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Nonhermiticity in quantum Hamiltonians leads to non-unitary time evolution and possibly complex energy eigenvalues, which can lead to a rich phenomenology with no Hermitian counterpart. In this work, we study the dynamics of an exactly solvable non-Hermitian system, hosting both $\mathcal{PT}$-symmetric and $\mathcal{PT}$-broken modes subject to a linear quench. Employing a fully consistent framework, in which the Hilbert space is endowed with a nontrivial dynamical metric, we analyze the dynamics of the generated defects. In contrast to Hermitian systems, our study reveals that $\mathcal{PT}$-broken time evolution leads to defect freezing and hence the violation of quantum adiabaticity. Additionally, no Kibble-Zurek scaling regime in the quasi-adiabatic limit exists in our model. This physics necessitates the quantum metric framework, as it is missed by the oft used approach of normalizing quantities by the time-dependent norm of the state. Our results are relevant for a wide class of experimental systems., Comment: Main text: 6 pages and 3 figures; Supplemental Material: 4 pages

We explore anomalous skin effects at non-Hermitian impurities by studying their interplay with potential disorder and by exactly solving a minimal lattice model. A striking feature of the solvable single-impurity model is that the presence of anisotropic hopping terms can induce a scale-invariant accumulation of all eigenstates opposite to the bulk hopping direction, although the non-monotonic behavior is fine-tuned and further increasing such hopping weakens and eventually reverses the effect. The interplay with bulk potential disorder, however, qualitatively enriches this phenomenology leading to a robust non-monotonic localization behavior as directional hopping strengths are tuned. These phenomena persist even in the limit of an entirely Hermitian bulk with a single non-Hermitian impurity., Comment: 7 pages, 3 figures; supplementary material (2 pages, 2 figures) included

We devise a generic and experimentally accessible recipe to prepare boundary states of topological or non-topological quantum systems through an interplay between coherent Hamiltonian dynamics and local dissipation. Intuitively, our recipe harnesses the spatial structure of boundary states which vanish on sublattices where losses are suitably engineered. This yields unique non-trivial steady states that populate the targeted boundary states with infinite life times while all other states are exponentially damped in time. Remarkably, applying loss only at one boundary can yield a unique steady state localized at the very same boundary. We detail our construction and rigorously derive full Liouvillian spectra and dissipative gaps in the presence of a spectral mirror symmetry for a one-dimensional Su-Schrieffer-Heeger model and a two-dimensional Chern insulator. We outline how our recipe extends to generic non-interacting systems.

In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials to circularly polarized light over a wide range of frequencies, measured in units of the fine structure constant, can be used to extract a spectral function that frequency-integrates to the Chern number, offering a simple optical experiment to measure it. This method is subsequently generalized to finite temperature and locally on every lattice site by a linear response theory, which helps to extract the Chern marker that maps the Chern number to lattice sites. The long range response in our theory corresponds to a Chern correlator that acts like the internal fluctuation of the Chern marker, and is found to be enhanced in the topologically nontrivial phase. Finally, from the Fourier transform of the valence band Berry curvature, a nonlocal Chern marker is further introduced, whose decay length diverges at topological phase transitions and therefore serves as a faithful indicator of the transitions, and moreover can be interpreted as a Wannier state correlation function. The concepts discussed in this work explore multi-faceted aspects of topology and should help address the impact of system inhomogeneities., Comment: Reworked version

We study a one-dimensional array of bosons with infinite-range interactions mediated by a laser-driven dissipative optical cavity. The cavity-mediated infinite-range interactions open up a new pathway to fermionization, hitherto only known for dipolar bosons due to their long-range interactions. In parameter ranges attainable in state-of-the-art experiments, we systematically compare observables for bosons and fermions with infinite-range interactions. At large enough laser pump power, many observables, including density distributions in real and momentum space, correlation functions, eigenvalues of the one-body density matrix, and superradiance order parameter, become identical for bosons and fermions. We map out the emergence of this cavity-induced fermionization as a function of pump power and contact interactions. We discover that cavity-mediated interactions can compensate a reduction by several orders of magnitude in the strength of the contact interactions needed to trigger fermionization., Comment: main text: 7 pages, 3 figures - supplement: 7 pages, 4 figures

We explore the role of atomic correlations in a harmonically trapped Bose-Einstein condensate coupled to a dissipative cavity, where both the atoms and the cavity are blue detuned from the external pumping laser. Using a genuine many-body approach that goes beyond mean-field, we extract density distributions and many-body correlations to unveil a pathway to chaos at large pump power through a hierarchical self-organization of the atoms, where the atoms transition from a single-well optical lattice to a double-well optical lattice. Correlated states of the atoms emerge and are characterized by local superfluid correlations in phases which are globally superfluid or Mott insulating. Local superfluid-Mott transitions are precluded by a dynamical instability to chaos which occurs via quasiperiodic attractors. Our results explain the mechanism behind the dynamical instabilities observed in experiments., 14 pages, 9 figures (including 7 pages, 5 figures in the supplementary material)

Out-of-equilibrium many-body physics is the fascinating study of complex systems that are subjected to driving, dissipation, or both. Through such procedures it is possible to generate exciting new dynamical phases of matter that have no static counterpart. In this thesis, we investigate the interplay between driving and dissipation in several paradigmatic many-body quantum systems. In particular, we analyze the impact of nonequilibrium phenomena on the stability of topological matter and light-matter interactions. We begin by addressing how to characterize the topological criticality of lower-dimensional systems whose parameters are periodically driven in time. We first introduce a curvature renormalization group method that extends the notions of Landau criticality to the realm of topological phase transitions. We show how this framework presents a simple and efficient way to map out topological phase diagrams of static and Floquet systems in any dimension. Furthermore, we illustrate its ability to precisely capture topological critical phenomena. We then apply it to prototypical static and Floquet topological systems to extract correlation lengths, critical exponents, scaling laws, and universality classes. In one dimension, we apply this methodology to the periodically driven Kitaev chain hosting Majorana end modes. As an interlude, we also examine the consequences of multifrequency driving, and reveal that it can be used as a valuable tool to dynamically control the number and the stability of the topological modes. In two dimensions, we analyze a Floquet-Chern insulator and the periodically driven Kitaev model on the honeycomb lattice. We also establish that periodic driving can induce very exotic topological semimetal phases hosting nodal loop gap closures. We demonstrate that the corresponding phase transitions belong to a different universality class than the ones described by Dirac low-energy theories, but both can coexist at multicritical points. We then discuss the physical origin of nodal loop gap closures and establish that they emerge as a consequence of enhanced symmetries introduced by the driving scheme. We separately analyze symmetry protection and provide concrete examples of how to induce it in both static and driven settings. In realistic settings, one has to often deal with open systems. To incorporate dissipation in our analysis, we re-examine the periodically driven Kitaev chain additionally subjected to a coupling with end reservoirs. In this context we discover that the Floquet-Majorana edge modes survive despite dissipation, and have strong signatures in stroboscopic observables that can reliably track their appearance and disappearance in different phases. Another challenge of contemporary physics is to understand the role of many-body interactions in driven-dissipative settings. As a first step in this direction, we present a very efficient numerical algorithm — the MultiConfigurational Time-Dependent Hartree method — tailored at reliably simulating the time-evolution of interacting many-body quantum systems. We illustrate its applications to several systems of ultracold atoms coupled with the radiation field of optical cavities that host intriguing light-matter phases stabilized by dissipation, such as superradiant phases, Mott insulating phases, and Tonks-Girardeau phases. We highlight how to calculate density distributions, correlation functions, and various order parameters for such setups, and how to simulate realistic single-shot experiments. We conclude this thesis by presenting a brief outlook on unresolved issues and new intriguing questions that have surfaced throughout our study.

We consider laser-pumped one-dimensional two-component bosons in a parabolic trap embedded in a high-finesse optical cavity. Above a threshold pump power, the photons that populate the cavity modify the effective atom trap and mediate a coupling between the two components of the Bose-Einstein condensate. We calculate the ground state of the laser-pumped system and find different stages of self-organization depending on the power of the laser. The modified potential and the laser-mediated coupling between the atomic components give rise to rich many-body physics: an increase of the pump power triggers a self-organization of the atoms while an even larger pump power causes correlations between the self-organized atoms -- the BEC becomes fragmented and the reduced density matrix acquires multiple macroscopic eigenvalues. In this fragmented superradiant state, the atoms can no longer be described as two-level systems and the mapping of the system to the Dicke model breaks down., 8 pages, 3 figures, software available at http://ultracold.org

We numerically obtain the full time-evolution of a parametrically-driven dissipative Bose-Einstein condensate in an optical cavity and investigate the implications of driving for the phase diagram. Beyond the normal and superradiant phases, a third nonequilibrium phase emerges as a manybody parametric resonance. This dynamical normal phase switches between two symmetry-broken superradiant configurations. The switching implies a breakdown of the system's mapping to the Dicke model. Unlike the other phases, the dynamical normal phase shows features of nonintegrability and thermalization., 5 pages, 3 figures

Topological order in solid state systems is often calculated from the integration of an appropriate curvature function over the entire Brillouin zone. At topological phase transitions where the single particle spectral gap closes, the curvature function diverges and changes sign at certain high symmetry points in the Brillouin zone. These generic properties suggest the introduction of a supervised machine learning scheme that uses only the curvature function at the high symmetry points as input data. We apply this scheme to a variety of interacting topological insulators in different dimensions and symmetry classes. We demonstrate that an artificial neural network trained with the noninteracting data can accurately predict all topological phases in the interacting cases with very little numerical effort. Intriguingly, the method uncovers a ubiquitous interaction-induced topological quantum multicriticality in the examples studied., SciPost Physics, 11 (3), ISSN:2542-4653

Single-shot images are the standard readout of experiments with ultracold atoms -- the tarnished looking glass into their many-body physics. The efficient extraction of observables from single-shot images is thus crucial. Here, we demonstrate how artificial neural networks can optimize this extraction. In contrast to standard averaging approaches, machine learning allows both one- and two-particle densities to be accurately obtained from a drastically reduced number of single-shot images. Quantum fluctuations and correlations are directly harnessed to obtain physical observables for bosons in a tilted double-well potential at an unprecedented accuracy. Strikingly, machine learning also enables a reliable extraction of momentum-space observables from real-space single-shot images and vice versa. This obviates the need for a reconfiguration of the experimental setup between in-situ and time-of-flight imaging, thus potentially granting an outstanding reduction in resources., 7+8 pages, 3+8 figures, software available at http://ultracold.org

The competition between short-range and cavity-mediated infinite-range interactions in a cavity-boson system leads to the existence of a superfluid phase and a Mott-insulator phase within the self-organized regime. In this work, we quantitatively compare the steady-state phase boundaries of this transition measured in experiments and simulated using the Multiconfigurational Time-Dependent Hartree Method for Indistinguishable Particles. To make the problem computationally feasible, we represent the full system by the exact many-body wave function of a two-dimensional four-well potential. We argue that the validity of this representation comes from the nature of both the cavity-atomic system and the Bose-Hubbard physics. Additionally, we show that the chosen representation only induces small systematic errors, and that the experimentally measured and theoretically predicted phase boundaries agree reasonably well. We thus demonstrate a new approach for the quantitative numerical modeling for the physics of the superfluid-Mott-insulator phase boundary., SciPost Physics, 11 (2), ISSN:2542-4653

The Kitaev model on the honeycomb lattice is a paradigmatic system known to host a wealth of nontrivial topological phases and Majorana edge modes. In the static case, the Majorana edge modes are nondispersive. When the system is periodically driven in time, such edge modes can disperse and become chiral. We obtain the full phase diagram of the driven model as a function of the coupling and the driving period. We characterize the quantum criticality of the different topological phase transitions in both the static and driven model via the notions of Majorana-Wannier state correlation functions and momentum-dependent fidelity susceptibilities. We show that the system hosts cross-dimensional universality classes: although the static Kitaev model is defined on a 2D honeycomb lattice, its criticality falls into the universality class of 1D linear Dirac models. For the periodically driven Kitaev model, besides the universality class of prototype 2D linear Dirac models, an additional 1D nodal loop type of criticality exists owing to emergent time-reversal and mirror symmetries, indicating the possibility of engineering multiple universality classes by periodic driving. The manipulation of time-reversal symmetry allows the periodic driving to control the chirality of the Majorana edge states., 14 pages, 11 figures