We introduce entanglement purification protocols for $d$-level systems (qudits) with improved efficiency as compared to previous protocols. While we focus on protocols for bipartite systems, we also propose generalizations to multipartite qudit systems. The schemes we introduce include recurrence protocols that operate on two copies, as well as hashing protocols that operate on large ensembles. We analyze properties of the protocols with respect to minimal required fidelity and yield, and study their performance in the presence of noise and imperfections. We determine error thresholds and study the dependence on local dimension. We find that our schemes do not only outperform previous approaches, but also show an improved robustness and better efficiency with increasing dimension. While error thresholds for different system sizes are not directly comparable, our results nevertheless suggest that quantum information processing using qudits, in particular for long-distance quantum communication, may offer an advantage over approaches based on qubit systems.

We propose a dissipative method for preparation of a maximally entangled steady state of two trapped ions in the Lamb-Dicke limit. By addressing the trapped-ion system with a monochromatic standing-wave laser pulse of frequency resonant with the ionic transition and a microwave field coupled to the ground-state transitions, we obtain an effective coupling between two particles, which is independent of the phonon-number fluctuations. Meanwhile, the controlled spontaneous emission of trapped ions is implemented via pumping the metastable states upwards to the short-lived ionic states by an auxiliary laser field. Combining the unitary processes with the engineered dissipation, a deterministic Bell state can be produced irrespective of the initial states of systems. Moreover, our result shows that the Clauser-Horne-Shimony-Holt inequality can be violated for a wide range of decoherence parameters, even at finite temperature.

CP violation effects produced by the nuclear magnetic quadrupole moment (MQM), electron electric dipole moment (EDM), and scalar-pseudoscalar nucleus-electron neutral current (SP) interaction in ${}^{177}\mathrm{Hf}{}^{19}\mathrm{F}^{+}$ and ${}^{179}\mathrm{Hf}{}^{19}\mathrm{F}^{+}$ are calculated. The role of the hyperfine interaction is investigated. It is shown that the MQM shift can be distinguished from the electron EDM and SP ones due to the implicit dependence of the MQM shift on the hyperfine sublevel. The MQM effect is expressed in terms of the proton (EDM), QCD vacuum angle $\theta$, and quark chromo-EDMs.

A theoretical study is conducted on the stability of exotic antiproton-hydrogen molecular anions ($\overline{p}\mathrm{H}$), which in the separated atom limit correlate with $\overline{p}+\mathrm{H}(n=2)$ ($n$ being the principal quantum number). The $\overline{p}\mathrm{H}$ molecule in the electronic ground state is highly unstable due to pair annihilation and autodetachment ($\to \overline{p}p+e$). However, if the $\overline{p}\mathrm{H}$ molecule is electronically excited, the molecular stability can be drastically improved. Since the excited states of the $\mathrm{H}$ atom have accidental degeneracy, the asymptotic form of the Born-Oppenheimer potential curve of $\overline{p}+\mathrm{H}(n=2)$ behaves as $1/R^2$ ($R$ being the relative distance), which can play a critical role in the bonding and stability of the molecule. It is found that the $\overline{p}\mathrm{H}$ molecule in the first electronic excited state and in a high rotational state is sufficiently stable and has a lifetime dominated by spontaneous radiative emission ($\to \overline{p}+\mathrm{H}+h\nu$). The $\overline{p}\mathrm{H}$ system is dynamically similar to ${\mathrm{H}}_2{}^{-}$, which had been commonly considered to be unstable due to autodetachment. However, recent measurements of ion-beam sputtering unambiguously verified the existence of long-lived ${\mathrm{H}}_2{}^{-}$ molecules in high rotational states. This suggests that the $\overline{p}\mathrm{H}$ molecules may actually be created if one employs experimental means such as the chemical sputtering of hydrogen-rich targets with $\overline{p}$ beams.

The elastic scattering of twisted electrons by diatomic molecules is studied within the framework of the nonrelativistic first Born approximation. In this process, the coherent interaction of incident electrons with two molecular centers may cause interference patterns in the angular distributions of outgoing particles. We investigate how this Young-type interference is influenced by the complex internal structure of twisted beams. In particular, we show that the corkscrewlike phase front and the inhomogeneous intensity profile of the incident beam can strongly modify the angular distribution of electrons, scattered off a single well-localized molecule. For the collision with a macroscopic target, composed of randomly distributed but aligned molecules, the angular-differential cross section may reveal valuable information about the transverse and longitudinal momenta of twisted states. To illustrate the difference between the scattering of twisted and plane-wave beams for both single-molecule and macroscopic-target scenarios, detailed calculations have been performed for a ${\mathrm{H}}_2$ target.

We demonstrate loading of a Li magneto-optical trap using light-induced atomic desorption. The magneto-optical trap confines up to approximately $4\times {10}^4$ ${}^7\mathrm{Li}$ atoms with loading rates up to approximately $4\times {10}^3$ atoms per second. We study the Li desorption rate as a function of the desorption wavelength and power. The extracted wavelength threshold for desorption of Li from fused silica is approximately 470 nm. In addition to desorption of lithium, we observe light-induced desorption of background gas molecules. The vacuum pressure increase due to the desorbed background molecules is $\lesssim 50\%$, and the vacuum pressure decreases back to its base value with characteristic timescales on the order of seconds when we extinguish the desorption light. By examining both the loading and decay curves of the magneto-optical trap, we are able to disentangle the trap decay rates due to background gases and desorbed lithium. Our results show that light-induced atomic desorption can be a viable Li vapor source for compact devices and sensors.

Tailored intense laser fields can be used to steer electron and nuclear dynamics in molecules and control chemical reactions. Here we demonstrate that inhomogeneous nanoscopic near fields provide an additional mechanism for controlling light-induced chemical reactions. This is investigated by quantum-dynamical calculations on dissociation of ${{\mathrm{H}}_2}^{+}$ in few-cycle near fields with a controlled carrier-envelope phase. Directional dissociation asymmetry analysis reveals that the spatial asymmetry of the field is critical in controlling and in modifying field-induced dissociation pathways such as zero-photon dissociation, bond softening, and above-threshold dissociation. The degree of impact strongly depends on the maximum length scale of coherent control in a dissociation channel. The results pave the way towards coherent control of molecular reactions in a wide range of molecules in inhomogeneous near fields.

In recent decades there has been a rapid development of methods to experimentally control individual quantum systems. A broad range of quantum control methods has been developed for two-level systems; however, the complexity of multilevel quantum systems make the development of analogous control methods extremely challenging. Here we exploit the equivalence between multilevel systems with SU(2) symmetry and spin-1/2 systems to develop a technique for generating new robust, high-fidelity, multilevel control methods. As a demonstration of this technique, we develop adiabatic and composite multilevel quantum control methods and experimentally realize these methods using a ${}^{171}\mathrm{Yb}^{+}$ ion system. We measure the average infidelity of the process in both cases to be around ${10}^{-4}$, demonstrating that this technique can be used to develop high-fidelity multilevel quantum control methods and can, for example, be applied to a wide range of quantum computing protocols, including implementations below the fault-tolerant threshold in trapped ions.

By exploring a phase-space hydrodynamics description of one-dimensional free Fermi gas, we discuss how systems settle down to steady states described by the generalized Gibbs ensembles through quantum quenches. We investigate time evolutions of the fermions which are trapped in external potentials or a circle for a variety of initial conditions and quench protocols. We analytically compute local observables such as particle density and show that they always exhibit power-law relaxation at late times. We find a simple rule which determines the power law exponent. Our findings are, in principle, observable in experiments in a one-dimensional free Fermi gas or Tonk's gas (Bose gas with infinite repulsion).

We introduce a scheme to reconstruct the quantum state of a mechanical mirror in a hybrid optomechanical system. The scheme involves sending a beam of two-level atoms to interact with a quantized cavity field which is weakly coupled to the mechanical mirror. We show that the measured data of the excited-state probability of the atoms can be used directly to reconstruct the initial state of the mechanical mirror. If the mechanical mirror is initially a pure quantum state, we can reconstruct both the probability and the phase of the mechanical state. If it is initially a mixed state, we can reconstruct all the diagonal matrix elements and the first two diagonals above and below them.

Understanding large-scale interacting quantum matter requires dealing with the huge number of quanta that are produced by scattering even a few particles against a complex quantum object. Prominent examples are found from high-energy cosmic ray showers, to the optical or electrical driving of degenerate Fermi gases. We tackle this challenge in the context of many-body quantum optics, as motivated by the recent developments of circuit quantum electrodynamics at ultrastrong coupling. The issue of particle production is addressed quantitatively with a simple yet powerful concept rooted in the quantum superposition principle of multimode coherent states. This key idea is illustrated by the study of multiphoton emission from a single two-level artificial atom coupled to a high impedance waveguide, driven by a nearly monochromatic coherent tone. We find surprisingly that the off-resonant inelastic emission line shape is dominated by broadband particle production, due to the large phase space associated with contributions that do not conserve the number of excitations. Such frequency conversion processes produce striking signatures in time correlation measurements, which can be tested experimentally in quantum waveguides. These ideas open new directions for the simulation of a variety of physical systems, from polaron dynamics in solids to complex superconducting quantum architectures.

A large-scale full-configuration-interaction calculation based on the Dirac-Coulomb-Breit (DCB) Hamiltonian is performed for the $2{}^1{S}_0$ and $2{}^3{S}_1$ states of helium. The operators of the normal and specific mass shifts are directly included in the DCB framework to take the finite nuclear mass correction into account. High-accuracy energies and matrix elements involved $n$ (the main quantum number) up to 13 are obtained from one diagonalization of Hamiltonian. The dynamic dipole polarizabilities are calculated by using the sum rule of intermediate states, and a series of magic wavelengths with QED and hyperfine effects included for the $2{}^3{S}_1\to 2{}^1{S}_0$ transition of helium are identified. In addition, the high-order ac Stark shift determined by the dynamic hyperpolarizabilities at the magic wavelengths are also evaluated. Since the most promising magic wavelength for application in experiment is 319.8 nm, the high-accuracy magic wavelength of 319.815 3(6) nm of ${}^4\mathrm{He}$ is in good agreement with the recent measurement value of 319.815 92(15) nm [R. J. Rengelink et al., arXiv:1804.06693], and the present magic wavelength of 319.830 2(7) nm for ${}^3\mathrm{He}$ would provide theoretical support for experimentally designing an optical dipole trap to precisely determine the nuclear charge radius of helium in the future.

We theoretically propose a circuit QED system implemented with a triple-leg stripline resonator (TSR). Unlike from a linear stripline resonator, the fundamental intracavity microwave modes of the TSR are twofold degenerate. When a superconducting qubit is placed near one of the TSR legs, one fundamental mode is directly coupled to the qubit, while the other one remains uncoupled. Using our circuit QED system, we have theoretically studied a two-qubit quantum gate operation in a hybrid qubit composed of a flying microwave qubit and a superconducting qubit. We have demonstrated that, for the hybrid qubit, the quantum controlled phase flip gate can be reliably implemented for the experimentally available set of parameters.

According to the Schiff theorem, an external electric field vanishes at the atomic nucleus in a neutral atom, i.e., it is completely shielded by electrons. This makes a nuclear electric dipole moment (EDM) unobservable. In this paper an extension of the Schiff theorem to an oscillating electric field is considered. Such a field can reach the nucleus and interact with the nuclear EDM. An enhancement effect appears if the field is in resonance with an atomic or molecular transition. The shielding by electrons strongly affects low-energy nuclear electric dipole transition amplitudes in different nuclear reactions, including radiative transitions, radiative nucleon capture, photo- or electro-excitation of nuclei, and laser-induced or laser-enhanced nuclear reactions.

We investigate the limitations of the single-electron time-dependent Schrödinger equation (TDSE) in the studies of solid high-order harmonic generation (HHG). Two main differences are found by comparing the harmonic spectra calculated by TDSE and semiconductor Bloch equations (SBEs) in the same conditions. One is that the spectrum obtained from SBEs only contains clear odd harmonics, but that derived from TDSE consists of even and odd harmonics. The other is that the two approaches derive different linear dependence of cutoff energy on electric strength and wavelengths of laser fields. These discrepancies can be attributed to the single-active-electron approximation used in TDSE. Moreover, we find that the phase mismatching between the dipole interaction and the intrinsic dynamical phase of the system is responsible for the generation of even harmonics in the single-active-electron approximation. Finally, an approach is proposed to expand the applicable range of TDSE further. Our results demonstrate that many-body effects must be taken into account in solid HHG simulations, though the Coulomb interaction between electrons can be neglected in some cases.

Coherent electron currents in circular charge transport are of great importance in photoinduced processes, magneto-optics, and reaction dynamics of molecules. We present ultrafast magnetic field generation by circularly polarized attosecond ultraviolet laser pulses in molecular media. Simulations in a one electron molecular model ${\mathrm{H}}_2^{+}$ show that the induced magnetic field exhibits periodic oscillations on attosecond time scales, which depends on the laser pulse and molecular alignment. We attribute it to the coherent electronic currents, arising from resonant coherent excitation between the ground and excited electronic states. The temporal evolution of the generated magnetic fields and the induced electronic currents relies on the molecular orbital superposition in the electron coherence, providing a way for controlling ultrafast magnetic field generation.

We study the screening of a homogeneous oscillating external electric field $E_0$ in noble-gas atoms using atomic many-body calculations. At zero frequency of the oscillations ($\omega =0$) the screened field $E\left(r\right)$ vanishes at the nucleus, $E\left(0\right)=0$. However, the profile of the field $E\left(r\right)$ is complicated, with the magnitude of the field exceeding the external field $E_0$ at certain points. For $\omega >0$ the field $E(r,\omega )$ strongly depends on $\omega$ and at some points may exceed the external field $E_0$ many times. The field at the nucleus is not totally screened and grows with $\omega$ faster than ${\omega }^2$. It can even be enhanced when $\omega$ comes close to resonance with a frequency of an atomic transition. This field interacts with CP-violating nuclear electric dipole moments creating new opportunities for studying them. The screening of the external field by atomic electrons may strongly suppress (or enhance near an atomic resonance) the low energy nuclear electric dipole transitions.

We show that indirect spin-spin interactions between effective spin-1/2 systems can be realized in two parallel one-dimensional optical lattices loaded with polar molecules and/or Rydberg atoms. The effective spin can be encoded into low-energy rotational states of polar molecules or long-lived states of Rydberg atoms, tightly trapped in a deep optical lattice. The spin-spin interactions can be mediated by Rydberg atoms, placed in a parallel shallow optical lattice, interacting with the effective spins by charge-dipole (for polar molecules) or dipole-dipole (for Rydberg atoms) interaction. Indirect $XX$, Ising, and $XXZ$ interactions with interaction coefficients $J^{\perp }$ and $J^{zz}$ sign varying with interspin distance can be realized, in particular, the $J_1-J_2 XXZ$ model with frustrated ferro-(antiferro-)magnetic nearest (next-nearest) neighbor interactions.

We consider polarization properties of the unpolarized emission of an ensemble of classical emitters with randomly varying polarization. The light is supposed to be unpolarized in the sense that all three polarization-related components of its Stokes vector are zero. At the same time, the mean-square values of these components should not be necessarily zero, may differ from each other, and, therefore, may provide additional information about properties of individual emitters. Experimentally, this information is revealed as dependence of the polarization noise on the azimuth of the quarter-wave plate placed before the polarization-sensitive detector. This dependence appears to be different for the emitters randomly polarized over the equator of the Poincaré sphere, or preferentially located on its poles, or uniformly covering the whole sphere. We show that full quantitative analysis of the polarization-noise anisotropy allows one, in the framework of the proposed model, to get information about polarization characteristics of individual emitters hidden in the emission of the ensemble. Vitality of the method is illustrated by its application to polarization analysis of the polariton laser emission, which is shown to predominantly arise from linearly polarized emitters.