An angle-resolved x-ray spectroscopic scheme is presented for determining the hyperfine splitting of highly charged ions. For heliumlike ions, in particular, we propose to measure either the angular distribution or polarization of the $1s2p{}^{3}P_1,F\to 1s^2{}^{1}S_0,F_f$ emission following the stimulated decay of the initial $1s2s{}^{1}S_0,F_i$ level. It is found that both the angular and polarization characteristics of the emitted x-ray photons strongly depend on the (relative) splitting of the partially overlapping hyperfine $1s2p{}^{3}P_1,F$ resonances and may thus help resolve their hyperfine structure. The proposed scheme is feasible with present-day photon detectors and allows a measurement of the hyperfine splitting of heliumlike ions with a relative accuracy of about ${10}^{-4}$.

We present an experimental determination of the $4S_{1/2}\to 6S_{1/2}$ transition frequency in atomic potassium ${}^{39}\mathrm{K}$, using direct frequency-comb spectroscopy. The output of a stabilized optical frequency comb was used to excite a thermal atomic vapor. The repetition rate of the frequency comb was scanned and the transitions were excited using stepwise two-photon excitation. The center-of-gravity frequency for the transition was found to be ${\nu }_{\mathrm{cog}}=822951698.09\left(13\right)$ MHz and the measured hyperfine $A$ coefficient of the $6S_{1/2}$ state was $21.93\left(11\right)$ MHz. The measurements are in agreement with previous values and represent an improvement by a factor of 700 in the uncertainty of the center-of-gravity measurement.

Formation of triply ionized states upon the creation of $4d$ inner-shell holes in atomic Hg is investigated by using synchrotron radiation of 730 eV photon energy and a versatile multielectron coincidence detection technique in combination with multiconfiguration Dirac-Fock calculations. By carefully selecting Coster-Kronig electrons detected only in coincidence with a $4d$ photoelectron, the Coster-Kronig spectrum has been extracted and the corresponding branching ratios of the $4d$ hole have been determined. The results are found to differ from previously established experimental ratios based on electron impact ionization but to agree now better with theory. We also present an Auger cascade analysis of pathways leading to triply ionized states of atomic Hg upon removal of a $4d$ inner-shell electron.

The origin of the complex structure of $L{\gamma }_1$ $\left(L_2{N}_4\right)$, $L{\gamma }_2$ $\left(L_1{N}_2\right)$, $L{\gamma }_3$ $\left(L_1{N}_3\right)$, and $L{\gamma }_6$ $\left(L_2{O}_4\right)$ x-ray lines of thorium in high-resolution spectra induced by oxygen projectiles has so far resisted reliable quantitative interpretation. Therefore, the detailed structure predictions for satellite (additional holes in $M,N,O$, and/or $P$ shells) and hypersatellite (additional hole in $L$ shell) $L\gamma$ x-ray lines of thorium being the results of extensive multiconfiguration Dirac-Fock calculations have been performed. Our predictions reproduce with the excellent precision the positions and shapes of characteristic parts of above high-resolution $L\gamma$ x-ray spectrum of thorium what indicates that our study has been carried out with very high accuracy. The results of this study are the precursor for proper quantitative interpretation of the complex origin of $L{\gamma }_1,L{\gamma }_2,L{\gamma }_3$, and $L{\gamma }_6$ lines in high-resolution x-ray spectra of thorium induced by different light and heavy projectiles.

We present a study of nonsequential double-recombination (NSDR) high-harmonic generation (HHG) in a molecularlike system. We have calculated the HHG spectrum for a wide range of internuclear distances, and using a Coulomb-corrected three-step model we are able to analyze and predict the observed NSDR HHG cutoffs precisely for all internuclear distances. It is shown through this Coulomb-corrected three-step (CC-TSM) model that there is an intrinsic dependence on the location of the nuclei in the NSDR HHG process not seen in one-electron HHG. This dependence originates from the strong electron correlation in the NSDR HHG process, and it modifies the classically allowed return energies which in return changes the cutoffs observed in the HHG spectra. It is observed that the CC-TSM correctly predicts cutoffs at all internuclear distances with differences of more than six harmonics being observed between the CC-TSM and the normal three-step model for the laser parameters used. We also observe that the NSDR HHG process changes for internuclear distances of $R\gtrsim 8–9$ a.u., which is proposed to stem from a change in the charge-transfer dynamics within the molecule. For large internuclear distances of $R\gtrsim 13$ a.u., we observe a clear signature of the point of emission for the first electron emitted in the NSDR HHG signal and we also see signs of molecular exchange paths contributing to the HHG spectrum for these internuclear distances.

We report a method for loading cold atoms into an optical trap with high initial phase-space density (PSD). When the trap beam is overlapped with atoms in optical molasses of optimized parameters including large cooling beam detuning compared with conventional detuning used for a magneto-optical trap (MOT), more than $3\times {10}^6$ rubidium atoms with an initial temperature less than 20 $\mu \mathrm{K}$ are loaded into a single beam trap. The obtained maximum initial PSD is estimated to be $1.1\times {10}^{-3}$, which is one or two orders of magnitude greater than that achieved with the conventional loading into an optical trap from atoms in a MOT. The proposed method is promising for creating a quantum gas with a large number of atoms in a short evaporation time.

We analyze the dynamics of two-component vector solitons, namely, dark-bright solitons, via the variational approximation in Bose-Einstein condensates. The system is described by a vector nonlinear Schrödinger equation appropriate to multicomponent Bose-Einstein condensates. The variational approximation is based on a hyperbolic tangent (hyperbolic secant) for the dark (bright) component, which leads to a system of coupled ordinary differential equations for the evolution of the ansatz parameters. We obtain the oscillation dynamics of two-component dark-bright solitons. Analytical calculations are performed for same-width components in the vector soliton, and numerical calculations extend the results to arbitrary widths. We calculate the binding energy of the system and find it to be proportional to the intercomponent coupling interaction and numerically demonstrate the breakup or unbinding of a dark-bright soliton. Our calculations explore observable eigenmodes, namely, the internal oscillation eigenmode and the Goldstone eigenmode. We find analytically that the number of atoms in the bright component is required to be less than the number of atoms displaced by the dark soliton in the other component in order to find the internal oscillation eigenmode of the vector soliton and support the existence of the dark-bright soliton. This outcome is confirmed by numerical results. Numerically, we find that the oscillation frequency is amplitude independent. For dark-bright solitons in ${}^{87}\mathrm{Rb}$ we find that the oscillation frequency range is 90 to 405 Hz and therefore observable in multicomponent Bose-Einstein condensate experiments.

We consider the formation of order in a quasi-two-dimensional antiferromagnetic spin-1 condensate quenched from an easy-axis to an easy-plane nematic phase. We define the relevant order parameter to quantify the spin-nematic degrees of freedom and study the evolution of the spin-nematic and superfluid order during the coarsening dynamics using numerical simulations. We observe dynamical scaling in the late-time dynamics, with both types of order extending across the system with a diffusive growth law. We identify half-quantum vortices as the relevant topological defects of the ordering dynamics and demonstrate that the growth of both types of order is determined by the mutual annihilation of these vortices.

The realization of experiments in ultracold multicomponent mixtures, also involving more atomic species, opened the way to the study of exotic quantum phases and unconventional superfluidity, as, for instance non-Abelian superfluid phases. In this paper we study the occurrence of non-Abelian symmetry-locked superfluid states in ultracold fermionic mixtures with four components, showing that such states can be studied in current day experiments with ${}^{171}\mathrm{Yb}\text{−}{}^{173}\mathrm{Yb}$ isotopes. We study the phase diagram in the presence of an attractive interaction between the species of two pairs of the mixture, and general (also repulsive) interactions between the species of each pair. This system can be physically realized, e.g., in mixtures of two different earth-alkaline species, both of them with two hyperfine levels selectively populated. We find an extended region of the diagram exhibiting a two-flavors superfluid symmetry-locking (TFSL) phase. The locking corresponds to the presence of a order parameter involving—in all the possible and distinct permitted ways—two fermions, one of them belonging to the first pair and the second to the other one. This TSFL phase is present also for not too large repulsive intrapair interactions and it is characterized by a global non-Abelian symmetry group obtained by locking together two independent invariance groups of the corresponding normal state. Explicit estimates are reported for the mixture of the fermionic isotopes ${}^{171}\mathrm{Yb}\text{−}{}^{173}\mathrm{Yb}$, indicating that the TFSL phase can be achieved also without tuning the interactions between $\mathrm{Yb}$ atoms.

Quenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA), focus on the role of motion near separatrices, and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as $O(1/lnN)$, where $N$ is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady-state value is a damped oscillation. The damping is Gaussian in time with a time scale of $O\left[{(lnN)}^2\right]$. We also give the quantitative dependence of the steady-state value and the damping time on the system parameters. Our results are confirmed with numerical TWA simulations.

We have investigated theoretically the reflectivity, quality factor, and eigenfrequency for a single slab with zero refractive index. We demonstrate that optical bound states in the continuum can be achieved by the various zero-refractive-index slabs made of epsilon-near-zero, impedance-machted zero-index, or mu-near-zero materials. Moreover, by analytically investigating the frequency of the resonant reflection and resonant transmission, when the quality factor becomes infinity, these two frequencies are precisely equal. For the mu-near-zero slab, the bound states in the continuum are observed at arbitrary incident angles by analyzing the behaviors of complex eigenfrequencies. Our findings may lead to unprecedented high-quality resonators in metamaterials.

We propose and analyze an effective scheme to enhance the optical higher-order sideband generation in a three-cavity array with local parity-time ($\mathcal{PT}$) symmetry. In this three-cavity configuration, a single cavity containing a quantum dot (QD) is coupled to an assisted $\mathcal{PT}$-symmetric combination of two cavities. Beyond the weak-excitation approximation, we derive the analytic formulas used to determine the nonlinear coefficient of the optical second-order sideband (OSS) by employing the perturbation technique. Using experimentally achievable parameters, we identify the conditions under which the assisted $\mathcal{PT}$-symmetric double-cavity system allows us to modify the transmission of the probe field and improve the efficiency of OSS generation beyond what is achievable in a loss-only QD-cavity system. We examine the influence of the $\mathcal{PT}$ phase transition from unbroken- to broken-$\mathcal{PT}$ regimes on the OSS generation. It is found that the efficiency of optical second-order sideband generation can be significantly enhanced when the assisted double-cavity system is in $\mathcal{PT}$-symmetric phase, extremely in the vicinity of the transition point. The present results illustrate the potential to utilize $\mathcal{PT}$-symmetric physical systems for enhancing optical higher-order sidebands and controlling optical frequency combs, as well as to guide the design of experimental implementation.

The threshold properties of very small lasers (down to the nanoscale) are a topic of active research in light of continuous progress in nanofabrication. With the help of a simple rate equation model, we analyze the intrinsic, macroscopic dynamics of threshold crossing for (class B) lasers whose response is adequately described by interplay of the intracavity photon number and the population inversion (energy reservoir). We use the deterministic aspects of the basic rate equations to extract some fundamental time constants from an approximate analysis of laser dynamics in the threshold region. Approximate solutions for the population inversion and the field intensity, up to the point where the latter reaches macroscopic levels, are found and discussed. The resulting time scales characterize the laser's ability to respond to perturbations (external modulation or intrinsic fluctuations in the lasing transition region). Numerical verifications test the accuracy of these solutions and confirm their validity. The predictions are used to interpret experimental results obtained in mesoscale lasers (VCSELs) and to speculate about their extension to nanolasers.

An all-optical method of setting a disordered password on different schemes of photonic memory is theoretically studied. While photons are regarded as ideal information carriers, it is imperative to implement such data protection on all-optical storage. However, we wish to address the intrinsic risk of data breaches in existing schemes of photonic memory. We theoretically demonstrate a protocol using spatially disordered laser fields to encrypt data stored on an optical memory, namely, encrypted photonic memory. To address the broadband storage, we also investigate a scheme of disordered echo memory with a high fidelity approaching unity. The proposed method increases the difficulty for the eavesdropper to retrieve the stored photon without the preset password even when the randomized and stored photon state is nearly perfectly cloned. Our results pave ways to significantly reduce the exposure of memories, required for long-distance communication, to eavesdropping and therefore restrict the optimal attack on communication protocols. The present scheme also increases the sensitivity of detecting any eavesdropper and so raises the security level of photonic information technology.

Free classical particles have well-defined momentum and position, while free quantum particles have well-defined momentum but a position fully delocalized over the sample volume. We develop a many-body formalism based on wave-packet operators that connects these two limits, the thermal energy being distributed between the state spatial extension and its thermal excitation. The corresponding mixed quantum-classical states, which render the Boltzmann operator diagonal, are the physically relevant states when the temperature is finite. The formulation of many-body Hamiltonians in terms of these thermally excited wave packets and the resulting effective scatterings is provided.

Optical communication channels are ultimately quantum mechanical in nature, and we must therefore look beyond classical information theory to determine their communication capacity as well as to find efficient encoding and decoding schemes of the highest rates. Thermal channels, which arise from linear coupling of the field to a thermal environment, are of particular practical relevance; their classical capacity has been recently established, but their quantum capacity remains unknown. While the capacity sets the ultimate limit on reliable communication rates, it does not promise that such rates are achievable by practical means. Here we construct efficiently encodable codes for thermal channels which achieve the classical capacity and the so-called Gaussian coherent information for transmission of classical and quantum information, respectively. Our codes are based on combining polar codes with a discretization of the channel input into a finite “constellation” of coherent states. Encoding of classical information can be done using linear optics.

We consider quantum cellular automata on a body-centered cubic lattice and provide a simple derivation of the only two homogenous, local, isotropic, and unitary two-dimensional automata [G. M. D'Ariano and P. Perinotti, Phys. Rev. A 90, 062106 (2014)]. Our derivation relies on the notion of Gram matrix and emphasizes the link between the transition matrices that characterize the automata and the body-centered cubic lattice: The transition matrices essentially are the matrix representation of the vertices of the lattice's primitive cell. As expected, the dynamics of these two automata reduce to the Weyl equation in the limit of small wave vectors and continuous time. We also briefly examine the four-dimensional case, where we find two one-parameter families of automata that reduce to the Dirac equation in a suitable limit.

We explore a possibility that astrophysical data may contain spectra of metastable nuclei belonging to the island of stability where the nuclei have a magic number of neutrons of $N=184$. The laboratory-produced nuclei have a significantly smaller number of neutrons. To identify spectra of the $N=184$ isotopes of these nuclei and their neutron-rich superheavy decay products in astrophysical data we calculate the isotope shift which should be added to the laboratory-measured wavelengths. The results for the isotope shifts in the strongest optical electromagnetic transitions in No, Lr, Nh, Fl, and $Z=120$ elements are presented.

The self-similar energy spectrum of a particle in a periodic potential under a magnetic field, known as the Hofstadter butterfly, is determined by the lattice geometry as well as the external field. Recent realizations of artificial gauge fields and adjustable optical lattices in cold-atom experiments necessitate the consideration of these self-similar spectra for the most general two-dimensional lattice. In a previous work [F. Yılmaz et al., Phys. Rev. A 91, 063628 (2015)], we investigated the evolution of the spectrum for an experimentally realized lattice which was tuned by changing the unit-cell structure but keeping the square Bravais lattice fixed. We now consider all possible Bravais lattices in two dimensions and investigate the structure of the Hofstadter butterfly as the lattice is deformed between lattices with different point-symmetry groups. We model the optical lattice with a sinusoidal real-space potential and obtain the tight-binding model for any lattice geometry by calculating the Wannier functions. We introduce the magnetic field via Peierls substitution and numerically calculate the energy spectrum. The transition between the two most symmetric lattices, i.e., the triangular and the square lattices, displays the importance of bipartite symmetry featuring deformation as well as closing of some of the major energy gaps. The transitions from the square to rectangular lattice and from the triangular to centered rectangular lattices are analyzed in terms of coupling of one-dimensional chains. We calculate the Chern numbers of the major gaps and Chern number transfer between bands during the transitions. We use gap Chern numbers to identify distinct topological regions in the space of Bravais lattices.