We investigate the behavior of two coupled nonlinear photonic cavities, in the presence of inhomogeneous coherent driving and local dissipations. By solving numerically the quantum master equation, either by diagonalizing the Liouvillian superoperator or by using the approximated truncated Wigner approach, we extrapolate the properties of the system in a thermodynamic limit of large photon occupation. When the mean-field Gross-Pitaevskii equation predicts a unique parametrically unstable steady-state solution, the open quantum many-body system presents highly nonclassical properties and its dynamics exhibits the long-lived Josephson-like oscillations typical of dissipative time crystals, as indicated by the presence of purely imaginary eigenvalues in the spectrum of the Liouvillian superoperator in the thermodynamic limit.

Optical fibers have been considered an optimal platform for third-order parametric down-conversion since they can potentially overcome the weak third-order nonlinearity by their long interaction length. Here we present, in the first part, a theoretical derivation for the conversion rate both in the case of spontaneous generation and in the presence of a seed beam. Then we review three types of optical fibers and we examine their properties in terms of conversion efficiency and practical feasibility.

In this work, we discuss the way in which electric and magnetic dipole resonances arising in the optical scattering spectrum of nonabsorbing dielectric nanospheres can be accurately approximated by means of simple explicit expressions that depend on the sphere's radius, incident wavelength, and relative refractive index. We find such expressions to hold not only for high- but also for moderate-refractive-index values, thus complementing the results reported in previous studies.

We studied the instability suppression of vector vortex solitons (VVS), comprised of two incoherently coupled vortices with different topological charges $m$ in thermal nonlocal nonlinear media with cylindrical symmetry. Using linear stability analysis, we found that the azimuthal instability of the higher-order ($\left|m\right|\ge 3$) vortex can be suppressed and even eliminated because of the presence of the other lower-order ($\left|m\right|\le 2$) vortex, including the fundamental beam. The VVS will be stable when the power ratio of the lower-order vortex exceeds a threshold. We also found that stable VVS exists in some combinational states with opposite-sign charges ($m_1=-1$, $m_2\ge 3$) when the two vortex components have equal Gaussian beam widths.

In this paper we analyze the limits of optical time transfer through atmospheric turbulence and relate those predictions to timing uncertainty analysis using the Allan timing variance (TVAR). The power spectrum of timing uncertainty due to atmospheric turbulence is expressed with the help of Taylor's frozen flow hypothesis, identifying a $f^{-8/3}$ and $f^{-2/3}$ power-law behavior for uncorrelated and partially correlated turbulence, respectively. The scaling of each power law is related to the geometry of the link and the turbulence profile. The power-law slopes are used to calculate two TVAR scaling coefficients relevant to turbulence timing noise, $c_{5/3}$ and $c_{-1/3}$, which can be applied to time-transfer analysis of timing data affected by turbulent fluctuations. Examples of a 2-km horizontal partially overlapping two-way link estimate the atmospheric contribution to timing fluctuations to be below $10\mathrm{fs}$, while a two-way link to a medium-Earth-orbit satellite experiences timing fluctuations on the order of $2\mathrm{fs}$. Comparison of turbulence theory to a recent two-way optical time transfer experiment shows good agreement with the expected power-law behavior and scaling factors.

A Wigner distributionlike function based on the improved strong-field approximation theory is proposed to calculate the rescattering time-energy distribution (RTED) of high-energy photoelectrons of atomic above-threshold ionization process in few-cycle laser fields with different frequencies. The RTED shows bell-like stripes and the outermost stripe is compared with semiclassical results given by the simple-man model with consideration of different positions of tunnel exit and different initial longitudinal momenta. Analysis indicates the existence of the tunnel exit. However, though it shifts farther away from the core with decreasing frequency, the position of the tunnel exit is significantly less than the prediction by adiabatic theory even for the low-frequency case which is well in the tunneling regime. Our results also imply that the effect of the tunnel exit is more important than that of the initial longitudinal momentum at the tunnel exit for the backward-scattering electrons. Moreover, the inner stripe structures in the RTED are attributed to interference between electrons with the same final energy emitted at different ionization times.

Within the BCS-Leggett mean-field model of a balanced mixture of two different spin fermionic atoms, we calculate the BCS pair probability distribution and the density correlation functions both between atoms with the same and different spin states, being able to accurately extract their spatial large-distance behavior along the BEC-BCS crossover. It is found that, after different initial transients, these distributions show an exponential decay and a well-defined periodic oscillatory behavior, which we analyze throughout the whole crossover. In addition, we derive analytic expressions for the mean pair size and the correlation lengths of the same and different density correlation functions. While in general, in the BCS side, there are long-range correlations and, in the BEC region, the behavior is dominated by tight-pair formation, each distribution shows its own characteristic behavior, yielding all together a quite complete description of the spatial structure of the superfluid along the crossover.

It is known that photon pairs generated from pulse-pumped spontaneous parametric processes can be described by independent temporal modes and form a multitemporal mode entangled state. However, the exact form of the temporal modes is not known even though the joint spectral intensity of photon pairs can be measured by the method of stimulated emission tomography. In this paper, we describe a feedback-iteration method which, combined with the stimulated emission method, can give rise to the exact forms of the independent temporal modes for the temporally entangled photon pairs.

The problem of the position and spin in relativistic quantum mechanics is analyzed in detail. It is definitively shown that the position and spin operators in the Foldy-Wouthuysen representation (but not in the Dirac one) are quantum-mechanical counterparts of the classical position and spin variables. The probabilistic interpretation is valid only for Foldy-Wouthuysen wave functions. The relativistic spin operators are discussed. The spin-orbit interaction does not exist for a free particle if the conventional operators of the orbital angular momentum and the rest-frame spin are used. Alternative definitions of the orbital angular momentum and the spin are based on noncommutative geometry, do not satisfy standard commutation relations, and can allow the spin-orbit interaction.

Quantum transduction between microwaves and optics can be realized by quantum teleportation if given reliable microwave-optical entanglement, namely, entanglement-based quantum transduction. To realize this protocol, an entangled source with a high fidelity between the two frequencies is necessary. In this paper, we study microwave and optical entanglement generation based on a generic cavity electro-optomechanical system in the strong coupling regime. Splittings are shown in the microwave and optical output spectra and the frequency entanglement between the two modes is quantified. We show that entanglement can be straightforwardly encoded in the frequency-bin degree of freedom and propose a feasible experiment to verify entangled photon pairs. The experimental implementation is systematically analyzed, and the preferable parameter regime for entanglement verification is identified. An inequality is given as a criterion for good entanglement verification with analysis of practical imperfections.

Grover's quantum search algorithm provides a quadratic speedup over the classical one. The computational complexity is based on the number of queries to the oracle. However, depth is a more modern metric for noisy intermediate-scale quantum computers. We propose a depth optimization method for the quantum search algorithm. We show that Grover's algorithm is not optimal in depth. We propose a quantum search algorithm, which can be divided into several stages. Each stage has a new initialization, which is a rescaling of the database. This decreases errors. The multistage design is natural for parallel running of the quantum search algorithm.

The jellium model of free electron gas and its extended version have been widely used to understand the neutralization of alkali-metal ions on metal surfaces. We report an unexpected deviation from its prediction that we observed in the neutralization of $\mathrm{N}{\mathrm{a}}^{+}$ ions scattering from an Al(111) surface. We find that the neutralization probability decreases monotonically with increasing ion velocity for the specular scattering condition, which is consistent with the well-known parallel velocity effect. However, the neutralization probability exhibits an unexpected bell shape with the variation of outgoing angle for a given incident energy. Calculations based on the jellium model using the rate equation and including the dynamic parallel velocity effect are presented. Their results agree with the velocity dependence of the neutral fraction, but completely fail in reproducing the angle dependence. This anomalous angle dependence could be due to the appearance of inelastic processes, corresponding to inner $2p$ electron promotion in hard encounters with Al atoms for large incidence angles, when the interatomic distances become small. This can lead to the formation of autoionizing Na states that result in the formation of extra $\mathrm{N}{\mathrm{a}}^{+}$ ions, not accounted for in the jellium model.

We consider a system of weakly interacting bosons confined on a planar double lattice ring subjected to two artificial gauge fields. This system is known to display three phases: the Meissner phase, where the flow of particles is carried at the edges of the system without transverse current; a vortex phase, characterized by nonzero transverse current; and a biased-ladder phase, characterized by an imbalance of the population of the two rings. We use the Bogoliubov approximation to determine the excitation spectrum in the three phases, the dynamic structure factor, and the quantum fluctuation corrections to the first-order correlation function. Our analysis reveals supersolid features as well as Josephson modes, corresponding to out-of-phase modes of the finite ring.

We propose a scheme to control the spin Hall effect (SHE) of light reflected from a Kretschmann configuration containing an N-type coherent atomic medium. Owing to the excitation of surface plasmon resonance (SPR), enhanced spin splitting occurs in the reflection dip for TM-polarized incident light. The magnitude and sign of the transverse shifts of spin components depend on the system internal damping which is closely related to the absorption coefficient of atoms. There is an optimal absorption around which the spin components undergo large transverse displacements. We also show that the direction of the photonic spin accumulations can be switched between positive and negative values by adjusting the system parameters. In addition, the resonance angle of SPR varies linearly with the refractivity of the medium. We can therefore coherently control the peak position of the transverse shift. Compared to the conventional SPR-based systems, the proposed scheme provides a more flexible pathway for manipulating and enhancing the SHE of light without changing the structure. This tunable SHE may find applications in spin photonic devices.

Many-mode Floquet theory [T.-S. Ho, S.-I. Chu, and J. V. Tietz, Chem. Phys. Lett. 96, 464 (1983)] is a technique for solving the time-dependent Schrödinger equation in the special case of multiple periodic fields, but its limitations are not well understood. We show that for a Hamiltonian consisting of two time-periodic couplings of commensurate frequencies (integer multiples of a common frequency), many-mode Floquet theory provides a correct expression for unitary time evolution. However, caution must be taken in the interpretation of the eigenvalues and eigenvectors of the corresponding many-mode Floquet Hamiltonian, as only part of its spectrum is directly relevant to time evolution. We give a physical interpretation for the remainder of the spectrum of the Hamiltonian. These results are relevant to the engineering of quantum systems using multiple controllable periodic fields.

The multiqubit bound entangled states that are uniformly mixed over the subspaces complementary to unextendible product bases (UPBs) are interesting members from the peculiar family of bound entangled states. Their entanglement is delocalized and they look separable with respect to any partition into a single party and all remaining parties. Only one example of quantifying the entanglement of this type of states in the case of three-qubit states has been studied [C. Branciard, H. Zhu, L. Chen, and V. Scarani, Evaluation of two different entanglement measures on a bound entangled state, Phys. Rev. A 82, 012327 (2010)]. We provide a systematic procedure for generating decompositions of such states in terms of minimally entangled states. This procedure enables us to measure entanglement in terms of the concurrence for a wide range of families of these bound entangled (BE) states with each family containing an infinite number of states. In particular, we study one family of three-qubit states in addition to six inequivalent families of four-qubit bound entangled states. These studied families are examples that represent all the known 1446 families of four-qubit UPB-based bound entangled states, which means that our method is applicable to all the 1446 families. In addition, a discussion on the matter of applicability of the proposed strategy to additional families is provided. Specifically, the proposed method looks promising for measuring entanglement of other families of UPB-based BE states in addition to some families of symmetric multipartite positive under partial transposition BE states.

In this article, we consider the monogamy relations for the generalized $W$-class states. Here we first present an analytical formula on Tsallis-$q$ entanglement ($\mathrm{T}q\mathrm{EE}$) and Tsallis-$q$ entanglement of assistance ($\mathrm{T}q\mathrm{EEoA}$) of a reduced density matrix for a generalized $W$-class state. By using the analytical formula, we present a monogamy relation in terms of the squared $\mathrm{T}q\mathrm{EE}$ for a generalized $W$-class state. Then we present generalized monogamy relations in terms of $\mathrm{T}q\mathrm{EE}$ for a generalized $W$-class state. We also present a monogamy relation in terms of an arbitrary power of $\mathrm{T}q\mathrm{EE}$ for a generalized $W$-class state. Last, we apply our results to quantum games and present the bound of the nonclassicality of the quantum games when restricting to the generalized $W$-class states.

We develop and study quantum and semiclassical models of Rydberg-atom spectroscopy in amplitude-modulated optical lattices. Both initial- and target-state Rydberg atoms are trapped in the lattice. Unlike in other spectroscopic schemes, the modulation-induced ponderomotive coupling between the Rydberg states is spatially periodic and perfectly phase-locked to the lattice trapping potentials. This leads to a type of sub-Doppler mechanism which we explain in detail. In our exact quantum model, we solve the time-dependent Schrödinger equation in the product space of center-of-mass (COM) momentum states and the internal-state space. We also develop a perturbative model based on the band structure in the lattice and Fermi's golden rule, as well as a semiclassical trajectory model in which the COM is treated classically and the internal-state dynamics quantum-mechanically. In all models we obtain the spectrum of the target Rydberg-state population versus the lattice modulation frequency, averaged over the initial thermal COM momentum distribution of the atoms. We investigate the quantum-classical correspondence of the problem in several parameter regimes and exhibit spectral features that arise from vibrational COM coherences and rotary-echo effects. Applications in Rydberg-atom spectroscopy are discussed.