We consider a nonstationary circuit quantum electrodynamics setup in which a three-level artificial atom in the $\mathrm{\Delta }$ configuration interacts with a single-mode cavity field of natural frequency $\omega$. It is demonstrated that when some atomic energy level(s) undergoes a weak harmonic modulation, photons can be generated from vacuum via effective one- and three-photon transitions, while the atom remains approximately in the ground state. These phenomena occur in the dispersive regime when the modulation frequency is accurately tuned near $\omega$ and $3\omega$, respectively, and the generated field states exhibit strikingly different statistics from the squeezed vacuum state attained in the standard cavity dynamical Casimir effect.

In this study, we present a statistical analysis of the level structures of four highly charged actinide ions: Bk xii, Cf xii, No xiii, and Md xiv. In these ions, $5f$ wave-function contraction gives rise to a manifold of levels arising from configurations with partially filled $5f$ and $6p$ subshells. The cumulative effects of configuration interaction (CI) between these configurations results in a complete breakdown of the independent particle model used in the labeling of the states and leads to the formation of so-called “compound” states. Properties of the calculated level structures have been analyzed using the techniques of random-matrix theory (RMT). Standard statistical measures, such as the repulsion parameter $q$, the covariance of adjacent spacings $\text{cov}(s_i,s_{i+1})$, and the Dyson-Mehta statistic ${\mathrm{\Delta }}_3\left(L\right)$, have been computed for specific $J^{\pi }$ interacting sets belonging to the four aforementioned ion stages. In the majority of cases, these calculations are found to be in very good agreement with the RMT-predicted values for these quantities. This study therefore extends previous identifications of RMT-like level fluctuations in the level spectra of lanthanide ions to high-$Z$, moderately charged actinide ions.

We study here higher-order two-loop and three-loop logarithmic contributions to the Lamb shift in light hydrogenlike atoms. We have found the leading logarithmic contributions in order ${\alpha }^2{\left(Z\alpha \right)}^{7}m$ and ${\alpha }^3{\left(Z\alpha \right)}^{6}m$ for the arbitrary states. Those terms are double logarithmic for the $ns$ states and single logarithmic for the $np$ states and vanish for the states with $l\ge 2$. We have also obtained the leading (single-logarithmic) contribution to the specially normalized difference for the Lamb shift of the $ns$ states ${\mathrm{\Delta }}_L\left(n\right)=E_L\left(1s\right)-n^3{E}_L\left(ns\right)$, which is important for a combined evaluation of the overall set of the experimental data available on various transitions in hydrogen and deuterium.

We perform two-photon photoassociation spectroscopy of the heteronuclear CsYb molecule to measure the binding energies of near-threshold vibrational levels of the $X{}^2{\mathrm{\Sigma }}_{1/2}^{+}$ molecular ground state. We report results for ${}^{133}\mathrm{Cs}{}^{170}\mathrm{Yb}$, ${}^{133}\mathrm{Cs}{}^{173}\mathrm{Yb}$, and ${}^{133}\mathrm{Cs}{}^{174}\mathrm{Yb}$, in each case determining the energy of several vibrational levels including the least-bound state. We fit an interaction potential based on electronic structure calculations to the binding energies for all three isotopologs and find that the ground-state potential supports 77 vibrational levels. We use the fitted potential to predict the interspecies $s$-wave scattering lengths for all seven Cs+Yb isotopic mixtures.

The creation of artificial gauge fields in neutral ultracold atom systems has opened the possibility to study the effects of spin-orbit coupling terms in clean environments. This work considers the multichannel scattering properties of two atoms confined by a waveguide in the presence of spin-orbit coupling terms within a $K$-matrix scattering framework. The tunability of resonances, induced by the interplay of the external waveguide geometry, the interactions, and the spin-orbit coupling terms, is demonstrated. Our results for the $K$-matrix elements as well as partial and total reflection coefficients for two identical fermions interacting through a finite-range interaction potential in the singlet channel only are compared with those obtained for a strictly one-dimensional effective low-energy Hamiltonian, which uses the effective coupling constant derived in Zhang et al. [Sci. Rep. 4, 4992 (2014)] and Zhang et al. [Phys. Rev. A 88, 053605 (2013)] as input. In the regime where the effective Hamiltonian is applicable, good agreement is obtained, provided the energy dependence of the coupling constant is accounted for. Our approach naturally describes the energy regime in which the bands associated with excited transverse modes lie below a subset of the bands associated with the lowest transverse modes. The threshold behavior is discussed and scattering observables are linked to bound state properties.

We propose a scheme to tailor nanostructured trapping potentials for ultracold atoms. Our trapping scheme combines an engineered extension of repulsive optical dipole forces at short distances and attractive Casimir-Polder forces at long distances between an atom and a nanostructured surface. This extended dipole force scheme takes advantage of excited-state dressing by plasmonically-enhanced optical fields to doubly dress the ground state and create a strongly repulsive potential with spatially tunable characteristics. In this paper, we show that, under realistic experimental conditions, this method can be used to trap Rubidium atoms close to surfaces (tens of nanometers). The influence of the various losses and heating rate mechanism in such traps is characterized. As an example we present a near-field optical lattice with subwavelength period (100 nm) and study the tunability of lattice and trapping depths. Such lattices can enhance energy scales with interesting perspectives for the simulation of strongly-correlated physics. Our method can be extended to other atomic species and to other cold atom near-field hybrid systems.

The intensity distribution in the core region of the Lyman-$\alpha$ line of hydrogen perturbed by neutral hydrogen atoms in the presence of an external cone-rotating electric field has been evaluated using an impact approximation. It was found that the line shape in this region can be described as the sum of four Lorentzian profiles representing contributions coming from transitions between various Stark and Berry sublevels of the resonance and ground states of the hydrogen atom. The effects due to Berry's phase are shown to produce a Lorentzian-shaped feature on each side of the Lyman-$\alpha$ line, with maxima located at frequencies linearly dependent on the angular frequency with which the electric field rotates about the laboratory fixed $z$ axis, as well as on the cosine of the polar angle that the field makes with respect to this axis. The remaining two Lorentzian profiles are due to the Stark effect, and their maxima are located on both sides of the Lyman-$\alpha$ line at frequencies corresponding to the Stark shift.

Recent experiments confirmed that fluctuations beyond the mean-field approximation can lead to self-bound liquid droplets of ultradilute binary Bose mixtures. We proceed beyond the beyond-mean-field approximation and study liquid Bose mixtures by using the variational hypernetted-chain Euler–Lagrange method, which accounts for correlations nonperturbatively. Focusing on the case of a mixture of uniform density, as realized inside large saturated droplets, we study the conditions for stability against evaporation of one of the components (both chemical potentials need to be negative) and against liquid-gas phase separation (spinodal instability), the latter being accompanied by a vanishing speed of sound. Dilute Bose mixtures are stable only in a narrow range near an optimal ratio ${\rho }_1/{\rho }_2$ and near the total energy minimum. Deviations from a universal dependence on the $s$-wave scattering lengths are significant despite the low density.

Magnetic properties of two-dimensional (2D) spin-polarized Fermi gas with dipole-dipole interaction are studied in the presence of external magnetic field at zero temperature. Within perturbation theory and the second quantization formalism, the total energy is explicitly obtained as a function of three dimensionless parameters: the spin polarization, dipolar coupling, and Zeeman parameters. We examine the effects of these agents on the magnetic properties of 2D Fermi gas. The results show that an induced ferromagnetic phase transition is observed only for adequately large values of magnetic field. This paper offers two controllable factors to change the spin polarization of the system.

In the 1930s, two main paradigms for the theoretical description of ferromagnetism were developed: Heisenberg ferromagnetism of localized fermions (e.g., in a lattice), and Bloch or Stoner ferromagnetism of nonlocalized fermions (i.e., in a gas), also called itinerant ferromagnetism. Despite many theoretical predictions, itinerant ferromagnetism has remained elusive in experiments. This ferromagnetic state is predicted to occur for strong repulsive interactions, corresponding to a regime that is very challenging to describe theoretically because there are multiple competing physical effects, including superfluid pairing. In this paper, we point out that the problem of itinerant ferromagnetism for atomic Fermi gases is different from that of electron gases in metals due to the short-range nature of the interatomic interactions. We also show that the standard saddle point used to describe itinerant ferromagnetism of the electron gas in metals does not apply, because in the short-range limit of this approximation the Pauli exclusion principle is violated. As a remedy, we introduce a modified interaction pseudopotential for ultracold gases which includes both local (Hartree) and nonlocal (Fock) terms while preserving the Pauli exclusion principle in the short-range regime. Furthermore, we demonstrate the usefulness of this method to study the existence and stability of itinerant ferromagnetism in ultracold atomic gases. Lastly, we obtain the critical temperature for the ferromagnetic transition as a function of the opposite-spin interaction strength and find a rather good agreement with recent experimental results.

We investigate theoretically the dynamics of the system that consists of a cascade three-level emitter interacting with a single-mode resonator in the deep-strong-coupling regime. We show that the dynamical evolution of the system can only occur in a certain parity chain decided by the initial state, in which the photon population and the initial state probability present periodic collapses and revivals. In particular, we find that the evolution of the dynamics can be controlled by feeding the time-control pulses into the system. Control pluses with specific arrival times can suddenly switch off and on the time evolutions of the system populations and initial state probability when the system is originally in a symmetry superposition state. Physically, the switch-off of the evolution originates from the symmetry breaking of the state, i.e., $\left(\right|g0\rangle +|f0\rangle )/\sqrt{2}\to \left(\right|g0\rangle -|f0\rangle )/\sqrt{2}$. This work offers an all-optical approach to manipulate the dynamics of the system, which might have potential application in modern quantum technology.

Geometrical frustration in either classical or quantum lattice systems is a phenomenon in which the impossibility of satisfying simultaneously all constraints of the system Hamiltonian leads to complex structures with degeneracy of the ground state. We show that geometrical frustration can be observed in a simple setup consisting of classical light propagating along a regular array of evanescently coupled photonic nonlinear waveguides arranged in a honeycomb geometry. Here, geometrical frustration emerges as competition between the number of waveguides and the need to satisfy the stationary constraints of the system. The phenomenology that exhibits these photonic arrays mimics the behavior observed in graphene-related spin lattices. Our results show that two-dimensional arrays of coupled photonic waveguides can be used as a proxy to study geometry frustration in diverse lattice systems.

We show that two-dimensional fractal subsystem symmetry-protected topological phases may serve as resources for universal measurement-based quantum computation. This is demonstrated explicitly for two cluster models known to lie within fractal symmetry-protected topological phases, and computational universality is shown to persist throughout those phases. One of the models considered is simply the cluster model on the honeycomb lattice in one limit. We discuss the importance of rigid subsystem symmetries, as opposed to global or $(D-1)$-form symmetries, in this context.

The paper presents a theory that solves analytically the time-dependent three-level problem of the scheme $\mathrm{discrete}|0\rangle \underset{\mathrm{as}\mathrm{pulse}{\omega }_1}{\overset{\mathrm{weak}}{\to }}\mathrm{resonance}|1\rangle \underset{\mathrm{fs}\mathrm{pulse}{\omega }_2}{\overset{\mathrm{moderately}\mathrm{strong}}{\to }}\mathrm{resonance}|2\rangle$, where $|0\rangle$ is a discrete state, and $|1\rangle$ and $|2\rangle$ are energy-normalized resonance states. The attosecond and femtosecond pulses with central frequencies ${\omega }_1$ and ${\omega }_2$ (${\omega }_1\gg {\omega }_2$) act with ultrashort time delay, $t_D$. The formalism leads to analytic expressions for photoelectron emission probabilities, $P_i(E,t)$, $i=1,2$, in the energy region of the two resonance states, whose calculation in terms of N-electron matrix elements and external control parameters can be carried out economically for any such three-level system. The problem is first solved analytically, within the rotating wave approximation, for the case where the femtosecond pulse is rectangular. The weak attosecond pulse can have any temporal shape. The final solution for two pulses with arbitrary shape (Gaussian in our case) is then achieved by fitting numerically the shape of the femtosecond pulse to a sum of rectangular pulses. The formulas for $P_i(E,t)$ involve, among other things, the Fano discrete-resonance asymmetry parameter $q$, and the resonance-resonance asymmetry parameter Q, defined by us in previous work. They also involve the complex energy poles of the two resonances, a result which accounts for the whole contribution of the open channels of energy-normalized scattering states into which they decay. The theory is applied to the calculation from first principles, using compact state-specific discrete and resonance wave functions, of observable aspects of the time-resolved dynamics associated with the processes $\mathrm{He}$ $1s^2$ ${}^{1}S$ $\to$ $\left(2s2p\right)$ ${}^{1}P^o$ $\leftrightarrow$ $\left(2p^2\right)$ ${}^{1}D$. Calculations show that the $\left(2p^2\right)$ ${}^{1}D$ resonance is 0.295 eV (4200 nm) below the energy of $\left(2s2p\right)$ ${}^{1}P^o$, (60.15 eV), and its width is 0.067 eV. For the transition $1s^2$ ${}^{1}S$ $\to$ $\left(2s2p\right)$ ${}^{1}P^o$, the full width at half maximum (FWHM) of the Gaussian pulse is 160 as. The few-cycle midinfrared pulse coupling the resonance states is also Gaussian, whose duration is varied in the range of a few decades of femtoseconds. Its intensity is in the range $5\times {10}^{10}–5\times {10}^{11}$ $\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. The external control parameters are the intensity and the FWHM of the femtosecond pulse, as well as the $t_D$. For a given value of $t_D$, the FWHM of the second pulse is a crucial control parameter. The results include the time-resolved formation of either the $\left(2s2p\right)$ ${}^{1}P^o$ or the $\left(2p^2\right)$ ${}^{1}D$ resonance, while they are coupled with each other. For the $\left(2s2p\right)$ ${}^{1}P^o$ state, comparison is made with the case where the time-dependent buildup of its asymmetric profile, excited from $1s^2$ ${}^{1}S$ by the same attosecond pulse, is calculated in the absence of coupling to another resonance. The result is in harmony with that of our earlier work on this problem. For the $\left(2p^2\right)$ ${}^{1}D$ resonance excited from $\left(2s2p\right)$ ${}^{1}P^o$, the time-resolved buildup of its profile does not develop into an asymmetric peak due to the fact that $Q$ has the very large value of $\approx -1300$. Instead, it finishes as an Autler-Townes doublet.

The bound states of a system consisting of two heavy identical atoms and one light electron interacting through finite-range pairwise potentials are explored, focusing on their dependence on the electron-atom scattering length. In the case of an exact resonance in the electron-atom interaction, the binding energy of an electron yields an effective $1/r^2$ potential for the relative motion of the atoms. One major finding is a universal potential that depends on the polarization length, which goes beyond the Efimov region. An analytic expression for that potential is extracted from numerical calculations. The spectrum of the $e+\mathrm{Rb}+\mathrm{Rb}$ system produced by the electron-atom polarization interaction exhibits three main sections: a nonuniversal transition region, a quasi-Efimov region, and a densely packed Efimov region.

Quantum manipulation of coupled mechanical resonators has become an important research topic in optomechanics because these systems can be used to study the quantum coherence effects involving multiple mechanical modes. A prerequisite for observing macroscopic mechanical coherence is to cool the mechanical resonators to their ground state. Here we propose a theoretical scheme to cool two coupled mechanical resonators by introducing an optomechanical interface. The final mean phonon numbers in the two mechanical resonators are calculated exactly and the results show that the ground-state cooling is achievable in the resolved-sideband regime and under the optimal driving. By adiabatically eliminating the cavity field in the large-decay regime, we obtain analytical results of the cooling limits, which show the smallest achievable phonon numbers and the parameter conditions under which the optimal cooling is achieved. Finally, the scheme is extended to the cooling of a chain of coupled mechanical resonators.

The interest in light-element nanomaterials stimulated the development of atomic-resolution low-voltage transmission electron microscopy. While geometric-aberration correction made high-resolution imaging at around 80-kV electron acceleration voltage possible, imaging at substantially lower voltages requested the development of chromatic-aberration correction in addition. Recently, the SALVE instrument was introduced with the capability of atomic resolution imaging at electron acceleration voltages from 80 kV down to 20 kV. Here, we show on the example of imaging graphene that at these electron energies, the residual geometric aberrations reintroduce contrast oscillations and delocalization. Also, we show an atomically resolved image of a single vacancy in graphene with a pronounced Jahn-Teller distortion.

We propose a theoretical method of detection of angular velocity based on a two-mode mechanical resonator placed on a rotating platform. The Coriolis force induced by rotation provides the coupling between the two intrinsic mechanical modes, which oscillate along two orthogonal directions perpendicular to the rotating axis of the platform. According to the relationship between the frequencies of mechanical normal modes and the angular velocity, the angular velocity of the rotating platform can be deduced by detecting the frequencies of the mechanical normal modes. It is also shown that our method is applicable to detection of high angular velocities and can protect against thermal drift of mechanical frequencies in the case of degenerate intrinsic mechanical modes.