Optical microcavities are often used to realize enhanced nonlinear optical interactions for highly efficient second-harmonic generation. With increased pump power, the efficiency of nonlinear frequency conversion can be increased further, whereas some other unwanted nonlinear effects will also emerge, leading to complicated dynamics or instability. Here, we study the interplay between cascaded second- and third-order nonlinear processes and investigate their impact on the second-harmonic generation in microcavities. It is found that the nondegenerate optical parametric oscillation (OPO) appears and the presence of a ${\chi }^{\left(3\right)}$ process can modify the OPO threshold significantly when the multimode cavity is strongly pumped at the fundamental optical mode. One can even break the efficiency limitation of the second-harmonic mode restricted by the OPO by utilizing the interference between the OPO and the four-wave mixing. The present coherent interplay between nonlinear optical processes in the microcavities is conducive to explore new physics in the cavity nonlinear photonics.

We consider a two-state quantum walk on a line where after the first step an absorbing sink is placed at the origin. The probability of finding the walker at position $j$, conditioned on that it has not returned to the origin, is investigated in the asymptotic limit. We prove a limit theorem for the conditional probability distribution and show that it is given by the Konno's density function modified by a prefactor ensuring that the distribution vanishes at the origin. In addition, we discuss the relation to the problem of recurrence of a quantum walk and determine the Pólya number. Our approach is based on path counting and the stationary phase approximation.

A plane-wave approximation in particle physics implies that a width of a massive wave packet ${\sigma }_{\perp }$ is much larger than its Compton wavelength ${\lambda }_c=\hslash /mc$. For Gaussian packets or for those with nonsingular phases (say, the Airy beams), corrections to this approximation are attenuated as ${\lambda }_c^2/{\sigma }_{\perp }^2\ll 1$ and usually negligible. Here we show that this situation drastically changes for particles with the phase vortices associated with an orbital angular momentum $\ell \hslash$. For highly twisted beams with $\left|\ell \right|\gg 1$, the nonparaxial corrections get $\left|\ell \right|$ times enhanced and $\left|\ell \right|$ can already be as large as ${10}^3$. We describe the relativistic wave packets, both for vortex bosons and fermions, which transform correctly under the Lorentz boosts, are localized in a three-dimensional space, and represent a nonparaxial generalization of the massive Laguerre-Gaussian beams. We compare such states with their paraxial counterparts, paying specific attention to relativistic effects and to the differences from the twisted photons. In particular, a Gouy phase is found to be Lorentz invariant and it generally depends on time rather than on a distance $z$. By calculating the electron packet's mean invariant mass, magnetic moment, etc., we demonstrate that the nonparaxial corrections can already reach the relative values of ${10}^{-3}$. These states and the nonparaxial effects can be relevant for the proper description of spin-orbit phenomena in relativistic vortex beams, of scattering of the focused packets by atomic targets, of collision processes in particle and nuclear physics, and so forth.

We apply advanced methods of control theory to open quantum systems and we determine finite-time processes which are optimal with respect to thermodynamic performances. General properties and necessary conditions characterizing optimal drivings are derived, obtaining bang-bang-type solutions corresponding to control strategies switching between adiabatic and isothermal transformations. A direct application of these results is the maximization of the work produced by a generic quantum heat engine, where we show that the maximum power is directly linked to a particular conserved quantity naturally emerging from the control problem. Finally we apply our general approach to the specific case of a two-level system, which can be put in contact with two different baths at fixed temperatures, identifying the processes that minimize heat dissipation. Moreover, we explicitly solve the optimization problem for a cyclic two-level heat engine driven beyond the linear-response regime, determining the corresponding optimal cycle, the maximum power, and the efficiency at maximum power.

Quantum information processing in a modular architecture requires the distribution, stabilization, and distillation of entanglement in a qubit network. We present autonomous entanglement stabilization protocols between two superconducting qubits that are coupled to distant cavities. The coupling between cavities is mediated and controlled via a three-wave mixing device that generates either a two-mode squeezed state or a delocalized mode between the remote cavities depending on the pump applied to the mixer. Local drives on the qubits and the cavities steer and maintain the system to the desired qubit Bell state. Most spectacularly, even a weakly squeezed state can stabilize a maximally entangled Bell state of two distant qubits through an autonomous entanglement concentration process. Moreover, we show that such reservoir-engineering-based protocols can stabilize entanglement in the presence of qubit-cavity asymmetries and losses.

The decoy-state protocol has been considered to be one of the most important methods to protect the security of quantum key distribution (QKD) with a weak coherent source. Here we test two experimental approaches to generating the decoy states with different intensities: modulation of the pump current of a semiconductor laser diode, and external modulation by an optical intensity modulator. The former approach shows a side channel in the time domain that allows an attacker to distinguish s signal state from a decoy state, breaking a basic assumption in the protocol. We model a photon-number-splitting attack based on our experimental data, and show that it compromises the system's security. Then, based on the work of Tamaki et al. [New J. Phys. 18, 065008 (2016)], we obtain two analytical formulas to estimate the yield and error rate of single-photon pulses when the signal and decoy states are distinguishable. The distinguishability reduces the secure key rate below that of a perfect decoy-state protocol. To mitigate this reduction, we propose to calibrate the transmittance of the receiver (Bob's) unit. We apply our method to three QKD systems and estimate their secure key rates.

Robust quantum state transfer (QST) is an indispensable ingredient in scalable quantum information processing. Here we present an experimentally feasible mechanism for realizing robust QST via topologically protected edge states in superconducting qubit chains. Using superconducting Xmon qubits with tunable couplings, we construct generalized Su-Schrieffer-Heeger models and analytically derive the wave functions of topological edge states. We find that such edge states can be employed as a quantum channel to realize robust QST between remote qubits. With a numerical simulation, we show that both single-qubit states and two-qubit entangled states can be robustly transferred in the presence of sizable imperfections in the qubit couplings. The transfer fidelity demonstrates a wide plateau at the value of unity in the imperfection magnitude. This approach is general and can be implemented in a variety of quantum computing platforms.

We calculate the nonretarded dispersion force exerted on an electrically polarizable quantum particle by a perfectly conducting toroid, which is one of the most common objects exhibiting a nontrivial topology. We employ a convenient method developed by Eberlein and Zietal that essentially relates the quantum problem of calculating dispersion forces between a quantum particle and a perfectly conducting surface of arbitrary shape to a corresponding classical problem of electrostatics. Considering the quantum particle in the symmetry axis of the toroid, we use this method to find an exact analytical result for the van der Waals interaction between the quantum particle and the conducting toroid. Surprisingly, we show that for appropriate values of the two radii of the toroid the dispersive force on the quantum particle is repulsive. This is a remarkable result since repulsion in dispersive interactions involving only electric objects (and particles) in vacuum is rarely reported in the literature. Final comments are made about particular limiting cases as, for instance, the quantum particle-nanoring system.

We report on observations of spin dynamics in single ${\mathrm{Yb}}^{+}$ ions immersed in a cold cloud of spin-polarized ${}^6\mathrm{Li}$ atoms. This species combination has been proposed to be the most suitable system to reach the quantum regime in atom-ion experiments. For ${}^{174}\mathrm{Yb}^{+}$, we find that the atomic bath polarizes the spin of the ion by 93(4)% after a few Langevin collisions, pointing to strong spin-exchange rates. For the hyperfine ground states of ${}^{171}\mathrm{Yb}^{+}$, we also find strong rates towards spin polarization. However, relaxation towards the $F=0$ ground state occurs after 7.7(1.5) Langevin collisions. We investigate spin impurity atoms as a possible source of apparent spin-relaxation leading us to interpret the observed spin-relaxation rates as an upper limit. Using ab initio electronic structure and quantum scattering calculations, we explain the observed rates and analyze their implications for the possible observation of Feshbach resonances between atoms and ions once the quantum regime is reached.

We focus on the post-collision interaction in Auger processes where the photoelectron energy is near or below the ionization threshold. Time-dependent quantum and classical calculations are performed. When the photoelectron is more deeply bound, interference patterns can be seen in the angular and photoelectron energy distributions. These interference patterns are visible in quantum calculations, but not in purely classical calculations. A semiclassical analysis using actions from two-path trajectories gives the relative locations of the interference maxima very close to those from the full quantum calculations.

We investigate dissipative extensions of the Su-Schrieffer-Heeger model with regard to different approaches of modeling dissipation. In doing so, we use two distinct frameworks to describe the gain and loss of particles: One uses Lindblad operators within the scope of Lindblad master equations, and the other uses complex potentials as an effective description of dissipation. The reservoirs are chosen in such a way that the non-Hermitian complex potentials are $\mathcal{PT}$-symmetric. From the effective theory we extract a state which has similar properties as the nonequilibrium steady state following from Lindblad master equations with respect to lattice site occupation. We find considerable similarities in the spectra of the effective Hamiltonian and the corresponding Liouvillian. Further, we generalize the concept of the Zak phase to the dissipative scenario in terms of the Lindblad description and relate it to the topological phases of the underlying Hermitian Hamiltonian.

Quantum spectroscopy with single two-level systems has considerably improved our ability to detect weak signals. Recently it was realized that for classical signals, precision and resolution of quantum spectroscopy is limited mainly by coherence of the signal and the stability of the clock used to measure time. The coherence time of the quantum probe, which can be significantly shorter, is not a major limiting factor in resolution measurements. Here, we address a similar question for spectroscopy of quantum signals, for example, a quantum sensor is used to detect a single nuclear spin. We present and analyze a novel correlation spectroscopy technique with performance that is limited by the coherence time of the target spins and the stability of the clock.

We investigate quantum nonlinear effects at a level of individual quanta in a double-tripod atom-light coupling scheme involving two atomic Rydberg states. In such a scheme the slow light coherently coupled to strongly interacting Rydberg states represents a two-component or spinor light. The scheme provides additional possibilities for the control and manipulation of light quanta. A distinctive feature of the proposed setup is that it combines the spin-orbit coupling for the spinor slow light with an interaction between the photons, enabling generation of the second probe beam even when two-photon detuning is zero. Furthermore, the interaction between the photons can become repulsive if the one-photon detunings have opposite signs. This is different from a single-ladder atom-light coupling scheme in which the interaction between the photons is attractive for both positive and negative detunings as long as the Rabi frequency of the control beam is not too high.

Recently, the creation of a strong magnetic field in a photonic cavity system has been demonstrated [N. Schine et al., Nature (London) 534, 671 (2016).]. Using this setup, we propose a scheme to adiabatically transfer flux quanta simultaneously to all cavity photons. The flux transfer is achieved using external light fields with orbital angular momentum and a near-resonant dense atomic medium as a mediator. Furthermore, by coupling the cavity fields to a Rydberg state, strong photon-photon interactions can be realized and fractional quantum Hall states can be prepared. To this end, a growing protocol is discussed consisting of a sequence of flux insertion and subsequent single-photon insertion. Specifically, we discuss the growing of the $\nu =1/2$ bosonic Laughlin state. First we adiabatically insert two photonic flux quanta, creating a two-quasihole excitation, and second we refill the hole with a single photon using the strong photon-photon interactions.

We consider self-pulsing regimes in chains of Kerr nonlinear optical microresonators. By means of a supermodal diagonalization procedure of the conventional coupled-mode theory in time, we theoretically and numerically study the bifurcation diagrams of a singly pumped three-cavity and a doubly pumped four-cavity system: the latter allows us to predict thresholdless frequency tripling of a GHz modulation. These self-pulsing regimes are proven robust and will find applications in the generation and conversion of microwaves on an optical carrier.

In the calculation of probabilities of physical processes occurring in a background classical field, the local-constant-field approximation (LCFA) relies on the possibility of neglecting the space-time variation of the external field within the region of formation of the process. This approximation is widely employed in strong-field QED as it allows one to evaluate probabilities of processes occurring in arbitrary electromagnetic fields starting from the corresponding quantities computed in a constant electromagnetic field. Here, we scrutinize the validity of the LCFA in the case of nonlinear Compton scattering focusing on the role played by the energy of the emitted photon on the formation length of this process. In particular, we derive analytically the asymptotic behavior of the emission probability per unit of photon light-cone energy $k_{-}$ and show that it tends to a constant for $k_{-}\to 0$. With numerical codes being an essential tool for the interpretation of present and upcoming experiments in strong-field QED, we obtained an improved approximation for the photon emission probability, implemented it numerically, and showed that it amends the inaccurate behavior of the LCFA in the infrared region, such that it is in qualitative and good quantitative agreement with the full strong-field QED probability also in the infrared region.

In this work, we study the decay behavior of a two-level system under the competing influence of a dissipative environment and repetitive measurements. The sign of the second derivative of the environmental spectral density function with respect to the system transition frequency is found to be a sufficient condition to distinguish between the quantum Zeno (negative) and the anti-Zeno (positive) effects raised by the measurements. We check our criterion for practical measurement intervals, which are larger than the conceptual Zeno time, in various environments. In particular, with the Lorentzian spectrum, the quantum Zeno and anti-Zeno phenomena are found to emerge respectively in the near-resonant and off-resonant cases. For the interacting spectra of hydrogenlike atoms, the quantum Zeno effect usually occurs and the anti-Zeno effect can rarely occur unless the transition frequency is close to the cut-off frequency. With a power-law spectrum, we find that sub-Ohmic and super-Ohmic environments lead to the quantum Zeno and anti-Zeno effects, respectively.