Coherent time is a characteristic time in the extreme nonlinear optics regime and thus generally introduced as the dephasing time in simulations of solid-state high-harmonic generation. This characteristic time linked with the coherent decay of quantum trajectory controls the emergence of spectral splittings in high-harmonic spectroscopy, which has been attributed to the temporal interference between two adjacent harmonic emission channels. To reproduce the harmonic peaks and spectral splittings, a temporal two-slit interference model in the momentum space is introduced. In addition, mechanisms of spectral splitting provide a state-of-the-art avenue to probe the characteristic elapse between electron and hole. Based on the subfemtosecond resolution of the spectral interference opening and closing zones in the wavelength-dependent high-order harmonic spectra, we also propose an alternative scheme to probe the dephasing time of crystals with feasible laser pulses in present experimental setups.

We propose a general Zeeman slower scheme applicable to the majority of the laser-coolable molecules. Different from previous schemes, we apply a careful modulation on the repump laser and guarantee the velocity selectivity through the polarization selection rules. Only atoms or molecules with the right velocity will be laser slowed. Such a scheme is more feasible for molecules with complex energy structures. We apply this scheme for molecules with a large Landé $g$ factor of the excited states, i.e., $g_e>0.1$, and polyatomic molecules with one-dimensional numerical simulations. The results show a better slowing efficiency with about 62% of the BaF molecules and 99% of the SrOH molecules being successfully slowed down to a velocity below $15\mathrm{m}/\mathrm{s}$ without the consideration of transverse divergence.

The physical generalization of the system of the reduced Maxwell-Bloch equations describing the nonlinear interaction of the laser pulses with the multilevel quantum medium is obtained without using the slowly varying envelope approximation. It is shown that this system is integrable in the frameworks of the inverse scattering transformation method. The soliton and breather solutions in the form of the unipolar and few-cycle pulses are constructed. Their distinctive features caused solely by the multilevel structure of the medium are discussed. It is revealed that the collision of the solitons can lead to an appearance of the large-amplitude short-living pulse, whose dynamics resembles that of rogue waves.

The recently realized photonic-crystal Fano laser constitutes the first demonstration of passive pulse generation in nanolasers [Yi Yu et al., Nat. Photon. 11, 81 (2017)]. We show that the laser operation is confined to only two degrees of freedom after the initial transition stage. We show that the original five-dimensional dynamic model can be reduced to a one-dimensional model in a narrow region of the parameter space and it evolves into a two-dimensional (2D) model after the exceptional point, where the eigenvalues transition from being purely real to a complex conjugate pair. The 2D reduced model allows us to establish an effective band structure for the eigenvalue problem of the stability matrix and to explain the laser dynamics. The reduced model is used to associate an origin of instability with an unstable periodic orbit separating the stable steady state from the stable periodic orbit.

We study the controllable single-photon scattering via a one-dimensional waveguide which is coupled to a two-level emitter and a single-mode cavity simultaneously. The emitter and the cavity are also coupled to each other and form a three-level system with cyclic transitions within the zero- and single-excitation subspaces. As a result, the phase of emitter-cavity coupling strength serves as a sensitive control parameter. When the emitter and cavity locate at the same point of the waveguide, we demonstrate the Rabi splitting and quasidark-state-induced perfect transmission for the incident photons. More interestingly, when they locate at different points of the waveguide, a controllable nonreciprocal transmission can be realized and the nonreciprocity is robust to the weak coupling between the system and environment. Furthermore, we demonstrate that our theoretical model is experimentally feasible with currently available technologies.

A methodology is devised for building optimal bases for the generalized Dicke model based on the symmetry adapted variational solution to the problem. At order zero, the matter sector is constructed by distributing $N_a$ particles in all the possible two-level subsystems connected with electromagnetic radiation; the next order is obtained when the states of $N_a-1$ particles are added and distributed again into the two-level subsystems and so on. In the electromagnetic sector, the order zero for each mode is the direct sum of the Fock spaces, truncated to a value of the corresponding constants of motion of each two-level subsystem; by including contributions of the other modes, the next orders are obtained. As an example of the procedure, we consider four atoms in the $\mathrm{\Xi }$ configuration interacting dipolarly with two modes of electromagnetic radiation. The results may be applied to situations in quantum optics, quantum information, and quantum computing.

Pumping a nonlinear crystal by an intense radiation results in the optical parametric generation of photons in two modes (the signal and the idler). The quantized electromagnetic field in these modes is described by a continuous-variable quantum state, which is entangled if the pump is a coherent state produced by a laser. The signal and the idler modes remain populated by photons even if the pump becomes incoherent (dephased by a medium, superposed with a thermal state, or produced by an alternative source such as the superluminescent diode). However, the incoherent pump does effect the entanglement and purity of the signal and the idler modes, which is of vital importance for quantum information applications and interferometry. Here we develop an approach to infer the signal-idler entanglement and purity for a general quantum incoherent pump with the given Glauber-Sudarshan function. We show that the signal-idler entanglement is extremely sensitive to the phase distribution of the pump and illustrate our findings by physically relevant examples of the incoherent pump: the noisy coherent state, slightly dephased and phase-averaged coherent states, the thermal state, and states modulated by the Kerr medium. The effect of an incoherent pump on the combined quadratures is discussed as well.

We took a generalization of the conventional concept of the $q$-plate, allowing in its definition nonlinear functions of the azimuthal coordinate, and simulated the resulting fields of applying this kind of element to uniformly polarized input beams, both in the near-field (Fresnel diffraction) and the far-field (Fraunhofer diffraction) approximations. In general terms, when working in the near-field regime, the chosen function defines the output polarization structure for linearly polarized input beams and the phase of the output field for circularly polarized input beams. In the far-field regime, it is obtained that when there are nonlinearities in the azimuthal variable, the central singularity of the polarization field of a vector or vortex beam may divide into several singularities of lower topological charge, preserving the total charge. Depending on the chosen $q$-plate function, different particular behaviors on the output beam are observed, which offers a whole range of possibilities for creating alternative kinds of vector and vortex beams, as well as polarization critical points and singularity distributions.

We study theoretically an extended Bose-Hubbard model with the spatially modulated interaction strength, describing a one-dimensional array of tunneling-coupled nonlinear cavities. It is demonstrated that the spatial modulation of the nonlinearity induces bound two-photon edge states. The formation of these edge states has been understood analytically in terms of nonlinear self-localization. Our results show that the number of excitations and the modulation period of the interaction affect the photonic quantum walks in the universal way and both promote the edge states.

We theoretically investigate the dynamics and stability of a temporal cavity soliton (CS) excited inside a silicon-based microresonator that exhibits free-carrier generation as a result of two-photon absorption (TPA). The optical propagation of the CS is modeled through a mean-field Lugiato-Lefever equation (LLE) coupled with an ordinary differential equation accounting for the generation of free carriers owing to TPA. The CS experiences several perturbations [like intrapulse Raman scattering (IRS), TPA, free-carrier absorption (FCA), free-carrier dispersion (FCD), etc.] during its round-trip evolution inside the cavity. We develop a full variational analysis based on a Ritz optimization principle which is useful in deriving simple analytical expressions describing the dynamics of individual pulse parameters of the CS under perturbation. TPA and FCA limit the efficient comb generation and modify the stability condition of the CS. We determine the critical condition of stability modified due to TPA and derive closed-form expressions of the saturated amplitude and width of the stable CS. We perform detailed modulation-instability analysis and obtain stability conditions against perturbations of the steady-state solution of LLE. The CS experiences FCD, which leads to a temporal acceleration resulting in spectral blueshift. Exploiting the variational analysis, we estimate these temporal and spectral shifts. We also include IRS in our perturbation theory and analytically estimate the frequency redshifting. Finally, we study the effect of pump-phase modulation on a stable CS. All our analytical results are found to be in good agreement with the data obtained from the full numerical solution of LLE.

Low-dissipation, tunable coupling to other quantum systems and unique features of phonons in the aspects of propagation, detection, and other areas suggest the applications of quantized mechanical oscillators in phonon-based quantum information processing (QIP) in a way different from their photonic counterpart. In this paper, we propose a protocol of entanglement concentration for nonlocal phonons from quantized mechanical vibration. We combine the optomechanical cross-Kerr interaction with the Mach-Zehnder interferometer and, by means of twice optomechanical interactions and the photon analysis with respect to the output of the interferometer, achieve ideal entanglement concentration about less-entangled nonlocal phonon Bell and Greenberger-Horne-Zeilinger states. Our protocol is useful for preserving the entangled phonons for the use of high-quality phonon-based QIP in the future.

The standard Bloch oscillation normally refers to the oscillatory tunneling dynamics of quantum particles in a periodic lattice plus a linear gradient. In this paper we theoretically investigate the generalized form of the Bloch oscillation in the presence of additional higher-order gradients and demonstrate that the higher-order gradients can significantly modify the tunneling dynamics, particularly in the spectrum of the density oscillation. The spectrum of the standard Bloch oscillation is composed of a single prime frequency and its higher harmonics, while the higher-order gradients in the external potential give rise to fine structures in the spectrum around each of these Bloch frequencies, which are composed of series of frequency peaks. Our investigation leads to a twofold consequence to the applications of Bloch oscillations for measuring external forces. For one thing, under a limited resolution of the measured spectrum, the fine structures would manifest as a blur to the spectrum and lead to intrinsic errors to the measurement. For another, given that the fine structures could be experimentally resolved, they can supply more information on the external force than the strength of the linear gradient, and be used to measure more complicated forces.

We explore the consequences of incorporating parity and time reversal ($\mathcal{PT}$) symmetries on the dynamics of nonreciprocal light propagation exhibited by a class of nonuniform periodic structures known as chirped $\mathcal{PT}$-symmetric fiber Bragg gratings. The interplay among various grating parameters such as chirping, detuning, nonlinearities, and gain or loss gives rise to bi- and multistable states in the unbroken as well as broken $\mathcal{PT}$-symmetric regimes. The role of chirping on the steering dynamics of the hysteresis curve is influenced by the type of nonlinearities and the nature of the detuning parameter. Also, incident directions of the input light robustly impact the steering dynamics of bistable and multistable states, both in the unbroken and broken $\mathcal{PT}$-symmetric regimes. When the light launching direction is reversed, critical stable states are found to occur at very low intensities, which opens up an avenue for an additional way of controlling light with light. We also analyze the phenomenon of unidirectional wave transport and the reflective bi- and multistable characteristics at the so-called $\mathcal{PT}$-symmetry breaking point.

The decay of quasistable quantum systems involves primarily an outgoing probability current density. However, during the transition from exponential to inverse-power-law decay there are time intervals during which this current, although small, is inward. In this paper this inward flow is associated with quantum backflow. Furthermore substantial backflow exists for time-evolving free wave packets which are initially confined in space.

Transport in a non-Hermitian trimerized lattice with one lossy site per unit cell exhibits a quantized mean displacement before decay characterized by a two-step phase transition from zero to unity through a fractional value. Such a peculiar behavior, sensitive to both the lattice parameters and the initial state, is shown to be closely related to the presence of two nondegenerate dark states decoupled from the lossy sites and correspond to two staggered band closing points. We further check that distinct topological phases can also be characterized by the total Zak phase and by the number of midgap edge states. Moreover, we demonstrate that the edge states are topologically protected and their localization can be controlled via the couplings imbalance. Our results are expected to be relevant for implementations of topological photonics such as those based on arrays of evanescently coupled waveguides.

We introduce a probabilistic version of the one-shot quantum dense coding protocol in both two- and multiport scenarios in which the sender(s) transmit(s) only complete messages unambiguously, to a single receiver, and we refer to it as conclusive quantum dense coding. We derive the relevant form of the mutual information between encoded information and measurement results in the scenario considered. We analyze the corresponding capacities of shared states between two, three, and more qubits, and two qutrits. We identify cases where Pauli and generalized Pauli operators are not sufficient as encoders to attain the optimal one-shot conclusive quantum dense coding capacities. We find that there is a rich connection between the capacities and the bipartite as well as multipartite entanglements of the shared state.

The maximal evolution speed of a quantum system can be represented by quantum speed limit time (QSLT). We investigate the QSLT of a two-qubit system passing through a correlated channel (amplitude damping, phase damping, and depolarizing). By adjusting the correlation parameter of the channel and the initial entanglement, a method to accelerate the evolution speed of the system for some specific channels is proposed. It is shown that, in the amplitude damping channel and the depolarizing channel, QSLT may be shortened in some cases by increasing the correlation parameter of the channel and the initial entanglement, which are in sharp contrast to the phase damping channel. In particular, under depolarizing channels, the transition from no-speedup evolution to speedup evolution for the system can be realized by changing the correlation strength of the channel.

Properties of the ground state of an unpolarized ultracold Fermi gas along the BCS-BEC crossover are investigated by the variational and diffusion Monte Carlo methods. We apply the Wigner-Bethe-Peierls boundary condition in our calculations to avoid any bias from using an interatomic potential with finite effective range. Properties for several values of the scattering length are studied in the range $-8\le 1/a{k}_F\le 4$, including the unitary limit. The contact parameters as a function of scattering length are obtained by fitting the pair distribution functions for particles with different spins. The energies and contact parameters are in very good agreement with experimental data reported in the literature.