Table of contents

Canonical quantum mechanics postulates Hermitian Hamiltonians to ensure real eigenvalues. Counterintuitively, a non-Hermitian Hamiltonian, satisfying combined parity-time (PT) symmetry, could display entirely real spectra above some phase-transition threshold. This stems from the existence of a parameter in the Hamiltonian governing characteristics features of eigenvalues and eigenfunctions. Varying this parameter causes real eigenvalues to coalesce and become complex conjugate pairs, signaling the occurrence of a nontrivial phase transition and the breakdown of PT symmetry. Such an appealing discovery has aroused extensive theoretical interest in extending canonical quantum theory by including non-Hermitian but PT-symmetric operators in the last two decades. Despite much fundamental theoretical success in the development of PT-symmetric quantum mechanics, an experimental observation of pseudo-Hermiticity remains elusive as these systems with complex potential seem absent in Nature. But nevertheless, the notion of PT symmetry has survived in many other branches of physics including optics, photonics, AMO physics, acoustics, electronic circuits, and material science over the past ten years, where a judicious balance of gain and loss constitutes ingeniously a PT-symmetric system. Here, although we concentrate upon reviewing recent progress on PT symmetry in optical microcavity systems, we also wish to present some new results that may help to accelerate the research in the area. These compound photonic structures with gain and loss provide a powerful platform for testing various theoretical proposals on PT symmetry, and initiate new possibilities for shaping optical beams and pulses beyond conservative structures. Throughout this article there is an effort to clearly present the physical aspects of PT-symmetry in optical microcavity systems, but mathematical formulations are reduced to the indispensable ones. Readers who prefer strict mathematical treatments should resort to the extensive list of references. Despite the rapid progress on the subject, new ideas and applications of PT symmetry using optical microcavities are still expected in the future.

We use finite element simulations in both the frequency and the time-domain to study the terahertz resonance characteristics of a metamaterial (MM) comprising a spiral connected to a straight arm. The MM acts as a RLC circuit whose resonance frequency can be precisely tuned by varying the characteristic geometrical parameters of the spiral: inner and outer radius, width and number of turns. We provide a simple analytical model that uses these geometrical parameters as input to give accurate estimates of the resonance frequency. Finite element simulations show that linearly polarized terahertz radiation efficiently couples to the MM thanks to the straight arm, inducing a current in the spiral, which in turn induces a resonant magnetic field enhancement at the center of the spiral. We observe a large (approximately 40 times) and uniform (over an area of ∼10 μm²) enhancement of the magnetic field for narrowband terahertz radiation with frequency matching the resonance frequency of the MM. When a broadband, single-cycle terahertz pulse propagates towards the MM, the peak magnetic field of the resulting band-passed waveform still maintains a six-fold enhancement compared to the peak impinging field. Using existing laser-based terahertz sources, our MM design allows to generate magnetic fields of the order of 2 T over a time scale of several picoseconds, enabling the investigation of nonlinear ultrafast spin dynamics in table-top experiments. Furthermore, our MM can be implemented to generate intense near-field narrowband, multi-cycle electromagnetic fields to study generic ultrafast resonant terahertz dynamics in condensed matter.

The nonequilibrium quantum dynamics of few boson ensembles which experience a spatially modulated interaction strength and are confined in finite optical lattices is investigated. We utilize a cosinusoidal spatially modulated effective interaction strength which is characterized by its wavevector, inhomogeneity amplitude, interaction offset and a phase. Performing quenches either on the wavevector or the phase of the interaction profile an enhanced imbalance of the interatomic repulsion between distinct spatial regions of the lattice is induced. Following both quench protocols triggers various tunneling channels and a rich excitation dynamics consisting of a breathing and a cradle mode. All modes are shown to be amplified for increasing inhomogeneity amplitude of the interaction strength. Especially the phase quench induces a directional transport enabling us to discern energetically, otherwise, degenerate tunneling pathways. Moreover, a periodic population transfer between distinct momenta for quenches of increasing wavevector is observed, while a directed occupation of higher momenta can be achieved following a phase quench. Finally, during the evolution regions of partial coherence are revealed between the predominantly occupied wells.

We report on the precision measurement of aluminum atoms ${}^{2}{P}_{1/2}-{}^{2}{S}_{1/2}$ transition at 394 nm and ${}^{2}{P}_{3/2}-{}^{2}{S}_{1/2}$ transition at 396 nm in a hollow-cathode lamp. Both absorption and saturated absorption spectra are measured. From the absorption spectra, the Doppler linewidth is estimated to be 2.65 GHz. The saturated absorption spectra are analyzed based on a velocity-changing collisions model. With a frequency comb calibrated wavemeter, the frequencies of ${}^{2}{P}_{1/2}(F^{\prime} =3)-{}^{2}{S}_{1/2}(F=2)$ transition and ${}^{2}{P}_{3/2}(F^{\prime} =4)-{}^{2}{S}_{1/2}(F=3)$ transition are measured to be 759.905 204(1) THz and 756.547 133(3) THz, respectively. The hyperfine coupling constants of aluminum atoms are determined, and are compared with previously reported measurement results and theoretical calculation results. Reasonable agreement is found for the magnetic dipole constant (A constant), while the electric quadrupole constant (B constant) has a large deviation.

We report absolute measurements of doubly differential electron–atom bremsstrahlung cross sections for energies in the keV region and elements with atomic numbers 6, 13, 52, 73 and 79. Thin targets were irradiated at the low-energy beam line of the São Paulo Microtron with 20, 50, 75 and 100 keV electrons. For each element and energy, the photon spectra were collected simultaneously with three HPGe detectors at the emission angles of 35°, 90° and 131°. The deconvolution of the bremsstrahlung spectra was done adopting an analytical model for the spectrometers' response functions. The resulting doubly differential cross sections are compared with the available partial-wave calculations of ordinary bremsstrahlung. Based on this comparison, we discuss some features of the experimental spectra that might be related to the emission of polarization bremsstrahlung.

This paper analyzes the absorption line profile at 21 cm for the hydrogen atom in the interstellar medium (ISM). The hydrogen atom is treated as a three-level system illuminated by a powerful light source at neighboring resonances corresponding to the hyperfine splitting of the ground state and Lyman-α (Ly_α) transition. The field acting upon the resonances gives rise to physical processes, which can be explained as interfering pathways between different transitions. The paper considers particular cases when the 21 cm line profile is substantially modified by the Ly_α transition. A correction to the optical depth is introduced as a result of theory. It is shown that the correction can be considerable and should be taken into account when determining the column density of hydrogen atoms in the ISM. The paper also deals with the effects of non-Doppler broadening and frequency shift.

The theory of fast coplanar symmetric (e, 2e) reactions is analyzed. The calculation is performed in the framework of Coulomb-Volkov-Born approximation, where the initial and final electrons are described by Volkov wave functions, while the interaction of the fast incident electron with the target atom is treated in the first Born approximation. The state of the ejected electron is described by a Coulomb-Volkov wave function. We have considered two (e, 2e) spectroscopy regimes: (i) the regime in which the momentum transfer K is large, but the recoil momentum Q of the ion is small or moderate; and (ii) the regime of large K and large Q. The influence of the laser frequency on the angular distribution is analyzed and several illustrative examples are discussed.

This paper reports the rotational excitation of the alkali sodium hydroxide molecule (${X}^{1}{{\rm{\Sigma }}}^{+}$) by collision with helium atom. We present a new 2D potential energy surface (PES) for NaOH–He van der Waals complex. The PES was computed at the coupled cluster level of theory with single, double and perturbative triple excitation (CCSD(T)) using the aug-cc-pVQZ basis sets for the four atoms with bound functions. A global minimum of −100.15 cm⁻¹ is found at linear geometry He–NaOH and a local minimum of −21.94 cm⁻¹ is located at linear geometry He–HONa. The scattering calculations were performed, via close coupling approach, for a grid of total energies up to 1500 cm⁻¹ to ensure converged state-to-state rate coefficients for kinetic temperatures ranging from 5 K up to 300 K among the first 13 rotational levels. Propensity rules that favor Δj = ±1 transitions are found. These new rates have great potential for NaOH detection in the interstellar medium.

A theoretical scheme is proposed to investigate the formation of three coupled slow temporal vector optical solitons in a lifetime-broadened seven-state atomic medium. We demonstrate that the three polarized components of a low intensity linear-polarized pulsed probe field can evolve into three coupled slow temporal vector optical solitons due to the fact that group-velocity dispersion can be well compensated by the self- and cross-phase-modulation effects. Moreover, this atomic system could support the existence of various types of three coupled slow temporal vector solitons, such as bright–bright–bright, bright–dark–bright, dark–dark–dark, and bright–dark–dark vector solitons.

We performed photoelectron spectroscopy using femtosecond extreme-ultraviolet (XUV) pulses from a free-electron laser and femtosecond near-infrared (NIR) pulses from a synchronized laser, and succeeded in measuring photoelectrons from highly excited Rydberg states of molecular ions ${{{\rm{CS}}}_{2}}^{+}.$ Such excited states are prepared via a sequential process of photoionization and subsequent photoexcitation during a short pulse of XUV, and then a band of the Rydberg excited states is probed with a synchronized NIR pulse. The photoelectron spectrum has been well explained by our hydrogenic Rydberg orbital model. The present result demonstrates that the two-color experiments of XUV free-electron lasers and NIR laser makes it possible to observe highly excited states of molecular ions. This implies that the present approach provides ones a new spectroscopic tool for studying excited states of various molecular ions.

Analytical solutions for the emitted nonlinear Thomson scattering spectrum with radiation reaction (RR) included are provided for a single electron colliding with a high intensity laser pulse. Further expressions are derived for the peak intensity for a given harmonic order and the downshift of the frequency when RR is included. Controlling the spectrum with shaping of the laser pulse frequency (chirp) has been investigated. It is shown that chirping of the laser pulse gives a distinct fingerprint of the effect of RR in the spectrum.