We study a continuous-variable dense coding protocol, originally proposed to employ a two-mode squeezed state, using a general two-mode Gaussian state as a quantum channel. We particularly obtain conditions to manifest quantum advantage by beating two well-known single-mode schemes, namely, the squeezed-state scheme (best Gaussian scheme) and the number-state scheme (optimal scheme achieving the Holevo bound). We then extend our study to a multipartite Gaussian state and investigate the monogamy of operational entanglement measured by the communication capacity under the dense coding protocol. We show that this operational entanglement represents a strict monogamy relation, by means of Heisenberg's uncertainty principle among different parties; i.e., the quantum advantage for communication can be possible for only one pair of two-mode systems among many parties.

Quantum states can, in a sense, be thought of as generalizations of classical probability distributions, but are more powerful than probability distributions when used for computation or communication. Quantum speedup therefore requires some feature of quantum states that classical probability distributions lack. One such feature is interference. We quantify interference and show that there can be no quantum speedup due to a small number of operations incapable of generating large amounts of interference (although large numbers of such operations can, in fact, lead to quantum speedup). Low-interference operations include sparse unitaries, Grover reflections, short-time and low-energy Hamiltonian evolutions, and the Haar wavelet transform. Circuits built from such operations can be classically simulated via a Monte Carlo technique making use of a convex combination of two Markov chains. Applications to query complexity, communication complexity, and the Wigner representation are discussed.

Using well-known scaling techniques we present that for a given laser intensity the photoionization decay rate $\Gamma$ of the core electron in the $1s$ orbital of an atom is varied with the laser frequency $\omega$ such that $\Gamma {\mathcal{Z}}^4$ vs $\omega /{\mathcal{Z}}^2$ has a universal behavior that does not depend on the nuclear charge $\mathcal{Z}$. One can conclude that the laser frequency required to stabilize the $1s$ core electron is larger by the factor ${\mathcal{Z}}^2$ than the laser frequency required to stabilize the electron in the most diffused orbital. This condition ensures the applicability of the Kramers-Henneberger approximation (KHA) for all electrons including the core electrons. However, simple analytical arguments, which are confirmed by our numerical results, show that when the photoionization of the core electron is due to the absorption of one photon only, then the KHA is applicable for a lower frequency that is linearly proportional to $\mathcal{Z}$ and not to the square of atomic number as expected. This condition is a lower bound for the laser frequency which is needed to stabilize a many-electron atom in the presence of high-frequency strong laser fields.

We propose to generate an artificial non-Abelian U(3) gauge field by using a two-tripod scheme, namely, two tripod configurations sharing a common ground-state level and driven by resonant one-photon transitions. Using an appropriate combination of four Laguerre-Gauss and two Hermite-Gauss laser beams, we are able to produce a U(3) monopole and a U(3) spin-orbit coupling for both alkali-metal and alkaline-earth-metal atoms. This two-tripod scheme could open the way to the study of interacting spinor condensates subjected to U(3) monopoles.

The inverse Compton scattering of laser light on high-energetic twisted electrons is investigated with the aim to construct spatially structured x-ray beams. In particular, we analyze how the properties of the twisted electrons, such as the topological charge and aperture angle of the electron Bessel beam, affect the energy and angular distribution of scattered x rays. We show that with suitably chosen initial twisted electron states one can synthesize tailor-made x-ray beam profiles with a well-defined spatial structure, in a way not possible with ordinary plane-wave electron beams.

For eight-dimensional quantum systems there is a Kochen-Specker (KS) set of 40 quantum yes-no tests that is related to the Greenberger-Horne-Zeilinger (GHZ) proof of Bell's theorem. Here we experimentally implement this KS set using an eight-dimensional Hilbert space spanned by the transverse momentum of single photons. We show that the experimental results of these tests violate a state-independent noncontextuality inequality. In addition, we show that, if the system is prepared in states that are formally equivalent to a three-qubit GHZ and W states, then the results of a subset of 16 tests violate a noncontextuality inequality that is formally equivalent to the three-party Mermin's Bell inequality, but for single eight-dimensional quantum systems. These experimental results highlight the connection between quantum contextuality and nonlocality for eight-dimensional quantum systems.

We analyze two families of three-state quantum walks which show the localization effect. We focus on the role of the initial coin state and its coherence in controlling the properties of the quantum walk. In particular, we show that the description of the walk simplifies considerably when the initial coin state is decomposed in the basis formed by the eigenvectors of the coin operator. This allows us to express the limit distributions in a much more convenient form. Consequently, striking features which are hidden in the standard basis description are easily identified. Moreover, the dependence of moments of the position distribution on the initial coin state can be analyzed in full detail. In particular, we find that in the eigenvector basis the even moments and the localization probability at the origin depend only on incoherent combination of probabilities. In contrast, odd moments and localization outside the origin are affected by the coherence of the initial coin state.

We present elastic cross sections for electron interactions with arsine (${\mathrm{AsH}}_3$) in gas phase over an extensive energy range from 0.5 to 5000 eV by combining two computational methods. The ab initio R-matrix method is employed for low-energy computations up to 15 eV and the intermediate to high-energy calculations were performed using the spherical complex optical potential (SCOP) method. The elastic cross section computed through the $R$ matrix and SCOP formalism shows consistency at crossover energy (11–12 eV) and gives reasonable accord with the available data. Besides elastic cross sections, the differential cross section at low and intermediate incident electron energies is reported. The electronic excitation cross section is also reported at low energies. Shape resonance is observed at around 2.4 eV due to the formation of a transient negative ion state.

We apply a numerical basis-state method to determine the electric susceptibility of atomic hydrogen via calculations of the terms of the perturbative power series expansion up to eleventh order as well as from ab initio calculations of the field-induced polarization. The results of the perturbative calculations indicate that the applicability of the power series expansion is limited to intensities of a uniform electric field below $2\times {10}^{13}$ $\mathrm{W}/\mathrm{cm}{}^2$ at a wavelength of 800 nm. While the predictions for the electric susceptibility from the perturbative power series tend to strongly increase beyond this intensity regime, those from ab initio calculations have a negative slope as a function of intensity. We therefore interpret that the latter feature is due to the nonperturbative interaction between the atom and the external field and an explanation via higher-order nonlinear terms is not applicable.

We investigate $\mathrm{SU}\left(N\right)$ attractive Fermi systems with disorder using a Bogoliubov-de Gennes method at zero temperature with particular focus on the SU(3) case. The charge correlation function, the distribution function of the superfluid (SF) order parameter, and the free energy are calculated for a two-dimensional square lattice system at half filling. From the disorder average of these quantities, we find that disorder triggers a transition from the charge-density-wave (CDW) phase to the SF phase; disorder suppresses the CDW order, making the SF state stable. This disorder-driven phase transition is of first order and is unique for SU(3) systems; it has not been observed for the disordered SU(2) systems studied so far. We elucidate the properties of the CDW-SF transition from the disorder-averaged density of states and the distribution function of the particle density and thus obtain the ground-state phase diagram. We also address the SU(4) case and find that the CDW state is driven directly to the Anderson localized state, but the SF phase is not stabilized. We argue what will be expected for generic $N$ cases.

We consider interacting bosons in a two-dimensional square and a three-dimensional cubic optical lattice with a periodic modulation of the $s$-wave scattering length. At first we map the underlying periodically driven Bose-Hubbard model for large enough driving frequencies approximately to an effective time-independent Hamiltonian with a conditional hopping. Combining different analytical approaches with quantum Monte Carlo simulations then reveals that the superfluid–Mott-insulator quantum phase transition still exists despite the periodic driving and that the location of the quantum phase boundary turns out to depend quite sensitively on the driving amplitude. A more detailed quantitative analysis shows that the effect of driving can even be described within the usual Bose-Hubbard model provided that the hopping is rescaled appropriately with the driving amplitude.

The properties of a dual-frequency vertical-external-cavity surface-emitting laser (VECSEL), in which two linear orthogonal polarization modes are oscillating simultaneously, are theoretically investigated. We derive a model based on the ideas introduced by San Miguel et al. [San Miguel, Feng, and Moloney, Phys. Rev. A 52, 1728 (1995)], taking into account the spin dynamics of the carriers inside the quantum well based gain medium of the dual-frequency VECSEL. This model is shown to succeed in describing quite a few properties of the dual-frequency VECSEL, such as the behavior of nonlinear coupling strength between the modes, the spectral behavior of intensity noises of the modes, and also the correlation between these intensity noises. A good agreement is found with experimental data. The variables associated with the spin-dependent carrier dynamics can be adiabatically eliminated due to the class-A dynamical behavior of the considered laser which is based on a cm-long external cavity. This leads to a simple analytical description of the dynamics of the dual-frequency VECSEL, providing a better understanding of the physics involved.

Optical instabilities in moving media are linked to a spontaneous parity-time-symmetry breaking of the system. It is shown that in general the time evolution of the electromagnetic waves in moving media is determined by a non-Hermitian parity-time-symmetric operator. For lossless systems the frequency spectrum of the time evolution operator may be complex valued, and has a mirror symmetry with respect to the real-frequency axis. The possibility of optical amplification of a light pulse in the broken parity-time-symmetry regime is demonstrated.

When the initial state in a collision involves indeterminate momenta, the conservation law for momentum no longer applies to the individual event with a sharpness beyond the indeterminacy. As a consequence, there are collisions that are recoilless in the sense that the state of one of the quanta is unchanged by the collision while the other quantum emerges in a superposition of momenta. Recoilless collisions that avoid entanglement are basic for experiments studying coherence effects for individual quanta involving interactions of the quantum with reflectors or diaphragms. The idea that in interference experiments there is an inevitable recoil that can be made unobservable by firmly bolting the reflector or diaphragm to a solid support is false since in interference with individual quanta there $\mathit{is}$ no recoil to control. The highly quantal character of the reflector or diaphragm in the interference experiment apparently went unnoticed in the conception of complementarity.

We generalize the notion of the best separable approximation (BSA) and best $W$-class approximation (BWA) to arbitrary pure-state entanglement measures, defining the best zero-$E$ approximation (BEA). We show that for any polynomial entanglement measure $E$, any mixed state $\rho$ admits at least one “$S$ decomposition,” i.e., a decomposition in terms of a mixed state on which $E$ is equal to zero, and a single additional pure state with (possibly) nonzero $E$. We show that the BEA is not, in general, the optimal $S$ decomposition from the point of view of bounding the entanglement of $\rho$ and describe an algorithm to construct the entanglement-minimizing $S$ decomposition for $\rho$ and place an upper bound on $E\left(\rho \right)$. When applied to the three-tangle, the cost of the algorithm is linear in the rank $d$ of the density matrix and has an accuracy comparable to a steepest-descent algorithm whose cost scales as $d^{8}logd$. We compare the upper bound to a lower-bound algorithm given by C. Eltschka and J. Siewert [Phys. Rev. Lett. 108, 020502 (2012)] for the three-tangle and find that on random rank-2 three-qubit density matrices, the difference between the upper and lower bounds is $0.14$ on average. We also find that the three-tangle of random full-rank three-qubit density matrices is less than $0.023$ on average.

We present a method to construct high-fidelity quantum phase gates, which are insensitive to errors in various experimental parameters. The phase gates consist of a pair of two sequential broadband composite pulses, with a phase difference $\pi +\alpha /2$ between them, where $\alpha$ is the desired gate phase. By using composite pulses which compensate systematic errors in the pulse area, the frequency detuning, or both the area and the detuning, we thereby construct composite phase gates which compensate errors in the same parameters. Particularly interesting are phase gates which use the recently discovered universal composite pulses, which compensate systematic errors in any parameter of the driving field, which keep the evolution Hermitian (e.g., pulse amplitude and duration, pulse shape, frequency detuning, Stark shifts, residual frequency chirps, etc.).

The multiconfiguration Dirac-Hartree-Fock method is employed to calculate atomic electric dipole moments in the ground states of ${}^{225}\mathrm{Ra}$, ${}^{199}\mathrm{Hg}$, and ${}^{171}\mathrm{Yb}$. For the calculations of the matrix elements we extend the relativistic atomic structure package grasp2k. The extension includes programs to evaluate matrix elements of $\mathcal{P}\mathcal{T}$-odd electron-nucleus tensor-pseudotensor and pseudoscalar-scalar interactions, the atomic electric dipole operator, the nuclear Schiff moment, and the interaction of the electron electric dipole moment with nuclear magnetic moments. The interelectronic interactions are accounted for through valence and core-valence electron correlation effects. The electron shell relaxation is included with separately optimized wave functions of opposite parities.

We experimentally investigate strong-field ionization of noble-gas atoms in elliptically polarized laser fields with the Keldysh parameter $\gamma \sim 1$, which is typical for most current strong-field experiments. Our data show that the single-ionization yields exhibit a rapid decrease with increasing elipticity and, moreover, the decrease becomes more dramatic for lower laser intensity. The experimental results are compared with the simulations of the Ammosov-Delone-Krainov (ADK) theory based on the quasistatic tunneling ionization picture and the strong-field approximation (SFA) theory, which involves the nonadiabatic effect in the tunneling ionization process. Our results show that although both the ADK simulations and the SFA calculations can qualitatively reproduce the experimental results, the SFA calculations are in a better agreement with the experimental data than the ADK simulations, which implies a nonadiabatic effect during strong-field atomic ionization for elliptical polarization with $\gamma \sim 1$.

We present a numerical ab-initio simulation of the time delay in the photoionization of the simplest diatomic molecule ${\mathrm{H}}_2^{+}$ as observed by attosecond streaking. We show that the strong variation of the Eisenbud-Wigner-Smith time delay $t_{\mathrm{EWS}}$ as a function of energy and emission angle becomes observable in the streaking time shift $t_{\mathrm{S}}$ provided laser field induced components are accounted for. The strongly enhanced photoemission time shifts are traced to destructive Cohen-Fano (or two-center) interferences. Signatures of these interferences in the streaking trace are shown to be enhanced when the ionic fragments are detected in coincidence.