A “quasideterministic” scheme to generate a two-photon generalized binomial state in a single-mode high-$Q$ cavity is proposed. We also suggest a single-shot scheme to measure the generated state based on a probe two-level atom that “reads” the cavity field. The possibility of implementing the schemes is discussed.

We propose an experimental setup of ultracold fermions in an optical lattice to determine the pairing gap in a superfluid state and the spin ordering in a Mott-insulating state. The idea is to apply a periodic modulation of the lattice potential and to use the thereby induced double occupancy to probe the system. We show by full time-dependent calculation using the adaptive time-dependent density-matrix renormalization-group method that the position of the peak in the spectrum of the induced double occupancy gives the pairing energy in a superfluid and the interaction energy in a Mott insulator, respectively. In the Mott insulator we relate the spectral weight of the peak to the spin ordering at finite temperature using perturbative calculations.

The Coulomb fragmentation patterns of multicharged sodium clusters $\mathrm{Na}_n{}^{Q+}$ are theoretically investigated in broad size range $55⩽n⩽923$ and for charges $Q⩽50$ below and accross the Rayleigh stability limit. An empirical many-body potential is used to model the main cohesion energy in the neutral clusters. The extra electrostatic interaction is described using a specific fluctuating-charge model, which correctly reproduces the surface localization but can be tuned to represent a uniform distribution. Molecular dynamics simulations are performed by sampling the liquidlike state of the neutral clusters, then charging them instantaneously and following their fragmentation behavior. In order to achieve meaningful statistics, an extended Lagrangian scheme is used to accelerate the propagation when a surface charge is simulated. It is generally found that clusters with charge on the surface decay by emitting small fragments, essentially monomers, both above and below the Rayleigh limit. For fissilities close to 1, large clusters lost about 30%–40% of their charge but only a few percent of the mass is lost. These values agree with experimental data on mesoscopic conducting droplets. In contrast, the uniform charge distribution leads to fission into two or more large fragments when the fissility parameter approaches 1 and the fragmentation becomes more and more asymmetric as the charge increases. The distributions of fragments, average fragment sizes, and charges are estimated. The time scales for fragmentation show that fission into large fragments is much slower than the emission of surface atoms, particularly close to the Rayleigh threshold. In the case of surface-charged clusters, Coulomb multifragmentation appears to be mainly isotropic.

An intensive study for both the weak coupling and strong coupling limits of the ground state properties of this classic system is presented. Detailed results for specific values of finite $N$ are given and from them results for general $N$ are determined. We focus on the density matrix and concomitantly its Fourier transform, the occupation numbers, along with the pair correlation function and concomitantly its Fourier transform, the structure factor. These are the signature quantities of the Bose gas. One specific result is that for weak coupling a rational polynomial structure holds despite the transcendental nature of the Bethe equations. All these results are predicated on the Bethe ansatz and are built upon the seminal works of the past.

The hyperfine splitting of energy levels in the ${{\mathrm{H}}_2}^{+}$ molecular ion is calculated within the framework of the spin-dependent part of the Breit-Pauli Hamiltonian. This is the first ab initio calculation based on the precise variational solution of the three-body Schrödinger equation. It is shown that inclusion of the nuclear spin-spin tensor interaction, neglected in previous theoretical considerations, brings agreement with the most precise hyperfine transition measurements obtained by Jefferts to about $1\mathrm{kHz}$ for the lower-frequency intervals in the $5–100\mathrm{MHz}$ range. Finally, we investigate the hyperfine structure of some transitions, candidates for high-precision two-photon spectroscopy.

In this paper, I study the coherent control and suppression of the free-induction-decay emission associated with the decay from an excited multilevel atom to its ground state. It is shown here that a strong and ultrashort coupling pulse, resonant with the excited states and a lower state other than the ground state, can induce destructive quantum interferences in the decay process. The suppression is temporary and the free-induction-decay signal reappears one quantum-beat period (of the excited states) later. A sequence of equally spaced, ultrashort coupling pulses can control the moment the free-induction-decay emission occurs.

Translational transverse shifts drastically affect pattern formation in a noisy system with optical feedback. These strong nonlocal interactions may give rise to large domains of convective instability resulting in various types of two-dimensional (2D) noise-sustained structures. These “basic patterns” are investigated and their thresholds and properties are analytically derived. Corresponding 2D experimental patterns are shown to be in complete agreement with theory. Surprisingly enough, some patterns that are purely sustained by noise are found to be nondrifting in contrast with the commonly widespread situation in which convective instabilities lead to traveling patterns.

The spin state of an atomic ensemble can be viewed as two bosonic modes, i.e., a quantum signal mode and a $c$-numbered “local oscillator” mode when large numbers of spin-1/2 atoms are spin polarized along a certain axis and collectively manipulated within the vicinity of the axis. We present a concrete procedure, which determines the spin-excitation-number distribution, i.e., the diagonal elements of the density matrix in the Dicke basis for the collective spin state. By seeing the collective spin state as a statistical mixture of the inherently entangled Dicke states, the physical picture of its multiparticle entanglement is made clear.

We analyze a nondegenerate three-level cascade laser coupled to a two-mode vacuum reservoir employing the stochastic differential equations associated with the normal ordering. We study the squeezing properties and entanglement amplification of the cavity radiation. We also calculate the correlation of the photon numbers and the fluctuations of the intensity difference. It turns out that the generated light exhibits a two-mode squeezing and entanglement when initially there are more atoms in the lower level. Moreover, a strong correlation between photon numbers along with a significant fluctuation in the intensity difference is found.

Using a velocity formula derived by matched asymptotic expansion, we study the dynamics of a vortex ring in an axisymmetric Bose-Einstein condensate in the Thomas-Fermi limit. The trajectory for an axisymmetrically placed and oriented vortex ring shows that it generally precesses in a condensate. The linear instability due to bending waves is investigated both numerically and analytically. General stability boundaries for various perturbed wave numbers are computed. Our analysis suggests that a slightly oblate trap is needed to prevent the vortex ring from becoming unstable.

There has been much recent effort to realize quantum devices in many different physical systems. Among them, nuclear magnetic resonance (NMR) has been the first to demonstrate nontrivial quantum algorithms with small numbers of qubits and hence is a prototype for the key ingredients needed to build quantum computers. An important building block in many quantum applications is the scattering circuit, which can be used as a quantum multimeter to perform various quantum information processing tasks directly without recourse to quantum tomography. We implement in NMR a three-qubit version of the multimeter and also demonstrate a single-qubit fingerprinting.

The majorization theory has been applied to analyze the mathematical structure of quantum algorithms. An empirical conclusion by numerical simulations obtained in the previous literature indicates that step-by-step majorization seems to appear universally in quantum adiabatic algorithms. In this paper, a rigorous analysis of the majorization arrow in a special class of quantum adiabatic algorithms is carried out. In particular, we prove that for any adiabatic algorithm of this class, step-by-step majorization of the ground state holds exactly. For the actual state, we show that step-by-step majorization holds approximately, and furthermore that the longer the running time of the algorithm, the better the approximation.

Quantum electrodynamic (QED) corrections to $4p\text{−}4d$ transition energies of several copperlike ions with $Z=70–92$ are calculated nonperturbatively in strong external fields to all orders in binding corrections. Dirac-Kohn-Sham potentials are used to account for screening and core-relaxation effects. For the $4p_{1∕2}\text{−}4d_{3∕2}$ transition in copperlike bismuth, thorium, and uranium, results are in good agreement with empirical QED corrections deduced from differences between transition energies obtained from recent high-precision electron-beam ion-trap measurements and those calculated with the relativistic many-body perturbation theory (RMBPT). These comparisons provide sensitive tests of QED corrections for high-angular-momentum states in many-electron heavy ions and illustrate the importance of core-relaxation corrections. Comparisons are also made with other theories and with experiments on the $4s\text{−}4p$ transition energies of high-$Z$ Cu-like ions as accuracy checks of the present RMBPT and QED calculations.

The differential cross sections for low-energy muonic hydrogen atom scattering from hydrogenic molecules are directly expressed by the corresponding amplitudes for muonic atom scattering from hydrogen-isotope nuclei. The energy and angular dependence of these three-body amplitudes is thus taken naturally into account in scattering from molecules, without involving any pseudopotentials. Effects of the internal motion of nuclei inside the target molecules are included for every initial rotational-vibrational state. These effects are very significant as the considered three-body amplitudes often vary strongly within the energy interval $\lesssim 0.1\mathrm{eV}$. The differential cross sections, calculated using the presented method, have been successfully used for planning and interpreting many experiments in low-energy muon physics. Studies of ${\mu }^{-}$ nuclear capture in $p\mu$ and the measurement of the Lamb shift in $p\mu$ atoms created in ${\mathrm{H}}_2$ gaseous targets are recent examples.

An extension of the recently proposed approach [O. I. Tolstikhin, Phys. Rev. A 73, 062705 (2006)] to the whole-axis problem is presented. Here, the motion in a one-dimensional time-dependent potential is considered. The solution to the time-dependent Schrödinger equation is expanded in terms of Siegert states. A set of coupled equations defining time evolution of the coefficients in the expansion is derived, in pseudodifferential and integral forms, and physical observables (probabilities of transitions to discrete states and the spectrum of ejected particles) are expressed in terms of these coefficients. The approach is implemented in terms of Siegert pseudostates and illustrated by calculations for a model system.

In controlled quantum dynamics, a level set is defined as the collection of control fields that produce a specific value for a particular observable. This paper explores the relationship between individual solutions to a control problem, and presents the first experimentally observed quantum control level sets, which are found to be continuous submanifolds. Level sets are observed for two photon transitions where the control is the spectral phase function, which is expressed as a fourth-order polynomial. For the systems studied here, the level sets are shown to be closed surfaces in the spectral phase control space. A perturbation analysis provides insight into the observed topology of the level set, which is shown to be preserved by the low-order polynomial phase representation. Each of the multiple control fields forming a level set preserves the observable value by its own distinct manipulation of constructive and destructive quantum interferences. Thus, the richness of quantum control fields meeting a particular observable value is accompanied by an equally diverse family of control mechanisms.

We consider the motion of a vortex in an asymptotically homogeneous condensate bounded by a solid wall where the wave function of the condensate vanishes. For a vortex parallel to the wall, the motion is essentially equivalent to that generated by an image vortex, but the depleted surface layer induces an effective shift in the position of the image compared to the case of a vortex pair in an otherwise uniform flow. Specifically, the velocity of the vortex can be approximated by $U\approx (\hslash ∕2m){(y_0-\sqrt{2}\xi )}^{-1}$, where $y_0$ is the distance from the center of the vortex to the wall, $\xi$ is the healing length of the condensate, and $m$ is the mass of the boson.

We analyze photoionization and ion detection as a means of accurately counting ultracold atoms. We show that it is possible to count clouds containing many thousands of atoms with accuracies better than $N^{-1∕2}$ with current technology. This allows the direct probing of sub-Poissonian number statistics of atomic samples. The scheme can also be used for efficient single-atom detection with high spatiotemporal resolution. All aspects of a realistic detection scheme are considered, and we discuss experimental situations in which such a scheme could be implemented.

The form and stability properties of axisymmetric and spherically symmetric stationary states in two and three dimensions, respectively, are elucidated for Bose-Einstein condensates. These states include the ground state, central vortices, and radial excitations of both. The latter are called ring solitons in two dimensions and spherical shells in three. The nonlinear Schrödinger equation is taken as the fundamental model; both extended and harmonically trapped condensates are considered. It is found that the instability times of ring solitons can be long compared to experimental time scales, making them effectively stable over the lifetime of an experiment.

The self-guiding of femtosecond light pulses in dense materials is investigated both theoretically and numerically for various laser wavelengths. Special attention is paid on chromatic dispersion, plasma gain, and multiphoton absorption in the nonlinear evolution of ultrashort filaments. First, by mapping the dispersion versus the ratio of beam power over the critical power for self-focusing we justify the existence of special propagation regimes, in which the beam self-channels with weak plasma response. Second, we prove that at low wavelengths multiphoton losses can quench the emission of free electrons, which justifies recent experimental observations of no apparent electron emission in water.