Bloch oscillations of spatiotemporal light wave packets in arrays of nonlinear fibers with high-order dispersion are studied. The light wave experiences discrete spatial diffraction along the waveguide array coordinate together with continuous temporal dispersion including higher-order terms. When a gradient in the waveguide light confinement strength is considered, the wave packet features robust long-lived Bloch oscillations with temporal and spatial spreading in the presence of a Kerr nonlinearity. The effect of spatial Bloch oscillations on the emission of the dispersive radiation by the solitary wave is analyzed. It is shown that Bloch oscillations result in the generation of new frequencies. The condition of resonant emission of dispersive waves is derived and it is demonstrated that it matches very well with the results of direct numerical simulations.

We show that a transition-metal dichalcogenide monolayer with a radiatively broadened exciton resonance would exhibit perfect extinction of the transmitted field. This result holds for $s$- or $p$-polarized weak resonant light fields at any incidence angle, due to the conservation of the in-plane momentum of excitons and photons in a flat defect-free two-dimensional crystal. In contrast to extinction experiments with single quantum emitters, exciton-exciton interactions lead to an enhancement of reflection with increasing power for incident fields that are blue detuned with respect to the exciton resonance. By taking into account quantum fluctuations, we show that the extinction of such a nonlinear mirror is limited; for light intensities leading to maximal reflection, the transmitted field is in a multimode squeezed state.

We investigate the maximum rates for transmitting quantum information, distilling entanglement, and distributing secret keys between a sender and a receiver in a multipoint communication scenario, with the assistance of unlimited two-way classical communication involving all parties. First we consider the case where a sender communicates with an arbitrary number of receivers, a so-called quantum broadcast channel. Here we also provide a simple analysis in the bosonic setting where we consider quantum broadcasting through a sequence of beamsplitters. Then, we consider the opposite case where an arbitrary number of senders communicate with a single receiver, a so-called quantum multiple-access channel. Finally, we study the general case of all-in-all quantum communication where an arbitrary number of senders communicate with an arbitrary number of receivers. Since our bounds are formulated for quantum systems of arbitrary dimension, they can be applied to many different physical scenarios involving multipoint quantum communication.

We analyze the problem of quantum phase estimation in which the set of allowed phases forms a discrete $N$-element subset of the whole $[0,2\pi ]$ interval, ${\phi }_n=2\pi n/N, n=0,\cdots ,N-1$, and study the discrete-to-continuous transition $N\to \infty$ for various cost functions as well as the mutual information. We also analyze the relation between the problems of phase discrimination and estimation by considering a step cost function of a given width $\sigma$ around the true estimated value. We show that in general a direct application of the theory of covariant measurements for a discrete subgroup of the $\text{U}\left(1\right)$ group leads to suboptimal strategies due to an implicit requirement of estimating only the phases that appear in the prior distribution. We develop the theory of subcovariant measurements to remedy this situation and demonstrate truly optimal estimation strategies when performing a transition from discrete to continuous phase estimation.

We consider the situation when the signal propagating through each arm of an interferometer has a complicated multimode structure. We demonstrate that the shot-noise level for such a setup is the same as for the common two-mode case for as long as the interferometric transformation treats each arm as a whole and does not penetrate its inner structure. We find the relation between the particle entanglement and the possibility to surpass the shot-noise limit of the phase estimation. Our results are general—they apply to pure and mixed states of identical and distinguishable particles (or combinations of both) for a fixed and fluctuating number of particles. An important result is that the method for detecting the entanglement often used in a two-mode system—based on the measurement of the visibility of fringes and the population imbalance fluctuations—can give misleading results when applied to the multimode case. Our main result is that the additional modes do not boost the sensitivity for as long as they are not interacting. Therefore, the improvement above the shot-noise level established for the two-mode systems can safely be treated as an entanglement criterion also in the complex multimode case.

A central result in the study of quantum Hamiltonian complexity is that the $k$-local Hamiltonian problem is quantum-Merlin-Arthur–complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above another, promised one of these is true. Given the ground state of the Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently quantum preparable. Kitaev's proof of QMA-completeness encodes a unitary quantum circuit in QMA into the ground space of a Hamiltonian. However, we now have quantum computing models based on measurement instead of unitary evolution; furthermore, we can use postselected measurement as an additional computational tool. In this work, we generalize Kitaev's construction to allow for nonunitary evolution including postselection. Furthermore, we consider a type of postselection under which the construction is consistent, which we call tame postselection. We consider the computational complexity consequences of this construction and then consider how the probability of an event upon which we are postselecting affects the gap between the ground-state energy and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the two are not immediately related by giving a family of circuits where the probability of an event upon which we postselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial.

We investigate genuinely entangled $N$-qubit states with no $N$-partite correlations in the case of symmetric states. Using a tensor representation for mixed symmetric states, we obtain a simple characterization of the absence of $N$-partite correlations. We show that symmetric states with no $N$-partite correlations cannot exist for an even number of qubits. We fully identify the set of genuinely entangled symmetric states with no $N$-partite correlations in the case of three qubits, and in the case of rank-2 states. We present a general procedure to construct families for an arbitrary odd number of qubits.

A combined adiabatic approach is proposed in which orbital expectations of the Kohn-Sham operator (KSEs) are embedded into the matrix environment of time-dependent phase-including natural-orbital functional theory (TDPINOFT). Analytical diagonalization of a model molecular matrix eigenvalue problem shows that the resultant TDNOFT-KSE combines strong sides of both adiabatic time-dependent density functional theory (TDDFT) and TDPINOFT. Around the equilibrium, like in TDDFT, the energy of a single excitation of the model is evaluated with the KSEs. In its turn, the TDPINOFT environment provides an effective Hartree-exchange-correlation (Hxc) kernel, which properly diverges in the bond dissociation limit. This environment also generates a double excitation, the energy of which is related to the ratio of fractional occupation numbers of the natural orbitals.

As an extension to powerful two-dimensional coherent spectroscopy, optical three-dimensional (3D) coherent spectroscopy has been experimentally implemented and found beneficial in studying various systems in physics and chemistry. A critical challenge is how to interpret 3D spectra and extract useful quantitative information, given the richness and complexity of 3D data. Here, we demonstrate how the information of a system's optical response is manifested in 3D spectra by theoretical simulations of a few representative examples including a homogeneous three-level V system, an inhomogeneous three-level V system, and an inhomogeneous three-level ladder system. These examples show that important parameters of the system can be extracted from the spectral pattern, peak positions, amplitudes, and line shapes. The method developed here can be used to analyze 3D spectra of more sophisticated systems which might be a generalization or combination of the three examples, contributing to develop a general approach for the interpretation of 3D spectra.

The antidynamical Casimir effect (ADCE) is a term coined to designate the coherent annihilation of excitations due to resonant external perturbation of system parameters, allowing for extraction of quantum work from nonvacuum states of some field. Originally proposed for a two-level atom (qubit) coupled to a single-cavity mode in the context of the nonstationary quantum Rabi model, it suffered from a very low transition rate and correspondingly narrow resonance linewidth. In this paper we show analytically and numerically that the ADCE rate can be increased by at least one order of magnitude by replacing the qubit by an artificial three-level atom (qutrit) in a properly chosen configuration. For the cavity thermal state we demonstrate that the dynamics of the average photon number and atomic excitation is completely different from the qubit's case, while the behavior of the total number of excitations is qualitatively similar yet significantly faster.

Theoretical total cross-section results for all ionization and capture processes in the ${\mathrm{He}}^{+}$-He collision system are presented in the approximate impact energy range of 10–1000 keV/amu. Calculations were performed within the framework of time-dependent spin-density functional theory. The Krieger-Li-Iafrate approximation was used to determine an accurate exchange-correlation potential in the exchange-only limit. The results of two models, one where electron translation factors in the orbitals used to calculate the potential are ignored and another where partial electron translation factors are included, are compared with available experimental data as well as a selection of previous theoretical calculations.

We present a numerical method to calculate the macroscopic harmonic spectrum generated from the gas-exposed nanostructure. This method includes the propagation of plasmonic and harmonic fields in the macroscopic medium as well as the response of the single atom exposed to plasmonic field. Based on the simulation, we demonstrate that the macroscopic harmonic yields drop dramatically in the high-energy region. This result well interprets the disagreement in the cutoff between the single-atom prediction and the experimental detection. Moreover, we also show that the harmonic cutoff difference induced by a $\pi$ shift in carrier-envelope phase (CEP) of laser pulses depends sensitively on the spatial position. However, when the collective effect of plasmon-driven high-order-harmonic generation is considered, this cutoff difference is eliminated.

We report on direct measurements of the emission character of quantum cascade laser based frequency combs, using intensity autocorrelation. Our implementation is based on fast electro-optic sampling, with a detection spectral bandwidth matching the emission bandwidth of the comb laser, around 2.5 THz. We find the output of these frequency combs to be continuous even in the locked regime, but accompanied by a strong intensity modulation. Moreover, with our record temporal resolution of only few hundreds of femtoseconds, we can resolve correlated intensity modulation occurring on time scales as short as the gain recovery time, about 4 ps. By direct comparison with pulsed terahertz light originating from a photoconductive emitter, we demonstrate the peculiar emission pattern of these lasers. The measurement technique is self-referenced and ultrafast, and requires no reconstruction. It will be of significant importance in future measurements of ultrashort pulses from quantum cascade lasers.

The computation of light scattering by the superposition $T$-matrix scheme has been restricted thus far to systems made of particles that are either sparsely distributed or of near-spherical shape. In this work, we extend the range of applicability of the $T$-matrix method by accounting for the coupling of scattered fields between highly nonspherical particles in close vicinity. This is achieved using an alternative formulation of the translation operator for spherical vector wave functions, based on a plane-wave expansion of the particle's scattered electromagnetic field. The accuracy and versatility of the present approach is demonstrated by simulating arbitrarily oriented and densely packed spheroids, for both dielectric and metallic particles.

A precise, accurate, and relatively straightforward in situ method to measure and control the ellipticity of light resonantly interacting with an atomic vapor is described. The technique can be used to minimize vector light shifts. The method involves measurement of ellipticity-induced resonances in the magnetic-field dependence of nonlinear magneto-optical rotation of frequency-modulated light. The light propagation direction is orthogonal to the applied magnetic field $\mathbf{B}$ and the major axis of the light polarization ellipse is along $\mathbf{B}$. When the light modulation frequency matches the Larmor frequency, elliptically polarized light produces a precessing atomic spin orientation transverse to $\mathbf{B}$ via synchronous optical pumping. The precessing spin orientation causes optical rotation oscillating at the Larmor frequency by modulating the atomic vapor's circular birefringence. Based on this technique's precision, in situ nature (which avoids systematic errors arising from optical interfaces) and independent control of the most important systematic errors, it is shown that the accuracy of light ellipticity measurements achievable with this technique can exceed that of existing methods by orders of magnitude.

We study guided modes in non-Hermitian optical waveguides with dielectric layers having either gain or loss. For the case of a three-layer waveguide, we describe stationary regimes for guided modes when gain and loss compensate each other in the entire structure rather than in each layer. We demonstrate that, by adding a lossless dielectric layer to a double-layer waveguide with the property of parity-time ($\mathcal{PT}$) symmetry, we can control a ratio of gain and loss required to support propagating and nondecaying optical guided modes. This novel feature becomes possible due to the modification of the mode structure, and it can allow using materials with a lower gain to balance losses in various optical waveguiding structures. In addition, we find a non-$\mathcal{PT}$-symmetric regime when all guided modes of the system have their losses perfectly compensated.

Both conservation laws and practical restrictions impose symmetry constraints on the dynamics of open quantum systems. In the case of time-translation symmetry, which arises naturally in many physically relevant scenarios, the quantum coherence between energy eigenstates becomes a valuable resource for quantum information processing. In this work, we identify the minimum amount of decoherence compatible with this symmetry for a given population dynamics. This yields a generalization to higher-dimensional systems of the relation $T_2\le 2T_1$ for qubit decoherence and relaxation times. It also enables us to witness and assess the role of non-Markovianity as a resource for coherence preservation and transfer. Moreover, we discuss the relationship between ergodicity and the ability of Markovian dynamics to indefinitely sustain a superposition of different energy states. Finally, we establish a formal connection between the resource-theoretic and the master equation approaches to thermodynamics, with the former being a non-Markovian generalization of the latter. Our work thus brings the abstract study of quantum coherence as a resource towards the realm of actual physical applications.

We map the quantum entanglement problem onto the mathematically well-studied truncated moment problem. This yields a necessary and sufficient condition for separability that can be checked by a hierarchy of semidefinite programs. The algorithm always gives a certificate of entanglement if the state is entangled. If the state is separable, typically a certificate of separability is obtained in a finite number of steps and an explicit decomposition into separable pure states can be extracted.

Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constraints on the accuracy of two noncommuting observables. The existing uncertainty relations adopt variance or entropic measures, which are functions of observed outcome distributions, to quantify the uncertainty. According to recent studies of quantum coherence, such uncertainty measures contain both classical (predictable) and quantum (unpredictable) components. In order to extract out the quantum effects, we define quantum uncertainty to be the coherence of the state on the measurement basis. We discover a quantum uncertainty relation using coherence between two measurement noncommuting bases. Furthermore, we analytically derive the quantum uncertainty relation for the qubit case with three widely adopted coherence measures, the relative entropy of coherence, the coherence of formation, and the $l_1$ norm of coherence.

We show that arbitrary $N$-qubit interactions among nuclear spins can be achieved efficiently in solid state quantum platforms, such as nitrogen vacancy centers in diamond, by exerting control only on the electron spin coupled to the nuclei. This allows to exploit nuclear spins as robust quantum registers and the direct measurement of nuclear many-body correlators. The method takes advantage of recently introduced dynamical decoupling techniques and avoids the necessity of external, slow, control on the nuclei. Our protocol is general, being applicable to other nuclear spin-based platforms with electronic spin defects acting as mediators as silicon carbide.