The four-body continuum-distorted-wave model is formulated and used to investigate single electron capture in fast collisions of hydrogenlike projectiles with one- and multi-electron targets. The presented method of an analytical calculation of scattering integrals yields the total cross sections in terms of four-dimensional numerical quadratures. As an illustration, total cross sections are computed for electron capture processes in ${\mathrm{He}}^{+}\text{−}\mathrm{H}$, ${\mathrm{He}}^{+}\text{−}\mathrm{He}$, and ${\mathrm{Li}}^{2+}\text{−}\mathrm{He}$ collisions at intermediate and high impact energies. The contribution from the interelectron interaction during the collision is evaluated. The prior and post total cross sections are found to be in good agreement with the available experimental data.

Elucidating the mechanisms of dephasing in the alkali-metal ground state hyperfine transition has remained an unsatisfactorily resolved problem since the mid-1960s, even though its solution has relevance to next-generation atomic clocks. Recently, however, measurements of electronic spin relaxation in strong magnetic fields have resolved a number of outstanding ambiguities, and the situation has greatly improved. Unfortunately, while these studies have illuminated the processes contributing to hyperfine transition dephasing, they only allow one to infer actual dephasing rates, $\gamma$. The direct measurement of dephasing rates remains problematic, primarily as a result of temperature gradient inhomogeneous broadening, which makes it nearly impossible to distinguish systematic from physical effects. Here, we demonstrate that by measuring $\gamma$ as a function of mole fraction in mixed buffer-gas systems we can isolate temperature gradient effects, thereby allowing a direct comparison between theory and experiment. In the present work, we examine the linewidth of the ${}^{87}\mathrm{Rb}$ hyperfine transition in $\mathrm{Ar}\text{−}{\mathrm{N}}_2$ mixed buffer-gas systems. We obtain good agreement between theory and experiment so long as we include the full dephasing contribution from RbAr van der Waals molecules: the spin-rotation contribution, ${\gamma }_{\mathrm{SR}}$, and the contribution from the change in ${}^{87}\mathrm{Rb}$ hyperfine coupling, ${\Gamma }_B$, which we refer to as the Bouchiat rate. We have been able to measure ${\Gamma }_B$, obtaining ${\Gamma }_B=87\pm 6{\mathrm{s}}^{-1}$ for RbAr.

A condensate in an optical lattice, prepared in the ground state of the superfluid regime, is stimulated first by suddenly increasing the optical lattice amplitude and then, after a waiting time, by abruptly decreasing this amplitude to its initial value. Thus the system is first taken to the Mott regime and then back to the initial superfluid regime. We show that, as a consequence of this nonadiabatic process, the system falls into a configuration far from equilibrium whose superfluid order parameter is described in terms of a particular superposition of Glauber coherent states that we derive. We also show that the classical equations of motion describing the time evolution of this system are inequivalent to the standard discrete nonlinear Schrödinger equations. By numerically integrating such equations with several initial conditions, we show that the system loses coherence, becoming insulating.

We propose a Pfaffian-like ansatz for the ground state of bosons subject to three-body infinite repulsive interactions in a one-dimensional (1D) lattice. Our ansatz consists of symmetrization over all possible ways of distributing the particles in two identical Tonks-Girardeau gases. We support the quality of our ansatz with numerical calculations and propose an experimental scheme based on mixtures of bosonic atoms and molecules in 1D optical lattices in which this Pfaffian-like state could be realized. Our findings may open the way for the creation of non-Abelian anyons in 1D systems.

We analyze the quantum theory of the two-mode micromaser pumped by cold three-level atoms with a $\Lambda$-configuration under the two-photon resonance condition. We focus more specifically on the large detuning limit where the detuning between the two cavity mode frequencies and the two atomic transition frequencies is large in comparison with the atom-cavity coupling constants. We show that this regime can mimic a virtual two-level atom micromaser without spontaneous emission where the cavity acts for the atoms as a potential barrier or a potential well (depending on the sign of the detuning) and a zero potential but no more both as a potential barrier and a potential well as it is the case for the usual cold two-level atom micromaser [M. O. Scully, G. M. Meyer, and H. Walther, Phys. Rev. Lett. 76, 4144 (1996)]. This introduces interesting options for engineering the interaction between the cold atoms and the cavity. The elimination of the spontaneous emission solves a major issue of the conventional cold two-level atom micromaser as the transit time of cold atoms inside and in the vicinity of the cavity is usually much larger than the atomic level lifetimes. It is also shown that the cold atom regime is very sensitive to the sign of the detuning (in contrast to the hot atom regime) and that, according to this sign, the cavity may speed up or slow down the incident three-level atoms after their interaction with the field.

We study a system of two-dimensional Bose gases trapped in minima of a deep one-dimensional optical lattice potential. Increasing the tunneling amplitude between adjacent gases drives a deconfinement transition to a phase where coherence is established between neighboring two-dimensional gases. We compute the signature of this transition in the interference pattern of the system as well as in its rotational response, which provides a direct measurement of the superfluidity in the system.

We propose a model, based on a quantum stochastic differential equation (QSDE), to describe the scattering of polarized laser light by an atomic gas. The gauge terms in the QSDE account for the direct scattering of the laser light into different field channels. Once the model has been set, we can rigorously derive quantum filtering equations for balanced polarimetry and homodyne detection experiments, study the statistics of output processes, and investigate a strong driving, weak coupling limit.

We derive different relations quantifying duality in a generic two-way interferometer. These relations set different upper bounds to the visibility $\mathcal{V}$ of the fringes measured at the output port of the interferometer. A hierarchy of inequalities is presented which exhibits the influence of the availability to the experimenter of different sources of which-way information contributing to the total distinguishability $\mathcal{D}$ of the ways. For mixed states and unbalanced interferometers an inequality is derived, ${\mathcal{V}}^2+{\Xi }^2\le 1$, which can be more stringent than the one associated with the distinguishability $({\mathcal{V}}^2+{\mathcal{D}}^2\le 1)$.

It is shown that quantum information stored in a two-level system coupled to a super-Ohmic bosonic bath is coherently distributed between the system and the environment. A different two-level subsystem, including a proper coherent state of the environment, satisfies all control, reset, and measurement conditions required for a qubit, including two-qubit conditional gates. Such a dressed qubit is decoupled from the remaining environmental degrees of freedom but its control imposes specific adiabaticity conditions. The dressed qubit is the actual physical medium in which quantum information is encoded whenever control operations are slower than the environment dynamics.

We present a control-theoretic analysis of a system consisting of a two-level atom coupled with a quantum harmonic oscillator. We show that, by applying external fields with just two resonant frequencies, any desired unitary operator can be generated.

The collective modes in a uniform fermionic atomic gas with Feshbach resonance are investigated with the path integral method in the frame of a fermion-boson model Hamiltonian. We mainly concentrated on the long-wavelength and low-frequency limits at $T=0\mathrm{K}$ and got an analytical expression for the collective modes across the whole BCS-Bose-Einstein condensate (BEC) crossover. We completely recover the Anderson-Bogoliubov modes in the BCS limit and the Bogoliubov modes of the bosonic systems in the BEC limit. The numerical results show that there exists a continuous interpolation for sound velocity between BCS and BEC limits.

We derive the frequency spectrum of the lowest compressional oscillations of a three-dimensional harmonically trapped Fermi superfluid in the presence of a vortex lattice, treated in the diffused vorticity approximation within a hydrodynamic approach. We consider the general case of a superfluid at $T=0$ characterized by a polytropic equation of state $(\sim n^{\gamma })$, which includes both the Bose-Einstein condensed regime of dimers $(\gamma =1)$ and the unitary limit of infinite scattering length $(\gamma =2∕3)$. Important limiting cases are considered, including the centrifugal limit, the isotropic trapping, and the cigar geometry. The conditions required to enter the lowest Landau level and quantum Hall regimes at unitarity are also discussed.

The modulational instability of continuous waves in nonlocal focusing and defocusing Kerr media with stochastically varying diffraction (dispersion) and nonlinearity coefficients is studied both analytically and numerically. It is shown that nonlocality with sign-definite Fourier images of the medium response functions considerably suppresses the growth rate peak and bandwidth of instability caused by stochasticity. In contrast, nonlocality can enhance modulational instability growth for a response function with negative-sign bands.

We present a linear optics quantum computation scheme with a greatly reduced cost in resources compared to that proposed by Knill, Laflamme, and Milburn (KLM). The scheme makes use of elements from cluster state computation but retains the circuit based approach of KLM.

We discuss the scaling of entanglement entropy in the random singlet phase (RSP) of disordered quantum magnetic chains of general spin $S$. Through an analysis of the general structure of the RSP, we show that the entanglement entropy scales logarithmically with the size of a block, and we provide a closed expression for this scaling. This result is applicable for arbitrary quantum spin chains in the RSP, being dependent only on the magnitude $S$ of the spin. Remarkably, the logarithmic scaling holds for the disordered chain even if the pure chain with no disorder does not exhibit conformal invariance, as is the case for Heisenberg integer-spin chains. Our conclusions are supported by explicit evaluations of the entanglement entropy for random spin-1 and spin-$3∕2$ chains using an asymptotically exact real-space renormalization group approach.

A general quantum theory is presented for unconventional anionic states supported by the presence of an external magnetic field. The theory applies to atomic anions and allows for straightforward extensions to anions formed in magnetic fields by other species, e.g., by clusters or small molecules. A special focus of the theory is on the coupling of the anion’s motion across the magnetic field to the motion of the attached electron. Neglecting this coupling, the magnetically induced anionic states are known to constitute an infinite manifold of bound states. In reality, the number of bound anionic states is finite. Typically, the quantized motion of the anion in the field results in sequences of excitations. These might include, depending on properties of the anion and on the magnetic field strengths, a few or a substantial number of states. Explicit results obtained by quantum ab initio calculations are presented and discussed on bound states and radiative transitions for some experimentally relevant atomic anions.

We use a Rb-stabilized ring-cavity resonator to measure the frequencies of the $D$ lines in ${}^{6,7}\mathrm{Li}$. Li spectroscopy is done by exciting a well-collimated atomic beam with a perpendicular diode laser beam and monitoring the resulting fluorescence. We obtain frequencies of $446789597.791\left(30\right)\mathrm{MHz}$ and $446800132.006\left(25\right)\mathrm{MHz}$ for the $D_1$ line and $446799650.653\left(60\right)\mathrm{MHz}$ and $446810184.005\left(33\right)\mathrm{MHz}$ for the $D_2$ line in the two isotopes. These values are consistent with earlier measurements, but represent an order-of-magnitude improvement in uncertainty. The measurements allow us to determine precisely the isotope shift in the $D$ lines and the fine-structure interval in the $2P$ state, which resolve several discrepancies among earlier measurements. The small negative isotope shift in the interval appears inconsistent with theoretical estimates.

For atoms with large scattering length, the dependence of the three-body recombination rate on the collision energy is determined by the scattering length and the Efimov three-body parameters and can be expressed in terms of universal functions of a single scaling variable. We use published results on the three-body recombination rate for ${}^4\mathrm{He}$ atoms to constrain the universal functions. We then use those universal functions to calculate the three-body recombination rate for other atoms with large scattering length at nonzero temperature. The constraints from the ${}^4\mathrm{He}$ results are strong if the scattering length is near the minimum of the three-body recombination rate at threshold. We apply our results to ${}^{133}\mathrm{Cs}$ atoms with a large positive scattering length, and compare them with experimental results from the Innsbruck group.

Absolute cross sections for electron-impact dissociation of $\mathrm{C}{\mathrm{H}}_2^{+}$ producing $\mathrm{C}{\mathrm{H}}^{+}$ and ${\mathrm{C}}^{+}$ fragment ions were measured in the $3–100\mathrm{eV}$ range using a crossed electron-ion beams technique with total uncertainties of about 11% near the cross section peak. The cross sections are nearly identical for energies above $15\mathrm{eV}$, but they are dramatically different at lower energies. The $\mathrm{C}{\mathrm{H}}^{+}$ channel exhibits a strong peak rising from an observed threshold of about $6\mathrm{eV}$; the ${\mathrm{C}}^{+}$ channel is relatively flat down to the lowest measured energy. Ionization cross sections for the $\mathrm{C}{\mathrm{H}}_2^{+}$ ion are also presented.

We consider a conducting and a permeable plate immersed in the vacuum of a scalar field. We calculate the photon production rate when two plates at a distance $H$ oscillate with a frequency ${\omega }_p$. For $H{\omega }_p∕\left(\pi c\right)<2$, the angular spectrum and photon production rates are significantly different from those of a conventional cavity with two conducting or two permeable plates.