We theoretically show that a nonlinear oscillator network with controllable parameters can be used for universal quantum computation. The initialization is achieved by a quantum-mechanical bifurcation based on quantum adiabatic evolution, which yields a Schrödinger cat state. All the elementary quantum gates are also achieved by quantum adiabatic evolution, in which dynamical phases accompanying the adiabatic evolutions are controlled by the system parameters. Numerical simulation results indicate that high gate fidelities can be achieved, where no dissipation is assumed.

Doubly excited Rydberg states of helium (He) have been studied in nanodroplets using synchrotron radiation. Although qualitatively similar to their atomic counterparts, the Fano resonances in droplets are broader and exhibit blueshifts which increase for the higher excited states. However, varying the droplet size hardly affects the shapes of the resonances. Furthermore, additional dipole-forbidden resonances appear which are not seen in the He atom. We discuss these features in terms of localized atomic states perturbed by the surrounding He atoms.

We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic evolution with geometric phases is provided, and we determine that in the adiabatic evolution, while the eigenstates are slowly varying, the eigenenergies and degeneracy of the Hamiltonian can change rapidly. We exemplify this result by the example of the adiabatic evolution driven by parametrized pulse sequences. For driving fields that are rotating slowly with the same average energy and evolution path, fast modulation fields can have smaller nonadiabatic errors than obtained under the traditional approach with a constant amplitude.

We measured the branching fractions for the decay of the $5p{}^{2}P_{1/2}$ state of ${}^{88}\mathrm{Sr}^{+}$ by applying a recently demonstrated photon-counting sequential method [M. Ramm, T. Pruttivarasin, M. Kokish, I. Talukdar, and H. Häffner, Phys. Rev. Lett. 111, 023004 (2013)] to a single ion laser cooled in a microfabricated surface trap. The branching fraction for the decay into the $5s{}^{2}S_{1/2}$ ground level was found to be $p=0.9449\left(5\right)$. This result is in good agreement with recent theoretical calculations but disagrees with previous experimental measurements, however affected by a one-order-of-magnitude larger uncertainty. This experiment demonstrates that microtrap technology is also applicable in the domain of precision measurements and spectroscopy.

We numerically demonstrate two-dimensional (2D) matter-wave solitons in the disk-shaped dipolar Bose-Einstein condensates (BECs) trapped in strongly anisotropic optical lattices (OLs) in a disk's plane. The considered OLs are square lattices which can be formed by interfering two pairs of plane waves with different intensities. The hopping rates of the condensates between two adjacent lattices in the orthogonal directions are different, which gives rise to a linearly anisotropic system. We find that when the polarized orientation of the dipoles is parallel to disk's plane with the same direction, the combined effects of the linearly anisotropy and the nonlocal nonlinear anisotropy strongly influence the formations, as well as the dynamics of the lattice solitons. Particularly, the isotropy-pattern solitons (IPSs) are found when these combined effects reach a balance. Motion, collision, and rotation of the IPSs are also studied in detail by means of systematic simulations. We further find that these IPSs can move freely in the 2D anisotropic discrete system, hence giving rise to an anisotropic effective mass. Four types of collisions between the IPSs are identified. By rotating an external magnetic field up to a critical angular velocity, the IPSs can still remain localized and play as a breather. Finally, the influences from the combined effects between the linear and the nonlocal nonlinear anisotropy with consideration of the contact and/or local nonlinearity are discussed too.

We study $s$-wave superconductivity in the two-dimensional attractive Hubbard model in an applied magnetic field, assume the extreme Pauli limit, and examine the role of spatial fluctuations in the coupling regime corresponding to BCS-BEC crossover. We use a decomposition of the interaction in terms of an auxiliary pairing field, retain the static mode, and sample the pairing field via a Monte Carlo approach. The method requires iterative solution of the Bogoliubov–de-Gennes equations for amplitude- and phase-fluctuating configurations of the pairing field. We establish the full thermal phase diagram of this strong-coupling problem. At low field we observe the magnetized but homogeneous “breached pair” superfluid phase. It reveals that $T_c$ scales an order of magnitude below the mean-field estimate, spontaneous inhomogeneity in the field-induced magnetization, and a strong nonmonotonicity in the temperature dependence of the low-energy density of states. We compare our results to the experimental phase diagram of the imbalanced Fermi gas at unitarity. At higher field we obtain the modulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases. The thermal transition from the FFLO phases to the normal state is strongly first order. We track the fermionic momentum distribution, the density of states, and the pairing structure factor deep into the normal state. The pairing structure factor retains weak signature of finite momentum pairing to a high temperature despite the low $T_c$ itself, while the spin-resolved density of states changes from the “pseudogapped” FFLO character to gapless and pseudogapped again with increasing temperature.

We consider recurrence to the initial state after repeated actions of a quantum channel. After each iteration a projective measurement is applied to check recurrence. The corresponding return time is known to be an integer for the special case of unital channels, including unitary channels. We prove that for a more general class of quantum channels the expected return time can be given as the inverse of the weight of the initial state in the steady state. This statement is a generalization of the Kac lemma for classical Markov chains.

We show that the electrons, produced in strong-bicircular-field-induced above-threshold ionization of inert-gas atoms, have a large spin asymmetry if the ions exhibit fine-structure splitting. For a bicircular field, which consists of two coplanar counterrotating circularly polarized fields of frequencies $\omega$ and $2\omega$, the spin-asymmetry parameter changes rapidly with the electron energy. Since the electron–parent-ion rescattering in a counterrotating bicircular field is characterized on the attosecond time scale, this spin asymmetry may introduce the spin degree of freedom into attoscience. We show that the high-energy backward and low-energy forward scattered electrons, which are produced on the scale of a fraction of the laser cycle, exhibit spin asymmetry.

The reflectivity properties of graphene with a nonzero mass-gap parameter are investigated in the framework of a Dirac model using the polarization tensor in $(2+1)$-dimensional space-time. For this purpose, a more simple explicit representation for the polarization tensor along the real frequency axis is found. The approximate analytic expressions for the polarization tensor and for the reflectivities of graphene are obtained in different frequency regions at any temperature. We show that the nonzero mass-gap parameter has a profound effect on the reflectivity of graphene. Specifically, at zero temperature the reflectivity of gapped graphene goes to zero with vanishing frequency. At nonzero temperature the same reflectivities are equal to unity at zero frequency. We also find the resonance behavior of the reflectivities of gapped graphene at both zero and nonzero temperature at the border frequency determined by the width of the gap. At nonzero temperature the reflectivities of graphene drop to zero in the vicinity of some frequency smaller than the border frequency. Our analytic results are accompanied with numerical computations performed over a wide frequency region. The developed formalism can be used in devising nanoscale optical detectors and optoelectronic switches and in other optical applications of graphene.

We investigate the entanglement patterns of photon-added and photon-subtracted four-mode squeezed vacuum states. Entanglements in different scenarios are analyzed by varying the number of photons added or subtracted in certain modes, which are referred to as the “player” modes, the others being “spectators.” We find that the photon-subtracted state can give us higher entanglement than the photon-added state which is in contrast to the two-mode situation. We also study the logarithmic negativity of the two-mode reduced density matrix obtained from the four-mode state which again shows that the state after photon subtraction can possess higher entanglement than that of the photon-added state, and we then compare it to that of the two-mode squeezed vacuum state. Moreover, we examine the non-Gaussianity of the photon-added and photon-subtracted states to find that the rich features provided by entanglement cannot be captured by the measure of nonclassicality.

Zero-frequency Casimir theory is analyzed from different viewpoints, with the aim of obtaining further insight into the delicate Drude-plasma issue that turns up when one considers thermal corrections to the Casimir force. The problem is essentially that the plasma model, physically inferior in comparison to the Drude model since it leaves out dissipation in the material, apparently gives the best results when comparing with recent experiments. Our geometric setup is quite conventional, namely, a dielectric plate separated from a dielectric half-space by a vacuum gap, both media being made of the same material. Our investigation is divided into the following categories: (1) Making use of the statistical-mechanical method developed by J. S. Høye and I. Brevik [Physica A (Amsterdam, Neth.) 259, 165 (1998)], implying that the quantized electromagnetic field is replaced by interaction between dipole moments oscillating in harmonic potentials, we first verify that the Casimir force is in agreement with the Drude prediction. No use of Fresnel's reflection coefficients is made at this stage. (2) Then turning to the field-theoretic description implying use of the reflection coefficients, we derive results in agreement with the forgoing when first setting the frequency equal to zero, before letting the permittivity become large. With the plasma relation the reflection coefficient for TE zero-frequency modes depends on the component of the wave vector parallel to the surfaces and lies between 0 and 1. This contradicts basic electrostatic theory. (3) Turning to high-permeability magnetic materials, the TE zero-frequency mode describes the static magnetic field in the same way the TM zero-frequency modes describe the static electric fields in electrostatics. With the plasma model magnetic fields, except for a small part, cannot pass through metals; that is, metals effectively become superconductors. However, recent experimental results clearly favor the plasma model. We briefly discuss a possible explanation for this apparent conflict with electrostatics.

We consider the dissipative single-qubit circuit QED architecture in which the atomic transition frequency undergoes a weak external time modulation. For sinusoidal modulation with linearly varying frequency we derive effective Hamiltonians that resemble the Landau-Zener problem of finite duration associated with a two- or multilevel systems. The corresponding off-diagonal coupling coefficients originate either from the rotating or the counter-rotating terms in the Rabi Hamiltonian, depending on the values of the modulation frequency. It is demonstrated that in the dissipationless case one can accomplish almost complete transitions between the eigenstates of the bare Rabi Hamiltonian even for relatively short durations of the frequency sweep. To assess the experimental feasibility of our scheme we solved numerically the phenomenological and the microscopic quantum master equations in the Markovian regime at zero temperature. Both models exhibit qualitatively similar behavior and indicate that photon generation from vacuum via effective Landau-Zener transitions could be implemented with the current technology on the time scales of a few microseconds. Moreover, unlike the harmonic dynamical Casimir effect implementations, our proposal does not require precise knowledge of the resonant modulation frequency to accomplish meaningful photon generation.

Experimentally measured and theoretically calculated rate coefficients for the recombination of ${\mathrm{W}}^{19+}(\left[\mathrm{Kr}\right]4d^{10}4f^9$) ions with free electrons (forming ${\mathrm{W}}^{18+}$) are presented. At low electron-ion collision energies, the merged-beam rate coefficient is dominated by strong, mutually overlapping, recombination resonances as already found previously for the neighboring charge-state ions ${\mathrm{W}}^{18+}$ and ${\mathrm{W}}^{20+}$. In the temperature range where ${\mathrm{W}}^{19+}$ is expected to form in a collisionally ionized plasma, the experimentally derived recombination rate coefficient deviates by up to a factor of about 20 from the theoretical rate coefficient obtained from the Atomic Data and Analysis Structure database. The present calculations, which employ a Breit–Wigner redistributive partitioning of autoionizing widths for dielectronic recombination via multi-electron resonances, reproduce the experimental findings over the entire temperature range.

Many systems under control with an applied field also interact with the surrounding environment. Understanding the control mechanisms has remained a challenge, especially the role played by the interaction between the field and the environment. In order to address this need, here we expand the scope of the Hamiltonian-encoding and observable-decoding (HE-OD) technique. HE-OD was originally introduced as a theoretical and experimental tool for revealing the mechanism induced by control fields in closed quantum systems. The results of open-system HE-OD analysis presented here provide quantitative mechanistic insights into the roles played by a Markovian environment. Two model open quantum systems are considered for illustration. In these systems, transitions are induced by either an applied field linked to a dipole operator or Lindblad operators coupled to the system. For modest control yields, the HE-OD results clearly show distinct cooperation between the dynamics induced by the optimal field and the environment. Although the HE-OD methodology introduced here is considered in simulations, it has an analogous direct experimental formulation, which we suggest may be applied to open systems in the laboratory to reveal mechanistic insights.

We study the effects of quasiparticle interactions in a quasi-two-dimensional (quasi-2D), zero-temperature Bose-Einstein condensate of dipolar atoms, which can exhibit a roton-maxon feature in its quasiparticle spectrum. Our focus is the Beliaev damping process, in which a quasiparticle collides with the condensate and resonantly decays into a pair of quasiparticles. Remarkably, the rate for this process exhibits a highly nontrivial dependence on the quasiparticle momentum and the dipolar interaction strength. For weak interactions, low-energy phonons experience no damping, and higher-energy quasiparticles undergo anomalously weak damping. In contrast, the Beliaev damping rates become anomalously large for stronger dipolar interactions, as rotons become energetically accessible as final states. When the dipoles are tilted off the axis of symmetry, the damping rates acquire an anisotropic character. Surprisingly, this anisotropy does not simply track the anisotropy of the dipolar interactions, rather, the mechanisms for damping are qualitatively modified in the anisotropic case. Our study reveals the unconventional nature of Beliaev damping in dipolar condensates, and has important implications for ongoing studies of equilibrium and nonequilibrium dynamics in these systems. Further, our results are relevant for other 2D superfluids with roton excitations, including spin-orbit-coupled Bose gases, magnon condensates, and ${}^4\mathrm{He}$ films.

We study the behavior of interacting ultracold bosons in optical lattices in synthetic magnetic fields with wide range of in-cell fluxes $\alpha =p/q$. The problem is similar to the one of an electron moving in a tight-binding scheme in the magnetic field and becomes difficult to tackle for a growing number of magnetic subbands, $q$. To overcome this, we focus on the interplay of the width, shape, and number of the subbands on the formation of the coherent state of cold bosons. Using the quantum rotor approach, which goes beyond the mean-field approximation, we are able to pinpoint the elements of the band structure, which are the most significant in a proper theoretical description of the synthetic magnetic field in a bosonic lattice system. As a result, we propose a method of reconstruction of the Hofstadter butterfly spectrum by replacing the magnetic subbands with renormalized bands of a square lattice. This allows us to effectively investigate the properties of the studied system for a wide range of magnetic fluxes and their impact on the Mott-insulator–superfluid transition.

In the field of optomechanics, radiation forces have provided a particularly high level of control over the frequency and dissipation of mechanical elements. Here we propose a class of optomechanical systems in which light exerts a similarly profound influence over two other fundamental parameters: geometry and mass. By applying an optical trap to one lattice site of an extended phononic crystal, we show it is possible to create a tunable, localized mechanical mode. Owing to light's simultaneous and constructive coupling with the structure's continuum of modes, we estimate that a trap power at the level of a single intracavity photon should be capable of producing a significant effect within a realistic, chip-scale device.

We develop an approach describing nonlinear-optical processes in the strong-field domain characterized by the nonperturbative field-with-matter interaction. The polarization of an isolated atom in the external field calculated via the numerical solution of the time-dependent Schrödinger equation agrees with our analytical findings. For the practically important case of one strong laser field and several weaker fields, we derive and analytically solve propagation equations describing high-order (HO) wave mixing, HO parametric amplification, and HO stimulated scattering. These processes provide a way of efficient coherent xuv generation. Some properties of HO processes are new in nonlinear optics: essentially complex values of the coefficients in the propagation equations, the superexponential (hyperbolic) growing solutions, etc. Finally, we suggest conditions for the practical realization of these processes and discuss published numerical and experimental results where such processes could have been observed.