The use of entanglement renormalization in the presence of scale invariance is investigated. We explain how to compute an accurate approximation of the critical ground state of a lattice model and how to evaluate local observables, correlators, and critical exponents. Our results unveil a precise connection between the multiscale entanglement renormalization ansatz and conformal field theory (CFT). Given a critical Hamiltonian on the lattice, this connection can be exploited to extract most of the conformal data of the CFT that describes the model in the continuum limit.

Optical ${\chi }^{\left(2\right)}$ nonlinearity can be used for parametric amplification and producing down-converted entangled photon pairs that have broad applications. It is known that weak nonlinear media exhibit dispersion and produce a frequency response. It is therefore of interest to know how spectral effects of a strong ${\chi }^{\left(2\right)}$ crystal affect the performance. Here we model the spectral effects of the dispersion of a strong ${\chi }^{\left(2\right)}$ crystal and illustrate how this affects its ability to perform Bell measurements and influence the performance of a quantum gates that employ such a Bell measurement. We show that a Dyson series expansion of the unitary operator is necessary in general, leading to unwanted spectral entanglement. We identify a limiting situation employing periodic poling, in which a Taylor series expansion is a good approximation and this entanglement can be removed.

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple tensor. We exploit this result in order to prove and extend a version of the Lieb-Schultz-Mattis theorem, one of the basic results in many-body physics, in the context of MPS. We illustrate the results with an exhaustive search of SU(2)-invariant two-body Hamiltonians which have such MPS as exact ground states or excitations.

The radiative charge transfer for ${\text{H}}^{+}+\text{Na}\left(3s\right)$ collisions has been investigated by using both the optical-potential and semiclassical methods in the energy ranges of ${10}^{-6}–10$ and ${10}^{-2}–100\text{eV}$, respectively, which are in agreement in the overlapping energy region. The relevant molecular potentials and dipole matrix elements were obtained from the multireference single- and double-excitation configuration interaction approach. The radiative charge-transfer cross sections display rich resonance structures, due to the formation of quasibound rotational-vibrational molecular states, in the energy range below 0.2 eV. The present radiative charge-transfer cross-section results disagree with the calculations of Watanabe et al. [Phys. Rev. A 66, 044701 (2002)]. The rate coefficient is obtained for temperatures between 0.1 and $20000\text{K}$. Below 7000 K, it has a nearly constant value of approximately $1.7\times {10}^{-13}{\text{cm}}^3{\text{s}}^{-1}$, which is about 1/3 of that of Watanabe et al. The nonradiative charge transfer becomes dominant at energies above 4 eV.

We develop a method for extracting fully differential cross sections for ionization from an impact-parameter treatment of the collision. The approach uses pseudostates. The method is applied to antiproton-impact ionization of H and He. It is not restricted to antiprotons but can be used with other projectiles. The method automatically includes the interaction between the projectile and the target nucleus. This interaction is shown to be very important in low-energy antiproton ionization. Integrated cross sections for elastic scattering, discrete excitation, ionization, and total scattering are also calculated. For ionization, these are compared with experimental data on H and He. At impact energies greater than 30 keV there is agreement with these data. At lower energies the calculated cross sections for He are in disagreement with the trend of the older experimental data of Andersen et al. and Hvelplund et al. but are in qualitative accord with the recent measurement of Knudsen et al. However, there is no overall quantitative agreement with the new measurements. First-order Born calculations are also presented as a benchmark for checking the pseudostate approximation.

Drawing from an analogy with a linear particle-chain model, we develop a picture of the dark optical soliton as a composite of a background and notch each enjoying a certain degree of independence. The semiclassical quantization procedure of Dashen et al. [Phys. Rev. D 11, 3424 (1975)] is modified to allow for the separate quantization of these two entities. We apply our results to the one-kink and two-kink dark solitons. For both we find that the fluctuations about the notch can be understood as a bound state of bosons held by an attractive delta potential while the background fluctuations are seen as an ensemble of oscillators with a slightly repulsive interaction. We show that the collision effects are small for the two-kink soliton. The quantum numbers emerging from this analysis are interpreted in terms of the number of particles. Moreover, the topological character of the dark soliton also appears naturally in our description. We speculate on the possibility of fractional quantum numbers and derive the repulsive interaction of two dark solitons from the framework developed for the two-kink soliton.

Carrier-envelope-phase-dependent effects of high-harmonic generation for two-level atoms interacting with Gaussian shape few-cycle pulses (with $\varphi =0$ and $\varphi =\pi /2$) have been investigated theoretically by using a time-frequency analysis. The differences in energies and populations of the two adiabatic states and the harmonic spectra in the cutoff region are illustrated. We find that, by tuning the carrier-envelope phase, the high-harmonic generation in the cutoff region can be controlled. Our results also show that the model of two-level atoms driven by few-cycle pulses can be used to study carrier-envelope phase effects.

Electromagnetically-induced transparency (EIT) of atomic medium interacting with two laser beams can exhibit effects of reciprocal influence of both beams on optical properties of the medium. If the probe beam reaches instantaneous intensity comparable to that of the control beam, considerable energy is transferred to the latter. Resulting increase in the control-beam intensity temporarily modifies EIT conditions and consequently affects propagation of probe-beam pulses. The effect is particularly strong in atomic media exhibiting significant dissipation of radiation energy due to relaxation processes efficiently counteracting the optical pumping. Coherent interaction of atoms with both beams causes reduction of dissipation of the control beam (reciprocal EIT conditions). Our experiments with hot rubidium vapor demonstrate the possibility of dual control over slow propagation of light pulses in such media. Besides the well-known dependence on input control-beam intensity, the delays of output probe pulses depended significantly also on the energy of input probe pulses. Moreover, for relatively short input pulses, very specific shape of output pulses was observed, invariant in wide ranges of input probe pulse energies and control-beam intensities. The shapes of the output pulses were also the same for short input pulses of different shapes as well as for pulses temporarily stored in the medium by switching off the control beam during their propagation.

By attributing a circulating Josephson current induced diamagnetic moment to a superconducting quantum interference device type three-level qubit, a wireless connection between such qubits is proposed based only on dipole-dipole interaction between their moments. The estimates of the model parameters suggest quite an optimistic possibility to experimentally realize the suggested coupling scheme.

We present a time-dependent density-functional-theory approach for the ab initio study of the effect of correlated multielectron responses on the multiphoton ionization (MPI) of diatomic molecules ${\text{N}}_2$, ${\text{O}}_2$, and ${\text{F}}_2$ in intense short laser pulse fields with arbitrary molecular orientation. We show that the contributions of inner molecular orbitals to the total MPI probability can be significant or even dominant over the highest-occupied molecular orbital, depending on detailed electronic structure and symmetry, laser field intensity, and orientation angle.

We experimentally demonstrate how the two-photon field generated by spontaneous parametric down-conversion contains an intriguing fine structure associated with the positional spread within the photon pair. The obtained results provide a three-dimensional picture of the near-field correlations, which are determined by the phase-matching conditions. These correlations are compared with previous results on second-harmonic generation, spatial antibunching, and transverse entanglement in parametric down-conversion.

The definition of a cluster state naturally suggests an implementation scheme: find a physical system with an Ising coupling topology identical to that of the target state and evolve freely for a time of $\frac{1}{2J}$. Using the tools of optimal control theory, we address the question of whether or not this implementation is time-optimal. We present some examples where it is not and provide an explanation in terms of geodesics on the Bloch sphere.

We propose a scheme for performing quantum simulations with atoms in cavities based on a photon detection feedback loop that requires only linear optical elements. Atoms can be stored individually without the need of directly interacting with one another. The scheme is able to simulate any time evolution that can be written as a sum of two-qubit Hamiltonians, e.g., any nearest-neighbor interaction on a lattice. It can also be made robust against photon losses.

The scheme of quantum teleportation, where Bob has multiple $\left(N\right)$ output ports and obtains the teleported state by simply selecting one of the $N$ ports, is thoroughly studied. We consider both the deterministic version and probabilistic version of the teleportation scheme aiming to teleport an unknown state of a qubit. Moreover, we consider two cases for each version: (i) the state employed for the teleportation is fixed to a maximally entangled state and (ii) the state is also optimized as well as Alice’s measurement. We analytically determine the optimal protocols for all the four cases and show the corresponding optimal fidelity or optimal success probability. All these protocols can achieve the perfect teleportation in the asymptotic limit of $N\to \infty$. The entanglement properties of the teleportation scheme are also discussed.

We report the experimentally determined oscillator strengths for the $5s6s$ ${{}^{1}S}_0\to 5snp$ ${{}^{1}P}_1$ Rydberg transitions of strontium using two-step excitation in conjunction with a thermionic diode ion detector. The absolute photoionization cross section from the $5s6s$ ${{}^{1}S}_0$ excited state has been determined by adjusting the polarization vector of the ionizing laser beam parallel, perpendicular, and at the magic angle with respect to that of the exciting dye laser. The measured absolute value of the photoionization cross section $0.9\pm 0.2\text{Mb}$ at the $5s$ threshold is used to extract the $f$ values of the $5s6s$ ${{}^{1}S}_0\to 5snp$ ${{}^{1}P}_1$ $\left(26\le n\le 73\right)$ Rydberg transitions. The oscillator strength in the discrete region merges smoothly to the oscillator strength density at the ionization threshold.

We apply a field-theoretic functional renormalization-group technique to the few-body (vacuum) physics of nonrelativistic atoms near a Feshbach resonance. Three systems are considered: one-component bosons with a U(1) symmetry, two-component fermions with a $\text{U}\left(1\right)\times \text{SU}\left(2\right)$ symmetry, and three-component fermions with a $\text{U}\left(1\right)\times \text{SU}\left(3\right)$ symmetry. We focus on the scale-invariant unitarity limit of an infinite scattering length. The exact solution for the two-body sector is consistent with the unitary fixed-point behavior of the considered systems. Nevertheless, the numerical three-body solution in the $s$-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3) fermions. The Efimov parameter for the one-component bosons and the three-component fermions is found to be $s\approx 1.006$, consistent with the result of Efimov.

Within the Born-Oppenheimer approximation, scaling laws are derived for isotopic homonuclear diatomic molecules interacting with strong few-cycles laser pulses. As a consequence of an approximate scaling of the transition dipole moment function between charge-resonant states, the Schrödinger equation describing the nuclear dynamics on the initial bonding Born-Oppenheimer curve for a given isotope can approximately be mapped to a reference molecule within that isotope. For other channels the presence of the external field inhibits a scaling even though in the field-free case scaling can be performed by a channel specific mapping. By comparing the scaling predictions with the results of ab initio calculations, insight is gained into the nature of the highly nonlinear dissociative ionization mechanisms.

We study the flow of a spinor $\left(F=1\right)$ Bose-Einstein condensate in the presence of an obstacle. We consider the cases of ferromagnetic and polar spin-dependent interactions, and find that the system demonstrates two speeds of sound that are identified analytically. Numerical simulations reveal the nucleation of macroscopic nonlinear structures, such as dark solitons and vortex-antivortex pairs, as well as vortex rings in one- and higher-dimensional settings, respectively, when a localized defect (e.g., a blue-detuned laser beam) is dragged through the spinor condensate at a speed larger than the second critical speed.

The Lamb shift in a Kerr nonlinear blackbody (KNB) is studied in the framework of nonrelativistic quantum electrodynamics theory. It is found that the Lamb shift in a KNB depends on the absolute temperature and the Kerr nonlinear coefficient. Below a transition temperature $T_c$, the Lamb shift is larger than that in a nonabsorbing linear medium. Under some conditions, the Lamb shift in a KNB can become much larger than that in a nonabsorbing linear medium or in free space. Above $T_c$, the Lamb shift equals that in a nonabsorbing linear medium. The application of our theory is also discussed.

In this paper, single-molecule spectroscopy experiments based on continuous laser excitation are characterized through an open quantum system approach. The evolution of the fluorophore system follows from an effective Hamiltonian microscopic dynamic where its characteristic parameters, i.e., its electric dipole, transition frequency, and Rabi frequency, as well as the quantization of the background electromagnetic field and their mutual interaction, are defined in an extended Hilbert space associated to the different configurational states of the local nanoenvironment. After tracing out the electromagnetic field and the configurational states, the fluorophore density matrix is written in terms of a Lindblad rate equation. Observables associated to the scattered laser field, such as optical spectrum, intensity-intensity correlation, and photon-counting statistics, are obtained from a quantum-electrodynamic calculation also based on the effective microscopic dynamic. In contrast with stochastic models, this approach allows one to describe in a unified way both the full quantum nature of the scattered laser field as well as the classical nature of the environment fluctuations. By analyzing different processes such as spectral diffusion, lifetime fluctuations, and light assisted processes, we exemplify the power of the present approach.