High-order harmonic generation (HHG) from aligned acetylene molecules interacting with mid infra-red (IR), linearly polarized laser pulses is studied theoretically using a mixed quantum-classical approach in which the electrons are described using time-dependent density-functional theory while the ions are treated classically. We find that for molecules aligned perpendicular to the laser polarization axis, HHG arises from the highest-occupied molecular orbital (HOMO), while for molecules aligned along the laser polarization axis, HHG is dominated by the HOMO-1. In the parallel orientation we observe a double plateau with an inner plateau that is produced by ionization from and recombination back to an autoionizing state. Two pieces of evidence support this idea. First, by choosing a suitably tuned vacuum ultraviolet pump pulse that directly excites the autoionizing state we observe a dramatic enhancement of all harmonics in the inner plateau. Second, in certain circumstances, the position of the inner plateau cutoff does not agree with the classical three-step model. We show that this discrepancy can be understood in terms of a minimum in the dipole recombination matrix element from the continuum to the autoionizing state.

Motivated by recent experimental progress, we make an investigation of $p$- and $d$-wave resonant Bose gas. An explanation of the Nozières and Schmitt-Rink (NSR) scheme in terms of two-channel model is provided. Different from the $s$-wave case, high-partial-wave interaction supports a quasibound state in the weak-coupling regime. Within the NSR approximation, we study the equation of state, critical temperature, and particle population distributions. We clarify the effect of the quasibound state on the phase diagram and the dimer production. A multicritical point where normal phase, atomic superfluid phase, and molecular superfluid phase meet is predicted within the phase diagram. We also show the occurrence of a resonant conversion between solitary atoms and dimers when temperature $k_{B}T$ approximates the quasibound energy.

The Creutz ladder model is studied in the presence of unconventional flux induced by complex tunneling rates along and between the two legs. In the vortex phase, the double-minima band structure is regarded as a double well. By introducing a tunable coupling between the two momentum minima, we demonstrate a phenomenon of Josephson oscillations in momentum space. The condensate density locked in one of the momentum valleys is referred to as macroscopic quantum self-trapping. The on-site interaction of the lattice provides an effective analogy to the double-well model within the two-mode approximation which allows for a quantitative understanding of the Josephson effect and the self-trapping in momentum space.

We study the Higgs mode of superfluid Bose gases in a three-dimensional optical lattice, which emerges near the quantum phase transition to the Mott insulator at commensurate fillings. Specifically, we consider responses of the Higgs mode to temporal modulations of the onsite interaction and the hopping energy. In order to calculate the response functions including the effects of quantum and thermal fluctuations, we map the Bose-Hubbard model onto an effective pseudospin-1 model and use a perturbative expansion based on the imaginary-time Green's function theory. We also include the effects of an inhomogeneous trapping potential by means of a local density approximation. We find that the response function for the hopping modulation is equal to that for the interaction modulation within our approximation. At the unit filling rate and in the absence of a trapping potential, we show that the Higgs mode can exist as a sharp resonance peak in the dynamical susceptibilities at typical temperatures. However, the resonance peak is significantly broadened due to the trapping potential when the modulations are applied globally to the entire system. We suggest that the Higgs mode can be detected as a sharp resonance peak by partial modulations around the trap center.

We demonstrate experimentally the control of the polarization (ellipticity and polarization axis) of femtosecond high-order harmonics. The method relies on a two-color ($\omega$ – $2\omega$) configuration, where both $\omega$ and $2\omega$ generating fields have linear polarizations with a variable crossing angle. We correlate our measurements with the conservation rules of energy and linear momentum accounting for harmonic generation in a two-color field. We evidence that the generation process, and especially the number of $\omega$ and $2\omega$ photons absorbed for generating a given harmonic, strongly depends on the crossing angle. Finally, relying on a simple formalism, we derive analytical formulæ for calculating both polarization axis and ellipticity of the separate harmonics. The model corroborates our results and represents a base for future investigations.

The Dicke model is of fundamental importance in quantum mechanics for understanding the collective behavior of atoms coupled to a single electromagnetic mode. Here, we demonstrate a Dicke-model simulation via cavity-assisted Raman transitions in a configuration using counterpropagating laser beams. The observations indicate that motional effects should be included to fully account for the results. These results are contrary to experiments using single-beam and copropagating configurations. We give a theoretical description that accounts for the beam geometries used in the experiments and indicates the potential role of motional effects. In particular, a model is given that highlights the influence of Doppler broadening on the observed phase-transition thresholds.

Quantum Brownian motion is the random motion of quantum particles suspended in a field (or an effective field) resulting from their collision with fast-moving modes in the field. It provides us with a fundamental model to understand various physical features concerning open systems in chemistry, condensed-matter physics, biophysics, and optomechanics. In this paper, without either the Born-Markovian or rotating-wave approximation, we derive a master equation for a charged-Brownian particle in one dimension coupled with a thermal reservoir in electric fields. The effect of the reservoir and the electric fields is manifested as time-dependent coefficients and coherent terms, respectively, in the master equation. The two-photon correlation between the Brownian particle and the reservoir can induce nontrivial squeezing dynamics to the particle. We derive a current equation including the source from the driving fields, transient current from the system flowing into the environment, and the two-photon current caused by the non-rotating-wave term. The presented results then are compared with that given by the rotating-wave approximation in the weak-coupling limit, and these results are extended to a more general quantum network involving an arbitrary number of coupled-Brownian particles. The presented formalism might open a way to better understand exactly the non-Markovian quantum network.

In the quest to achieve scalable quantum information processing technologies, gradient-based optimal control algorithms (e.g., grape) are broadly used for implementing high-precision quantum gates, but their performance is often hindered by deterministic or random errors in the system model and the control electronics. In this paper, we show that grape can be taught to be more effective by jointly learning from the design model and the experimental data obtained from process tomography. The resulting data-driven gradient optimization algorithm (d-grape) can in principle correct all deterministic gate errors, with a mild efficiency loss. The d-grape algorithm may become more powerful with broadband controls that involve a large number of control parameters, while other algorithms usually slow down due to the increased size of the search space. These advantages are demonstrated by simulating the implementation of a two-qubit controlled-not gate.

Two initially correlated coherent states, each interacting with its own independent dissipative environment, exhibit a sudden transition from classical to quantum decoherence. This change in the dynamics is a turning point in the decoherence in the sense that depending on the average number of photons of each harmonic oscillator, decoherence can even be suppressed. Indeed, the quantum state is time independent for a time span in the mesoscopic regime, revealing a decoherence-free subspace. Furthermore, the absence of decoherence is manifested in the apparition of a metastable pointer-state basis.

Quantifying entanglement in a quantum system generally requires a complete quantum tomography followed by the NP-hard computation of an entanglement monotone—requirements that rapidly become intractable at higher dimensions. Observing entanglement in large quantum systems has consequently been relegated to witnesses that only verify its existence. In this article, we show that the violation of recent entropic witnesses of the Einstein-Podolsky-Rosen paradox also provides tight lower bounds to multiple entanglement measures, such as the entanglement of formation and the distillable entanglement, among others. Our approach only requires the measurement of correlations between two pairs of complementary observables—not a tomography—so it scales efficiently at high dimension. Despite this, our technique captures almost all the entanglement in common high-dimensional quantum systems, such as spatially or temporally entangled photons from parametric down-conversion.

Detecting quantumness of correlations (especially entanglement) is a very hard task even in the simplest case, i.e., two-partite quantum systems. Here we provide an analysis of whether there exists a relation between two of the most popular types of entanglement identifiers: the first one based on positive maps and not directly applicable in the laboratory and the second one a geometric entanglement identifier which is based on specific Hermiticity-preserving maps. We show a profound relation between those two types of entanglement criteria. Hereunder we have proposed a general framework of nonlinear functional entanglement identifiers which allows us to construct experimentally friendly entanglement criteria.

Quantum steering means that in some bipartite quantum systems the local measurements on one side can determine the state of the other side. Here we show that in high-dimensional systems there exists a specific entangled state which can display a kind of chaos effect when being adopted for steering. That is, a subtle difference in the measurement results on one side can steer the other side into completely orthogonal states. Moreover, by expanding the result to infinite-dimensional systems, we find two sets of states for which, contrary to common belief, even though their density matrices approach being identical, the steering between them is impossible. This property makes them very useful for quantum cryptography.

We consider a one-dimensional two-component extended Fermi-Hubbard model with nearest-neighbor interactions and mass imbalance between the two species. We study the binding energy of trimers, various observables for detecting them, and expansion dynamics. We generalize the definition of the trimer gap to include the formation of different types of clusters originating from nearest-neighbor interactions. Expansion dynamics reveal rapidly propagating trimers, with speeds exceeding doublon propagation in the strongly interacting regime. We present a simple model for understanding this unique feature of the movement of the trimers, and we discuss the potential for experimental realization.

Already a few bosons with contact interparticle interactions in small optical lattices feature a variety of quantum phases: superfluid, Mott-insulator, and fermionized Tonks gases can be probed in such systems. To detect these phases—pivotal for both experiment and theory—as well as their many-body properties we analyze several distinct measures for the one-body and many-body Shannon information entropies. We exemplify the connection of these entropies with spatial correlations in the many-body state by contrasting them to the Glauber normalized correlation functions. To obtain the ground state for lattices with commensurate filling (i.e., an integer number of particles per site) for the full range of repulsive interparticle interactions we utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) in order to solve the many-boson Schrödinger equation. We demonstrate that all emergent phases—the superfluid, the Mott insulator, and the fermionized gas can be characterized equivalently by many-body entropy measures and by Glauber's normalized correlation functions. In sharp contrast, single-particle entropy cannot capture these phases.

We show that transverse-magnetic (TM) leaky modes can propagate further than transverse electric (TE) modes in real-index dielectric waveguides. We compute the density of states and find that while the TE spectrum contains only overlapping resonances, the TM spectrum typically contains several isolated peaks. By transforming the TM equation into a Schrödinger-type equation, we show that these isolated peaks arise due to $\delta$-function barriers at the core-cladding interface. Our theory is useful for a range of applications, including filtering TM modes from initially unpolarized light and transferring information between distant waveguides.

A spectral representation for the static electric potential field in a two-constituent composite medium is presented. A theory is developed for calculating the quasistatic eigenstates of Maxwell's equations for such a composite. The local physical potential field produced in the system by a given source charge density is expanded in this set of orthogonal eigenstates for any position r. The source charges can be located anywhere, i.e., inside any of the constituents. This is shown to work even if the eigenfunctions are normalized in an infinite volume. If the microstructure consists of a cluster of separate inclusions in a uniform host medium, then the quasistatic eigenstates of all the separate isolated inclusions can be used to calculate the eigenstates of the total structure as well as the local potential field. Once the eigenstates are known for a given host and a given microstructure, then calculation of the local field only involves calculating three-dimensional integrals of known functions and solving sets of linear algebraic equations.

We propose and analyze a cascaded optical parametric system which involves three interacting modes across two octaves of frequency difference. Our system, combining degenerate optical parametric oscillation (OPO) with second harmonic generation (SHG), promises to be a useful source of squeezed and entangled light at three differing frequencies. We show how changes in damping rates and the ratio of the two concurrent nonlinearities affect the quantum correlations in the output fields. We analyze the threshold behavior, showing how the normal OPO threshold is changed by the addition of the SHG interactions. We also find that the inclusion of the OPO interaction removes the self-pulsing behavior found in normal SHG. Finally, we show how the Einstein-Podolsky-Rosen correlations can be controlled by the injection of a coherent seed field at the lower frequency.

Topological edge states appear at the interface of two topologically distinct Hermitian insulators. We study the extension of this idea to non-Hermitian systems. We consider $\mathcal{P}T$-symmetric and topologically distinct non-Hermitian insulators with real spectra and study topological edge states at the interface of them. We show that $\mathcal{P}T$ symmetry is spontaneously broken at the interface during the topological phase transition. Therefore, topological edge states with complex energy eigenvalues appear at the interface. We apply our idea to a complex extension of the Su-Schrieffer-Heeger model.