The problem of the evaluation of the two-photon decay width of excited states in hydrogen is considered. Two different approaches to the evaluation of the width including cascades channels are employed: the summation of the transition probabilities for various decay channels and the evaluation of the imaginary part of the Lamb shift. As application, the two-photon decay channels for the $3s$ level of the hydrogen atom are evaluated, including the cascade transition probability $3s\text{−}2p\text{−}1s$. An important role is assigned to the two-photon decays in astrophysics context, since processes of this kind provide a possibility for the decoupling of radiation and matter in the early universe. We demonstrate the ambiguity of separation of the “pure” two-photon contribution and criticize the existing methods for such a separation.

We propose a quantum optical interface between an atomic and solid-state system. We show that quantum states in a single trapped atom can be entangled with the states of a semiconductor quantum dot through their common interaction with a classical laser field. The interference and detection of the resulting scattered photons can then herald the entanglement of the disparate atomic and solid-state quantum bits. We develop a protocol that can succeed despite a significant mismatch in the radiative characteristics of the two matter-based qubits. We study in detail a particular case of this interface applied to a single trapped ${{}^{171}\text{Y}\text{b}}^{+}$ ion and a cavity-coupled InAs semiconductor quantum dot. Entanglement fidelity and success rates are found to be robust to a broad range of experimental nonideal effects such as dispersion mismatch, atom recoil, and multiphoton scattering. We conclude that it should be possible to produce highly entangled states of these complementary qubit systems under realistic experimental conditions.

We analyze the magnetic dipole contribution to atom-surface dispersion forces. Unlike its electrical counterpart, it involves small transition frequencies that are comparable to thermal energy scales. A significant temperature dependence is found near surfaces with a nonzero dc conductivity, leading to a strong suppression of the dispersion force at $T>0$. We use thermal response theory for the surface material and discuss both normal metals and superconductors. The asymptotes of the free energy of interaction and of the entropy are calculated analytically over a large range of distances. Near a superconductor, the onset of dissipation at the phase transition strongly changes the interaction, including a discontinuous entropy. We discuss the similarities with the Casimir interaction between two surfaces and suggest that precision measurements of the atom-surface interaction may shed light upon open questions around the temperature dependence of dispersion forces between lossy media.

We study the stability of superfluid Fermi gases in deep optical lattices in the BCS–Bose-Einstein condensation (BEC) crossover at zero temperature. Within the tight-binding attractive Hubbard model, we calculate the spectrum of the low-energy Anderson-Bogoliubov (AB) mode as well as the single-particle excitations in the presence of superfluid flow in order to determine the critical velocities. To obtain the spectrum of the AB mode, we calculate the density response function in the generalized random-phase approximation applying the Green’s function formalism developed by Côté and Griffin to the Hubbard model. We find that the spectrum of the AB mode is separated from the particle-hole continuum having the characteristic rotonlike minimum at short wavelength due to the strong charge-density-wave fluctuations. The energy of the rotonlike minimum decreases with increasing the lattice velocity and it reaches zero at the critical velocity which is smaller than the pair-breaking velocity. This indicates that the superfluid state is energetically unstable due to the spontaneous emission of the short-wavelength rotonlike excitations of the AB mode instead due to pair breaking. We determine the critical velocities as functions of the interaction strength across the BCS-BEC crossover regime.

We provide analytical three-dimensional bright multisoliton solutions to the $\left(3+1\right)$-dimensional Gross-Pitaevskii equation with time- and space-dependent potential, time-dependent nonlinearity, and gain or loss. The zigzag propagation trace and the breathing behavior of solitons are observed. Different shapes of bright solitons and fascinating interactions between two solitons can be achieved with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.

The conjunction of atom-cavity physics and photonic structures (“solid light” systems) offers new opportunities in terms of more device functionality and the probing of designed emulators of condensed-matter systems. By analogy to the canonical one-electron approximation of solid-state physics, we propose a one-polariton approximation to study these systems. Using this approximation, we apply Bloch states to the uniformly tuned Jaynes-Cummings-Hubbard model to analytically determine the energy-band structure. By analyzing the response of the band structure to local atom-cavity control, we explore its application as a quantum simulator and show phase-transition features absent in mean-field theory. Using this approach for solid light systems, we extend the analysis to include detuning impurities to show the solid light analogy of the semiconductor. This investigation also shows features with no semiconductor analog.

Angular distributions of the ${\text{CO}}^{+}\left(A{}^2\Pi \right)$ photoelectrons and of the ${\text{CO}}^{+}\left(A{}^2\Pi \to X{{}^2\Sigma }^{+}\right)$ fluorescence are computed in the vicinity of the $1s^{-1}{\pi }^{\ast }$ resonant excitation of the ${\text{C}}^{\ast }\text{O}$ molecule. In the calculations, lifetime vibrational interference and the direct transition amplitude for population of the $A{}^2\Pi \left(v^{\prime }\right)$ states were taken into account ab initio. The weak direct photoionization channel induces broad exciting-photon energy range dispersions of the angular distribution parameters ${\beta }_A^e\left(\omega \right)$ and $\beta 2_A^X\left(\omega \right)$, and the nuclear vibrational motion causes variations of the computed parameters across the positions of the ${\text{C}}^{\ast }\text{O}\left(v_r\right)$ vibronic states. Present calculations are in good agreement with available vibrationally and angularly resolved resonant Auger spectra. Theoretical $\beta 2_A^X\left(\omega \right)$ parameters are in agreement with the experimental results from the polarization analysis of the ${\text{CO}}^{+}\left(A\text{−}X\right)$ fluorescence induced by linearly polarized synchrotron radiation.

We demonstrate that the characteristics of the high-order harmonic spectra generated by few-cycle carrier-envelope phase-stabilized pulses can be finely adjusted by controlling the time-dependent ellipticity. The experimental measurements show evidence for the generation of single, pairs, and trains of attosecond pulses by controlling the time window of linear polarization of the driving pulses. The influence of the carrier-envelope phase on the generation process in different confinement configurations is interpreted and analyzed using a nonadiabatic stationary phase model. We show that the xuv emission depends critically on particular aspects of the fundamental electric field that allows us to steer the electron trajectories on the time scale of tens of attoseconds.

We study the statistics of quantum interference for completely positive maps. We calculate analytically the mean interference and its second moment for finite-dimensional quantum systems interacting with a simple environment consisting of one or several spins (qudits). The joint propagation of the entire system is taken as unitary with an evolution operator drawn from the circular unitary ensemble (CUE). We show that the mean interference decays with a power law as function of the dimension of the Hilbert space of the environment, with a power that depends on the temperature of the environment.

We describe a low-pressure flow-through apparatus for generating hyperpolarized ${}^{129}\text{X}\text{e}$ and report its performance by examining both the output ${}^{129}\text{X}\text{e}$ polarization $P_{\text{Xe}}$ by NMR and the in situ Rb polarization profile by optically detected electron paramagnetic resonance. The polarizer is based on a previously presented design employing a long optical pumping cell, lean Xe mixture at low pressure, Rb presaturation, and counterflow of gas with respect to the direction of light propagation. The numerical model to which we compare the polarizer’s performance includes the temperature dependence of the $\text{Rb-}{}^{129}\text{X}\text{e}$ spin-exchange rate, which has not previously been treated. The qualitative trends in the data mostly follow those in the model, although the model predicts $P_{\text{Xe}}$ to be up to a factor of two higher than observed. This discrepancy cannot be attributed to low Rb polarization: the model and the optically detected electron paramagnetic resonance data (acquired at six points along the length of the heated portion of the optical pumping cell) are in reasonable agreement and show typical values of 85%–95%, although measurements also reveal an anomalous region of depressed Rb polarization near the middle of the cell. The highest output ${}^{129}\text{X}\text{e}$ polarization $P_{\text{Xe}}=84\pm 16\%$, was recorded using $\approx 60\text{W}$ of frequency-narrowed laser light at a Xe partial pressure (referenced to $20°\text{C}$) of $1.1\pm 0.2\text{mbar}$, flowing at 1 sccm of Xe; typical values were $P_{\text{Xe}}\approx 20\%$ flowing at 10 sccm of Xe with $\approx 30\text{W}$ of laser light.

The pressure broadening and shift rates for the cesium $D_1$ $\left(6{{}^{2}P}_{1/2}\leftarrow 6{{}^{2}S}_{1/2}\right)$ transition with the noble gases and ${\text{N}}_2$, ${\text{H}}_2$, HD, ${\text{D}}_2$, ${\text{CH}}_4$, ${\text{C}}_2{\text{H}}_6$, ${\text{CF}}_4$, and ${}^3\text{H}\text{e}$ were obtained for pressures less than 300 torr at temperatures under $65°\text{C}$ by means of laser absorption spectroscopy. The collisional broadening rate, ${\gamma }_L$, for He, Ne, Ar, Kr, Xe, ${\text{N}}_2$, ${\text{H}}_2$, HD, ${\text{D}}_2$, ${\text{CH}}_4$, ${\text{C}}_2{\text{H}}_6$, ${\text{CF}}_4$, and ${}^3\text{H}\text{e}$ are 24.13, 10.85, 18.31, 17.82, 19.74, 16.64, 20.81, 20.06, 18.04, 29.00, 26.70, 18.84, and 26.00 MHz/torr, respectively. The corresponding pressure-induced shift rates, $\delta$, are 4.24, $-1.60$, $-6.47$, $-5.46$, $-6.43$, $-7.76$, 1.11, 0.47, 0.00, $-9.28$, $-8.54$, $-6.06$, and 6.01 MHz/torr. These rates have then been utilized to calculate Lennard-Jones potential coefficients to quantify the interatomic potential surfaces. The broadening cross section has also been shown to correlate with the polarizability of the collision partner.

We investigate magnetism and quantum phase transitions in a one-dimensional system of integrable spin-1 bosons with strongly repulsive density-density interaction and antiferromagnetic spin-exchange interaction via the thermodynamic Bethe ansatz method. At zero temperature, the system exhibits three quantum phases: (i) a singlet phase of boson pairs when the external magnetic field $H$ is less than the lower critical field $H_{c1}$; (ii) a ferromagnetic phase of atoms in the hyperfine state $|F=1,m_F=1⟩$ when the external magnetic field exceeds the upper critical field $H_{c2}$; and (iii) a mixed phase of singlet pairs and unpaired atoms in the intermediate region $H_{c1}<H<H_{c2}$. At finite temperatures, the spin fluctuations affect the thermodynamics of the model through coupling the spin bound states to the dressed energy for the unpaired $m_F=1$ bosons. However, such spin dynamics is suppressed by a sufficiently strong external field at low temperatures. Thus the singlet pairs and unpaired bosons may form a two-component Luttinger liquid in the strong coupling regime.

We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct “phases”—one in which every state is a universal resource for quantum computation, and another in which any local measurement sequence can be simulated efficiently on a classical computer. Remarkably, this transition in computational power does not coincide with any phase transition, classical, or quantum in the underlying spin-lattice model.

We report improved precision measurements of the van der Waals potential strength $\left(C_3\right)$ for Na atoms and a silicon-nitride $\left({\text{SiN}}_x\right)$ surface. We studied diffraction from nanofabricated gratings with a particular “magic” open fraction that allows us to determine $C_3$ without the need for separate measurements of the width of the grating openings. Therefore, finding the magic open fraction improves the precision of $C_3$ measurements. The same effect is demonstrated for a grating with an arbitrary open fraction by rotating it to a particular “magic” angle, yielding $C_3=3.42\pm 0.19\text{eV}{\text{Å}}^3$ for Na and a ${\text{SiN}}_x$ surface. This precision is sufficient to detect a change in $C_3$ due to a thin metal coating on the grating surface. We discuss the contribution to $C_3$ of core electrons and edge effects.

We propose a scheme to trap cold atoms (or molecules) by using an improved red- or blue-detuned far-field optical trap, which is formed by an optical system composed of a binary phase plate and a circular aperture illuminated by a plane light wave. We calculate the relative intensity distribution of the far-field trap and study its dependence on the phase $\phi$ of the binary phase plate. Our study shows that the binary phase plate can be used to improve some geometric and optical parameters of the far-field optical trap, and realize the evolution of the far-field optical trap from a red-detuned trap to a blue-detuned one. In particular, when the phase $\phi$ of the binary phase plate is changed from 0 to $-\pi$, the maximum intensity of the far-field trap and its well depth will be enhanced by $\sim 4$ times, and the corresponding trapping volume will be increased by $\sim 8$ times, with respect to a trapping beam obtained from the diffraction by a circular aperture.

Numerical solution of the time-dependent Schrödinger equation for a two-dimension model of ${\text{H}}_2$ ionization by intense ultrashort (few cycles) extreme ultraviolet (XUV) laser pulses are presented to compare linear and circular polarization angular distributions for aligned molecules. Both ground $\left(X{{}^1\Sigma }_g^{+}\right)$ and excited $\left(A{{}^3\Sigma }_u^{+}\right)$ states ionization is calculated at equilibrium and for extended large internuclear distance configurations to study the effect of electron delocalization via molecular orbitals vs electron localization in Heitler-London atomic wave functions. It is found that at large distance for ionized electron wavelengths less than the internuclear distance, circular polarization ionization angular distributions exhibit signature of the entanglement of electrons by exchange, thus, allowing for a measure of exchange entanglement.

We investigate the exact nature of the superfluid–to–Mott-insulator crossover for interacting bosons on an optical lattice in a one-dimensional harmonic trap by high-precision density-matrix renormalization-group calculations. The results reveal an intermediate regime characterized by a cascade of microscopic steps. These arise as a consequence of individual boson “squeezing” events and display an even-odd alternation dependent on the trap symmetry. We discuss the experimental observation of this behavior, which is generic in an external trapping potential.

Inconsistencies are pointed out in the usual quantum versions of the classical linear Boltzmann equation constructed for a quantized test particle in a gas. These are related to the incorrect formal treatment of momentum decoherence. We prove that ideal collisions with the molecules would result in complete momentum decoherence, the persistence of coherence is only due to the finite intercollision time. A corresponding quantum linear Boltzmann equation is proposed.

Quantum random walks have received much interest due to their nonintuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable and not limited to special connectivity criteria. We present a scheme for walking on arbitrarily complex graphs, which can be realized using a variety of quantum systems such as a Bose-Einstein condensate trapped inside an optical lattice. This scheme is particularly elegant since the walker is not required to physically step between the nodes; only flipping coins is sufficient.

The scattering wave function and the transition amplitude for the two-body Coulomb problem are written as power series of the Sommerfeld parameter. Making use of a mathematical study of the $n\text{th}$ derivatives of Kummer function with respect to its first parameter, the series coefficients are expressed analytically in terms of multivariable hypergeometric functions. We establish the connection with the Born series based on the free particle Green’s function and show its applicability to long-range potentials. We also relate our analysis to recent works on the distorted-wave theory for the Coulomb problem. For the transition amplitude, the Born series is presented and compared to the series obtained from the exact well-known Rutherford result. Since the two series differ, care must be taken when extracting the relevant information about the scattering. Finally, implications for three-body problems are discussed.