We propose here a setup to generate and evaluate the entanglement between two mechanical resonators in a cavity optomechanical setting. As in previous proposals, our scheme includes two driving pumps allowing for the generation of two-mode mechanical squeezing. In addition, we include here four additional probing tones, which allow for the separate evaluation of the collective mechanical quadratures required to estimate the Duan quantity, thus allowing us to infer whether the mechanical resonators are entangled.

We found theoretically that optical rectification of an ultrashort laser pulse in an electro-optic crystal can produce a terahertz pulse with a quasistatic electromagnetic precursor propagating ahead of the pulse. The strengths of the electric and magnetic fields in the precursor can be comparable to those in the main terahertz pulse. This effect occurs if the pump optical pulse is intense enough to produce two-photon or multiphoton ionization in the crystal. The precursor is generated by the current of the optically created carriers, which are accelerated by the electric field of the terahertz pulse. The optically generated strong quasistatic precursors can be used for particle acceleration, control of magnetic materials, and in streaking techniques.

The emergence of long-range phase coherence among random nonlinear waves is a fascinating effect that characterizes fundamental phenomena such as the condensation of nonlinear waves and the related manifestation of superfluidity of certain turbulent flows. Here we report a previously unrecognized phenomenon of spontaneous emergence of long-range phase coherence among incoherent waves interacting through a nonlocal nonlinearity. The theory reveals that the establishment of long-range phase coherence constitutes a generic property of a conservative (Hamiltonian) system of highly nonlocal random waves that evolve in the strongly nonlinear regime. Aside from phase coherence, the field exhibits intensity fluctuations whose coherence length is shown to increase in a dramatic way during the evolution of the system. The analysis can be transposed to the temporal domain, revealing the emergence of temporal phase coherence among incoherent waves propagating in nonlinear materials featured by a noninstantaneous nonlinear response.

Xe $1s$ photoelectron spectra were measured at SPring-8, Japan. The core-hole lifetime broadening was found to be 9.6 eV, yielding a lifetime of $\sim 68$ as. The amount of radiative versus nonradiative decay was assessed by recording Auger LMM spectra below and above the $K$ edge. Below the $K$ edge, $L$ vacancies are produced only by direct photoionization, while above the $K$ edge some of these vacancies are mainly produced by $KL$ emission following $1s$ photoionization. Due to the dipole selection rule for x-ray emission, the dominant role of the $KL$ relaxation process is rather directly observed.

Analytic solutions of the quantum relativistic two-body problem are obtained for an interaction potential modeled as a one-dimensional smooth square well. Both stationary and moving pairs are considered and the limit of the $\delta$-function interaction is studied in depth. Our result can be utilized for understanding excitonic states in narrow-gap carbon nanotubes. We also show the existence of bound states within the gap for a pair of particles of the same charge.

We discuss the relation between fermion entanglement and bipartite entanglement. We first show that an exact correspondence between them arises when the states are constrained to have a definite local number parity. Moreover, for arbitrary states in a four-dimensional single-particle Hilbert space, the fermion entanglement is shown to measure the entanglement between two distinguishable qubits defined by a suitable partition of this space. Such entanglement can be used as a resource for tasks like quantum teleportation. On the other hand, this fermionic entanglement provides a lower bound to the entanglement of an arbitrary bipartition, although in this case the local states involved will generally have different number parities. Finally, the fermionic implementation of the teleportation and superdense coding protocols based on qubits with odd and even number parity is discussed, together with the role of the previous types of entanglement.

Performing qubit gate operations as quickly as possible can be important to minimize the effects of decoherence. For resonant gates, this requires applying a strong ac drive. However, strong driving can present control challenges by causing leakage to levels that lie outside the qubit subspace. Strong driving can also present theoretical challenges because preferred tools such as the rotating wave approximation can break down, resulting in complex dynamics that are difficult to control. Here we analyze resonant $X$ rotations of a silicon-quantum-double-dot hybrid qubit within a dressed-state formalism, obtaining results beyond the rotating wave approximation. We obtain analytic formulas for the optimum driving frequency and the Rabi frequency, which are both affected by strong driving. While the qubit states exhibit fast oscillations due to counter-rotating terms and leakage, we show that they can be suppressed to the point that gate fidelities above $99.99\%$ are possible, in the absence of decoherence. Hence decoherence mechanisms, rather than strong-driving effects, should represent the limiting factor for resonant-gate fidelities in quantum dot hybrid qubits.

A semiclassical model supporting the destructive interference interpretation of zero-width resonances (ZWRs) is extended to wavelengths inducing $c^{-}$-type curve crossing situations in ${\mathrm{Na}}_2$ strong-field dissociation. This opens the possibility to get critical couples of wavelengths $\lambda$ and field intensities $I$ to reach ZWRs associated with the ground vibrationless level $v=0$, that, contrary to other vibrational states ($v>0$), is not attainable for the commonly referred $c^{+}$-type crossings. The morphology of such ZWRs in the laser $(I,\lambda )$ parameter plane and their usefulness in filtration strategies aiming at molecular cooling down to the ground $v=0$ state are examined within the frame of an adiabatic transport scheme.

The ionization of the prealigned nitric oxide molecule by strong circularly polarized laser fields is studied via theoretical simulations of the spin-resolved photoelectron momentum distributions by solving numerically the three-dimensional time-dependent Schrödinger equation. Due to the spin-orbit entanglement in the ground state of nitric oxide and the sensitivity of the tunnel ionization of its doubly degenerate valence $2{\pi }_{\pm }$ orbitals carrying opposite electron ring currents to the sense of the laser-field rotation, the momentum-resolved spin-polarized photoelectrons are produced. We show that the spin polarization exhibits strong dependence on the kinetic energy as well as the emitting angle of the photoelectron. In addition to the laser control, the momentum gate in strong-field experiments would enable full control of the spin polarization.

According to the quantitative rescattering theory, the laser features are imbedded in the returning electron wave packets. By analyzing high-energy photoelectron wave packets on the two sides of the linearly polarization axis we can retrieve the experimental laser pulse irrespective of the atomic targets. Laser parameters including its carrier-envelope phase, pulse duration, and peak intensity can be retrieved within a small range simultaneously from the output of the genetic algorithm. This is a simple direct retrieval method for characterizing a phase-stabilized few-cycle laser pulse based only on one set of photoelectron spectra.

We investigate the universal dynamics of a continuous magnetic phase transition from a unmagnetized phase to a ferromagnetic phase in a spin-1 spin-orbit-coupled Bose-Einstein condensate. When the system approaches the critical point, the Landau critical velocity gradually decreases to zero and so the correlation length diverges. Therefore, during the slow passage through the critical point, ferromagnetic domains are spontaneously created according to the Kibble-Zurek mechanism. Through calculating the Bogoliubov excitations, we give the Landau critical velocity and the correlation length, from which we derive the Kibble-Zurek scalings. Furthermore, we numerically simulate the critical spatial-temporal dynamics of the bifurcation delay and spontaneous domain formation, and extract the universal scaling exponents. The numerical scalings extracted from the critical spatial-temporal dynamics are very consistent with the scalings derived from the correlation length.

We theoretically investigate the interparticle force between a pair of spherical aerosol nanoparticles in a dual counterpropagating Bessel beam configuration. We study the dependence of optical binding in the aerosol phase on the wavelength of the electromagnetic radiation, the particle radius, and the refractive index, including the cases of weak, moderate, and strong light absorption by the particles. We also investigate the relation between optical binding and the time-averaged intensity of the incident and scattered light. Our results show that optical binding in the aerosol phase depends strongly on the specific values of these parameters. This explains some of the difficulties associated with optical binding experiments with aerosol nanoparticles.

We show that a type of two-body interaction, which depends on the momentum of the center of mass (COM) of these two particles, can be realized in ultracold atom gases with a laser-modulated magnetic Feshbach resonance (MFR). Here the MFR is modulated by two laser beams propagating along different directions, which can induce Raman transition between two-body bound states. The Doppler effect causes the two-atom scattering length to be strongly dependent on the COM momentum of these two atoms. As a result, the effective two-atom interaction is COM-momentum dependent, while the one-atom free Hamiltonian is still the simple kinetic energy ${\mathbf{p}}^2/\left(2m\right)$.

Although it is well-known that all quantum states can be produced by single-qubit measurements on the cluster states, it is not a simple task to explicitly find which measurement patterns on the cluster states can generate different quantum states. In this paper, we introduce a general scheme to find measurement patterns corresponding to Calderbank–Shor–Steane (CSS) topological states containing Kitaev's toric code states and color code states on different lattices and in different dimensions. Furthermore, we find a measurement pattern for generating non-Abelian anyons where measurement-induced defects on a toric code state play the role of Ising anyons. We also support our scheme by a graphical notation where, by following a few simple graphical transformations, one will be able to convert a CSS topological state to a cluster state. Our scheme can also be used for experimental realization of anyons on cluster states.

Inspired by a class of algorithms proposed by Farhi et al. (arXiv:1411.4028), namely, the quantum approximate optimization algorithm (QAOA), we present a circuit-based quantum algorithm to search for a needle in a haystack, obtaining the same quadratic speedup achieved by Grover's original algorithm. In our algorithm, the problem Hamiltonian (oracle) and a transverse field are applied alternately to the system in a periodic manner. We introduce a technique, based on spin-coherent states, to analyze the composite unitary in a single period. This composite unitary drives a closed transition between two states that have high degrees of overlap with the initial state and the target state, respectively. The transition rate in our algorithm is of order $\mathrm{\Theta }(1/\sqrt{N})$, and the overlaps are of order $\mathrm{\Theta }\left(1\right)$, yielding a nearly optimal query complexity of $T\simeq \sqrt{N}(\pi /2\sqrt{2})$. Our algorithm is a QAOA circuit that demonstrates a quantum advantage with a large number of iterations that is not derived from Trotterization of an adiabatic quantum optimization (AQO) algorithm. It also suggests that the analysis required to understand QAOA circuits involves a very different process from estimating the energy gap of a Hamiltonian in AQO.

A bipartite quantum system in a mixed state can exhibit nonclassical correlations which can go beyond quantum entanglement. While quantum discord is the standard measure of quantifying such general quantum correlations, the nonclassicality can be determined by simpler means via the measurement of witness operators. We experimentally construct a positive map to witness nonclassicality of two qubits in an NMR system. The map can be decomposed in terms of measurable spin magnetizations so that a single run of an experiment on an ensemble of spins suffices to detect the nonclassicality in the state, if present. We let the state evolve in time and use the map to detect nonclassicality as a function of time. To evaluate the efficacy of the witness operator as a means to detect nonclassicality, we measure quantum discord by performing full quantum-state tomography at each time instant and obtain a fairly good match between the two methods.

We present a general approach to speed up the adiabatic process without adding the traditional counterdiabatic driving Hamiltonian. The strategy is to design an easy-to-get intermediate Hamiltonian to connect the original Hamiltonian and final transitionless Hamiltonian. With a final transitionless Hamiltonian, the same target can be achieved as in the adiabatic process governed by the original Hamiltonian, but in a shorter time. We apply the present approach to a three-level system and the result shows that the final transitionless Hamiltonian usually has the same structure as the original Hamiltonian but with different time-dependent coefficients, allowing speedup to be achieved in a much easier way compared to previous methods.

The strong-field-approximation theory of high-order above-threshold ionization of atoms is generalized to include the electron spin. The obtained rescattering amplitude consists of a direct and exchange part. On the examples of excited He atoms as well as ${\mathrm{Li}}^{+}$ and ${\mathrm{Be}}^{++}$ ions, it is shown that the interference of these two amplitudes leads to an observable difference between the photoelectron momentum distributions corresponding to different initial spin states: Pronounced minima appear for singlet states, which are absent for triplet states.