Microdisk cavities with a smoothly deformed boundary allow for highly directional light emission. The conventional direct problem is to determine the far-field emission pattern of an optical mode for a given cavity shape by solving Maxwell's equations. We introduce the inverse problem of finding the cavity shape for which the far-field intensity pattern of the optical mode best fits a desired profile. We find an optimal solution within a second-order perturbation theory for weakly deformed cavities with a mirror reflection symmetry. Surprisingly, in this case the optimal solution is unique for specified mode numbers and refractive index. The perturbative results are confirmed by full numerical simulations.

It is well known that standing waves, as special bound states in the radiation continuum, may exist on a periodic array of dielectric cylinders at a discrete set of frequencies if the medium is linear. Recent numerical studies indicate that nonlinear standing waves could exist continuously with respect to the frequency on a periodic array of cylinders with a Kerr nonlinearity. In this paper, we study the diffraction of a normal incident plane wave by a periodic array of circular cylinders with a Kerr nonlinearity. Using a perturbation method and a highly accurate numerical method, we show that a plane incident wave may couple to a nonlinear standing wave, and in general, there are four different couplings leading to four asymmetric solutions in two pairs. The existence of these asymmetric solutions provides another example for the symmetry-breaking phenomenon. Importantly, it seems that the asymmetric solutions (thus the symmetry-breaking phenomenon) appear for incident waves of arbitrarily low intensity.

Frequent observation of a quantum system leads to quantum Zeno physics, where the system evolution is constrained to states commensurate with the measurement outcome. We show that, more generally, the system can evolve between such states through higher-order virtual processes that pass through states outside the measurement subspace. We derive effective Hamiltonians to describe this evolution, and the dependence on the time between measurements. We demonstrate application of this phenomena to prototypical quantum many-body system examples, spin chains and atoms in optical lattices, where it facilitates correlated dynamical effects.

We investigate the problem of what evolutions an open quantum system described by a time-local master equation can undergo with universal coherent controls. A series of conditions is given which exclude channels from being reachable by any unitary controls, assuming that the coupling to the environment is not being modified. These conditions primarily arise by defining decay rates for the generator of the dynamics of the open system, and then showing that controlling the system can only make these rates more isotropic. This forms a series of constraints on the shape and nonunitality of allowed evolutions, as well as an expression for the time required to reach a given goal. We give numerical examples of the usefulness of these criteria and explore some similarities they have with quantum thermodynamics.

The role of the generalized Pauli constraints (GPCs) in higher spatial dimensions and by incorporating spin degrees of freedom is systematically explored for a system of interacting fermions confined by a harmonic trap. Physical relevance of the GPCs is confirmed by analytical means for the ground state in the regime of weak couplings by finding its vector of natural occupation numbers close to the boundary of the allowed region. Such quasipinning is found to become weaker in the intermediate- and strong-coupling regime. The study of crossovers between different spatial dimensions by detuning the harmonic trap frequencies suggests that quasipinning is essentially an effect for systems with reduced spatial dimensionality. In addition, we find that quasipinning becomes stronger by increasing the degree of spin polarization. Consequently, the number of states available around the Fermi level plays a key role for the occurrence of quasipinning. This suggests that quasipinning emerges from the conflict between energy minimization and fermionic exchange symmetry.

Fock states are a fundamental resource for many quantum technologies such as quantum metrology. While much progress has been made in single-photon source technologies, preparing Fock states with a large photon number remains challenging. We present and analyze a bootstrapped approach for nondeterministically preparing large photon-number Fock states by iteratively fusing smaller Fock states on a beamsplitter. We show that by employing state recycling we are able to exponentially improve the preparation rate over conventional schemes, allowing the efficient preparation of large Fock states. The scheme requires single-photon sources, beamsplitters, number-resolved photodetectors, fast-feedforward, and an optical quantum memory.

We consider the van der Waals force involving excited atoms in general environments, constituted by magnetodielectric bodies. We develop a dynamical approach studying the dynamics of the atoms and the field, mutually coupled. When only one atom is excited, our dynamical theory suggests that for large distances the van der Waals force acting on the ground-state atom is monotonic, while the force acting in the excited atom is spatially oscillating. We show how this latter force can be related to the known oscillating Casimir-Polder force on an excited atom near a (ground-state) body. Our force also reveals a population-induced dynamics: for times much larger that the atomic lifetime the atoms will decay to their ground states leading to the van der Waals interaction between ground-state atoms.

We present our experimental investigation of an optical Raman transition between the magnetic clock states of ${}^{87}\mathrm{Rb}$ in an atom chip magnetic trap. The transfer of atomic population is induced by a pair of diode lasers which couple the two clock states off-resonantly to an intermediate state manifold. This transition is subject to destructive interference of two excitation paths, which leads to a reduction of the effective two-photon Rabi frequency. Furthermore, we find that the transition frequency is highly sensitive to the intensity ratio of the diode lasers. Our results are well described in terms of light shifts in the multilevel structure of ${}^{87}\mathrm{Rb}$. The differential light shifts vanish at an optimal intensity ratio, which we observe as a narrowing of the transition linewidth. We also observe the temporal dynamics of the population transfer and find good agreement with a model based on the system's master equation and a Gaussian laser beam profile. Finally, we identify several sources of decoherence in our system, and discuss possible improvements.

The properties of molecule-optical elements such as lenses or prisms based on the interaction of molecules with optical fields depend in a crucial way on the molecular quantum state and its alignment created by the optical field. Herein, we consider the effects of state-dependent alignment in estimating the optical dipole force acting on the molecules and, to this end, introduce an effective polarizability which takes proper account of molecular alignment and is directly related to the alignment-dependent optical dipole force. We illustrate the significance of including molecular alignment in the optical dipole force by a trajectory study that compares previously used approximations with the present approach. The trajectory simulations were carried out for an ensemble of linear molecules subject to either propagating or standing-wave optical fields for a range of temperatures and laser intensities. The results demonstrate that the alignment-dependent effective polarizability can serve to provide correct estimates of the optical dipole force, on which a state-selection method applicable to nonpolar molecules could be based. We note that an analogous analysis of the forces acting on polar molecules subject to an inhomogeneous static electric field reveals a similarly strong dependence on molecular orientation.

The coherent photon scattering of atoms in an atomic array is studied. It is found that due to cooperative photon exchanges, the excitation probability of an atom in an array parallel to the direction of laser propagation ($\widehat{\mathit{k}}$) will either grow or decay along $\widehat{\mathit{k}}$, depending on the detuning of the laser. The symmetry of the system for atomic separations of $a=j\lambda /2$ causes the excitation distribution and scattered radiation to abruptly become symmetric about the center of the array, where $j$ is an integer and $\lambda$ is the transition wavelength. For atomic separations of $a<\lambda /2$, a collection of nonradiating states ($\mathrm{\Gamma }\sim 0$) disrupts the described trend. In order to interpret this surprising result, a band-structure calculation in the $N\to \infty$ limit is conducted, where the decay rates and the collective Lamb shifts of the eigenmodes versus quasimomentum are obtained. This calculation shows that the collective exchange of photons in an array strongly affects its scattered radiation, allowing one to easily manipulate the collective Lamb shift and directly excite either superradiant or subradiant eigenmodes by correctly choosing the angle of the driving laser.

Witnessing entanglement is crucial in quantum information processing. With properly preparing ancillary states, it has been shown previously that genuine entanglement can be witnessed without trusting measurement devices. In this work we generalize the scenario and show that generic multipartite entanglement structures, including entanglement of subsystems and entanglement depth, can be witnessed via measurement-device-independent means. As the original measurement-device-independent entanglement witness scheme exploits only one out of four Bell measurement outcomes for each party, a direct generalization to multipartite quantum states will inevitably cause inefficiency in entanglement detection after taking account of statistical fluctuations. To resolve this problem, we also present a way to utilize all the measurement outcomes. The scheme is efficient for multipartite entanglement detection and can be realized with state-of-the-art technologies.

Dynamic second-order hyperpolarizabilities of atomic noble gases and their multiply ionized ions are computed using ab initio multiconfigurational self-consistent field cubic response theory. For each species, the calculations are performed at wavelengths ranging from the static regime to those about 100 nm above the first multiphoton resonance. The second-order hyperpolarizability coefficients progressively decrease as the electrons are removed from the system, in qualitative agreement with phenomenological calculations. In higher ionization states, the resulting nonlinear refractive index becomes less dispersive as a function of wavelength. At each ionization stage, the sign of the optical response depends on the number of electrons in the system and, if multiple state symmetries are possible, on the spin of the particular quantum state. Thus, for $\mathrm{N}{\mathrm{e}}^{3+}$ and $\mathrm{N}{\mathrm{e}}^{4+}$, the hyperpolarizability coefficients in the low-spin states (${}^{2}P_u$, and ${}^{1}S_g$, respectively) are positive, while in the high-spin states (${}^{4}S_u$, and ${}^{3}P_g$) they are negative. However, for doubly, triply, and quadruply charged Ar and Kr these coefficients do not undergo a sign change.

Nonresonant spontaneous bremsstrahlung of an electron scattered by a nucleus in the field of two moderately strong pulsed waves is studied theoretically. The process is studied in detail within the interference kinematic region. This region is determined by scattering of particles in the same plane at predetermined angles, at which stimulated absorption and emission of photons of external pulsed waves by an electron occur in a correlated manner. It is shown that the probability of the partial process with correlated emission (absorption) by an electron of the equal number of photons of the both waves is of an order of the magnitude greater than the corresponding probability in any other scattering kinematics. The cross section of spontaneous bremsstrahlung in two pulsed waves may be two times greater than the cross section of a free-field process after summation over all stimulated processes of correlated emission and absorption. Obtained results may be experimentally verified, for example, by scientific facilities at sources of pulsed laser radiation (SLAC, FAIR, ELI, XCELS).

We study the photon energy sharing between the photoelectron and the nuclei in the process of above-threshold multiphoton dissociative ionization of CO molecules by measuring the joint energy spectra. The experimental observation shows that the electron-nuclear energy sharing strongly depends on the vibrational state. The experimental observation shows that both the energy deposited to the nuclei of $\mathrm{C}{\mathrm{O}}^{+}$ and the emitted photoelectron decrease with increasing the vibrational level. Through studying the vibrationally resolved nuclear kinetic energy release and photoelectron energy spectra at different laser intensities, for each vibrational level of $\mathrm{C}{\mathrm{O}}^{+}$, the nuclei always tend to take the same amount of energy in every vibrational level regardless of the laser intensity, while the energy deposited to the photoelectron varies with respect to the laser intensity because of the ponderomotive shifted energy and the distinct dissociative ionization mechanisms.

The capability of generating two intense, femtosecond x-ray pulses with a controlled time delay opens the possibility of performing time-resolved experiments for x-ray-induced phenomena. We have applied this capability to study the photoinduced dynamics in diatomic molecules. In molecules composed of low-$Z$ elements, $K$-shell ionization creates a core-hole state in which the main decay mode is an Auger process involving two electrons in the valence shell. After Auger decay, the nuclear wave packets of the transient two-valence-hole states continue evolving on the femtosecond time scale, leading either to separated atomic ions or long-lived quasibound states. By using an x-ray pump and an x-ray probe pulse tuned above the $K$-shell ionization threshold of the nitrogen molecule, we are able to observe ion dissociation in progress by measuring the time-dependent kinetic energy releases of different breakup channels. We simulated the measurements on ${\mathrm{N}}_2$ with a molecular dynamics model that accounts for $K$-shell ionization, Auger decay, and the time evolution of the nuclear wave packets. In addition to explaining the time-dependent feature in the measured kinetic energy release distributions from the dissociative states, the simulation also reveals the contributions of quasibound states.

Tripartite entangled states, such as Greenberger-Horne-Zeilinger and W states, are typically generated by manipulating two pairs of polarization-entangled photons in bulk optics. Here we propose a scheme to generate W states that are entangled in the energy degree of freedom in an integrated optical circuit. Our approach employs photon pairs generated by spontaneous four-wave mixing in a microring resonator. We also present a feasible procedure for demonstrating the generation of such a state, and we compare polarization-entangled and energy-entangled schemes for the preparation of W states.

High-order-harmonic generation in α-quartz $\mathrm{Si}{\mathrm{O}}_2$ is theoretically investigated under a strong laser field by solving the extended semiconductor Bloch equations. The accurate band structures as well as dipole moments between different bands are obtained from state-of-the-art first-principles calculations. We find that the shapes of $k$-space-dependent dipole moments play an important role in harmonic generation. The calculated results show that harmonic conversion efficiency is significantly enhanced and the cutoff energy is distinctly increased when the dipole moments change greatly along a valley in the $k$ direction in the solid. Based on that dependence on the dipole moment, we also show that symmetry groups greatly affect the harmonic spectra from the solid materials. Moreover, a two-color synthesized field is used to achieve a supercontinuum harmonic spectrum near the cutoff region, and isolated attosecond pulses can be obtained directly by filtering out the harmonic radiation. We hope the contribution presented in this work provides a useful reference for future studies on laser-crystal interactions.

We first show that the many-body Hamiltonian governing the physical properties of an alkaline-earth ${}^{173}\mathrm{Yb}$ Fermi gas across the recently realized orbital Feshbach resonance is exactly analogous to that of two-band $s$-wave superconductors with contact interactions; i.e., even though the free-particle bands have a tunable energy offset in between and are coupled by a Josephson-type attractive interband pair scattering, the intraband interactions have exactly the same strength. We then introduce two intraband order parameters within the BCS mean-field approximation and investigate the competition between their in-phase and out-of-phase (i.e., the so-called $\pi$-phase) solutions in the entire BCS-BEC evolution at zero temperature.

The photonic analog of the paramagnetic to spin-glass phase transition in disordered magnetic systems, signaled by the phenomenon of replica symmetry breaking, has been reported using random lasers as the photonic platform. We report here a demonstration of replica symmetry breaking in a one-dimensional photonic system consisting of an erbium-doped random fiber laser operating in the continuous-wave regime. The system is based on a unique random fiber grating system which plays the role of random scattering, providing the disordered feedback mechanism. The clear transition from a photonic paramagnetic to a photonic spin-glass phase, characterized by the Parisi overlap parameter, was verified and indicates the glassy random-fiber-laser behavior.

Although superconducting systems provide a promising platform for quantum computing, their networking poses a challenge because they cannot be interfaced to light, the medium used to send quantum signals through channels at room temperature. We show that mechanical oscillators can mediate such coupling and light can be used to measure the joint state of two distant qubits. The measurement provides information on the total spin of the two qubits such that entangled qubit states can be postselected. Entanglement generation is possible without ground-state cooling of the mechanical oscillators for systems with optomechanical cooperativity moderately larger than unity; in addition, our setup tolerates a substantial transmission loss. The approach is scalable to the generation of multipartite entanglement and represents a crucial step towards quantum networks with superconducting circuits.