We present an analytical theory of topologically protected photonic states for the two-dimensional Maxwell equations for a class of continuous periodic dielectric structures, modulated by a domain wall. We further numerically confirm the applicability of this theory for three-dimensional structures.

We address Berry phases that have been predicted to appear when a two-level system interacts with a quantized field, including the vacuum state. The issue became controversial after it was argued that the appearance of such Berry phases is an artifact of the rotating-wave approximation (RWA). As is widely believed, whenever the RWA applies, one may replace the Rabi model of a two-level system interacting with a quantized field by the analytically solvable Jaynes-Cummings model. Conflicting predictions of these two models under conditions that validate the RWA would signal a serious inconsistency of this approximation. We show that this is not the case and that claims to the contrary are inconsistent with analytical results concerning the Rabi model. We provide also numerical evidence supporting our analytical approach. Furthermore, we argue that the appearance of Berry phases in the addressed cases does not depend on adiabatic conditions nor on any particular Hamiltonian, but on the underlying vector space. Thus, the appropriate framework is given by the kinematic approach to geometric phases, which contains Berry's phase as a special case.

We explore theoretically the physics of dynamic hysteresis for driven-dissipative nonlinear photonic resonators. In the regime where the semiclassical mean-field theory predicts bistability, the exact steady-state density matrix is known to be unique, being a statistical mixture of two states; in particular, no static hysteresis cycle of the excited population occurs as a function of the driving intensity. Here, we predict that in the quantum regime a dynamic hysteresis with a rich phenomenology does appear when sweeping the driving amplitude in a finite time. The hysteresis area as a function of the sweep time reveals a double power-law decay, with a behavior qualitatively different from the mean-field predictions. The dynamic hysteresis power-law in the slow sweep limit defines a characteristic time, which depends dramatically on the size of the nonlinearity and on the frequency detuning between the driving and the resonator. In the strong nonlinearity regime, the characteristic time oscillates as a function of the intrinsic system parameters due to multiphotonic resonances. We show that the dynamic hysteresis for the considered class of driven-dissipative systems is due to a nonadiabatic response region with connections to the Kibble-Zurek mechanism for quenched phase transitions. We also consider the case of two coupled driven-dissipative nonlinear resonators, showing that dynamic hysteresis and power-law behavior occur also in the presence of correlations between resonators. Our theoretical predictions can be explored in a broad variety of physical systems, e.g., circuit QED superconducting resonators and semiconductor optical microcavities.

We investigate the preparation of a target initial state for a two-level (qubit) system from a system-environment equilibrium or correlated state by an external field. The system-environment equilibrium or correlated state results from the inevitable interaction of the system with its environment. An efficient method in an extended auxiliary Liouville space is introduced to describe the dynamics of the non-Markovian open quantum system in the presence of a strong field and an initial system-environment correlation. By using the time evolutions of the population difference, the state trajectory in the Bloch sphere representation, and the trace distance between two reduced system states of the open quantum system, the effect of initial system-environment correlations on the preparation of a system state is studied. We introduce an upper bound and a lower bound for the trace distance within our perturbation formalism to describe the diverse behaviors of the dynamics of the trace distance between various correlated states after the system state preparation. These bounds, that are much more computable than similar bounds in the literature, give a sufficient condition and a necessary condition for the increase of the trace distance and are related to the witnesses of non-Markovianity and initial system-bath correlation.

We derive two types of sets of higher-order conditions for bipartite entanglement in terms of continuous variables. One corresponds to an extension of the well-known Duan inequalities from second to higher moments describing a kind of higher-order Einstein-Podolsky-Rosen (EPR) correlations. Only the second type, however, expressed by powers of the mode operators leads to tight conditions with a hierarchical structure. We start with a minimization problem for the single-partite case and, using the results obtained, establish relevant inequalities for higher-order moments satisfied by all bipartite separable states. We give an explicit example of a non-Gaussian state that exhibits fourth-order but no second-order EPR correlations. Similarly, a certain fourth-order condition cannot be violated by any Gaussian state and we present non-Gaussian states whose entanglement is detected by that condition. Violations of all our conditions are provided, so they can all be used as entanglement tests.

We study the propagation of information through a Kitaev chain with long-range pairing interactions. Although the Lieb-Robinson bound is violated in the strict sense for long-range interacting systems, we illustrate that a major amount of information in this model still propagates ballistically on a light cone. We find a pronounced effect of the interaction range on the decay of the mutual information between spatially disconnected subsystems. A significant amount of information is shared at timelike separations. This regime is accompanied by very slow equilibration of local observables. As the Kitaev model is quasifree, we illustrate how the distribution of quasiparticle group velocities explains the physics of this system qualitatively.

We present a scheme for realizing passive quantum key distribution with heralded single-photon sources. In this scheme, the idler light from the parametric down-conversion process is split into two parts and sent into two local detectors individually. Then all the clicking and nonclicking events are used to herald the arrival and nonarrival of the signal light. As a result, a precise estimation of the behavior of the single-photon pulses can be achieved without changing the light intensity. Furthermore, we compare our scheme with other existing methods with the Bennett-Brassard 1984 (BB84) protocol through numerical simulations. Our simulations demonstrate that the performance of our scheme can greatly overcome other existing practical methods and approach very close to the asymptotic case of using infinite-decoy-state methods.

We investigate the effects of systematic errors of the control parameters on single-qubit gates based on nonadiabatic non-Abelian geometric holonomies and those relying on purely dynamical evolution. It is explicitly shown that the systematic error in the Rabi frequency of the control fields affects these two kinds of gates in different ways. In the presence of this systematic error, the transformation produced by the nonadiabatic non-Abelian geometric gate is not unitary in the computational space, and the resulting gate infidelity is larger than that with the dynamical method. Our results provide a theoretical basis for choosing a suitable method for implementing elementary quantum gates in physical systems, where the systematic noises are the dominant noise source.

We present theoretical and experimental fully differential cross sections, in coplanar scattering geometry, for the double ionization of helium by electron impacting at 2 keV. The observed structures for both equal and unequal sharing of the excess energy are analyzed. Although the incident energy could, in principle, be regarded as high enough for the applicability of the first Born approximation in the projectile-target interaction, the experimental cross sections, measured with a COLTRIMS apparatus, show that further orders' effects can be appreciated. The theoretical cross sections are calculated with the generalized Sturmian functions method, which exactly solves the three-body problem that stems from a first-order projectile-target perturbative treatment.

A method for the calculation of transition amplitudes of two-photon ionization processes is developed. It is based on computing a correlation function, which enables the summation over intermediate states of two-photon transitions. Two-photon ionization transition amplitudes were calculated in the lowest order of perturbation theory with taking into account many-electron correlations. The noniterative numerical scheme provided a solution of the differential equation for the correlation function at exciting-photon energies close to the intermediate discrete resonance states. Cross section and angular distribution parameters for photoelectrons of the two-photon $3p$ photoionization of Ar were calculated. The exciting-photon energy ranged from 8 eV to 15 eV. For the first time an ab initio polarization potential considers the polarization of the atomic core by the excited photoelectron was included in the calculation. This effect increases the photoionization cross section at the photon energy from 8 eV to 10 eV by approximately 15% and shifts the computed energies of the intermediate discrete-state resonances, bringing them to excellent agreement with the experimental energies.

The linear polarization of the characteristic lines $L{\alpha }_1$ $\left(3d_{5/2}\to 2p_{3/2}\right)$ and $L{\alpha }_2$ $(3d_{3/2}\to 2p_{3/2})$, following inner-shell photoionization of neutral tungsten, is analyzed both experimentally and theoretically. In the experiment, a tungsten target is photoionized by the primary emission of an x-ray tube with incident photon energies in the range of 10.2–30 keV. The $\sigma$ and $\pi$ components of the emitted fluorescence are measured by using a spectropolarimeter, based on x-ray diffraction at Bragg angles close to ${45}^{\circ }$. The degree of linear polarization of the $L{\alpha }_1$ and $L{\alpha }_2$ lines is determined to be $+(1.6\pm 0.5)\%$ and $-(7\pm 2)\%$, respectively. In addition, this degree of polarization is calculated within the framework of the density-matrix theory as a function of the incident photon energy. These calculations are in good agreement with the experimental results and show only a weak dependence of the degree of polarization on the energy of the incident photoionizing photon.

We address the problem of computing the thermodynamic properties of the repulsive one-dimensional two-component Fermi gas with contact interaction, also known as the Gaudin-Yang model. Using a specific lattice embedding and the quantum transfer matrix we derive an exact system of only two nonlinear integral equations for the thermodynamics of the homogeneous model which is valid for all temperatures and values of the chemical potential, magnetic field, and coupling strength. This system allows for an easy and extremely accurate calculation of thermodynamic properties circumventing the difficulties associated with the truncation of the thermodynamic Bethe ansatz system of equations. We present extensive results for the densities, polarization, magnetic susceptibility, specific heat, interaction energy, Tan contact, and local correlation function of opposite spins. Our results show that at low and intermediate temperatures the experimentally accessible contact is a nonmonotonic function of the coupling strength. As a function of the temperature the contact presents a pronounced local minimum in the Tonks-Girardeau regime which signals an abrupt change of the momentum distribution in a small interval of temperature. The density profiles of the system in the presence of a harmonic trapping potential are computed using the exact solution of the homogeneous model coupled with the local density approximation. We find that at finite temperature the density profile presents a double shell structure (partially polarized center and fully polarized wings) only when the polarization in the center of the trap is above a critical value which is monotonically increasing with temperature.

In this work we present a generic feature of $\mathcal{PT}$-symmetric Bose-Einstein condensates by studying the many-particle description of a two-mode condensate with balanced gain and loss. This is achieved using a master equation in Lindblad form whose mean-field limit is a $\mathcal{PT}$-symmetric Gross-Pitaevskii equation. It is shown that the purity of the condensate periodically drops to small values but then is nearly completely restored. This has a direct impact on the average contrast in interference experiments which cannot be covered by the mean-field approximation, in which a completely pure condensate is assumed.

We analyze the dynamics of Josephson vortex states in two-component Bose-Einstein condensates with Rashba-Dresselhaus spin-orbit coupling by using the Gross-Pitaevskii equation. In one dimension, both in homogeneous and harmonically trapped systems, we report on stationary states containing doubly charged, static Josephson vortices. In multidimensional systems, we find stable Josephson vortices in a regime of parameters typical of current experiments with ${}^{87}\text{Rb}$ atoms. In addition, we discuss the instability regime of Josephson vortices in disk-shaped condensates, where the snake instability operates and vortex dipoles emerge. We study the rich dynamics that they exhibit in different regimes of the spin-orbit-coupled condensate depending on the orientation of the Josephson vortices.

We prove feasibility of high-fidelity pulsed optomechanical interface based on all-optical presqueezing of non-Gaussian quantum states of light before they enter the optomechanical system. We demonstrate that feasible presqueezing of optical states effectively increases the low noise transfer of them to mechanical oscillator. It allows one to surpass the limit necessary to transfer highly nonclassical states with negative Wigner function. In particular, we verify that with this help single photon states of light can be efficiently turned to single phonon states of mechanical oscillator, keeping the negativity of the Wigner function. It opens the possibility to merge quantum optomechanics with the recent methods of quantum optics.

We discuss the effect of external noisy magnetic fields on mesoscopic spin fluctuations that can be probed in semiconductors and atomic vapors by means of optical spin-noise spectroscopy. We show that conventional arguments of the law of large numbers do not apply to spin correlations induced by external fields, namely, the magnitude of the 4th-order spin cumulant grows as $\sim N^2$ with the number $N$ of observed spins, i.e., it is not suppressed in comparison to the 2nd-order cumulant. This allows us to design a simple experiment to measure the 4th-order cumulant of spin fluctuations in an atomic system near thermodynamic equilibrium and develop a quantitative theory that explains all observations.

We study narrowband biphoton generation from spontaneous four-wave mixing with electromagnetically induced transparency in a laser-cooled atomic ensemble. We compare two formalisms in the interaction and Heisenberg pictures and find that they agree in the low-gain regime but disagree in the high-gain regime. We extend both formalisms to account for the nonuniformity of the atomic density and the driving laser fields. We find that for a fixed optical depth and a weak and far-detuned pump laser beam, the two-photon waveform is independent of the atomic density distribution. However, the spatial profiles of the two driving laser beams have significant effects on the biphoton temporal waveform. We predict that waveform shaping in the time domain can be achieved by controlling the spatial profiles of the driving laser fields.

We investigate polarization squeezing in squeezed coherent states with varying coherent amplitudes. In contrast to the traditional characterization based on the full Stokes parameters, we experimentally determine the Stokes vector of each excitation subspace separately. Only for states with a fixed photon number do the methods coincide; when the photon number is indefinite, we parse the state in Fock layers, finding that substantially higher squeezing can be observed in some of the single layers. By capitalizing on the properties of the Husimi $Q$ function, we map this notion onto the Poincaré space, providing a full account of the measured squeezing.