A relativistic wave equation for bound states of two fermions with arbitrary masses, which are exposed to a magnetic field, is derived from quantum electrodynamics. The interaction kernels are based upon the generalized invariant $\tilde{\mathcal{M}}$-matrices for interfermion and fermion-field interactions. As an application we calculate the energy corrections in a weak homogeneous $\mathbf{B}$ field to obtain the Zeeman splitting of the hyperfine structure and $g$ factors in the lowest order [i.e., to $O\left({\alpha }^4\right)$]. Landé $g$ factors are presented for several of the first excited states of hydrogen, muonium, and muonic hydrogen.

We numerically investigate a particular type of spin soliton inside a trapped atomic spin-1 Bose-Einstein condensate with ferromagnetic interactions. Within the mean-field theory approximation, our study of the solitonic dynamics shows that the solitonic wave function, its center-of-mass motion, and the local spin evolutions are stable and are intimately related to the domain structures studied recently in spin-1 ${}^{87}\mathrm{Rb}$ condensates. We discuss a rotating reference frame wherein the dynamics of the solitonic local spatial spin distribution becomes time independent.

We report on the origin of fragmentation of ultracold atoms observed on a magnetic film atom chip. Radio frequency spectroscopy and optical imaging of the trapped atoms is used to characterize small spatial variations of the magnetic field near the film surface. Direct observations indicate the fragmentation is due to a corrugation of the magnetic potential caused by long range inhomogeneity in the film magnetization. A model which takes into account two-dimensional variations of the film magnetization is consistent with the observations.

Conditional preparation of photon number states from a continuous-wave nondegenerate optical parametric oscillator is investigated. We derive the phase space Wigner function for the output state conditioned on photodetection events that are not necessarily simultaneous, and we maximize its overlap with the desired photon number state by choosing the optimal temporal output state mode function. We present a detailed numerical analysis for the case of two-photon state generation from a parametric oscillator driven with an arbitrary intensity below threshold, and in the low-intensity limit we present a formalism that yields the optimal output state mode function and fidelity for higher-photon-number states.

In a previous work [Phys. Rev. A. 73, 023421 (2006)] we investigated various forms of the Keldysh-Faisal-Reiss (KFR) theory for the ground state of a hydrogen atom when both conditions: $\omega ⪡1\mathrm{a.u.}$ and $\gamma ⪡1$ are satisfied. ($\omega$ is the laser frequency and $\gamma$ the Keldysh parameter.) We concluded, among other things, that when $F⪡1\mathrm{a.u.}$ ($F$ is the electric laser field) only the length gauge form of the WKB Coulomb corrected KFR theory may be consistent with the static field results in the limit $\omega \to 0$, $\gamma \to 0$. In the present paper, after making more accurate analytical calculations, we show that the velocity gauge counterpart of this theory behaves much better in this limit than it was suggested in our previous paper.

We report the observation of a coherent multimode instability in quantum cascade lasers (QCLs), which is driven by the same fundamental mechanism of Rabi oscillations as the elusive Risken-Nummedal-Graham-Haken (RNGH) instability predicted $40\text{years}$ ago for ring lasers. The threshold of the observed instability is significantly lower than in the original RNGH instability, which we attribute to saturable-absorption nonlinearity in the laser. Coherent effects, which cannot be reproduced by standard laser rate equations, can play therefore a key role in the multimode dynamics of QCLs, and in lasers with fast gain recovery in general.

We show that a cavity field can evolve from an initial displaced mixed thermal state to a macroscopic superpositions of displaced thermal states via resonant interaction with a two-level atom. As a macroscopic system (meter) is really in a mixed state before coupling with the microscopic system at some temperature, our result is important for studying the quantum measurement problem and decoherence under real conditions. For the two-mode case, entanglement of displaced thermal states between the modes can be obtained.

With the chiral representation, the Friedel sum rule for chiral fermions in odd space dimensions is given and the Levinson theorem which determines the number of discrete zero modes is obtained. Furthermore, the connections among the Friedel sum, Levinson theorem, and the Atiyah-Singer index are discussed, thereby proving that the Euclidean Atiyah-Singer index for the background field that describes an arbitrary short-range central force is zero.

We demonstrate that spin chains are experimentally feasible using electrons confined in micro-Penning traps, supplemented with local magnetic field gradients. The resulting Heisenberg-like system is characterized by coupling strengths showing a dipolar decay. These spin chains can be used as a channel for short-distance quantum communication. Our scheme offers high accuracy in reproducing an effective spin chain with relatively large transmission rate.

A general method for implementing multipartite unitary operations that are close to the identity using a small amount of entanglement and classical communication is presented. For cases where methods were previously known, our approach requires less entanglement. In addition, it is shown that, via compression, the average communication required from all parties except one may be reduced to the same as the entanglement. This improves upon previous methods which required a large amount of communication that did not scale down with the strength of the interaction.

We evaluate the exact concurrence between any two spins in a cyclic $XX$ chain of $n$ spins placed in a uniform transverse magnetic field, at both zero and finite temperature, by means of the Jordan-Wigner transformation plus a number-parity-projected statistics. It is shown that, while at $T=0$ there is always entanglement between any two spins in a narrow field interval before the transition to the aligned state, at low but nonzero temperatures the entanglement remains nonzero for arbitrarily high fields, for any pair separation $L$, although its magnitude decreases exponentially with increasing field. It is also demonstrated that the associated limit temperatures approach a constant nonzero value in this limit, which decreases as $L^{-2}$ for $L⪡n$, but exhibit special finite-size effects for distant qubits $(L\approx n∕2)$. Related aspects such as the different behavior of even and odd antiferromagnetic chains, the existence of $n$ ground-state transitions, and the thermodynamic limit $n\to \infty$ are also discussed.

We discuss quantum random walk of two photons using linear optical elements. We analyze the quantum random walk using photons in a variety of quantum states including entangled states. We find that for photons initially in separable Fock states, the final state is entangled. For polarization entangled photons produced by type-II downconverter, we calculate the joint probability of detecting two photons at a given site. We show the remarkable dependence of the two photon detection probability on the quantum nature of the state. In order to understand the quantum random walk, we present exact analytical results for small number of steps such as five. We present in detail numerical results for a number of cases and supplement the numerical results with asymptotic analytical results.

In Ebbinghaus et al. [Plasma Sources Sci. Technol. 15, 72 (2006)] we reported terahertz time-domain spectroscopy in a plasma at low pressure, we observed a simultaneous absorption and amplification process within each single rotational transition. Here we show that this observation is a direct consequence of the short interaction time of the pulsed terahertz radiation with the plasma, which is shorter than the average collision time between the molecules. Thus, during the measurement time the molecular states may be considered entangled. Solution of the time-dependent Schrödinger equation yields a linear term that may be neglected for long observation times, large frequencies, or nonentangled states. We determine the restrictions for the observation of this effect and calculate the spectrum of a simple diatomic molecule. Using this model we are able to explain the spectral features showing a change from emission to absorption as observed previously. In addition we find that the amplification and absorption do not follow the typical Lambert-Beer exponential law but an approximate square law.

The transition between $n=55$ and $n=109$ Rydberg levels of ${\mathrm{Kr}}^{5+}$ has been studied at high resolution using the resonant excitation stark ionization spectroscopy method. Resolved excitation of $L=6$, 7, 8, and 9 levels in $n=55$ lead to a determination of the fine-structure energies of these levels. Interpreted with the long-range polarization model, this leads to a measurement of the dipole polarizabilities of Zn-like ${\mathrm{Kr}}^{6+}$, ${\alpha }_d=2.69\left(4\right)a_0^3$. Obtaining a value of the quadrupole polarizability from the data will require additional theoretical input. Factors contributing to the signal and noise levels in measurements of this type are discussed.

Very recently, Ohsawa et al. have presented a new experimental apparatus for measuring doubly differential cross sections of electron emission from water vapor with fast heavy-ion impact $(6–25\mathrm{MeV})$. Successful measured energy and angular distributions of secondary electrons were produced for a collision of $6.0\mathrm{MeV}∕\mathrm{u}$ ${\mathrm{He}}^{2+}$ ions with vapor water [Nucl. Instrum. Methods Phys. Res. B 227, 431 (2005)] and for $10.0\mathrm{MeV}∕\mathrm{u}$ ${\mathrm{He}}^{2+}$ ions [Phys. Rev. A 72, 062710 (2005)]. The present theoretical work aims to reproduce these very recent measurements as well as more former existing data dedicated to low-energy alpha particles. Doubly, singly differential, and total ionization cross sections have then been studied.

We report the formation rate constants and the dissociation cross sections of ${\mathrm{Ba}}^{+*}\text{−}\mathrm{He}$ exciplexes in an environment of cold gaseous helium at temperatures of $3–25\mathrm{K}$. We have observed laser-induced fluorescence spectra of ${\mathrm{Ba}}^{+}$ and ${\mathrm{Ba}}^{+*}\text{−}\mathrm{He}$ exciplexes by means of $D2$ excitation of ${\mathrm{Ba}}^{+}$ ions. Using the rate equation analyses of fluorescence intensities of ${\mathrm{Ba}}^{+*}\text{−}\mathrm{He}$ and ${\mathrm{Ba}}^{+}$, we have determined the rate constant of exciplex formation (${\mathrm{Ba}}^{+}$: $6p$ ${}^{2}P_{3∕2}+2\mathrm{He}\to {\mathrm{Ba}}^{+*}\text{−}\mathrm{He}$: $6p$ ${}^2\Pi _{3∕2}+\mathrm{He}$) attributable to three-body collision at 5, 10, 15, and $20\mathrm{K}$. The formation rate constant was found to have irregular temperature dependence, with a local maximum $k_f=(6.0\pm 0.8)\times {10}^{-44}{\mathrm{m}}^6{\mathrm{s}}^{-1}$ at $15\mathrm{K}$. Results of this study also indicate peculiar temperature dependence of the dissociation cross section (${\mathrm{Ba}}^{+*}\text{−}\mathrm{He}$: $6p$ ${}^2\Pi _{3∕2}\to {\mathrm{Ba}}^{+}$: $6p$ ${}^{2}P_{1∕2}+\mathrm{He}$). It has a local maximum ${\sigma }_{\mathrm{dis}}=(3.1\pm 0.4)\times {10}^{-21}{\mathrm{m}}^2$ at $3.6\mathrm{K}$. In cold He gas at $25\mathrm{K}$ or lower, a new channel of population transfer from the $6p$ ${}^{2}P_{3∕2}$ state to the $6p$ ${}^{2}P_{1∕2}$ state of ${\mathrm{Ba}}^{+}$ is opened because both exciplex formation and dissociation start to occur frequently.

The energy levels involving the $0^{+}$, $(-1{)}^{+}$, $(-2{)}^{+}$ states of the lithium atom in strong magnetic fields up to $2.35\times {10}^7\mathrm{T}$ are investigated. Our computational approach is a full-core-plus-correlation (FCPC) method based on a set of anisotropic Gaussian orbitals nonlinearly optimized for different field strength. A detailed comparison between our method, the FCPC method in spherical coordinates, and the full configuration-interaction method is made. The dipole oscillator strengths of $1^2{0}^{+}\text{−}{1}^2(-1{)}^{+}$ and $1^2(-1{)}^{+}\text{−}{1}^2(-2{)}^{+}$ transitions, as well as the transition wavelengths for the transitions ${\nu }^2{0}^{+}\to {\mu }^2(-1{)}^{+}$ and ${\nu }^2(-1{)}^{+}\to {\mu }^2(-2{)}^{+}$ are also presented.

Within the framework of a mean-field description, we investigate atomic Bose-Einstein condensates, with attraction between atoms, under the action of a strong transverse confinement and periodic [optical-lattice (OL)] axial potential. Using a combination of the variational approximation, one-dimensional (1D) nonpolynomial Schrödinger equation, and direct numerical solutions of the underlying 3D Gross-Pitaevskii equation, we show that the ground state of the condensate is a soliton belonging to the semi-infinite band gap of the periodic potential. The soliton may be confined to a single cell of the lattice or extended to several cells, depending on the effective self-attraction strength $g$ (which is proportional to the number of atoms bound in the soliton) and depth of the potential, $V_0$, the increase of $V_0$ leading to strong compression of the soliton. We demonstrate that the OL is an effective tool to control the soliton’s shape. It is found that, due to the 3D character of the underlying setting, the ground-state soliton collapses at a critical value of the strength, $g=g_c$, which gradually decreases with the increase of $V_0$; under typical experimental conditions, the corresponding maximum number of ${}^7\mathrm{Li}$ atoms in the soliton, $N_{\max }$, ranges between 8000 and 4000. Examples of stable multipeaked solitons are also found in the first finite band gap of the lattice spectrum. The respective critical value $g_c$ again slowly decreases with the increase of $V_0$, corresponding to $N_{\max }\simeq 5000$.

Comprehensive numerical analysis of chirped-solitary-pulse stability in the positive-dispersion regime is presented. It is found that such a regime allowing generation of femtosecond pulses with energy above the microjoule level directly from a mode-locked oscillator is unstable against long-period pulsations. Pulsations are caused by the internal modes of solitary pulse and result in both symmetrical and asymmetrical perturbations of the pulse spectrum. This reduces a region of pulse stability and its coherence.

Strong-field phenomena are currently described as being multiphoton or tunneling, based on whether the Keldysh parameter $\gamma$ is greater than or less than unity. There are disqualifying features in this categorization. It is specific to the length gauge, dependent on only one intensity parameter, and backward in the sense that ionization with $\gamma ⪢1$ can occur only by tunneling, and ionization with $\gamma ⪡1$ must be over the barrier, and hence is not achieved by tunneling. As $\gamma$ becomes smaller, ionization becomes increasingly distant from tunneling, and eventually reaches conditions where the dipole approximation fails and there is no meaningful scalar-potential diagram at all.