We examine the switching dynamics of discrete solitons propagating along two coupled discrete arrays which are twisted to form a Möbius strip. We analyze the potential of the topological switches by comparing the differences between the Möbius strip and untwisted discrete arrays. We employ the Ablowitz-Ladik (AL) model and reveal a nontrivial Berry phase associated with the monopole spectra in parameter space. We study the dynamical evolution of the AL soliton launched into one of the chains and observe its switching behavior. While in the untwisted discrete case, the soliton splits in nearly identical portions as the interchain coupling is increased, in the Möbius case and for weak coupling, we observe a well-defined “switching time” where the soliton switches completely from one chain to the other.

We investigate the transient dynamics of photon statistics through two-time correlation functions for optical field coupled to a non-Markovian environment, described by the Fano-type Hamiltonian. We exactly solve the time-evolution of an initially nonclassical state which exhibits photon antibunching. We find that the transient correlations at different times $t$ yield a smooth transition from antibunching to bunching photon statistics in the weak system-environment coupling regime. In the strong-coupling regime, the two-time correlations exhibit oscillations that persists both in the transient process and in the steady-state limit. The oscillatory behavior of photon statistics is a manifestation of strong non-Markovian memory dynamics where the system remains in nonequilibrium from its environment. We also find that the antibunching-to-bunching transition in the weak-coupling regime and the photon statistical oscillations in the strong-coupling regime are strongly influenced by the environment temperature.

We study theoretically two-photon states in a periodic array of coupled cavities with both on-site and nonlocal Kerr-type nonlinearities. In the absence of nonlinearity the structure is topologically trivial and possesses no edge states. The interplay of two nonlinear interaction mechanisms described by the extended Hubbard model facilitates the formation of edge states of bound photon pairs. Numerical and exact analytical results for the two-photon wave functions are presented. Our findings thus shed light onto the edge states of composite particles and their localization properties.

Almost one and a half centuries ago, Abbe [Arch. Mikrosk. Anat. 9, 413 (1873)] and shortly after Lord Rayleigh [Philos. Mag. Ser. 5 8, 261 (1879)] showed that, when an optical lens is illuminated by a plane wave, a diffraction-limited spot with radius $0.61\lambda /sin\alpha$ is obtained, where $\lambda$ is the wavelength and $\alpha$ is the semiangle of the beam's convergence cone. However, spots with much smaller features can be obtained at the focal plane when the lens is illuminated by an appropriately structured beam. Whereas this concept is known for light beams, here, we show how to realize it for a massive-particle wave function, namely, a free electron. We experimentally demonstrate an electron central spot of radius 106 pm, which is more than two times smaller than the diffraction limit of the experimental setup used. In addition, we demonstrate that this central spot can be structured by adding orbital angular momentum to it. The resulting superoscillating vortex beam has a smaller dark core with respect to a regular vortex beam. This family of electron beams having hot spots with arbitrarily small features and tailored structures could be useful for studying electron-matter interactions with subatomic resolution.

A many-body Wannier-Stark system coupled to an effective reservoir is studied within a non-Hermitian approach in the presence of a periodic driving. We show how the interplay of dissipation and driving dynamically induces a subspace of states which are very robust against dissipation. We numerically probe the structure of these asymptotic states and their robustness to imperfections in the initial-state preparation and to the size of the system. Moreover, the asymptotic states are found to be strongly entangled making them interesting for further applications.

Theoretical description and simulation of large quantum coherent systems out of equilibrium remains a daunting task. Here we are developing an approach to it based on the Pechukas-Yukawa formalism, which is especially convenient in the case of an adiabatically slow external perturbation, though it is not restricted to adiabatic systems. In this formalism the dynamics of energy levels in an externally perturbed quantum system as a function of the perturbation parameter is mapped on that of a fictitious one-dimensional classical gas of particles with cubic repulsion. Equilibrium statistical mechanics of this Pechukas gas allows us to reproduce the random matrix theory of energy levels. In the present work, we develop the nonequilibrium statistical mechanics of the Pechukas gas, starting with the derivation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) chain of equations for the appropriate generalized distribution functions. Sets of approximate kinetic equations can be consistently obtained by breaking this chain at a particular point (i.e., approximating all higher-order distribution functions by the products of the lower-order ones). When complemented by the equations for the level occupation numbers and interlevel transition amplitudes, they allow us to describe the nonequilibrium evolution of the quantum state of the system, which can describe better a large quantum coherent system than the currently used approaches. In particular, we find that corrections to the factorized approximation of the distribution function scale as $1/N$, where $N$ is the number of the “Pechukas gas particles” (i.e., energy levels in the system).

We quantify the intrinsic noise content of an observable in a general probabilistic theory and derive a noise content inequality for incompatible observables. We apply the derived inequality to standard quantum theory, the quantum theory of processes, and polytope state spaces. The noise content for positive operator-valued measures takes a particularly simple form and equals the sum of minimal eigenvalues of all the effects. We illustrate our findings with a number of examples including the introduced notion of reverse observables.

We examine two proposals for marginally-self-correcting quantum memory: the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their Gibbs ensembles can be prepared via a short-depth quantum circuit from classical ensembles. Our proof technique naturally gives rise to the notion of free energy associated with excitations. Further, we develop a framework for an ergodic decomposition of Davies generators in CSS codes which enables formal reduction to simpler classical memory problems. We then show that memory time in the welded code is doubly exponential in inverse temperature via the Peierls argument. These results introduce further connections between thermal topological order and self-correction from the viewpoint of free energy and quantum circuit depth.

We show how to calculate the secure final key rate in the four-intensity decoy-state measurement-device-independent quantum key distribution protocol with both source errors and statistical fluctuations with a certain failure probability. Our results rely only on the range of only a few parameters in the source state. All imperfections in this protocol have been taken into consideration without assuming any specific error patterns of the source.

We formulate a general family of entanglement criteria for multipartite states on arbitrary Hilbert spaces. Fisher information criteria compare the sensitivity to unitary rotations with the variances of suitable local observables. Generalized squeezing-type criteria provide lower bounds that are less stringent but require only measurements of second moments. The enhancement due to local access to the individual subsystems is studied in detail for the case of $N$ spin-$1/2$ particles. The discussed techniques can be readily implemented in current experiments with trapped ions in Paul traps and neutral atoms in optical lattices.

We determine effective collisional radii of positronium (Ps) by considering Ps states in hard-wall spherical cavities. $B$-spline basis sets of electron and positron states inside the cavity are used to construct the states of Ps. Accurate Ps energy eigenvalues are obtained by extrapolation with respect to the numbers of partial waves and radial states included in the bases. Comparison of the extrapolated energies with those of a point-like particle provides values of the effective radius ${\rho }_{nl}$ of Ps($nl$) in collisions with a hard wall. We show that, for $1s, 2s$, and $2p$ states of Ps, the effective radius decreases with the increasing Ps center-of-mass momentum and find ${\rho }_{1s}=1.65$ a.u., ${\rho }_{2s}=7.00$ a.u., and ${\rho }_{2p}=5.35$ a.u. in the zero-momentum limit.

We show that the processes of $\pi -{\pi }^{*}$ transitions imprint themselves on the high-harmonic spectra when conjugated molecules interact with intense femtosecond laser pulses. It is found that a noninteger order peak appears in the harmonic spectrum with the photon energy equaling the excitation energy of the $\pi -{\pi }^{*}$ excitation. Further studies prove that this radiation is caused by the $\pi -{\pi }^{*}$ transition. The transition signals are prominent and can be easily measured as the corresponding radiation intensities are comparable to those of integer order harmonics. Our results pave the way for the study of excited-state electron-ion dynamics using high-harmonic spectroscopy. In comparison to the traditional absorption spectroscopy method relying on the synchrotron radiation source, the present approach is easily accessible for the use of a tabletop laser-based source. Furthermore, our study also provides a potential tool to probe the $\pi -{\pi }^{*}$ transition processes in femtosecond resolution.

The dynamics of ${\mathrm{CO}}_2$ excited into Rydberg states lying 0.2 eV below the ionization threshold is studied by means of time resolved photoelectron imaging. Over 3 eV broad photoelectron spectra are measured for all pump-probe delay times. Quantum mechanical calculations demonstrate that the spectral broadening is due to ultrafast electronic relaxation of Rydberg states and identify the likely relaxation pathways. Experiment and theory bracket the relaxation time between 15 and 65 fs. A weak time independent ionization signal is attributed to ${\mathrm{CO}}_2$ trapped in near-threshold triplet states.

The purpose of this paper is to investigate system identification for single-input–single-output general (active or passive) quantum linear systems. For a given input we address the following questions: (1) Which parameters can be identified by measuring the output? (2) How can we construct a system realization from sufficient input-output data? We show that for time-dependent inputs, the systems which cannot be distinguished are related by symplectic transformations acting on the space of system modes. This complements a previous result of Guţă and Yamamoto [IEEE Trans. Autom. Control 61, 921 (2016)] for passive linear systems. In the regime of stationary quantum noise input, the output is completely determined by the power spectrum. We define the notion of global minimality for a given power spectrum, and characterize globally minimal systems as those with a fully mixed stationary state. We show that in the case of systems with a cascade realization, the power spectrum completely fixes the transfer function, so the system can be identified up to a symplectic transformation. We give a method for constructing a globally minimal subsystem direct from the power spectrum. Restricting to passive systems the analysis simplifies so that identifiability may be completely understood from the eigenvalues of a particular system matrix.

Motivated by new technologies for designing and tailoring metamaterials, we seek properties for certain classes of nonlinear optical materials that allow room for a reversibly controlled opacity-to-transparency phase transition through the application of external electromagnetic fields. We examine some mathematically simple models for the dielectric parameters of the medium and compute the relevant geometric quantities that describe the speed and polarization of light rays.

We observe time-correlated emission between a single CdSe/CdS/ZnS quantum dot exhibiting single-photon statistics and a fluorescent nanobead located micrometers apart. This is accomplished by coupling both emitters to a silver nanowire. Single plasmons are created on the latter from the quantum dot, and transfer energy to excite in turn the fluorescent nanobead. We demonstrate that the molecules inside the bead show the same blinking behavior as the quantum dot.

We investigate the dynamics of a coupled waveguide system with competing linear and nonlinear loss-gain profiles which can facilitate power saturation. We show the usefulness of the model in achieving unidirectional beam propagation. In this regard, the considered type of coupled waveguide system has two drawbacks: (i) difficulty in achieving perfect isolation of light in a waveguide and (ii) existence of blow-up-type behavior for certain input power situations. We here show a nonlinear $\mathcal{PT}$-symmetric coupling that helps to overcome these two drawbacks. Such a nonlinear coupling has close connection with the phenomenon of stimulated Raman scattering. In particular, we have elucidated the role of this nonlinear coupling using an integrable $\mathcal{PT}$-symmetric situation. In particular, using the integrals of motion, we have reduced this coupled waveguide problem to the problem of dynamics of a particle in a potential. With the latter picture, we have clearly illustrated the role of the considered nonlinear coupling. The above $\mathcal{PT}$-symmetric case corresponds to a limiting form of a general equation describing the phenomenon of stimulated Raman scattering. We also point out the ability to transport light unidirectionally even in this general case.