Extensive numerical computations are often required to optimize the optical properties of nanostructures. Here, we use the Weierstrass factorization theorem to express the scattering matrix in terms of spectral singularities. We show that the location of poles and zeros of the scattering matrix fully determines all scattering properties, and that the scattering spectra of nanostructures can be decomposed into Lorentzian resonances over an arbitrary range of frequencies. This technique is applied to design nanoshell particles with enhanced absorption.

Changes in the magnetic moment of an electron near a dielectric or conducting surface due to boundary-dependent radiative corrections are investigated. The electromagnetic field is quantized by normal mode expansion for a nondispersive dielectric and an undamped plasma, but the electron is described by the Dirac equation without matter-field quantization. Perturbation theory in the Dirac equation leads to a general formula for the magnetic-moment shift in terms of integrals over products of electromagnetic mode functions. In each of the models investigated, contour integration techniques over a complex wave vector can be used to derive a general formula featuring just integrals over transverse electric and transverse magnetic reflection coefficients of the surface. Analysis of the magnetic-moment shift for several classes of materials yields markedly different results from the previously considered simplistic “perfect-reflector” model, due to the inclusion of physically important features of the electromagnetic response of the surface such as evanescent field modes and dispersion in the material. For a general dispersive dielectric surface, the magnetic-moment shift of a nearby electron can exceed the previous prediction of the perfect-reflector model by several orders of magnitude.

Multiphoton quantum walks in integrated optics comprise an attractive controlled quantum system, that can mimic less readily accessible quantum systems and exhibit behavior that cannot in general be accurately replicated by classical light without an exponential overhead in resources. The ability to observe the time evolution of such systems is important for characterizing multiparticle quantum dynamics—notably this includes the effects of boundary conditions for walks in spaces of finite size. Here we demonstrate the coherent evolution of quantum walks of two indistinguishable photons using planar arrays of 21 evanescently coupled waveguides fabricated in silicon oxynitride technology. We compare three time evolutions, that follow closely a model assuming unitary evolution, corresponding to three different lengths of the array—in each case we observe quantum interference features that violate classical predictions. The longest array includes reflecting boundary conditions.

We propose a two-dimensional model for a multilayer stack of dipolar Bose-Einstein condensates formed by a strong optical lattice. We derive effective intra- and interlayer dipole-dipole interaction potentials and provide simple analytical approximations for a given number of lattice sites at arbitrary polarization. We find that the interlayer dipole-dipole interaction changes the transverse aspect ratio of the ground state in the central layers depending on its polarization and the number of lattice sites. The changing aspect ratio should be observable in time-of-flight images. Furthermore, we show that the interlayer dipole-dipole interaction reduces the excitation energy of local perturbations affecting the development of a roton minimum.

We discuss the possible cooling of different phonon modes via three-wave mixing interactions of vibrational and optical modes. Since phonon modes exhibit a variety of dispersion relations or frequency spectra with diverse spatial structures, depending on the shape and size of the sample, we formulate our theory in terms of relevant spatial mode functions for the interacting fields in any given geometry. Our general formulation is applicable to cooling of any low-frequency excitation mode in matter which can give appreciable inelastic light scattering via the modulation of the optical dielectric function. We discuss the possibility of Dicke-like collective effects in phonon cooling and present explicit results for simultaneous cooling of two-phonon modes via the anti-Stokes up-conversions. We show that the bimodal cooling should be observable experimentally.

The most important ability of a quantum channel is to preserve the quantum properties of transmitted quantum states. We experimentally demonstrate a continuous-variable system for efficient benchmarking of quantum channels. We probe the tested quantum channels for a wide range of experimental parameters such as amplitude, phase noise, and channel lengths up to 40 km. The data is analyzed using the framework of effective entanglement. We subsequently are able to deduce an optimal point of operation for each quantum channel with respect to the rate of distributed entanglement. This procedure is a promising candidate for benchmarking quantum nodes and individual links in large quantum networks of different physical implementations.

Having the advantages of inherent robustness and fault tolerance, adiabatic quantum algorithms have attracted much attention in recent years. In this paper, we report the NMR experimental realization of adiabatic algorithms for the modified Simon's problem in a NMR quantum information processor. We first realized an adiabatic quantum algorithm by Rao [Phys. Rev. A 67, 052306 (2003)] and then proposed a quantum algorithm by using the method of enhanced symmetry of the Hamiltonian given in Schaller and Schtzhold [Quantum Inf. Comput. 10, 109 (2010)]. We demonstrated this symmetry-enhanced algorithm in experiment. We studied the effects of the number of Trotter evolution steps on the validity of adiabatic evolution and decoherence. In practical applications, a trade-off between pulse imperfection and adiabatic requirement must be made in the Trotter evolution step number. An optimal evolution step number and run time were indicated by our results. The experimental demonstration also showed that the symmetry-enhanced algorithm gave a better performance.

Quantum mechanics sets limits on how fast quantum processes can run given some system energy through time-energy uncertainty relations, and they imply that time and energy are tradeoffs against each other. Thus, we propose to measure the time energy as a single unit for quantum channels. We consider a time-energy measure for quantum channels and compute lower and upper bounds of it using the channel Kraus operators. For a special class of channels (which includes the depolarizing channel), we can obtain the exact value of the time-energy measure. One consequence of our result is that erasing quantum information requires $\sqrt{(n+1)/n}$ times more time-energy resource than erasing classical information, where $n$ is the system dimension.

The variational Feynman formalism for the polaron, extended to an all-coupling treatment of bipolarons, is applied for two impurity atoms in a Bose-Einstein condensate. This shows that if the polaronic coupling strength is large enough, the impurities will form a bound state (the bipolaron). As a function of the mutual repulsion between the impurities, two types of bipolaron are distinguished: a tightly bound bipolaron at weak repulsion and a dumbbell bipolaron at strong repulsion. Apart from the binding energy, the evolution of the bipolaron radius and its effective mass are also examined as a function of the strength of the repulsive interaction between the impurities and of the polaronic coupling strength. We then apply the strong-coupling formalism to multiple-impurity atoms in a condensate, which leads to the prediction of multipolaron formation in the strong-coupling regime. The results of the two formalisms are compared for two impurities in a condensate, which results in a general qualitative agreement and a quantitative agreement at strong coupling. Typically, the system of impurity atoms in a Bose-Einstein condensate is expected to exhibit the polaronic weak-coupling regime. However, the polaronic coupling strength is, in principle, tunable with a Feshbach resonance.

We examine the stability of quasi-two-dimensional dipolar Bose-Einstein condensates in the presence of weak optical lattices of various geometries. We find that when the condensate possesses a roton-maxon quasiparticle dispersion, the conditions for stability exhibit a strong dependence both on the lattice geometry and the polarization tilt. This results in rich structures in the system's stability diagram akin to spectroscopic signatures. We show how these structures originate from the mode matching of rotons to the perturbing lattice. In the case of a one-dimensional lattice, some of the features emerge only when the polarization axis is tilted into the plane of the condensate. Our results suggest that the stability diagram may be used as a novel means to spectroscopically measure rotons in dipolar condensates.

We study peculiarities of Bose-Einstein condensation of photons that are in thermodynamic equilibrium with atoms of noninteracting gases. General equations of the thermodynamic equilibrium of the system under study are obtained. We examine solutions of these equations in the case of high temperatures, when the atomic components of the system can be considered as nondegenerated ideal gases of atoms, and the photonic component can form a state with the Bose condensate. Transcendental equation for transition temperature and expression for the density of condensed photons in the considered system are derived. We also obtain analytical solutions of the equation for the critical temperature in a number of particular cases. The existence of two regimes of Bose condensation of photons, which differ significantly in nature of transition temperature dependence on the total density of photons pumped into the system, is revealed. In one case, this dependence is a traditional fractional-power law, and in another one it is the logarithmic law. Applying numerical methods, we determine boundaries of existence and implementation conditions for different regimes of condensation depending on the physical parameters of the system under study. We also show that for a large range of physical systems that are in equilibrium with photons (from ultracold gases of alkali metals to certain types of ideal plasma), the condensation of photons should occur according to the logarithmic regime.

An analytic approach is developed for obtaining the normalized surface height autocorrelation function of a one-dimensional randomly rough dielectric surface from experimental scattering data. It is based on the contribution to the mean differential reflection coefficient, obtained in the Kirchhoff approximation, from the light scattered incoherently. The incident light is $s$ polarized, and its plane of incidence is perpendicular to the generators of the surface. Good agreement with numerically generated experimental data is obtained.

The inverted spectral structure of coupled-resonator-induced transparency was experimentally demonstrated using an amplifying optical ring resonator, to which another dark ring resonator was coupled. A nonamplifying spectral window was induced by the dark resonator in an otherwise strongly amplifying spectral region. Within the induced window, sharp anomalous dispersion was expected. Propagation of nearly Gaussian-shaped optical pulses was observed; the pulses propagated through the amplifying medium with a negative delay of $-$20.8 ns, without significant amplification, attenuation, or pulse deformation. The inverted induced-transparency system, producing tunable fast light, is a complementary system to traditional induced-transparency systems that produce slow light and could be potentially useful in numerous applications.

In the standard theory of cavity quantum electrodynamics (QED), coupling between photons inside and outside a cavity (cavity system and environment) is given conserving the total number of photons. However, when the cavity photons (ultrastrongly) interact with atoms or excitations in matters, the system-environment coupling must be determined from a more fundamental viewpoint. Based on the Maxwell's boundary conditions in the QED theory for dielectric media, we derive the quantum Langevin equation and input-output relation, in which the total number of polaritons (not photons) inside the cavity and photons outside is conserved.

By solving the two-electron time-dependent Schrödinger equation, we study carrier-envelope-phase (CEP) effects on ionization plus excitation of He to He${}^{+}(n=2)$ states by a few-cycle attosecond pulse with a carrier frequency of 51 eV. For most CEPs the asymmetries in the photoelectron angular distributions with excitation of He${}^{+}\left(2s\right)$ or He${}^{+}\left(2p\right)$ have opposite signs and are two orders of magnitude larger than for ionization without excitation. These results indicate that attosecond pulse CEP effects may be significantly amplified in correlated two-electron ionization processes.

The atomic dipoles in the Rabi lattice model exhibit quantum Ising dynamics in the limit of strong atom-photon interaction. It governs the paraelectric to ferroelectric phase transition in the ground state. On an open chain, it implies the existence of two Majorana-like, albeit topologically unprotected, edge modes in the ordered phase. The relation ${\rho }_{1L}^x=p^8$ between the end-to-end dipole correlation ${\rho }_{1L}^x$ and the spontaneous polarization $p$ is proposed as an observable signature of these edge modes. The density-matrix renormalization-group calculations on the one-dimensional Rabi lattice support the strong-coupling quantum Ising behavior and correctly yield the proposed end-to-end dipole correlation. The conditions that protect the edge modes against the adverse perturbations are also identified.

We present a first-principles derivation of the Markovian semigroup master equation without invoking the rotating-wave approximation (RWA). Instead we use a time coarse-graining approach that leaves us with a free time-scale parameter, which we can optimize. Comparing this approach to the standard RWA-based Markovian master equation, we find that significantly better agreement is possible using the coarse-graining approach, for a three-level model coupled to a bath of oscillators, whose exact dynamics we can solve for at zero temperature. The model has the important feature that the RWA has a nontrivial effect on the dynamics of the populations. We show that the two different master equations can exhibit strong qualitative differences for the population of the energy eigenstates even for such a simple model. The RWA-based master equation misses an important feature which the coarse-graining-based scheme does not. By optimizing the coarse-graining time scale the latter scheme can be made to approach the exact solution much more closely than the RWA-based master equation.

In this work, we derived a semiclassical approximation for the matrix elements of a quantum propagator in coherent states (CS) basis that avoids complex trajectories; it only involves real ones. For that purpose, we used the symplectically invariant semiclassical Weyl propagator obtained by performing a stationary phase approximation (SPA) for the path integral in the Weyl representation. After that, for the transformation to CS representation SPA is avoided; instead a quadratic expansion of the complex exponent is used. This procedure also allows us to express the semiclassical CS propagator uniquely in terms of the classical evolution of the initial point without the need of any root search typical of van Vleck–Gutzwiller-based propagators. For the case of chaotic Hamiltonian systems, the explicit time dependence of the CS propagator has been obtained. The comparison with a realistic chaotic system that derives from a quadratic Hamiltonian, the cat map, reveals that the expression here derived is exact up to quadratic Hamiltonian systems.

We study the non-Markovianity of the dynamics of open quantum systems, focusing on the cases of independent and common environmental interactions. We investigate the degree of non-Markovianity quantified by two distinct measures proposed by Luo, Fu, and Song and Breuer, Laine, and Pillo. We show that the amount of non-Markovianity, for a single qubit and a pair of qubits, depends on the quantum process, the proposed measure, and whether the environmental interaction is collective or independent. In particular, we demonstrate that while the degree of non-Markovianity generally increases with the number of qubits in the system for independent environments, the same behavior is not always observed for common environments. In the latter case, our analysis suggests that the amount of non-Markovianity could increase or decrease depending on the properties of the considered quantum process.

The momentum spectrum of multiphoton-created electrons in the presence of a a static potential well as well as an alternating field is found to be related to the electron energy levels in the potential well and the energy of the photons. A simple relation among three energies, the created electron energy associated with the momentum distribution, the level energy of the electron bound state, and the photon energy, is obtained. Pair production can be significantly enhanced by this two-field configuration. In this case, the depth of the static potential well and the frequency of the alternating field also need not be supercritical.