Given a protocol $\mathcal{P}$ that implements multipartite quantum channel $\mathcal{E}$ by repeated rounds of local operations and classical communication (LOCC), we construct an alternate LOCC protocol for $\mathcal{E}$ in no more rounds than $\mathcal{P}$ and no more than a fixed, constant number of outcomes for each local measurement, the same constant number for every party and every round. We then obtain another upper bound on the number of outcomes that, under certain conditions, improves on the first. The latter bound shows that for LOCC channels that are extreme points of the convex set of all quantum channels, the parties can restrict the number of outcomes in their individual local measurements to no more than the square of their local Hilbert space dimension, $d_{\alpha }$, suggesting a possible link between the required resources for LOCC and the convex structure of the set of all quantum channels. Our bounds on the number of outcomes indicating the need for only constant resources per round, independent of the number of rounds $r$ including when that number is infinite, are a stark contrast to the exponential $r$ dependence in the only previously published bound of which we are aware. If a lower bound is known on the number of product operators needed to represent the channel, we obtain a lower bound on the number of rounds required to implement the given channel by LOCC. Finally, we show that when the quantum channel is not required but only that a given task be implemented deterministically, then no more than $d_{\alpha }^2$ outcomes are needed for each local measurement by party $\alpha$.

Macroscopic realism (MR) is the view that a system may possess definite properties at any time independent of past or future measurements and may be tested experimentally using the Leggett-Garg inequalities (LGIs). In this work we advance the study of LGIs in two ways using experiments carried out on a nuclear magnetic resonance spectrometer. First, we addresses the fact that the LGIs are only necessary conditions for MR but not sufficient ones. We implement a recently proposed test of necessary and sufficient conditions for MR which consists of a combination of the original four three-time LGIs augmented with a set of 12 two-time LGIs. We explore different regimes in which the two- and three-time LGIs may each be satisfied or violated. Second, we implement a recent proposal for a measurement protocol which determines the temporal correlation functions in an approximately noninvasive manner. It employs a measurement of the velocity of a dichotomic variable $Q$, continuous in time, from which a possible sign change of $Q$ may be determined in a single measurement of an ancilla coupled to the velocity. This protocol involves a significantly different set of assumptions to the traditional ideal negative measurement protocol, and a comparison with the latter is carried out.

We investigate roles of electron correlation effects in the determination of $g_j$ factors of the $ns{}^{2}S_{1/2}$ $(n=5,6,7)$, $np{}^{2}P_{1/2,3/2}$ $(n=5,6)$, $5d{}^{2}D_{3/2,5/2}$, and $4f{}^{2}F_{5/2,7/2}$ states of the singly ionized cadmium $\left({\mathrm{Cd}}^{+}\right)$ ion. Single and double excited configurations along with important valence triple excited configurations through relativistic coupled-cluster (RCC) theory are taken into account for incorporating electron correlation effects in our calculations. We find significant contributions from the triples to the lower $S$ and $P$ states for attaining high accuracy results. The contributions of Breit interaction and lower-order quantum electrodynamics effects, such as vacuum polarization and self-energy corrections, are also estimated using the RCC theory and are quoted explicitly. In addition, we present energies of the aforementioned states from our calculations and compare them with the experimental results to validate $g_j$ values. Using the $g_j$ factor of the ground state, systematical shift due to the Zeeman effect in the microwave clock frequency of the $|5s{}^{2}S_{1/2},F=0,m_F=0\rangle \leftrightarrow |5s{}^{2}S_{1/2},F=1,m_F=0\rangle$ transition in the ${}^{113}\mathrm{Cd}^{+}$ ion has been estimated.

In this paper, we report an application of the Hylleraas-$B$-spline basis to the calculation of the nonrelativistic Bethe logarithm of helium. The Bethe logarithms for the $n{}^{1}S$ states of helium, where $n$ is up to 10, are calculated precisely in the acceleration and the velocity-acceleration gauges, which greatly improves the accuracy of the traditional B-spline basis. In addition, to overcome numerical instability problem emerging from the use of this basis, a multiple-precision generalized symmetric eigenvalue problem solver is developed.

It was shown recently that the discrete scaling symmetry, which underlies the Efimov effect in the three identical boson system with two-body short-range interactions, survives when single-particle one-dimensional (1D) spin-orbit coupling terms are added to the Hamiltonian. Each three-body energy level in the ordinary Efimov scenario turns into an energy manifold that contains four energy levels in the presence of 1D spin-orbit coupling (equal mixture of Rashba-Dresselhaus coupling). This work provides a detailed characterization of the energy levels in these manifolds. The two-boson energies, which enter into the three-boson scattering threshold, are analyzed in detail. Moreover, the structural properties, e.g., momentum distributions of the two- and three-boson systems, are analyzed for various parameter combinations.

Double ionization in intense laser fields can comprise electron correlations which manifest in the nonindependent emission of two electrons from an atom or molecule. However, experimental methods that directly access the electron emission times have been scarce. Here we explore the application of an all-optical streaking technique to strong-field double ionization, both theoretically and experimentally. We show that both sequential and nonsequential double-ionization processes lead to streaking delays that are distinct from each other and single ionization. Moreover, coincidence detection of ions and electrons provides access to the emission time difference, which is encoded in the two-electron momentum distributions. The experimental data agree very well with simulations of sequential double ionization. We further test and discuss the application of this method to nonsequential double ionization, which is strongly affected by the presence of the streaking field.

Spectroscopic experiments have identified long-lived coherences in several light-harvesting systems, suggesting that coherent effects may be relevant to their performance. However, there is limited experimental evidence of coherence enhancing light-harvesting efficiency, largely due to the difficulty of turning coherences on and off to create an experimental control. Here we show that coherence can indeed enhance light harvesting and that this effect can be controlled. We construct a model system in which initial coherence can be controlled using the incident light and which is significantly more efficient under coherent, rather than incoherent, excitation. Our proposal would allow for an unambiguous demonstration of light harvesting enhanced by intermolecular coherence, as well as demonstrate the potential for coherent control of excitonic energy transfer.

Photoemission from solid targets includes the excitation and motion of electrons inside the substrate, followed by their propagation in vacuum and detection. It thus depends on the electronic band structure of the solid in the two distinct spectral domains of bound initial and continuum final states. While the imprint of the static (initial-state) valence electronic structure of solids on photoemission spectra is routinely examined in standard photoemission spectroscopy in the energy domain, state-of-the-art time-resolved photoelectron spectroscopy allows, in addition, the scrutiny of photoelectron propagation in the electronic continuum. Within a quantum-mechanical model for attosecond time-resolved interferometric photoelectron emission from solids, we calculated photoemission spectra as a function of the delay between the exciting primary attosecond pulse train and assisting infrared (IR) laser pulse. Accounting for final-state interactions of the photoelectron with the IR laser electric field and the periodic substrate, our numerical results for interferometric photoemission from the $3d$-valence band of Cu(111) surfaces show a striking resonantly enhanced sideband yield at photoelectron kinetic energies near $24\mathrm{eV}$, in conjunction with a pronounced increase of the photoelectron wave-function amplitude inside the solid on a length scale of a few nanometers. This resonant shift of final-state photoelectron-probability density towards the bulk can be interpreted as an increase in the photoelectron propagation time in the solid and is commensurate with the resonantly enhanced spectral sideband-phase shifts observed in recent two-pathway two-photon interference spectra by Kasmi et al. [Optica 4, 1492 (2017)].

We propose to discriminate chiral molecules by combining one- and two-photon processes in a closed-loop configuration. The one-photon-coupling intrinsic $\pi$-phase difference between two enantiomers leads to their different superposition states, which is then followed by a two-photon process through three-mode parallel paths (3MPPs), enabling the discrimination of enantiomers by inducing their entirely different population distributions. The 3MPPs are constructed by “chosen paths,” a method of shortcuts to adiabaticity, exhibiting a fast two-photon process. As an example, we propose to perform the scheme in 1,2-propanediol molecules, which show relatively robust and highly efficient results under considering the experimental issues concerning unwanted transitions, imperfect initial state, pulse shaping, control errors, and the effect of energy relaxations. The present work may provide help for laboratory researchers in a robust separation of chiral molecules.

We present the point-coupling Hamiltonian as a model for frequency-independent linear optical devices acting on propagating optical modes described as a continua of harmonic oscillators. We formally integrate the Heisenberg equations of motion for this Hamiltonian, calculate its quantum scattering matrix, and show that an application of the quantum scattering matrix on an input state is equivalent to applying the inverse of classical scattering matrix on the annihilation operators describing the optical modes. We show how to construct the point-coupling Hamiltonian corresponding to a general linear optical device described by a classical scattering matrix, and provide examples of Hamiltonians for some commonly used linear optical devices. Finally, in order to demonstrate the practical utility of the point-coupling Hamiltonian, we use it to rigorously formulate a matrix-product-state based simulation for time-delayed feedback systems wherein the feedback is provided by a linear optical device described by a scattering matrix as opposed to a hard boundary condition (e.g., a mirror with less than unity reflectivity).

On the basis of the approximate method of the averaged Lagrangian, the propagation modes of spatiotemporal solitons in a graded-index optical fiber with a Kerr nonlinearity and anisotropic transverse distribution of the linear refractive index are investigated. It is shown that within the framework of the proposed approach, the equations for soliton parameters are formally similar to the dynamical equations of a two-dimensional quantum Bose liquid in an external field. Various modes of propagation in the form of light bullets localized in all directions were investigated. The conditions under which “dancing” light bullets can form are revealed. The trajectories of such objects are spatial Lissajous figures, turning into helical lines in the case of axially symmetric optical fibers. The fundamental spatiotemporal soliton is a special case of dancing light bullets. Under conditions when the diffraction spreading scale length is much shorter than the dispersion scale length, the transverse dynamics of a soliton does not depend on its longitudinal dynamics. In this case, the principal possibility of forming a wide class of light bullets with different transverse structures is shown. In addition, under these conditions, the spatiotemporal soliton mode of the self-imaging effect is described.

Spontaneous parametric down-conversion (SPDC) is the most widely used method to generate higher-order Fock states ($n\ge 2$). Yet, a consistent performance analysis from fundamental principles is missing. Here, we address this problem by introducing a framework for state fidelity and generation probability under the consideration of losses and multimode emission. With this analysis we show the fundamental limitations of this process as well as a trade-off between state fidelity and generation rate intrinsic to the probabilistic nature of the process. This identifies the parameter space for which SPDC is useful when generating higher-order Fock states for quantum applications. We experimentally investigate the multiphoton regime of SPDC and demonstrate heralded Fock states up to $|n\rangle =4$.

Quantum mechanical properties like entanglement, discord, and coherence act as fundamental resources in various quantum information processing tasks. Consequently, the technique of generating more resources from a few, typically termed as broadcasting, serves as a promising candidate for the design of quantum networks. One way to broadcast resources could be using a cloning operation. In this article, broadcasting of quantum resources beyond $2\otimes 2$ systems is investigated. In particular, in $2\otimes 3$ dimensions, a class of states not useful for broadcasting of entanglement is characterized considering an optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states and two-parameter class of states are obtained to exemplify our protocol. A significant derivative of our protocol is that the cloning operation generates a qutrit ($3\otimes 3$) entangled pair with positive partial transpose on one of the local sides, and an absolutely separable qubit ($2\otimes 2$) pair on the other side of the input bipartite $2\otimes 3$-dimensional resource state. Moving beyond entanglement, in $2\otimes d$ dimensions, the impossibility to optimally broadcast quantum discord and quantum coherence ($l_1$ norm) is established. However, some significant illustrations are provided to highlight that nonoptimal broadcasting of discord and coherence is still possible.

We analyze the dynamics of multiparticle discrete-time quantum walk on the two-dimensional lattice, with an interaction inspired on a classical model for gas collision, called the HPP model. In this classical model, the direction of motion changes only when the particles collide head-on, preserving momentum and energy. In our quantum model, the dynamics is driven by the usual quantum-walk evolution operator if the particles are on different nodes, and is driven by the HPP rules if the particles are in the same node, linearly extended for superpositions. Using this form of evolution operator, we numerically analyze three physical quantities for the two-walker case: The probability distribution of the position of one walker, the standard deviation of the position of one walker, and the entanglement between the walkers as a function of the number of steps. The numerical analysis implies that the entanglement between the walkers as a function of the number of steps initially increases and quickly tends to a constant value, which depends on the initial condition. We compare the results obtained using the HPP interaction with the equivalent ones using the phase interaction, which is based on an evolution operator that inverts the sign of the coin operator if the walkers are in the same position.

We investigate the phase diagram of interacting $p$-orbital Fermi atoms on honeycomb optical lattice. We find that the interatomic interactions play critical roles in such $p$-orbital systems, which can drive a first-order topological transition from normal phases with trivial topology to topological phases with nonvanishing Chern numbers. Due to the interplay among atomic interactions, the sublattice potential, and the filling factors, the phase diagram of the system exhibits rich phases, which are characterized by Chern numbers and corresponding edge states. Furthermore, the evolution of the band structures and the moving of Dirac cones along with the phase transitions are also discussed.

Bosonic atoms confined in optical lattices can exist in two different phases, Mott insulator and superfluid, depending on the strength of the system parameters, such as the on-site interaction between particles and the hopping parameter. This work is motivated by the fact that nondegenerate perturbation theory applied to the mean-field approximation of the Bose-Hubbard Hamiltonian at both zero and finite temperature fails to give consistent results in the vicinity of the Mott insulator–superfluid phase transition, e.g., the order parameter calculated via nondegenerate perturbation theory reveals an unphysical behavior between neighboring Mott lobes, which is an explicit consequence of degeneracy problems that artificially arise from such a treatment. This problem also appears in other bosonic systems that present similar Mott-lobe structures. Therefore, in order to fix this problem, we propose a finite-temperature degenerate perturbation theory approach based on a projection operator formalism which ends up solving such degeneracy problems in order to obtain physically consistent results for the order parameter near the phase transition.

We analyze the interaction of exciton-polariton condensates in a one-dimensional semiconductor microcavity with acoustic phonons. We consider the case of a coherently pumped condensate and demonstrate that upon passing of a certain threshold the parametric instability in the system leads to the generation of a coherent acoustic wave and additional polariton harmonics. The process is strongly affected by exciton-exciton interactions which lead to the appearance of the effects of the bistability and hysteresis in the system.

Cavity optomechanical systems involving an optical parametric amplifier (OPA) can exhibit rich classical and quantum dynamical behaviors. By simply modulating the frequency of the laser pumping the OPA, we find two interesting parameter regimes, with one of them enabling us to study quantum-classical correspondence in system dynamics, while there exist no classical counterparts of the quantum features for the other. For the detuning of the laser pumping around the mechanical frequency, as the parametric gain of OPA increases to a critical value, the classical dynamics of the optical or mechanical modes can experience a transition from the regular periodic oscillation to a period-doubling motion, in which case the light-mechanical entanglement can be well studied by the logarithmic negativity and can manifest the dynamical transition the classical nonlinear dynamics. In addition, the optomechanical entanglement shows a second-order transition characteristic at the critical parametric gain. For the laser detuning being about twice the mechanical frequency, the kind of normal mode splitting comes up in the laser detuning dependence of optomechanical entanglement, which is induced by the squeezing of the optical and mechanical hybrid modes and finds no classical correspondence. The OPA-assisted optomechanical systems therefore offer a simple way to study and exploit quantum manifestations of classical nonlinear dynamics.

We investigate the multiphonon interactions in a hybrid system composed of a nitrogen-vacancy center and a mechanical resonator. We show that, through appropriate sideband engineering analogy to the Mollow or Lamb-Dicke dynamics, the enhanced nonlinear interactions can dominate the coupled system. As an example, we show the preparation of nonclassical states of the mechanical motion and explore the quantum correlation of $n$-phonon bundles with the engineered dissipation, based on the large multiphonon coupling strength attainable in this sideband structure. This work may take full advantage of the structure and coherence features of defect centers in diamond and may be useful for quantum information processing.