We investigate the use of twin-mode quantum states of light with symmetric statistical features in their photon number for improving intensity-sensitive surface plasmon resonance (SPR) sensors. For this purpose, one of the modes is sent into a prism setup where the Kretschmann configuration is employed as a sensing platform and the analyte to be measured influences the SPR excitation conditions. This influence modifies the output state of light that is subsequently analyzed by an intensity-difference measurement scheme. We show that quantum noise reduction is achieved not only as a result of the sub-Poissonian statistical nature of a single mode, but also as a result of the nonclassical correlation of the photon number between the two modes. When combined with the high sensitivity of the SPR sensor, we show that the use of twin-mode quantum states of light notably enhances the estimation precision of the refractive index of an analyte. With this we are able to identify a clear strategy to further boost the performance of SPR sensors, which are already a mature technology in biochemical and medical sensing applications.

Suppose we measure the time-dependent spectrum of a single photon. That is, we first send the photon through a set of frequency filters (which we assume to have different filter frequencies but the same finite bandwidth $\mathrm{\Gamma }$) and then record at what time (with some finite precision $\mathrm{\Delta }t$ and some finite efficiency $\eta$) and after passing what filter the photon is detected. What is the positive-operator-valued measure (POVM), the most general description of a quantum measurement, corresponding to such a measurement? We show how to construct the POVM in various cases, with special interest in the case $\mathrm{\Gamma }\mathrm{\Delta }t\ll 1$ (time-frequency uncertainty still holds, even in that limit). One application of the formalism is to heralding single photons. We also find a Hong-Ou-Mandel type of interference effect with two photons entering a frequency filter.

We discuss the ground-state properties of a one-dimensional bosonic system doped with an impurity (the so-called Bose polaron problem). We introduce a formalism that allows us to calculate analytically the thermodynamic zero-temperature properties of this system with weak and moderate boson-boson interaction strengths for any boson-impurity interaction. Our approach is validated by comparison to exact quantum Monte Carlo calculations. In addition, we test the method in finite-size systems using numerical results based upon the similarity renormalization group. We argue that the introduced approach provides a simple analytical tool for studies of strongly interacting impurity problems in one dimension.

The purpose of physics is to describe nature from elementary particles all the way up to cosmological objects like cluster of galaxies and black holes. Although a unified description for all this spectrum of events is desirable, this would be highly impractical. To not get lost in unnecessary details, effective descriptions are mandatory. Here we analyze the dynamics that may emerge from a full quantum description when one does not have access to all the degrees of freedom of a system. More concretely, we describe the properties of the dynamics that arise from quantum mechanics if one has access only to a coarse-grained description of the system. We obtain that the effective maps are not necessarily of Kraus form, due to correlations between accessible and nonaccessible degrees of freedom, and that the distance between two effective states may increase under the action of the effective map. We expect our framework to be useful for addressing questions such as the thermalization of closed quantum systems, as well as the description of measurements in quantum mechanics.

We study theoretically the teleportation of a controlled-phase (cz) gate through measurement-based quantum-information processing for continuous-variable systems. We examine the degree of entanglement in the output modes of the teleported cz-gate for two classes of resource states: the canonical cluster states that are constructed via direct implementations of two-mode squeezing operations and the linear-optical version of cluster states which are built from linear-optical networks of beam splitters and phase shifters. In order to reduce the excess noise arising from finite-squeezed resource states, teleportation through resource states with different multirail designs will be considered and the enhancement of entanglement in the teleported cz gates will be analyzed. For multirail cluster with an arbitrary number of rails, we obtain analytical expressions for the entanglement in the output modes and analyze in detail the results for both classes of resource states. At the same time, we also show that for uniformly squeezed clusters the multirail noise reduction can be optimized when the excess noise is allocated uniformly to the rails. To facilitate the analysis, we develop a trick with manipulations of quadrature operators that can reveal rather efficiently the measurement sequence and corrective operations needed for the measurement-based gate teleportation, which will also be explained in detail.

We investigate the tunable quantum entanglement and the probabilities of excitations in a system of three qubits in a nonstationary cavity due to the dynamical Lamb effect, caused by nonadiabatic fast change of the boundary conditions of the cavity. The transition amplitudes and the probabilities of excitation of qubits due to the dynamical Lamb effect have been evaluated. The conditional concurrence and the conditional residual tangle for each fixed amount of created photons are introduced and calculated as measures of the pairwise or three-way dynamical quantum entanglement of the qubits. We also give a prescription on how to increase the values of those quantities by controlling the frequency of the cavity photons. A physical realization of the system with three superconducting qubits, coupled to a coplanar waveguide entangled due to the nonadiabatic fast change of boundary conditions of the cavity is proposed.

We propose a method for implementing automated state transformations on single-photon multipath qudits encoded in a one-dimensional transverse spatial domain. It relies on transferring the encoding from this domain to the orthogonal one by applying a spatial phase modulation with diffraction gratings, merging all the initial propagation paths by using a stable interferometric network, and filtering out the unwanted diffraction orders. The automation feature is attained by utilizing a programmable phase-only spatial light modulator (SLM) where properly designed diffraction gratings displayed on its screen will implement the desired transformations, including, among others, projections, permutations, and random operations. We discuss the losses in the process which is, in general, inherently nonunitary. Some examples of transformations are presented and, considering a realistic scenario, we analyze how they will be affected by the pixelated structure of the SLM screen. The method proposed here enables one to implement much more general transformations on multipath qudits than is possible with a SLM alone operating in the diagonal basis of which-path states. Therefore, it will extend the range of applicability for this encoding in high-dimensional quantum information and computing protocols as well as fundamental studies in quantum theory.

Single-electron capture from one-electron and multielectron atoms colliding with hydrogenlike projectiles at intermediate and high incident energies is examined by using the post version of the boundary-corrected four-body continuum-intermediate-state (BCIS-4B) method. This method satisfies the correct boundary conditions in the entrance and exit channels. In the entrance configuration, the BCIS-4B method takes into account the ionization channel through the electronic continuum intermediate states described by the full Coulomb wave function centered on the screened nuclear charge of the projectile. The presented analytical calculation yields the transition amplitude in terms of an efficiently computed two-dimensional numerical quadrature over real variables. Total cross sections are computed for electron capture in the ${\mathrm{He}}^{+}\text{−}\mathrm{H}$, ${\mathrm{He}}^{+}\text{−}\mathrm{He}$, and ${\mathrm{Li}}^{2+}\text{−}\mathrm{He}$ collisions at intermediate and high impact energies. Also, differential cross sections are obtained for the ${\mathrm{He}}^{+}\text{−}\mathrm{He}$ collisions. The present results from the BCIS-4B method are found to be in very good agreement with the available experimental data on differential and total cross sections.

A theoretical study of double-differential cross sections (DDCSs) for single ionization of ${\text{CH}}_{{}_4}$ and ${\text{NH}}_{{}_3}$ molecules by collision with proton is presented at 0.25, 1, and 2 MeV, respectively. For the final state, we use a continuum distorted wave that contains the product of three-Coulomb distortion due to pairwise Coulombic interactions for which it is called the three-Coulomb wave model. In the entrance channel, the Coulomb distortion between the incoming projectile and the target is taken. In this model, the ground state of the polyatomic molecule is described by means of an accurate one-center molecular wave function, which is a linear combination of atomic orbitals. The contributions of DDCSs for different molecular orbitals of the polyatomic molecules to the spectrum of angular distributions at different electron emission energies have also been analyzed. Generally the preference for ionization depends on the binding energy of the active electron in molecular orbital in the ascending order of loosely bound electrons to more tightly bound electrons. At large ejected electron and projectile energy, the lesser bound electrons in the molecules dominate the DDCS at extreme forward emission angles. The present DDCS results are compared with available experimental and the theoretical findings. In case of ammonia molecules, good agreement is observed at all projectile energies, showing that the present model is sufficient to explain all the experimental data for double-differential cross sections. However, some degree of discrepancy is observed at 2 MeV proton impact for small electron emission angles when ${\text{CH}}_{{}_4}$ molecular target is considered.

We present experimental results on the inelastic and elastic interspecies interactions between ytterbium (Yb) in the metastable ${}^{3}P{}_2$ state loaded into a deep optical lattice and spin polarized lithium (Li) in its ground state. Focusing on the $m_J=0$ magnetic sublevel of $\mathrm{Yb}({}^{3}P{}_2$), bias magnetic fields between 20 and $800\mathrm{G}$ are investigated and significantly enhanced inelastic collision rates with high magnetic fields are found. In addition, by direct spectroscopy of the Yb Mott insulator immersed in the Li Fermi gas an upper boundary of the background scattering length of the $\mathrm{Yb}({}^{3}P{}_2,m_J=0)-\mathrm{Li}{(}^2{S}_{1/2},F=1/2,m_F=+1/2$) system is estimated, revealing the absence of useful Feshbach resonances. These observations are qualitatively consistent with the theoretical calculations.

A quasiclassical model based on the resolution of Hamilton equations of motion is used to get evidence for Auger electron emission following double-electron capture in 150-keV $\mathrm{N}{\mathrm{e}}^{10+}+\mathrm{He}$ collisions. Electron-electron interaction is taken into account during the collision by using pure Coulombic potential. To make sure that the helium target is stable before the collision, phenomenological potentials for the electron-nucleus interactions that simulate the Heisenberg principle are included in addition to the Coulombic potential. First, single- and double-electron captures are determined and compared with previous experiments and theories. Then, integration time evolution is calculated for autoionizing and nonautoionizing double capture. In contrast with single capture, the number of electrons originating from autoionization slowly increases with integration time. A fit of the calculated cross sections by means of an exponential function indicates that the average lifetime is $4.4\times {10}^{-3}\mathrm{a}.\mathrm{u}.$, in very good agreement with the average lifetime deduced from experiments and a classical model introduced to calculate individual angular momentum distributions. The present calculation demonstrates the ability of classical models to treat the Auger effect, which is a pure quantum effect.

The photoionization of a helium atom by short intense laser pulses is studied theoretically in the vicinity of the $2s2p{}^{1}P$ doubly excited state with the intention to investigate the impact of the intensity and duration of the exciting pulse on the dynamics of the autoionization process. For that purpose, we solve numerically the corresponding time-dependent Schrödinger equation by applying the time-dependent restricted-active-space configuration-interaction method (TD-RASCI). The present numerical results clearly demonstrate that the Fano interferences can be controlled by a single high-frequency pulse. As long as the pulse duration is comparable to the autoionization lifetime, varying the peak intensity of the pulse enables manipulation of the underlying Fano interference. In particular, the asymmetric profile observed for the $2s2p{}^{1}P$ doubly excited state of He in the weak-field ionization can be smoothly transformed to a window-type interference profile.

The interplay between classical and quantum-mechanical evolution in the optical centrifuge (OC) is discussed. The analysis is based on the quantum-mechanical formalism starting from either the ground state or a thermal ensemble. Two resonant mechanisms are identified, i.e., the classical autoresonance and the quantum-mechanical ladder climbing, yielding different dynamics and rotational excitation efficiencies. The rotating-wave approximation is used to analyze the two resonant regimes in the associated dimensionless two-parameter space and calculate the OC excitation efficiency. The results show good agreement between numerical simulations and theory and are relevant to existing experimental setups.

The light-shift theory of many-electron systems in a laser field is described using the projection operators technique. In heavy ions, the electrons are tightly bound by the Coulomb potential of the nucleus, which prohibits ionization even by strong lasers. However, interaction with the monofrequent laser field leads to dynamic shifts of the electronic energy levels, and the process is treated by second-order time-dependent perturbation theory. In order to treat heliumlike systems, one decomposes the corresponding matrix elements into hydrogenlike matrix elements using the independent particle model. We are applying a fully relativistic description of the electronic states by means of the Dirac equation. Our formalism goes beyond the Stark long-wavelength dipole approximation and takes into account nondipole effects of retardation and interaction with the magnetic field components of the laser beam.

We introduce two- and one-dimensional (2D and 1D) systems of two linearly coupled Gross-Pitaevskii equations (GPEs) with the cubic self-attraction and harmonic-oscillator (HO) trapping potential in each GPE. The system models a Bose-Einstein condensate with a negative scattering length, loaded in a double-pancake trap, combined with the in-plane HO potential. In addition to that, the 1D version applies to the light transmission in a dual-core waveguide with the Kerr nonlinearity and in-core confinement represented by the HO potential. The subject of the analysis is spontaneous symmetry breaking in 2D and 1D ground-state (GS, alias fundamental) modes, as well as in 2D vortices and 1D dipole modes. (The latter ones do not exist without the HO potential.) By means of the variational approximation and numerical analysis, it is found that both the 2D and 1D systems give rise to a symmetry-breaking bifurcation (SBB) of the supercritical type. The stability of symmetric and asymmetric states, produced by the SBB, is analyzed through the computation of eigenvalues for perturbation modes and verified by direct simulations. The asymmetric GSs are always stable, while the stability region for vortices shrinks and eventually disappears with the increase of the linear-coupling constant, $\kappa$. The SBB in the 2D system does not occur if $\kappa$ is too large (at $\kappa >{\kappa }_{max}$); in that case, the two-component system behaves, essentially, as its single-component counterpart. In the 1D system, both asymmetric and symmetric dipole modes feature an additional oscillatory instability, unrelated to the symmetry breaking. This instability occurs in several regions which expand with the increase of $\kappa$.

Motivated by a recent experiment, which synthesizes Landau levels for photons on cones [Schine et al., Nature (London) 534, 671 (2016)], and more generally the interest in understanding gravitational responses of quantum Hall states, we study fractional quantum Hall states of bosons on cones. A variety of trial wave functions for conical systems are constructed and compared with exact diagonalization results. The tip of a cone is a localized geometrical defect with singular curvature, which can modify the density profiles of quantum Hall states. The density profiles on cones can be used to extract some universal information about quantum Hall states. The values of certain quantities are computed numerically using the density profiles of some quantum Hall states and they agree with analytical predictions.

We study computationally the collision dynamics of vortices in a two-dimensional spin-2 Bose-Einstein condensate. In contrast to Abelian vortex pairs, which annihilate or pass through each other, we observe non-Abelian vortex pairs to undergo rungihilation—an event that converts the colliding vortices into a rung vortex. The resulting rung defect subsequently decays to another pair of non-Abelian vortices of different type, accompanied by a magnetization reversal.

We introduce a frequency-dependent incoherent pump scheme with a square-shaped spectrum as a way to study strongly correlated photons in arrays of coupled nonlinear resonators. This scheme can be implemented via a reservoir of population-inverted two-level emitters with a broad distribution of transition frequencies. Our proposal is predicted to stabilize a nonequilibrium steady state sharing important features with a zero-temperature equilibrium state with a tunable chemical potential. We confirm the efficiency of our proposal for the Bose-Hubbard model by computing numerically the steady state for finite system sizes: first, we predict the occurrence of a sequence of incompressible Mott-insulator-like states with arbitrary integer densities presenting strong robustness against tunneling and losses. Secondly, for stronger tunneling amplitudes or noninteger densities, the system enters a coherent regime analogous to the superfluid state. In addition to an overall agreement with the zero-temperature equilibrium state, exotic nonequilibrium processes leading to a finite entropy generation are pointed out in specific regions of parameter space. The equilibrium ground state is shown to be recovered by adding frequency-dependent losses. The promise of this improved scheme in view of quantum simulation of the zero-temperature many-body physics is highlighted.

Dicke's original thought experiment with two spins (two-level atoms) coupled to a photon mode has recently been experimentally realized. We propose extending this experiment to many spins as a way to synthesize highly entangled states. We suggest a protocol in which we start with a direct product state of $M$ atoms in the excited state and $N$ atoms in the ground state, placed within a lossy cavity. A null observation for photon emission collapses the system onto a dark state which, remarkably, has resonating-valence-bond (RVB) character. We demonstrate this by taking advantage of the symmetry of the initial state under permutations of the $M$ excited atoms and of the $N$ unexcited atoms. Using angular momentum analysis, we reexpress the wave function of the dark state to illustrate its RVB character. We discuss two limiting cases in detail, with $M=1$ (one excited atom) and $M=N$ (equal number of excited and unexcited atoms). In the latter case, we show that the probability for null emission scales as $N^{-1}$, making it possible to generate highly entangled RVB states of 20 spins or more.

The quality of individual photons and their ability to interfere are traditionally tested by measuring the Hong-Ou-Mandel photon bunching effect. However, this phase-insensitive measurement only tests the particle aspect of the quantum interference, leaving out the phase-sensitive aspects relevant for continuous-variable processing. To overcome these limitations we formulate a witness capable of recognizing both the indistinguishability of the single photons and their quality with regard to their continuous-variable utilization. We exploit the conditional nonclassical squeezing and show that it can reveal both the particle and the wave aspects of the quantum interference in a single set of direct measurements. We experimentally test the witness by applying it to a pair of independent single photons retrieved on demand.