We present a theoretical study of a Berezinskii-Kosterlitz-Thouless-like phase transition in lattices of nonequilibrium photon condensates. Starting from linearized fluctuation theory and the properties of vortices, we propose an analytical formula for the critical point containing four fitting parameters, that captures well all our numerical simulations. We find that the ordered phase becomes more stable when driving and dissipation are increased.

We theoretically investigate light scattering from an array of atoms into the guided modes of a waveguide. We observe that the scattering of a plane-wave laser field into the waveguide modes is dramatically enhanced for angles that deviate from the geometric Bragg angle. This modified Bragg condition arises from the dispersive interactions between the guided light and the atoms. We analytically identify various parameter regimes in which the scattering rate features a qualitatively different dependence on the atom number, such as linear, quadratic, oscillatory, or constant behavior. In combination with rigorous numerical calculations, we demonstrate that these scalings are independent of a possible asymmetry of the atom-light coupling. Finally, we show that our findings are robust against voids in the atomic array, facilitating their experimental observation and potential applications. Our work sheds light on collective light scattering and the interplay between geometry and interaction effects, with implications reaching beyond the optical domain.

Dissipative systems often exhibit wavelength-dependent loss rates. One prominent example is Rydberg polaritons formed by electromagnetically induced transparency, which have long been a leading candidate for studying the physics of interacting photons and also hold promise as a platform for quantum information. In this system, dissipation is in the form of quantum diffusion, i.e., proportional to $k^2$ ($k$ being the wavevector) and vanishing at long wavelengths as $k\to 0$. Here, we show that one-dimensional condensates subject to this type of loss are unstable to long-wavelength density fluctuations in an unusual manner: after a prolonged period in which the condensate appears to relax to a uniform state, local depleted regions quickly form and spread ballistically throughout the system. We connect this behavior to the leading-order equation for the nearly uniform condensate—a dispersive analog to the Kardar-Parisi-Zhang equation—which develops singularities in finite time. Furthermore, we show that the wavefronts of the depleted regions are described by purely dissipative solitons within a pair of hydrodynamic equations, with no counterpart in lossless condensates. We close by discussing conditions under which such singularities and the resulting solitons can be physically realized.

One of the most important and useful entropic uncertainty relations concerns a $d$-dimensional system and two mutually unbiased measurements. In such a setting, the sum of two information entropies is lower bounded by $lnd$. It has recently been shown that projective measurements subject to operational mutual unbiasedness can also be constructed in a continuous domain, with the help of periodic coarse graining. Here we consider the whole family of Rényi entropies applied to these discretized observables and prove that such a scheme does also admit the entropic uncertainty relations mentioned above.

We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. This quantity is properly defined only for states that possess a positive Wigner function, which we name Wigner-positive states, but we argue that it is a proper measure of quantum uncertainty in phase space. It is invariant under symplectic transformations (displacements, rotations, and squeezing) and we conjecture that it is lower bounded by $ln\pi +1$ within the convex set of Wigner-positive states. It reaches this lower bound for Gaussian pure states, which are natural minimum-uncertainty states. This conjecture bears a resemblance with the Wehrl-Lieb conjecture, and we prove it over the subset of passive states of the harmonic oscillator which are of particular relevance in quantum thermodynamics. Along the way, we present a simple technique to build a broad class of Wigner-positive states exploiting an optical beam splitter and reveal an unexpectedly simple convex decomposition of extremal passive states. The Wigner entropy is anticipated to be a significant physical quantity, for example, in quantum optics where it allows us to establish a Wigner entropy-power inequality. It also opens a way towards stronger entropic uncertainty relations. Finally, we define the Wigner-Rényi entropy of Wigner-positive states and conjecture an extended lower bound that is reached for Gaussian pure states.

We analyze the task of encoding classical information into a quantum system under the restriction by symmetry. Motivated by an analogy between the resource theories of asymmetry and entanglement, we ask whether an analog of superdense coding is possible in the former. I.e., we investigate whether the classical information capacity of an asymmetric state can be strictly larger than that of any symmetric state whereas the latter is a strictly positive constant. We prove that this is possible if and only if the unitary representation of the symmetry is non-Abelian and reducible. The result provides an information-theoretical classification of symmetries of quantum systems. We also discuss the possibility of superdense coding in other resource theories.

We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized Hamiltonians composed of a constant number of interactions, i.e., linear combinations of ladder operator monomials of fixed form. Compact encoding leads to qubit requirements that are optimal up to logarithmic factors. We show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding, give explicit implementations for the required oracles, and analyze the methods. We also describe several example applications including the free boson and fermion theories, the ${\varphi }^4$-theory, and the massive Yukawa model, all in both equal-time and light-front quantization. Our methods provide a general-purpose tool for simulating second-quantized Hamiltonians, with optimal or near-optimal scaling with error and model parameters.

Systematic theoretical data of positron binding to atoms [C. Harabati, V. A. Dzuba, and V. V. Flambaum, Phys. Rev. A 89, 022517 (2014)] are handled by machine learning techniques. Despite the existence of unsystematic errors in the calculations, it becomes possible to identify, through bound-unbound classification, a descriptor as a function of just the polarizability and ionization potential of the isolated atoms. Details of the bonding mechanism appear to be less relevant and the binding seems to be described by simply these two atomic properties, with large predominance of the polarizability. The descriptor is shown to be useful in the discrimination of binding energies of atoms with approximately equal polarizabilities as well as to correct some possibly wrong energy data. Identified arguably wrong cases are withdrawn from the data set so that an adjusted simple relation for the binding energy as a function of the descriptor is obtained, allowing corrections and predictions of binding energies extended to atoms up to Rf (104), except lanthanides and actinides.

The nonequilibrium dynamics of vortices in two-dimensional quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a harmonically trapped fluid can be analyzed analytically to show that single vortices will move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself. This allows the vortex ellipticity to be estimated through observation of its trajectory. A combination of analysis and numerical simulation is then used to show that nonlinear interactions cause the vortex orientation to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex ellipticity and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate and control local vortex structure and vortex trajectory is expected to prove useful in designing few-vortex systems in which ellipticity is a ubiquitous, as-yet-unharnessed feature.

We investigate the universal nonequilibrium dynamics of the superradiant phase transition in the anisotropic quantum Rabi model. By introducing position and momentum operators, we find the generators and the displaced operators to diagonalize the anisotropic Hamiltonian, and then obtain the ground states and their excitation gaps. According to the Kibble-Zurek mechanism, we find that the excitation gap near the critical point vanishes as $\omega \sim {\left|\epsilon \right|}^{\nu z}$ with $\nu z=1/2$, and the length scale diverges according to $\zeta \sim {\epsilon }^{-\nu }$, which determines the universality class $(z=2,\nu =1/4)$ of the anisotropic quantum Rabi model. Moreover, by simulating the real-time dynamics across the critical point, we numerically extract the critical exponents from the phase transition delay ${\widehat{b}}_d\sim {\tau }_Q^{-1/(1+\nu z)}$ and the diverging length scale $\mathrm{\Delta }x$, $\mathrm{\Delta }p\sim {\tau }_Q^{\nu /(1+\nu z)}$ (where ${\tau }_Q$ is the quench time). The numerical critical exponents are well consistent with the analytical ones. Our study provides a dynamic way to explore universal critical behaviors in the anisotropic quantum Rabi model.

Topological photonics provides a new platform to control and manipulate the flow of light in photonic devices that exhibit topological phase transitions. One way to introduce such transition of geometric phases in photonic waveguides is to modulate the structure of the photonic crystals, array waveguides, or the metamaterials in such a way that it eventually changes the bulk topology. Such topological waveguides localize the light at the boundary of the two distinct bulk systems with different topological invariant. Based on this fundamental physics, we demonstrate a robust and controlled propagation of light in a class of specialty optical fiber which exhibits the topological phase transition between a nontrivial one-dimensional (1D) periodic cylinder and its topologically trivial counterpart. The key idea is to explore the possibility of topological phase transition of 1D photonic bands over the momentum space by tuning the unit-cell dimension and its individual thicknesses. We have systematically computed the trivial and the nontrivial topological invariants, the Zak phase, of designed cylindrical 1D lattices with inversion symmetry over the first Brillouin zone. To establish the presence and the robustness of the localized edge mode, we have studied the reflectance of the geometry in the presence of disorder. Also, the simulated field profile and the back-reflectionless propagation of the edge mode through the fiber have been shown. Besides conventional fibers, such topological optical fibers are definitely a waveguide geometry for robust delivery of light and thus would be very significant to open up a new paradigm in guided wave photonics.

Verifiable blind quantum computation provides a cloud scenario for scalable quantum information processing. However, constructing one resource-efficient verification protocol is still an open problem. In this paper, the context of verification we consider is the measurement-based model, in which the client receives the graph state prepared by the server and performs single-qubit measurements on it to drive the computation. We first utilize three entanglement witnesses to estimate the fidelity of the prepared graph state. Applying entanglement witnesses to design the test phase, we propose verification protocols. Our protocol requires overhead in terms of copies of the graph state that scales as $O(n^{2}logn)$, where $n$ is the number of qubits of the graph state. Furthermore, the soundness of our protocol is improved. The advantages of our protocol are derived from the fact that each entanglement witness can be implemented by the client with a fixed number of measurement settings.

We consider the problem of discriminating quantum states, where the task is to distinguish two different quantum states with a complete classical knowledge about them, and the problem of classifying quantum states, where the task is to distinguish two classes of quantum states where no prior classical information is available but a finite number of physical copies of each class is given. In the case the quantum states are represented by coherent states of light, we identify intermediate scenarios where partial prior information is available. We evaluate an analytical expression for the minimum error when the quantum states are opposite and a prior on the amplitudes is known. Such a threshold is attained by complex positive operator-valued measurements that involve a highly nonlinear optical procedure. A suboptimal procedure that can be implemented with current technology is presented that is based on a modification of the conventional Dolinar receiver. We study and compare the performance of the scheme under different assumptions on the prior information available.

The present paper provides a joint experimental and theoretical study of positron scattering from pyrazine. Experimental data were measured employing a low-energy positron beamline, and covered an energy range from 1 to 79 eV. Cross sections were measured for total scattering, total elastic scattering, positronium formation, direct ionization, and the sum of the total discrete electronic-state excitation processes. In addition, measured total electronic excitation cross sections for the individual $1^1{B}_{3u},$ $1^1{B}_{2u},$ $1^1{B}_{1u},$ and $2^1{B}_{2u}$ states are also reported. Finally, experimental elastic differential cross sections (DCSs), here in the energy range $1–20$ eV, are also presented. Results from two theoretical approaches are given: the R-matrix approach and the independent atom method with screening corrected additivity rule and interference terms. Where a comparison between our experimental and theoretical results could be made, the level of accord varied from being quite good to marginal depending on the actual scattering process under consideration. Last, a comparison between the present elastic DCS results and those from our earlier study on positron scattering from pyrimidine [Palihawadana et al., Phys. Rev. A 88, 012717 (2013)] showed a somewhat unexpected level of agreement.

Photoelectron holography in strong-field tunneling ionization is an efficient way to probe the structures and the ultrafast dynamics information of atoms and molecules. Manipulating the process of photoelectron holography is important for its application. Here, we study theoretically strong-field photoelectron holography in the spatially inhomogeneous field by solving the time-dependent Schrödinger equation. Our results show that the returning energy of the rescattering electron is greatly enhanced in the spatially inhomogeneous field, and the holographic interference pattern can be separated from other types of interference in the photoelectron momentum distribution. Moreover, our results show that the time window of tunneling ionization wherein the electron could be driven back to induce holography is broadened in the inhomogeneous field. These properties are beneficial for the application of photoelectron holography in probing the atomic and molecular structures and dynamics. The origin for these properties is analyzed with the classical trajectory model.

Cherenkov radiation is one of the central effects in relativistic electrodynamics, which lends its name to a vast class of optical phenomena in which a moving source emits off-axis radiation, giving rise to a signature Cherenkov emission cone. When a radiation source is confined to a finite path, however, translational symmetry of its motion is removed, giving rise to edge effects that modify the canonical picture of conical emission. Here, we focus on one class of such edge effects as the key to understanding the properties of secondary radiation by laser-induced filaments. Charge-current transients near the edges of laser filaments are shown to couple Cherenkov emission to bremsstrahlung and transition radiation, giving rise to filament-length-sensitive features in the radiation field structure. We present a unified description of this class of radiation phenomena with a continuous analytical crossover from the subluminal to the superluminal setting of radiating currents and with the low-frequency cutoff in the radiation spectrum defined by the filament length.

Parity-time $\left(\mathcal{PT}\right)$ symmetry, originally conceived for non-Hermitian open quantum systems, has opened an exciting avenue towards coherent control of light for significant applications. Here we propose a paradigm towards non-Hermitian photonics based on the charge-parity $\left(\mathcal{CP}\right)$ symmetry, in which the charge conjugation and parity symmetries are broken individually but preserved jointly. Such a symmetry-breaking scheme induces a transition from dielectric to hyperbolic dispersions in chiral dielectrics, leading to lossless all-dielectric hyperbolic metamaterials. More interestingly, the $\mathcal{CP}$-symmetry transition represents a non-Hermitian topological phase transition that occurs at infinite energy and requires no explicit band gap closing. We further showcase broad applications of $\mathcal{CP}$-symmetric photonics such as an all-angle polarization-dependent beam splitter and enhanced spontaneous emission. The $\mathcal{CP}$ symmetry opens an unexplored pathway for non-Hermitian topological photonics by bringing new physics into strong chiral metamaterials, therefore providing a powerful tool for engineering many promising applications in photonics and other related fields.

An optical ring resonator with third-order, or Kerr, nonlinearity will exhibit symmetry breaking between the two counterpropagating circulating powers when pumped with sufficient power in both the clockwise and counterclockwise directions. This is due to the effects of self- and cross-phase modulation on the resonance frequencies in the two directions. The critical point of this symmetry breaking exhibits universal behaviors including divergent responsivity to external perturbations, critical slowing down, and scaling invariance. Here we derive a model for the critical dynamics of this system, first for a symmetrically pumped resonator and then for the general case of asymmetric pumping conditions and self- and cross-phase modulation coefficients. This theory not only provides a detailed understanding of the dynamical response of critical-point-enhanced optical gyroscopes and near-field sensors, but is also applicable to nonlinear critical points in a wide range of systems.