Quantum mechanics allows processes to be superposed, leading to a genuinely quantum lack of causal structure. For example, the process known as the quantum switch applies two operations $\mathcal{A}$ and $\mathcal{B}$ in a superposition of the two possible orders, $\mathcal{A}$ before $\mathcal{B}$ and $\mathcal{B}$ before $\mathcal{A}$. Experimental implementations of the quantum switch have been challenged by some on the grounds that the operations $\mathcal{A}$ and $\mathcal{B}$ were implemented more than once, thereby simulating indefinite causal order rather than actually implementing it. Motivated by this debate, we consider a situation in which the quantum operations are physically described by a light-matter interaction model. While for our model the two processes are indistinguishable in the infinite-energy regime, restricting the energy available for the implementation of the operations introduces imperfections, which allow one to distinguish processes using different numbers of operations. We consider such an energetically constrained scenario and compare the quantum switch to one of its natural simulations, where each operation is implemented twice. Considering a commuting-versus-anticommuting unitary discrimination task, we find that within our model the quantum switch performs better, for some fixed amount of energy, than its simulation. In addition to the known computational or communication advantages of causal superpositions, our work raises questions about their potential energetic advantages.

Square-root topology describes models whose topological properties can be revealed upon squaring the Hamiltonian, which produces their respective parent topological insulators. This concept has recently been generalized to $2^n$-root topology, characterizing models where $n$ squaring operations must be applied to the Hamiltonian to arrive at the topological source of the model. In this paper, we analyze the Hofstadter regime of quasi-one-dimensional and two-dimensional $2^n$-root models, the latter of which has the square lattice (SL) (known for the Hofstadter Butterfly) as the source model. We show that upon increasing the root-degree of the model, there appear multiple magnetic flux insensitive flat bands, and we analytically determine corresponding eigenstates. These can be recast as compact localized states (CLSs) occupying a finite region of the lattice. For a finite flux, these CLSs correspond to different harmonics contained within the same Aharonov-Bohm cage. Furthermore, as the root-degree increases, a kaleidoscope of butterflies is seen to appear in the Hofstadter diagram, with each butterfly constituting a topologically equivalent replica of the original one of the SL. As such, the index $n$, which uniquely identifies the root-degree of the model, can be seen as an additional fractal dimension of the $2^n$-root model present in its Hofstadter diagram. We discuss how these dynamics could be realized in experiments with ultracold atoms, and measured by Bragg spectroscopy or through observing dynamics of initially localized atoms in a quantum gas microscope.

Ghost vortices constitute an elusive class of topological excitations in quantum fluids since the relevant phase singularities fall within regions where the superfluid density is almost zero. Here we present a platform that allows for the controlled generation and observation of such vortices. Upon rotating an imbalanced mixture of two-component Bose-Einstein condensates, one can obtain necklaces of real vortices in the majority component whose cores get filled by particles from the minority one. The wave function describing the state of the latter is shown to harbor a number of ghost vortices which are crucial to support the overall dynamics of the mixture. Their arrangement typically mirrors that of their real counterpart, hence resulting in a “dual” ghost-vortex necklace, whose properties are thoroughly investigated in the present paper. We also present a viable experimental protocol for the direct observation of ghost vortices in a ${}^{23}\mathrm{Na}+{}^{39}\mathrm{K}$ ultracold mixture. Quenching the intercomponent scattering length, some atoms are expelled from the vortex cores and, while diffusing, swirl around unpopulated phase singularities, thus turning them directly observable.

Within the Gross-Pitaevskii theory, we study precursory pattern formations to the nucleation of vortex dipoles in a two-dimensional Bose-Einstein condensate stirred by a Gaussian potential. We introduce a smooth superfluid vorticity field and its conservative current, which capture very well the gradual process of vortex nucleation as a mechanism of topological singularities acquiring smooth cores. This is characterized by the localization of the superfluid vorticity into core regions which harbor the phase slips. For more impenetrable obstacles, we find that there are additional phase slips that do not acquire cores, thus remaining pinned as ghost vortices to the potential. We show that the vortex kinematics is slaved to the superfluid vorticity current, which determines not only the onset of nucleation but also the shedding dynamics.

We consider the dynamics of a translocation process of a flexible linear polymer through a nanopore into an environment of active rods in the trans side. Using Langevin dynamics simulations, we show that the rods facilitate translocation to the trans side even when there are initially more monomers on the cis than on the trans side. Structural analysis of the translocating polymer reveals that active rods induce a folded structure to the trans-side subchain in the case of successful translocation events. By keeping the initial number of monomers on the cis-side subchain fixed, we map out a state diagram for successful events as a function of the rod number density for a variety of system parameters. This reveals competition between facilitation by the rods at low densities and crowding that hinders translocation at higher densities.

A plethora of computational models have been developed in recent decades to account for the morphogenesis of complex biological fluid networks, such as capillary beds. Contemporary adaptation models are based on optimization schemes where networks react and adapt vessel conductance toward given flow patterns. Recent numeric studies on network morphogenesis, incorporating uptake of metabolites by the embedding tissue, have indicated this conventional approach to be insufficient. Here, we systematically study a hybrid model intended to generate space-filling perfusion as well as optimal filtration of metabolites. As a result, we find hydrodynamic stimuli (wall-shear stress) and filtration based stimuli (uptake of metabolites) to be antagonistic as hydrodynamically optimized systems have suboptimal uptake qualities and vice versa. We show that a switch between optimization regimes is typically accompanied with a transition between topologically redundant meshes and spanning trees. Depending on the metabolite demand and uptake capabilities of the adapting networks, we further demonstrate the existence of nullity reentrance as a function of dissipation and the development of compromised phenotypes such as dangling nonperfused vessels and bottlenecks.

We investigate a population of swarmalators, mobile versions of phase oscillators that both sync in time and swarm through space. We focus on an $XY$-type model of identical swarmalators running on a one-dimensional ring and subject to thermal noise. We uncover four distinct collective states, some of which capture the behavior of real-world swarmalators such as vinegar eels and sperm. Among these, the most intriguing is the “mixed state,” which blends two of the other states. We present a comprehensive phase diagram from the Fourier mode analysis with a high accuracy, which is in excellent agreement with numerical simulation results. Our model serves as a tractable toy model for thermal systems that both self-synchronize and self-assemble interdependently.

We use first-principles-derived numerical simulations to investigate the long-time evolution of a half-quantum vortex ring, an Alice ring, arising from the decay dynamics of an isolated monopole in the polar phase of a dilute spin-1 Bose-Einstein condensate. In particular, we study the lifetime and decay characteristics of the Alice ring under different experimentally relevant conditions. We observe that, in a ${}^{87}\mathrm{Rb}$ condensate with a homogeneous external magnetic field, a well-centered Alice ring may survive for over 160 ms, and that during its lifetime it can contract back into a monopole, which again converts into an Alice ring. Interestingly, we notice an additional Alice ring, with an opposite topological charge, to emerge during the decay dynamics within the condensate, leading to the coexistence of two Alice rings in the same cloud. Shortly after this coexistence, the original Alice ring breaks into a line-like defect referred to as an Alice string. We find that the location of the initial isolated monopole correlates with the winding direction of the scalar phase in the produced vortex ring, a phenomenon which we utilize to create two Alice rings with opposite charges and opposite winding directions. Such created Alice ring and anti-Alice ring naturally annihilate each other in the subsequent evolution.

Stochastic systems that undergo random restarts to their initial state have been widely investigated in recent years, both theoretically and in experiments. Oftentimes, however, resetting to a fixed state is impossible due to thermal noise or other limitations. As a result, the system configuration after a resetting event is random. Here, we consider such a resetting protocol for an overdamped Brownian particle in a confining potential $V\left(x\right)$. We assume that the position of the particle is reset at a constant rate to a random location $x$, drawn from a distribution $p_R\left(x\right)$. To investigate the thermodynamic cost of resetting, we study the stochastic entropy production $S_{\mathrm{Total}}$. We derive a general expression for the average entropy production for any $V\left(x\right)$, and the full distribution $P\left(S_{\mathrm{Total}}\right|t)$ of the entropy production for $V\left(x\right)=0$. At late times, we show that this distribution assumes the large-deviation form $P\left(S_{\mathrm{Total}}\right|t)\sim exp\{-t^{2\alpha -1}\varphi [(S_{\mathrm{Total}}-\langle S_{\mathrm{Total}}\rangle )/t^{\alpha }]\}$, with $1/2<\alpha \le 1$. We compute the rate function $\varphi \left(z\right)$ and the exponent $\alpha$ for exponential and Gaussian resetting distributions $p_R\left(x\right)$. In the latter case, we find the anomalous exponent $\alpha =2/3$ and show that $\varphi \left(z\right)$ has a first-order singularity at a critical value of $z$, corresponding to a real-space condensation transition.

Localization of electronic wave functions in modern two-dimensional (2D) materials such as graphene can impact drastically their transport and magnetic properties. The recent localization landscape (LL) theory has brought many tools and theoretical results to understand such localization phenomena in the continuous setting, but with very few extensions so far to the discrete realm or to tight-binding Hamiltonians. In this paper, we show how this approach can be extended to almost all known 2D lattices and propose a systematic way of designing LL even for higher dimensions. We demonstrate in detail how this LL theory works and predicts accurately not only the locations, but also the energies of localized eigenfunctions in the low- and high-energy regimes for the honeycomb and hexagonal lattices, making it a highly promising tool for investigating the role of disorder in these materials.

The use of neural network parametrizations to represent the ground state in variational Monte Carlo (VMC) calculations has generated intense interest in recent years. However, as we demonstrate in the context of the periodic Heisenberg spin chain, this approach can produce unreliable wave function approximations. One of the most obvious signs of failure is the occurrence of random, persistent spikes in the energy estimate during training. These energy spikes are caused by regions of configuration space that are over-represented by the wave function density, which are called “spurious modes” in the machine learning literature. After exploring these spurious modes in detail, we demonstrate that a collective-variable-based penalization yields a substantially more robust training procedure, preventing the formation of spurious modes and improving the accuracy of energy estimates. Because the penalization scheme is cheap to implement and is not specific to the particular model studied here, it can be extended to other applications of VMC where a reasonable choice of collective variable is available.

We explore the quasi-one-dimensional (thin torus, or TT) limit of fractional Chern insulators (FCIs) as a starting point for their adiabatic preparation in quantum simulators. Our approach is based on tuning the hopping amplitude in one direction as an experimentally amenable knob to dynamically change the effective aspect ratio of the system. Similar to the TT limit of fractional quantum Hall systems in the continuum, we find that the hopping-induced TT limit adiabatically connects the FCI state to a trivial charge density wave (CDW) ground state. This adiabatic path may be harnessed for state preparation schemes relying on the initialization of a CDW state followed by the adiabatic decrease of a hopping anisotropy. Our findings are based on the calculation of the excitation gap in a number of FCI models, both on a lattice and consisting of coupled wires. By analytical calculation of the gap in the limit of strongly anisotropic hopping, we show that its scaling is compatible with the preparation of large-size FCIs for sufficiently large hopping anisotropy, where the amenable system sizes are only limited by the maximal hopping amplitude. Our numerical simulations in the framework of exact diagonalization explore the full anisotropy range to corroborate these results.

Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description of Hamiltonian families near self-dual points. We focus on tight-binding models (also known as coupled-mode theories), which provide an effective description of systems composed of coupled harmonic oscillators across physical domains. We start by considering the general case in which group-theoretical arguments suffice to construct families of Hamiltonians with dualities by combining irreducible representations of the duality operation in parameter space and in operator space. When additional constraints due to system-specific features are present, a purely group-theoretic approach is no longer sufficient. To overcome this complication, we reformulate the existence of a duality as a root-finding problem, which is amenable to standard optimization and numerical continuation algorithms. We illustrate the generality of our method by designing concrete toy models of photonic, mechanical, and thermal metamaterials with dualities.

Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate duration and gate error rate. We describe two-qubit gates with addressed Raman beams within a linear trapped-ion chain by a quantum master equation (QME). The QME incorporates the single-ion two-photon effective Rabi frequency, Autler-Townes and vibrational Bloch-Siegert energy shifts, off-resonant transitions, Raman and Rayleigh scattering, laser-power fluctuations, motional heating, cross-Kerr phonon coupling, laser spillover, asymmetric addressing beams, and an imperfect initial motional ground state, with no fitting parameters, whereas state-of-the-art methods are oblivious to these effects in the gate design procedure. We employ global optimization to design pulse sequences for achieving a robust rapid two-qubit gate for a simulated chain of seven trapped ${}^{171}\mathrm{Yb}^{+}$ ions by optimizing over numerically integrated QME solutions. Here, robust means resilient against slow drift of motional frequencies, and rapid means gate execution where the effective Rabi frequency is comparable to the detuning of the laser from the ion's bare electronic transition. Our robust quantum control delivers rapid high-quality two-qubit gates in long ion chains, enabling scalable quantum computing with trapped ions.