of the non-stationary regime of soliton "shooting" from the defect. Generalizing to two point contacts in a condensate at rest we show that noise tuning can be employed to control, stabilize or eventually shunt the superfluid transport of particles along the segment which connects them, with perspectives for an atomtronic analogue of a superfluid-current source for studying quantum transport phenomena., Comment: 11 pages, 6 figures

Self-Organized Criticality (SOC) is a ubiquitous dynamical phenomenon believed to be responsible for the emergence of universal scale-invariant behavior in many, seemingly unrelated systems, such as forest fires, virus spreading or atomic excitation dynamics. SOC describes the buildup of large-scale and long-range spatio-temporal correlations as a result of only local interactions and dissipation. The simulation of SOC dynamics is typically based on Monte-Carlo (MC) methods, which are however numerically expensive and do not scale beyond certain system sizes. We investigate the use of Graph Neural Networks (GNNs) as an effective surrogate model to learn the dynamics operator for a paradigmatic SOC system, inspired by an experimentally accessible physics example: driven Rydberg atoms. To this end, we generalize existing GNN simulation approaches to predict dynamics for the internal state of the node. We show that we can accurately reproduce the MC dynamics as well as generalize along the two important axes of particle number and particle density. This paves the way to model much larger systems beyond the limits of traditional MC methods. While the exact system is inspired by the dynamics of Rydberg atoms, the approach is quite general and can readily be applied to other systems.

We present a systematic approach for the semiclassical treatment of many-body dynamics of interacting, open spin systems. Our approach overcomes some of the shortcomings of the recently developed discrete truncated Wigner approximation (DTWA) based on Monte-Carlo sampling in a discrete phase space that improves the classical treatment by accounting for lowest-order quantum fluctuations. We provide a rigorous derivation of the DTWA by embedding it in a continuous phase space, thereby introducing a hybrid discrete-continuous truncated Wigner approximation (DCTWA). We derive a set of operator-differential mappings that yield an exact equation of motion (EOM) for the continuous SU(2) Wigner function of spins. The standard DTWA is then recovered by a systematic neglection of specific terms in this exact EOM. The hybrid approach permits us to determine the validity conditions and to gain detailed understanding of the quality of the approximation, paving the way for systematic improvements. Furthermore, we show that the continuous embedding allows for a straightforward extension of the method to open spin systems subject to dephasing, losses and incoherent drive, while preserving the key advantages of the discrete approach, such as a positive definite Wigner distribution of typical initial states. We derive exact stochastic differential equations for processes which cannot be described by the standard DTWA due to the presence of non-classical noise. We illustrate our approach by applying it to the dissipative dynamics of Rydberg excitation of one-dimensional arrays of laser-driven atoms and compare it to exact results for small systems., Comment: 16 pages, 5 figures

We comment on the recent paper by Ghosh and \v{Z}nidari\v{c} (Phys. Rev. B 105, 144203 (2022)) which studies the growth of the number entropy $S_N$ in the Heisenberg model with random magnetic fields after a quantum quench. The authors present arguments for an intermediate power-law growth in time $t$ and a sub-ergodic saturation value, claiming consistency of their results with many-body localization (MBL) for strong disorder. We show that these interpretations are inconsistent with other recent studies and discuss specific issues with the analysis of the numerical data. We point out, in particular, that (i) the saturation values $\widetilde{S}_N(L,W)$ for fixed length $L$ are only bounded from above by 'the ergodic value' and are already far below this value for $W\ll 1$. Furthermore, the saturation values can show non-monotonic scaling with $L$. (ii) Power-law fits $S_N(t)\sim 1/t^\alpha$ -- with $\alpha=1$ expected based on the resonance model described in the paper -- yield a system-size dependent exponent $\alpha$ while fits $S_N\sim \frac{1}{W^3}\ln\ln t$ do hold independent of system size and over several orders of magnitude in time. (iii) We also argue that for the cases where the effective resonance model works best and predicts a saturation of the number entropy, the same applies to the von-Neumann entropy, i.e.~the dynamics at the considered scales is of single particle type and unrelated to MBL.

Photoplethysmographic Imaging (PPGI) allows the determination of pulse rate variability from sequential beat-to-beat intervals (BBI) and pulse wave velocity from spatially resolved recorded pulse waves. In either case, sufficient temporal accuracy is essential. The presented work investigates the temporal accuracy of BBI estimation from photoplethysmographic signals. Within comprehensive numerical simulation, we systematically assess the impact of sampling rate, signal-to-noise ratio (SNR), and beat-to-beat shape variations on the root mean square error (RMSE) between real and estimated BBI. Our results show that at sampling rates beyond 14 Hz only small errors exist when interpolation is used. For example, the average RMSE is 3 ms for a sampling rate of 14 Hz and an SNR of 18 dB. Further increasing the sampling rate only results in marginal improvements, e.g. more than tripling the sampling rate to 50 Hz reduces the error by approx. 14%. The most important finding relates to the SNR, which is shown to have a much stronger influence on the error than the sampling rate. For example, increasing the SNR from 18 dB to 24 dB at 14 Hz sampling rate reduced the error by almost 50% to 1.5 ms. Subtle beat-to-beat shape variations, moreover, increase the error decisively by up to 800%. Our results are highly relevant in three regards: first, they partially explain different results in the literature on minimum sampling rates. Second, they emphasize the importance to consider SNR and possibly shape variation in investigations on the minimal sampling rate. Third, they underline the importance of appropriate processing techniques to increase SNR. Importantly, though our motivation is PPGI, the presented work immediately applies to contact PPG and PPG in other settings such as wearables. To enable further investigations, we make the scripts used in modelling and simulation freely available., Comment: 18 pages, 11 figures

We show that the nonlinear transport of bosonic excitations in a two-dimensional honeycomb lattice of spin-orbit coupled Rydberg atoms gives rise to disordered quantum phases which are candidates for quantum spin liquids. As recently demonstrated in [Lienhard et al. Phys. Rev. X, 10, 021031 (2020)] the spin-orbit coupling breaks time-reversal and chiral symmetries and leads to a tunable density-dependent complex hopping of the hard-core bosons or equivalently to complex XY spin interactions. Using exact diagonalization (ED) we numerically investigate the phase diagram resulting from the competition between density-dependent and direct transport terms. In mean-field approximation there is a phase transition from a quasi-condensate to a 120{\deg} phase when the amplitude of the complex hopping exceeds that of the direct one. In the full model a new phase with a finite spin gap emerges close to the mean-field critical point as a result of quantum fluctuations induced by the density-dependence of the complex hopping. We show that this phase is a genuine disordered one, has a non-vanishing spin chirality and is characterized by a non-trivial many-body Chern number. ED simulations of small lattices with up to 28 lattice sites point to a non-degenerate ground state and thus to a bosonic integer-quantum Hall (BIQH) phase, protected by U(1) symmetry. The Chern number of C = 1, which is robust to disorder, is however different from the even Chern numbers found in BIQH phases. For very strong, nonlinear hoppings of opposite sign we find another disordered regime with vanishing spin gap. This phase also has a large spin chirality and could be a gapless spin-liquid but lies outside the parameter regime accessible in the Rydberg system., Comment: Updated version as published in Phys. Rev. Res

We examine the adiabatic preparation of spatially-ordered Rydberg excitations of atoms in finite one-dimensional lattices by frequency-chirped laser pulses, as realized in a number of recent experiments simulating quantum Ising model. Our aims are to unravel the microscopic mechanism of the phase transition from the unexcited state of atoms to the antiferromagnetic-like state of Rydberg excitations by traversing an extended gapless phase, and to estimate the preparation fidelity of the target state in a moderately sized system amenable to detailed numerical analysis. We find that, in the basis of the bare atomic states, the system climbs the ladder of Rydberg excitations predominantly along the strongest-amplitude paths towards the final ordered state. We show that, despite its complexity, the interacting many-body system can be described as an effective two-level system involving a pair of lowest-energy instantaneous collective eigenstates of the time-dependent Hamiltonian. The final preparation fidelity of the target state can then be well approximated by the Landau-Zener formula, while the nonadiabatic population leakage during the passage can be estimated using a perturbative approach applied to the instantaneous collective eigenstates., Comment: close to the published version

Quantized particle or spin transport upon cyclic parameter variations, determined by topological invariants, is a key signature of Chern insulators in the ground state. While measurable many-body observables exist that preserve the integrity of topological invariants also at finite temperature, quantized transport is generically lost. We here show that a coupling of a one-dimensional Chern insulator at arbitrary finite temperature to an auxiliary lattice can induce quantized transport determined by the finite-temperature invariant. We show for the example of a Rice-Mele model that the spatial distribution of a single particle in the auxiliary chain moves by a quantized number of unit cells in a Thouless cycle when subtracting a spatially homogeneous offset even at a temperature exceeding the band gap.

The topological classification of fermion systems in mixed states is a long standing quest. For Gaussian states, reminiscent of non-interacting unitary fermions, some progress has been made. While the topological quantization of certain observables such as the Hall conductivity is lost for mixed states, directly observable many-body correlators exist which preserve the quantized nature and naturally connect to known topological invariants in the ground state. For systems which break time-reversal (TR) symmetry, the ensemble geometric phase was identified as such an observable which can be used to define a Chern number in $(1+1)$ and $2$ dimensions. Here we propose a corresponding $\mathbb{Z}_2$ topological invariant for systems with TR symmetry. We show that this mixed-state invariant is identical to well-known $\mathbb{Z}_2$ invariants for the ground state of the so-called fictitious Hamiltonian, which for thermal states is just the ground state of the system Hamiltonian itself. We illustrate our findings for finite-temperature states of a paradigmatic $\mathbb{Z}_2$ topological insulator, the Kane-Mele model.

As shown in recent experiments [V. Lienhard et al., Phys. Rev. X 10, 021031 (2020)], spin-orbit coupling in systems of Rydberg atoms can give rise to density-dependent Peierls Phases in second-order hoppings of Rydberg spin excitations and nearest-neighbor (NN) repulsion. We here study theoretically a one-dimensional zig-zag ladder system of such spin-orbit coupled Rydberg atoms at half filling. The second-order hopping is shown to be associated with an effective gauge field, which in mean-field approximation is static and homogeneous. Beyond the mean-field level the gauge potential attains a transverse quantum component whose amplitude is dynamical and linked to density modulations. We here study the effects of this to the possible ground-state phases of the system. In a phase where strong repulsion leads to a density wave, we find that as a consequence of the induced quantum gauge field a regular pattern of current vortices is formed. However also in the absence of density-density interactions the quantum gauge field attains a non-vanishing amplitude. Above a certain critical strength of the second-order hopping the energy gain due to gauge-field induced transport overcomes the energy cost from the associated build-up of density modulations leading to a spontaneous generation of the quantum gauge field.

We investigate and compare the particle number fluctuations in the putative many-body localized (MBL) phase of a spinless fermion model with potential disorder and nearest-neighbor interactions with those in the non-interacting case (Anderson localization) and in effective models where only interaction terms diagonal in the Anderson basis are kept. We demonstrate that these types of simple effective models cannot account for the particle number fluctuations observed in the MBL phase of the microscopic model. This implies that assisted and pair hopping terms---generated when transforming the microscopic Hamiltonian into the Anderson basis---cannot be neglected. As a consequence, it appears questionable if the microscopic model possesses an exponential number of exactly conserved local charges. If such exactly conserved local charges do not exist, then particles are expected to ultimately delocalize for any finite disorder strength.

We discuss the realization of a magnonic version of the STImulated-Raman-Adiabatic-Passage (m-STIRAP) mechanism using micromagnetic simulations. We consider the propagation of magnons in curved magnonic directional couplers. Our results demonstrate that quantum-classical analogy phenomena are accessible in magnonics. Specifically, the inherent advantages of the STIRAP mechanism, associated with dark states, can now be utilized in magnonics. Applications of this effect for future magnonic device functionalities and designs are discussed., Comment: 6 pages, 4 figures

The truncated Wigner approximation is an established approach that describes the dynamics of weakly interacting Bose gases beyond the mean-field level. Although it allows a quantum field to be expressed by a stochastic c-number field, the simulation of the time evolution is still very demanding for most applications. Here, we develop a numerically inexpensive approximation by decomposing the c-number field into a variational ansatz function and a residual field. The dynamics of the ansatz function is described by a tractable set of coupled ordinary stochastic differential equations for the respective variational parameters. We investigate the non-equilibrium dynamics of a three-dimensional Bose gas in a one-dimensional optical lattice with a transverse isotropic harmonic confinement and neglect the influence of the residual field. The accuracy and computational inexpensiveness of our method are demonstrated by comparing its predictions to experimental data., Comment: 22 pages, 6 figures

We generalize the concept of topological invariants for mixed states based on the ensemble geometric phase (EGP) introduced for one-dimensional lattice models to two dimensions. In contrast to the geometric phase for density matrices suggested by Uhlmann, the EGP leads a proper Chern number for Gaussian, finite-temperature or non-equilibrium steady states. The Chern number can be expressed as an integral of the Berry curvature of the so-called fictitious Hamiltonian, constructed from single-particle correlations, over the two-dimensional Brillouin zone. For the Chern number to be non-zero the fictitious Hamiltonian has to break time-reversal symmetry.

Bose polarons, quasi-particles composed of mobile impurities surrounded by cold Bose gas, can experience strong interactions mediated by the many-body environment and form bipolaron bound states. Here we present a detailed study of heavy polarons in a one-dimensional Bose gas by formulating a non-perturbative theory and complementing it with exact numerical simulations. We develop an analytic approach for weak boson-boson interactions and arbitrarily strong impurity-boson couplings. Our approach is based on a mean-field theory that accounts for deformations of the superfluid by the impurities and in this way minimizes quantum fluctuations. The mean-field equations are solved exactly in Born-Oppenheimer (BO) approximation leading to an analytic expression for the interaction potential of heavy polarons which is found to be in excellent agreement with quantum Monte-Carlo (QMC) results. In the strong-coupling limit the potential substantially deviates from the exponential form valid for weak coupling and has a linear shape at short distances. Taking into account the leading-order Born-Huang corrections we calculate bipolaron binding energies for impurity-boson mass ratios as low as 3 and find excellent agreement with QMC results.

We study quench dynamics in a t-V chain of spinless fermions (equivalent to the spin-1/2 Heisenberg chain) with strong potential disorder. For this prototypical model of many-body localization we have recently argued that -- contrary to the established picture -- particles do not become fully localized. Here we summarize and expand on our previous results for various entanglement measures such as the number and the Hartley number entropy. We investigate, in particular, possible alternative interpretations of our numerical data. We find that none of these alternative interpretations appears to hold and, in the process, discover further strong evidence for the absence of localization. Furthermore, we obtain more insights into the entanglement dynamics and the particle fluctuations by comparing with non-interacting systems where we derive several strict bounds. We find that renormalized versions of these bounds also hold in the interacting case where they provide support for numerically discovered scaling relations between number and entanglement entropies.

We have recently shown that the logarithmic growth of the entanglement entropy following a quantum quench in a many-body localized (MBL) phase is accompanied by a slow growth of the number entropy, $S_N\sim\ln\ln t$. Here we provide an in-depth numerical study of $S_N(t)$ for the disordered Heisenberg chain and show that this behavior is not transient and persists even for very strong disorder. Calculating the truncated R\'enyi number entropy $S_N^{(\alpha)}(t)=(1-\alpha)^{-1}\ln\sum_n p^\alpha(n)$ for $\alpha\ll 1$ and $p(n)>p_c$ -- which is sensitive to large number fluctuations occurring with low probability -- we demonstrate that the particle number distribution $p(n)$ in one half of the system has a continuously growing tail. This indicates a slow but steady increase of the number of particles crossing between the partitions in the interacting case, and is in sharp contrast to Anderson localization, for which we show that $S_N^{(\alpha\to 0)}(t)$ saturates for any cutoff $p_c>0$. We show, furthermore, that the growth of $S_N$ is $\mathit not$ the consequence of rare states or rare regions but rather represents typical behavior. These findings provide strong evidence that the interacting system is never fully localized even for very strong but finite disorder.

We show that a topological pump in a one-dimensional (1D) insulator can induce a strictly quantized transport in an auxiliary chain of non-interacting fermions weakly coupled to the first. The transported charge is determined by an integer topological invariant of the ficticious Hamiltonian of the insulator, given by the covariance matrix of single-particle correlations. If the original system consists of non-interacting fermions, this number is identical to the TKNN (Thouless, Kohmoto, Nightinghale, den Nijs) invariant of the original system and thus the coupling induces a transfer of topology to the auxiliary chain. When extended to particles with interactions, for which the TKNN number does not exist, the transported charge in the auxiliary chain defines a topological invariant for the interacting system. In certain cases this invariant agrees with the many-body generalization of the TKNN number introduced by Niu, Thouless, and Wu (NTW). We illustrate the topology transfer to the auxiliary system for the Rice-Mele model of non-interacting fermions at half filling and the extended superlattice Bose-Hubbard model at quarter filling. In the latter case the induced charge pump is fractional.

We study experimentally the dissipative dynamics of ultracold bosonic gases in a dynamic disorder potential with tunable correlation time. First, we measure the heating rate of thermal clouds exposed to the dynamic potential and present a model of the heating process, revealing the microscopic origin of dissipation from a thermal, trapped cloud of bosons. Second, for Bose-Einstein condensates, we measure the particle loss rate induced by the dynamic environment. Depending on the correlation time, the losses are either dominated by heating of residual thermal particles or the creation of excitations in the superfluid, a notion we substantiate with a rate model. Our results illuminate the interplay between superfluidity and time-dependent disorder and on more general grounds establish ultracold atoms as a platform for studying spatiotemporal noise and time-dependent disorder., Comment: 12 pages, 7 figures