The Casimir stress and energy density are widely used to study the Casimir force, but they diverge in inhomogeneous systems, making the force seem to be infinite as well. Here we characterize the asymptotic behavior of the Casimir stress and energy density in inhomogeneous systems. We show an unambiguous map of all cutoff-dependent terms in the asymptotic expansion to the pressure and the surface tension through the insertion of multiple boundary layers. This result reveals an elegant subtraction to retrieve a finite stress that yields a cutoff-independent force.

We present two complementary models to study stationary nonlinear solutions in one-dimensional plasmonic slot waveguides made of a finite-thickness nonlinear dielectric core surrounded by metal regions. The considered nonlinearity is of focusing Kerr type. In the first model, it is assumed that the nonlinear term depends only on the transverse component of the electric field and that the nonlinear refractive index change is small compared to the linear part of the refractive index. This first model allows us to describe analytically the field profiles in the whole waveguide using Jacobi elliptic special functions. It also provides a closed analytical formula for the nonlinear dispersion relation. In the second model, the full dependency of the Kerr nonlinearity on the electric-field components is taken into account and no assumption is required on the amplitude of the nonlinear term. The disadvantage of this approach is that the field profiles must be computed numerically. Nevertheless, analytical constraints are obtained to reduce the parameter space where the solutions of the nonlinear dispersion relations are sought.

We describe the results of the two methods we developed to calculate the stationary nonlinear solutions in one-dimensional plasmonic slot waveguides made of a finite-thickness nonlinear dielectric core surrounded by metal regions. These two methods are described in detail in the preceding article [Walasik and Renversez, preceding paper, Phys. Rev. A 93, 013825 (2016)]. For symmetric waveguides, we provide the nonlinear dispersion curves obtained using the two methods and compare them. We describe the well-known low-order modes and higher modes that were not described before. All the modes are classiffied into two families: modes with or without nodes. We also compare nonlinear modes with nodes with the linear modes in similar linear slot waveguides with a homogeneous core. We recover the symmetry breaking Hopf bifurcation of the first symmetric nonlinear mode toward an asymmetric mode and we show that some of the higher modes also exhibit a bifurcation. We study the behavior of the bifurcation of the fundamental mode as a function of the permittivities of the metal cladding and of the nonlinear core. We demonstrate that the bifurcation can be obtained at low power levels in structures with optimized parameters. Moreover, we provide the dispersion curves for asymmetric nonlinear slot waveguides. Finally, we give results concerning the stability of the fundamental symmetric mode and the asymmetric mode that bifurcates from it using both theoretical argument and numerical propagation simulations from two different full-vector methods. We also investigate the stability properties of the first antisymmetric mode using our two numerical propagation methods.

We theoretically study the driven-dissipative Harper-Hofstadter model on a two-dimensional square lattice in the presence of a weak harmonic trap. Without pumping and loss, the eigenstates of this system can be understood, in certain limits, as momentum-space toroidal Landau levels, where the Berry curvature, a geometrical property of an energy band, acts like a momentum-space magnetic field. We show that key features of these eigenstates can be observed in the steady state of the driven-dissipative system under a monochromatic coherent drive and present a realistic proposal for an optical experiment using state-of-the-art coupled cavity arrays. We discuss how such spectroscopic measurements may be used to probe effects associated both with the off-diagonal elements of the matrix-valued Berry connection and with the synthetic magnetic gauge.

We present a quantum-field-theoretical framework based on path integrals and Feynman diagrams for the investigation of the quantum-optical properties of one-dimensional waveguiding structures with embedded quantum impurities. In particular, we obtain the Green's functions for a waveguide with an embedded two-level system in the single- and two-excitation sector for arbitrary dispersion relations both in the time and the frequency domains. In the single-excitation sector, we show how to sum the diagrammatic perturbation series to all orders and thus obtain explicit expressions for physical quantities such as the spectral density and the scattering matrix. In the two-excitation sector, we show that strictly linear dispersion relations exhibit the special property that the corresponding diagrammatic perturbation series terminates after two terms, again allowing for closed-form expressions for physical quantities. In the case of general dispersion relations, notably those exhibiting a band edge or waveguide cutoff frequencies, the perturbation series cannot be summed explicitly. Instead, we derive a self-consistent $T\text{-matrix}$ equation that reduces the computational effort to that of a single-excitation computation. This analysis allows us to identify a Fano resonance between the occupied quantum impurity and a free photon in the waveguide as a unique signature of the few-photon nonlinearity inherent in such systems. In addition, our diagrammatic approach allows for the classification of different physical processes such as the creation of photon-photon correlations and interaction-induced radiation trapping, the latter being absent for strictly linear dispersion relations. Our framework can serve as the basis for further studies that involve more complex scenarios such as several and many-level quantum impurities, networks of coupled waveguides, disordered systems, and nonequilibrium effects.

We study theoretically the effects of pump-spot size and location on photon condensates. By exploring the inhomogeneous molecular excitation fraction, we make clear the relation between spatial equilibration, gain clamping, and thermalization in a photon condensate. This provides a simple understanding of several recent experimental results. We find that as thermalization breaks down, gain clamping is imperfect, leading to “transverse spatial hole burning” and multimode condensation. This opens the possibility of engineering the gain profile to control the condensate structure.

We consider the effect on the motion of a dissipative soliton of the diffusion term in the quintic complex Ginzburg-Landau (CGL) equation, which accounts for the finite bandwidth of the gain when this model describes light pulse evolution in a fiber laser. We show analytically that, if the velocity is small enough, this effect can be modeled by a viscous friction force acting on the soliton. Numerical resolution of the CGL equation shows that this analytical approximation is valid with good accuracy in the case of anomalous dispersion.

That superpositions of states can be useful for performing tasks in quantum systems has been known since the early days of quantum information, but only recently has a quantitative theory of quantum coherence been proposed. Here we apply that theory to an analysis of the Deutsch-Jozsa algorithm, which depends on quantum coherence for its operation. The Deutsch-Jozsa algorithm solves a decision problem, and we focus on a probabilistic version of that problem, comparing probability of being correct for both classical and quantum procedures. In addition, we study a related decision problem in which the quantum procedure has one-sided error while the classical procedure has two-sided error. The role of coherence on the quantum success probabilities in both of these problems is examined.

We study the time dependence of the decoherence factor (DF) of a qubit globally coupled to an environmental spin system (ESS) which is driven across the quantum critical point (QCP) by varying a parameter of its Hamiltonian in time $t$ as $1-t/\tau$ or $-t/\tau$, to which the qubit is coupled starting at the time $t\to -\infty$; here $\tau$ denotes the inverse quenching rate. In the limit of weak coupling we analyze the time evolution of the DF in the vicinity of the QCP (chosen to be at $t=0$) and define three quantities, namely, the generalized fidelity susceptibility ${\chi }_F\left(\tau \right)$ (defined right at the QCP), and the decay constants ${\alpha }_1\left(\tau \right)$ and ${\alpha }_2\left(\tau \right)$ which dictate the decay of the DF at a small but finite $t\left(>0\right)$. Using a dimensional analysis argument based on the Kibble-Zurek healing length, we show that ${\chi }_F\left(\tau \right)$ as well as ${\alpha }_1\left(\tau \right)$ and ${\alpha }_2\left(\tau \right)$ indeed satisfy universal power-law scaling relations with $\tau$ and the exponents are solely determined by the spatial dimensionality of the ESS and the exponents associated with its QCP. Remarkably, using the numerical t-DMRG method, these scaling relations are shown to be valid in both the situations when the ESS is integrable and nonintegrable and also for both linear and nonlinear variation of the parameter. Furthermore, when an integrable ESS is quenched far away from the QCP, there is a predominant Gaussian decay of the DF with a decay constant which also satisfies a universal scaling relation.

We analyze a coupling scheme for qubits in different cavities of circuit-QED architecture. In contrast to the usual scheme where the cavities are coupled by an interface capacitance we employ a bridge qubit connecting cavities to mediate two-qubit coupling. This active-coupling scheme makes it possible to switch on or off and adjust the strength of qubit-qubit coupling, which is essential for scalability of quantum circuits. By transforming the Hamiltonian we obtain an exact expression of two-qubit coupling in the rotating-wave approximation. For the general case of $n$ qubits the Hamiltonian can produce the $W$ state as an eigenstate of the system. We calculate the decay rate of the coupled qubit-resonator system to find that it is viable in real experiments.

All-electron configuration interaction theory in the framework of the Dirac-Coulomb Hamiltonian has been applied to the TaN molecule, a promising candidate in the search for physics beyond the standard model in both the hadron and the lepton sectors of matter. We obtain in the first excited ${}^3\mathrm{\Delta }_1$ state a $\mathcal{P},\mathcal{T}$-odd effective electric field of 36.0 GV/cm, a scalar-pseudoscalar $\mathcal{P},\mathcal{T}$-odd interaction constant of 32.8 kHz, and a nuclear magnetic-quadrupole moment interaction constant of $0.74\times {10}^{33} \mathrm{Hz}/\left(e \mathrm{cm}{}^2\right)$. The latter interaction constant has been obtained with an approach which we describe in detail. Using the same highly correlated all-electron wave functions with up to $2.5\times {10}^9$ expansion terms, we obtain a parallel magnetic hyperfine interaction constant of $-2954$ MHz for the ${}^{181}\mathrm{Ta}$ nucleus, a very large molecule-frame electric dipole moment of $-4.91$ D, and spectroscopic constants for the four lowest-lying electronic states of the molecule.

We report measurements and the results of calculations demonstrating that the annihilation dynamics of positronium (Ps) atoms can be controlled by Stark and Zeeman mixing of optically excited states. In the experiments a trap-based pulsed positron beam was employed to generate a dilute Ps gas with a density of $\sim {10}^7 \mathrm{cm}{}^{-3}$ using a porous silica target. These atoms were excited via $1{}^3{S}_1\to 2{}^3{P}_J$ transitions in parallel electric and magnetic fields using a nanosecond pulsed dye laser, and Ps annihilation was measured using single-shot lifetime spectroscopy. The composition of the excited $n=2$ sublevels was controlled by varying the polarization of the excitation laser radiation and the strength of the electric and magnetic fields in the excitation region. The overall decay rates of the excited states can vary by a large amount, owing to the enormous differences between the annihilation and florescence lifetimes of the accessible field-free states. The energy-level structure, spectral intensities, and florescence and annihilation lifetimes in the presence of the fields were determined from the eigenvalues and eigenvectors of the complete $n=2$ Hamiltonian matrix in an $|nS\ell J{M}_J\rangle$ basis. Using these data as the input to a Monte Carlo model yielded calculated values which could be compared with experimentally measured quantities; qualitative agreement with the measurements was found. Varying the electric field in the presence of a weak parallel magnetic field provides control over the amount of level mixing that occurs, making it possible to increase or decrease the Ps lifetime. Field-controlled Ps decay can be used as an ionization-free detection method. Conversely, increasing the excited-state lifetime can potentially be exploited to optimize multistep excitation processes using mixed intermediate states. This will be useful either in minimizing losses through intermediate-state decay during excitation or by making it possible to separate excitation laser pulses in time. In addition, the adiabatic extraction of appropriate eigenstates from the electric field in which they are excited can, in principle, be used to prepare pure $2{}^3{S}_1$ atoms. The availability of atoms in these states produced via single-photon excitation will facilitate high-resolution microwave spectroscopy of the Ps $n=2$ fine structure.

We present a kinematically complete and time-resolved study of the dissociation dynamics of ${\mathrm{H}}_2{}^{+}$ using ultrashort extreme-ultraviolet and near-infrared laser pulses. The reaction kinematics can be controlled by varying the time delay between the two pulses. We demonstrate that a time-dependent laser-dressed potential-energy curve enables the control of the nuclear motion. The dynamics is well reproduced by intuitive semiclassical trajectories on a time-dependent potential curve. From this most fundamental scenario we gain insight in the underlying mechanisms which may be applied as design principles for molecular quantum control, particularly for ultrafast molecular reactions involving the motion of protons.

We study the transport of an interacting Bose–Einstein condensate through a 1D correlated disorder potential. We use for this purpose the truncated Wigner method, which is, as we show, corresponding to the diagonal approximation of a semiclassical van Vleck–Gutzwiller representation of this many-body transport process. We also argue that semiclassical corrections beyond this diagonal approximation are vanishing under disorder average, thus confirming the validity of the truncated Wigner method in this context. Numerical calculations show that, while for weak atom-atom interaction strengths Anderson localization is preserved with a slight modification of the localization length, for larger interaction strengths a crossover to a delocalized regime exists due to inelastic scattering. In this case, the transport is fully incoherent.

We present observations of the emission of XUV continua in the 20–37-eV region by high-harmonic generation with 4–7-fs pulses focused onto a Kr gas jet. The underlying mechanism relies on coherent control of the relative delays and phases between individually generated attosecond pulses, achievable by adjusting the chirp of the driving pulses and the interaction geometry. Under adequate negative chirp and phase-matching conditions, the resulting interpulse interference yields a continuum XUV spectrum, which is due to both microscopic and macroscopic (propagation) contributions. This technique opens the route for modifying the phase of individual attosecond pulses and for the coherent synthesis of XUV continua from multicycle driving laser pulses without the need of an isolated attosecond burst.

The laser–phase-transition analogy is considered for a system of identical emitters interacting with a cavity mode. As in the case of equilibrium phase transitions, the thermodynamic limit is shown to be an essential condition for the appearance of an abrupt transition, with a well-defined threshold. The proof is discussed first in the simpler formalism of the rate equation and then at the higher level of the master equation for probabilities. The latter is derived from the von Neumann–Lindblad evolution of the density operator. In the thermodynamic limit and for two-level emitters the master equation becomes a two-dimensional dynamic flow with two possible fixed points, related to the normal and the lasing regimes, respectively. The master equation analysis confirms the threshold value deduced from the rate equation, but also provides further evidence of lasing by showing that all photonic autocorrelation functions converge to unity.

We propose a scheme to realize a giant Kerr nonlinearity and create stable high-dimensional nonlinear plasmon polaritons via plasmon-induced transparency (PIT) in a metamaterial, which is constructed by an array of unit cell consisting of a cut-wire and a pair of varactor-loaded split-ring resonators. We show that, due to the PIT effect and the nonlinearity contributed by the varactor, the system may possess very large second-order and third-order nonlinear susceptibilities. We further show that the system supports a resonant interaction between longwave and shortwave and hence effective third-order nonlinear susceptibility can be further enhanced one order of magnitude. Based on these peculiar properties, we derive Davey-Stewartson equations governing the evolution of longwave and shortwave envelope, and demonstrate that it possible to generate plasmon dromions [i.e., (2+1)-dimensional plasmon solitons with coupled longwave and shortwave components] with very low generation power. Our study raises the possibility for obtaining new, giant Kerr effect and stable high-dimensional nonlinear plasmon polaritons at very low radiation intensity by using nonlinear PIT metamaterials.

Using the density matrix formalism, we prove the existence of the periodic steady state for an arbitrary periodically driven system described by linear dynamic equations. This state has the same period as the modulated external influence, and it is realized as an asymptotic solution $\left(t\to +\infty \right)$ due to relaxation processes. The presented derivation simultaneously contains a simple and effective computational algorithm (without using either the Floquet or Fourier formalisms), which automatically guarantees a full account of all frequency components. As a particular example, for three-level $\mathrm{\Lambda }$ system we calculate the line shape and field-induced shift of the dark resonance formed by the field with a periodically modulated phase. Also we have analytically solved a basic theoretical problem of the direct frequency comb spectroscopy, when the two-level system is driven by the periodic sequence of rectangular pulses. In this case, the radical dependence of the spectroscopy line shape on pulse area is found. Moreover, the existence of quasiforbidden spectroscopic zones, in which the Ramsey fringes are significantly reduced, is predicted. Our results have a wide area of applications in laser physics, spectroscopy, atomic clocks, and magnetometry. Also they can be useful for any area of quantum physics where periodically driven systems are considered.

We consider a three-level atomic medium and discuss how to control the Goos-Hänchen (longitudinal) and Imbert-Fedorov (transverse) shifts for a circular polarized Gaussian beam via a pump field and a coherent driving field applied to the atomic medium. The susceptibility of the atomic medium can be adjusted by changing the driving and pump fields. Consequently, for a fixed driving field, by turning on and off the pump field the amplitude and the direction of the longitudinal and transverse shifts of such beam can be changed. We adopt stationary phase and beam simulation methods to derive our results.

Ghost imaging and interference using squeezed thermal light are investigated. We show that squeezed thermal light can have a very strong photon-bunching effect in the region of very weak squeezing and thermal excitation. As a result, the visibility of the image and interference pattern can be greatly enhanced and raised to be much higher than the limitation $1/3$ to thermal light. In the squeezed vacuum case, especially, the visibility can approach to the level of entangled photon pairs from spontaneous parametric down-conversion. The present investigation may open a new potential application of squeezed light.