In a trapped Bose-Einstein condensate, subject to the action of an alternating external field, coherent topological modes can be resonantly excited. Depending on the amplitude of the external field and detuning parameter, there are two principally different regimes of motion, with mode locking and without it. The change of the dynamic regime corresponds to a dynamic phase transition. This transition can be characterized by an effective order parameter defined as the difference between fractional mode populations averaged over the temporal period of oscillations. The behavior of this order parameter, as a function of detuning, pumping amplitude, and atomic interactions is carefully analyzed. Special attention is paid to numerical calculations for the realistic case of a quadrupole exciting field and the system parameters accessible in current experiments.

We propose a simple scheme to realize $1\to M$ economical phase-covariant quantum cloning machine (EPQCM) with superconducting quantum interference device (SQUID) qubits. In our scheme, multi-SQUIDs are fixed into a microwave cavity by adiabatic passage for their manipulation. Based on this model, we can realize the EPQCM with high fidelity via adiabatic quantum computation.

The use of off-resonant standing light waves to manipulate ultracold atoms is investigated. Previous work has illustrated that Bragg diffraction can provide efficient beam-splitting and reflection operations for atomic wave packets. The performance of these operations is characterized experimentally using Bose-Einstein condensates confined in a weak magnetic trap. Fidelities of 0.99 for beam splitting and 0.98 for reflection are observed, and splitting operations of up to third order are achieved. The dependence of the operations on light intensity and atomic velocity is measured and found to agree well with theoretical estimates.

In realistic continuous-variable quantum key distribution protocols, an eavesdropper may exploit the additional Gaussian noise generated during transmission to mask her presence. We present a theoretical framework for a post-selection-based protocol which explicitly takes into account excess Gaussian noise. We derive a quantitative expression of the secret key rates based on the Levitin and Holevo bounds. We experimentally demonstrate that the post-selection-based scheme is still secure against both individual and collective Gaussian attacks in the presence of this excess noise.

For the prototypical example of the Ising chain in a transverse field, we study the impact of decoherence on the sweep through a second-order quantum phase transition. Apart from the advance in the general understanding of the dynamics of quantum phase transitions, these findings are relevant for adiabatic quantum algorithms due to the similarities between them. It turns out that (in contrast to first-order transitions studied previously) the impact of decoherence caused by a weak coupling to a rather general environment increases with system size (i.e., number of spins or qubits), which might limit the scalability of the system.

We report ab initio relativistic correlation calculations of potential curves for ten low-lying electronic states, the effective electric field on the electron, and hyperfine constants for the ${}^3\Delta _1$ state of a cation of the heavy transition metal fluoride $\mathrm{Hf}{\mathrm{F}}^{+}$, which it is suggested can be used in experiments to search for the electric dipole moment of the electron. It is shown that $\mathrm{Hf}{\mathrm{F}}^{+}$ has a deeply bound ${}^1\Sigma ^{+}$ ground state; its dissociation energy is $D_e=6.4\mathrm{eV}$. The ${}^3\Delta _1$ state is obtained as the relatively long-lived first excited state lying about $0.2\mathrm{eV}$ higher. The calculated effective electric field $E_{\mathrm{eff}}=W_d\mid \Omega \mid$ acting on an electron in this state is $5.84\times {10}^{24}\mathrm{Hz}∕e\mathrm{cm}$.

The efficiency of time-dependent density matrix renormalization group methods is intrinsically connected to the rate of entanglement growth. We introduce a measure of entanglement in the space of operators and show, for a transverse Ising spin-$1∕2$ chain, that the simulation of observables, contrary to the simulation of typical pure quantum states, is efficient for initial local operators. For initial operators with a finite index in Majorana representation, the operator space entanglement entropy saturates with time to a level which is calculated analytically, while for initial operators with infinite index the growth of operator space entanglement entropy is shown to be logarithmic.

Searching for an accurate optical clock which can serve as a better time standard than the present-day atomic clock is highly demanding from several areas of science and technology. Several attempts have been made to build more accurate clocks with different ion species. In this paper, we discuss the electric quadrupole and hyperfine shifts in the $5d^{9}6s^2{{}^{2}D}_{5∕2}\left(F=0,m_F=0\right)\leftrightarrow 5d^{10}6s{{}^{2}S}_{1∕2}\left(F=2,m_F=0\right)$ clock transition in ${{}^{199}\text{H}\text{g}}^{+}$, one of the most promising candidates for next-generation optical clocks. We have applied Fock-space unitary coupled-cluster theory to study the electric quadrupole moment of the $5d^{9}6s^2{{}^{2}D}_{5∕2}$ state and magnetic dipole hyperfine constants of $5d^{9}6s^2{{}^{2}D}_{3∕2,5∕2}$ and $5d^{10}6s^1{{}^{2}S}_{1∕2}$ states, respectively, of ${{}^{199}\text{H}\text{g}}^{+}$. We have also compared our results with available data. To the best of our knowledge, this is the first time a variant of coupled-cluster theories has been applied to study these kinds of properties of ${\text{Hg}}^{+}$ and is the most accurate estimate of these quantities to date.

Collisions of antiprotons with He-, Ne-, Ni-like, bare, and neutral uranium are studied theoretically for scattering angles close to $180°$ and antiproton energies in the interval from $100\mathrm{eV}$ to $10\mathrm{keV}$. We investigate the Coulomb glory effect which is caused by a screening of the Coulomb potential of the nucleus and results in a prominent maximum of the differential cross section in the backward direction at some energies of the incident particle. We found that for larger numbers of electrons in the ion the effect becomes more pronounced and shifts to higher energies of the antiproton. On the other hand, a maximum of the differential cross section in the backward direction can also be found in the scattering of antiprotons on a bare uranium nucleus. The latter case can be regarded as a manifestation of the screening property of the vacuum-polarization potential in nonrelativistic collisions of heavy particles.

Using a three-dimensional semiclassical method, we perform a systematic analysis of the effects of an additional static electric field on nonsequential double ionization (NSDI) of a helium atom in an intense, linearly polarized laser field. It is found that the static electric field influences not only the ionization rate, but also the kinetic energy of the ionized electron returning to the parent ion, in such a way that, if the rate is increased, then the kinetic energy of the first returning electron is decreased, and vice versa. These two effects compete in NSDI. Since the effect of the static electric field on the ionization of the first electron plays a more crucial role in the competition, the symmetric double-peak structure of the ${\mathrm{He}}^{2+}$ momentum distribution parallel to the polarization of the laser field is destroyed. Furthermore, the contribution of the trajectories with multiple recollisions to the NSDI is also changed dramatically by the static electric field. As the static electric field increases, the trajectories with two recollisions, which start at the time when the laser and the static electric field are in the same direction, become increasingly important for the NSDI.

One of the important applications of electromagnetically induced transparency (EIT) is to delay and store light in atomic ensembles. In this paper, the noise spectrum of the delayed quantum light throughout an EIT medium is investigated. With zero detection frequency, we can have minimum noise of delayed light in two-photon resonance of EIT, and the noise is larger than the minimum noise at off two-photon resonance due to the phase-to-amplitude noise conversion. It is shown that the noise for nonzero detection frequency can be suppressed by operating the system at off two-photon resonance, even when the unavoidable dephasing is included.

We theoretically study the coherent interaction of a tripod-type atomic system with three laser fields, i.e., one probe and two coupling, or two probe and one coupling field. Our analytical and numerical results show that, when all three fields are on two-photon resonance, in addition to the Rabi frequencies of the coupling fields, the probe group velocities also depend on the spontaneous decay rates and the initial population distribution. So we can manipulate the probe pulses to achieve controllable ultraslow group velocities by preparing different initial atomic states. With an incoherent pump field applied, a narrow transparent window accompanied by abnormal dispersion may occur in the probe absorption spectrum, which then allows us to switch a probe pulse from ultraslow to superluminal propagation.

Localized vectorial modes, with equal frequencies and mutually orthogonal polarizations, are investigated both analytically and experimentally in a one-dimensional photonic lattice with defocusing saturable nonlinearity. It is shown that these modes may span over many lattice elements and that energy transfer among the two components is both phase and intensity dependent. The transverse electrically polarized mode exhibits a single-hump structure and spreads in cascades in saturation, while the transverse magnetically polarized mode exhibits splitting into a two-hump structure. Experimentally such discrete vector solitons are observed in lithium niobate lattices for both coherent and mutually incoherent excitations.

The effect of an intense external linearly polarized radiation field on the angular distributions and polarization states of the photons emitted during the radiative capture of a free electron by a bare nucleus into the ground state of the bound system is investigated. On symmetry grounds it is predicted that emission of elliptically polarized photons occurs when the momentum of the electron beam is not aligned to the direction of the oscillating field. The predictions are corroborated by numerical calculations of recombination rates carried out within a modified Keldysh-type treatment, in order to account for Coulomb effects. It is found that strong modifications to the angular distributions of the emitted photons are induced by the external radiation field.

We unveil the bifurcations underlying polarization switching and injection locking in a vertical-cavity surface-emitting laser subject to optical injection. A Hopf bifurcation, not reported for conventional edge-emitting lasers, delimits the injection locking region and influences the polarization switching conditions. We furthermore theoretically show and experimentally observe periodic dynamics at the relaxation oscillation frequency in the noninjected mode together with wave-mixing dynamics in the injected mode. These dynamics precede the polarization switching leading to injection locking and are attributed to a torus bifurcation arising on a two-polarization mode solution.

Quantum properties of the probes used to estimate a classical parameter can be used to attain accuracies that beat the standard quantum limit. When qubits are used to construct a quantum probe, it is known that initializing $n$ qubits in an entangled state, rather than in a separable state, can improve the measurement uncertainty by a factor of $1∕\sqrt{n}$. We investigate how the measurement uncertainty is affected when the individual qubits in a probe are subjected to decoherence. In the face of such decoherence, we regard the rate $R$ at which qubits can be generated and the total duration $\tau$ of a measurement as fixed resources, and we determine the optimal use of entanglement among the qubits and the resulting optimal measurement uncertainty as functions of $R$ and $\tau$.

We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the typical value of the second largest eigenvalue. The key idea is the use of Schwinger-Dyson equations from lattice gauge theory to efficiently compute averages over the unitary group.

Auger decay of ${\mathrm{Xe}}^{+}$ states arising from $4p$ ionization has been studied with a very efficient multielectron coincidence method. Coster-Kronig decay from ${\mathrm{Xe}}^{+}$ $4p^{-1}$ and the subsequent decay into ${\mathrm{Xe}}^{3+}$ states with three valence holes are identified. Formation of ${\mathrm{Xe}}^{4+}$ is also observed as quadruple coincidences between a $4p$ photoelectron and three Auger electrons. The relative probabilities of individual multi-ionization processes are determined from the coincidence yields.

Two-mode nonlinear interaction (second-harmonic and second-subharmonic generation) in a planar waveguide with a small periodic corrugation at the surface is studied. Scattering of the interacting fields on the corrugation leads to constructive interference that enhances the nonlinear process provided that all the interactions are phase matched. Conditions for the overall phase matching are found. Compared with a perfectly quasi-phase-matched waveguide, better values of squeezing as well as higher intensities are reached under these conditions. Procedure for finding optimum values of parameters for squeezed-light generation is described.