Electromagnetic driving in a honeycomb lattice can induce gaps and topological edge states with a structure of increasing complexity as the frequency of the driving lowers. While the high-frequency case is the most simple to analyze we focus on the multiple photon processes allowed in the low-frequency regime to unveil the hierarchy of Floquet edge states. In the case of low intensities an analytical approach allows us to derive effective Hamiltonians and address the topological character of each gap in a constructive manner. At high intensities we obtain the net number of edge states, given by the winding number, with a numerical calculation of the Chern numbers of each Floquet band. Using these methods, we find a hierarchy that resembles that of a Russian nesting doll. This hierarchy classifies the gaps and the associated edge states in different orders according to the electron-photon coupling strength. For large driving intensities, we rely on the numerical calculation of the winding number, illustrated in a map of topological phase transitions. The hierarchy unveiled with the low-energy effective Hamiltonians, along with the map of topological phase transitions, discloses the complexity of the Floquet band structure in the low-frequency regime. The proposed method for obtaining the effective Hamiltonian can be easily adapted to other Dirac Hamiltonians of two-dimensional materials and even the surface of a three-dimensional topological insulator.

We optimize a collision-induced cooling process for ultracold atoms in the nondegenerate regime. It makes use of a Feshbach resonance, instead of rf radiation in evaporative cooling, to selectively expel hot atoms from a trap. Using functional minimization we analytically show that for the optimal cooling process the resonance energy must be tuned such that it linearly follows the temperature. Here, optimal cooling is defined as maximizing the phase-space density after a fixed cooling duration. The analytical results are confirmed by numerical Monte Carlo simulations. In order to simulate more realistic experimental conditions, we show that background losses do not change our conclusions, while additional nonresonant two-body losses make a lower initial resonance energy with nonlinear dependence on temperature preferable.

We demonstrate an effective control of nonlinear interactions of lasing modes in a semiconductor microdisk cavity by shaping the pump profile. A target mode is selected at the expense of its competing modes either by increasing their lasing thresholds or suppressing their power slopes above the lasing threshold. Despite the strong spatial overlap of the lasing modes at the disk boundary, adaptive pumping enables an efficient selection of any lasing mode to be the dominant one, leading to a switch of lasing frequency. The theoretical analysis illustrates both linear and nonlinear effects of selective pumping and quantifies their contributions to lasing-mode selection. This work shows that adaptive pumping not only provides a powerful tool to control the nonlinear process in multimode lasers, but also enables the tuning of lasing characteristic after the lasers have been fabricated.

We experimentally study the phase-space distribution (PSD) of a mechanical resonator that is simultaneously coupled to two electromagnetic cavities. The first one, operating in the microwave band, is employed for inducing either cooling or self-excited oscillation (SEO), whereas the second one, operating in the optical band, is used for displacement detection. A tomography technique is employed for extracting the PSD from the signal reflected by the optical cavity. Measurements of PSD are performed in steady state near the threshold of SEO while sweeping the microwave cavity detuning. In addition, we monitor the time evolution of the transitions from an optomechanically cooled state to a state of self-excited oscillation. This transition is induced by abruptly switching the microwave driving frequency from the red-detuned region to the blue-detuned one. The experimental results are compared with theoretical predictions that are obtained by solving the Fokker-Planck equation. The feasibility of generating quantum superposition states in the system under study is briefly discussed.

We propose a method of measuring topological invariants of a photonic crystal through phase spectroscopy. We show how the Chern numbers can be deduced from the winding numbers of the reflection coefficient phase. An explicit proof of the existence of edge states in a system with a nonzero reflection phase winding number is given. The method is illustrated for one- and two-dimensional photonic crystals of nontrivial topology.

The branching fractions from the excited state $6P_{1/2}$ of singly charged barium ion has been measured with a precision $0.03\%$ in an ion trap experiment. This measurement along with the known value of the upper state lifetime allowed the determination of the dipole matrix elements for the transitions $P\text{−}S$ and $P\text{−}D$ to below the $1\%$ level. Therefore, it is now possible to compare the many-body calculations of these matrix elements at a level which is of significance to any parity-nonconservation experiment on barium ion. Moreover, these dipole matrix elements are the most significant contributors to the parity-violating matrix element between the $S\text{−}D$ transition, contributing up to $90\%$ to the total. Our results on the dipole matrix elements are $3.305\pm 0.014$ a.u. and $3.042\pm 0.016$ a.u. for the $S\text{−}P$ and $P\text{−}D$ transitions, respectively.

The principle of local distinguishability states that an arbitrary physical state of a bipartite system can be determined by the combined statistics of local measurements performed on the subsystems. A necessary and sufficient requirement for the local measurements is that each one must be able to distinguish between all pairs of states of the respective subsystems. We show that, if the task is changed into the determination of an arbitrary bipartite pure state, then at least in certain cases it is possible to restrict to local measurements which can distinguish all pure states but not all states. Moreover, we show that, if the local measurements are such that the purity of the bipartite state can be verified from the statistics without any prior assumption, then in these special cases also this property is carried over to the composite measurement. These surprising facts give evidence that the principle of local distinguishability may be expanded beyond its usual applicability.

The linear polarization of x rays produced by dielectronic recombination into highly charged xenon ions was measured at an electron beam ion trap using the Compton polarimetry technique. This opens numerous possibilities for diagnostics of anisotropies of hot plasmas. Moreover, it was observed that the polarization of x rays, following the dielectronic capture populating the ${\left[1s2s^{2}2p_{1/2}\right]}_1$ state, is highly sensitive to the Breit interaction. The experimental results for this transition rule out by $5\sigma$ calculations not taking the Breit interaction into account.

The electronic structure of the $(\mathrm{LiYb}{)}^{+}$ molecular ion is investigated with two variants of the coupled cluster method restricted to single, double, and noniterative or linear triple excitations. Potential-energy curves for the ground and excited states, permanent and transition electric dipole moments, and long-range interaction coefficients $C_4$ and $C_6$ are reported. The data are subsequently employed in scattering calculations and photoassociation studies. Feshbach resonances are shown to be measurable, despite the ion's micromotion in the Paul trap. Molecular ions can be formed in their singlet electronic ground state by one-photon photoassociation and in triplet states by two-photon photoassociation; and control of cold atom-ion chemistry based on Feshbach resonances should be feasible. Conditions for sympathetic cooling of an ${\mathrm{Yb}}^{+}$ ion by an ultracold gas of Li atoms are found to be favorable in the temperature range $10\mathrm{nK}–10\mathrm{mK}$, and further improvements using Feshbach resonances should be possible. Overall, these results suggest excellent prospects for building a quantum simulator with ultracold ${\mathrm{Yb}}^{+}$ ions and Li atoms.

The triple differential cross section for laser-assisted ionization of a helium target by slow electrons is analyzed within the framework of the second Born approximation. We evaluate the $S$-matrix elements using Volkov and Coulomb-Volkov wave functions for describing the continuum states of the scattered and the ejected electrons, respectively. The required scattering amplitudes are performed by expanding the atomic wave functions onto a complex-scaled Sturmian basis, which allows us to exactly take into account the contribution of the continuous spectrum to the dressing of the atomic states. Our results have been improved by taking into account exchange effects. Furthermore, the second-order Born correction is seen to be important and significantly affects the magnitudes of the binary and recoil peaks.

The growing successes in performing quantum control experiments motivated the development of control landscape analysis as a basis to explain these findings. When a quantum system is controlled by an electromagnetic field, the observable as a functional of the control field forms a landscape. Theoretical analyses have predicted the existence of critical points over the landscapes, including saddle points with indefinite Hessians. This paper presents a systematic experimental study of quantum control landscape saddle points. Nuclear magnetic resonance control experiments are performed on a coupled two-spin system in a ${}^{13}\mathrm{C}$-labeled chloroform $\left({}^{13}{\mathrm{CHCl}}_3\right)$ sample. We address the saddles with a combined theoretical and experimental approach, measure the Hessian at each identified saddle point, and study how their presence can influence the search effort utilizing a gradient algorithm to seek an optimal control outcome. The results have significance beyond spin systems, as landscape saddles are expected to be present for the control of broad classes of quantum systems.

Motivated by the recent experiment performed by the Berkeley group [G. E. Marti et al., Phys. Rev. Lett. 113, 165301 (2014)], we consider the dynamics of magnons in a spin-1 spinor-dipolar Bose-Einstein condensate, using mean-field theory. We show that the effective mass of a magnon is increased by the magnetic dipole-dipole interaction, as observed in the experiment. The magnon mass is also decreased by changing the direction of the magnetic field. The increase and decrease in the magnon mass manifest themselves in the acceleration of the magnons.

We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-$\frac{1}{2}$ network, on a lattice of any dimensionality. Under the assumptions that the network Hamiltonian preserves the magnetization and that a fully polarized initial state is taken for the lattice, we obtain a general formula for the average fidelity of the two qubits QST, linking it to the one- and two-particle transfer amplitudes of the spin excitations among the sites of the lattice. We then apply this formalism to a 1D spin chain with $XX$-Heisenberg type nearest-neighbour interactions adopting a protocol that is a generalization of the single qubit one proposed in Paganelli et al. [Phys. Rev. A 87, 062309 (2013)]. We find that a high-quality two qubit QST can be achieved provided one can control the local fields at sites near the sender and receiver. Under such conditions, we obtain an almost perfect transfer in a time that scales either linearly or, depending on the spin number, quadratically with the length of the chain.

We present a discussion of the continuous-time quantum error correction introduced by J. P. Paz and W. H. Zurek [Proc. R. Soc. A 454, 355 (1998)]. We study the general Lindbladian which describes the effects of both noise and error correction in the weak-noise (or strong-correction) regime through a perturbative expansion. We use this tool to derive quantitative aspects of the continuous-time dynamics both in general and through two illustrative examples: the three-qubit and five-qubit stabilizer codes, which can be independently solved by analytical and numerical methods and then used as benchmarks for the perturbative approach. The perturbatively accessible time frame features a short initial transient in which error correction is ineffective, followed by a slow decay of the information content consistent with the known facts about discrete-time error correction in the limit of fast operations. This behavior is explained in the two case studies through a geometric description of the continuous transformation of the state space induced by the combined action of noise and error correction.

For bipartite pure and mixed quantum states, in addition to the quantum mutual information, there is another measure of total correlation, namely, the entanglement of purification. We study the monogamy, polygamy, and additivity properties of the entanglement of purification for pure and mixed states. In this paper, we show that, in contrast to the quantum mutual information which is strictly monogamous for any tripartite pure states, the entanglement of purification is polygamous for the same. This shows that there can be genuinely two types of total correlation across any bipartite cross in a pure tripartite state. Furthermore, we find the lower bound and actual values of the entanglement of purification for different classes of tripartite and higher-dimensional bipartite mixed states. Thereafter, we show that if entanglement of purification is not additive on tensor product states, it is actually subadditive. Using these results, we identify some states which are additive on tensor products for entanglement of purification. The implications of these findings on the quantum advantage of dense coding are briefly discussed, whereby we show that for tripartite pure states, it is strictly monogamous and if it is nonadditive, then it is superadditive on tensor product states.

We analyze the influence of an external electric field on the $ns$ and $np$ Rydberg states. The impact of an electric field leads to a significant modification of the decay rate. Namely, the additional (linear and quadratic in the field) terms arise in the differential transition probabilities. In contrast to the quadratic term, the linear summand leads to a difference of the hydrogen $\left(\text{H}\right)$ and antihydrogen $\left(\overline{\text{H}}\right)$ spectra. However, this difference vanishes after the integration over photon-emission directions and does not contribute to the total emission probability. The quadratic term results in the significant change of the total decay rate and level width, respectively. The analysis of the linear and quadratic terms depending on the field strength is discussed.

Using the time-dependent density matrix renormalization-group method and exact diagonalization, we study the nonequilibrium dynamics of the one-dimensional Fermi-Hubbard model following a quantum quench or a ramp of the on-site interaction strength. We are particularly interested in the nonequilibrium evolution of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations, which, at finite spin polarizations and for attractive interactions, are the dominant two-body correlations in the ground state. For quenches from the noninteracting to the attractive regime, we investigate the dynamical emergence of FFLO correlations and their signatures in the pair quasi–momentum distribution function. We observe that the postquench double occupancy exhibits a maximum as the interaction strength becomes of the order of the bandwidth. Finally, we study quenches and ramps from attractive to repulsive interactions, which imprint FFLO correlations onto repulsively bound pairs. We show that a quite short ramp time is sufficient to wipe out the characteristic FFLO features in the postquench pair momentum distribution functions.

Using a variational method, we derive an exact upper bound for one-magnon excitation energy in ferromagnetic spinor gases, which limits the quantum corrections to the effective mass of a magnon to be positive. We also derive an upper bound for one-magnon excitation energy in lattice systems. The results hold for both Bose and Fermi systems in $d$ dimensions as long as the interaction is local and invariant under spin rotation.