We investigate the full spectrum in the two-level atomic system strongly driven by a fundamental laser field with its much weaker harmonic field whose frequency is within the cutoff domain and find that the spectrum lines are more plentiful and the plateau is significantly extended due to their interference.

We present results for the ground states of a system of spin-1 bosons in a rotating trap. We focus on the dilute, weakly interacting regime, and restrict the bosons to the quantum states in the lowest Landau level (LLL) in the plane (disk), sphere, or torus geometries. We map out parts of the zero-temperature phase diagram, using both exact quantum ground states and LLL mean-field configurations. For the case of a spin-independent interaction we present exact quantum ground states at angular momentum $L<~N.\mathrm{}$ For general values of the interaction parameters, we present mean-field studies of general ground states at slow rotation and of lattices of vortices and skyrmions at higher rotation rates. Finally, we discuss quantum Hall liquid states at ultrahigh rotation.

We examine an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a rotating toroidal trap, as the magnitude of the coupling constant and the rotational frequency are varied. Using both a variational mean-field approach, as well as a diagonalization technique, we identify the phase diagram between a uniform and a localized state and we describe the system in the two phases.

We consider a system of mutually interacting spins 1/2 embedded in a transverse magnetic field which undergoes a second-order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusplike singularity appears at the critical point ${\lambda }_c$ in the thermodynamical limit. We also show that there exists a value ${\lambda }_0>~{\lambda }_c$ above which the ground state is not spin squeezed despite a nonvanishing concurrence.

Fingerprinting is a technique in communication complexity in which two parties (Alice and Bob) with large data sets send short messages to a third party (a referee), who attempts to compute some function of the larger data sets. For the equality function, the referee attempts to determine whether Alice’s data and Bob’s data are the same. In this paper, we consider the extreme scenario of performing fingerprinting where Alice and Bob both send either one bit (classically) or one qubit (in the quantum regime) messages to the referee for the equality problem. Restrictive bounds are demonstrated for the error probability of one-bit fingerprinting schemes, and show that it is easy to construct one-qubit fingerprinting schemes which can outperform any one-bit fingerprinting scheme. The author hopes that this analysis will provide results useful for performing physical experiments, which may help to advance implementations for more general quantum communication protocols.

We introduce a family of separability criteria that are based on the existence of extensions of a bipartite quantum state ρ to a larger number of parties satisfying certain symmetry properties. It can be easily shown that all separable states have the required extensions, so the nonexistence of such an extension for a particular state implies that the state is entangled. One of the main advantages of this approach is that searching for the extension can be cast as a convex optimization problem known as a semidefinite program. Whenever an extension does not exist, the dual optimization constructs an explicit entanglement witness for the particular state. These separability tests can be ordered in a hierarchical structure whose first step corresponds to the well-known positive partial transpose (Peres-Horodecki) criterion, and each test in the hierarchy is at least as powerful as the preceding one. This hierarchy is complete, in the sense that any entangled state is guaranteed to fail a test at some finite point in the hierarchy, thus showing it is entangled. The entanglement witnesses corresponding to each step of the hierarchy have well-defined and very interesting algebraic properties that, in turn, allow for a characterization of the interior of the set of positive maps. Coupled with some recent results on the computational complexity of the separability problem, which has been shown to be NP hard, this hierarchy of tests gives a complete and also computationally and theoretically appealing characterization of mixed bipartite entangled states.

It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the “monogamous nature of entanglement.” In this paper we present a simple identity which captures the trade off between entanglement and classical correlation, which can be used to derive rigorous monogamy relations. We also prove various other trade offs of a monogamy nature for other entanglement measures and secret and total correlation measures.

Using the quadruple-ion-coincidence momentum imaging technique, we find that the momentum correlation of the four atomic ions departed from one ${\mathrm{BF}}_3^{4+}$ parent molecular ion produced via multiple Auger decay after $\mathrm{F}1s$ ionization exhibits asymmetric fragmentation in which the ${\mathrm{B}}^{+}$ ion is ejected in the direction opposite to one of the ${\mathrm{F}}^{+}$ ions. This observation provides evidence of symmetry lowering, from $D_{3h}$ to $C_{3v}$ in the $\mathrm{F}1s$–ionized state.

The duration-time concept, vastly successful for interpreting the frequency dependence of resonant radiative and nonradiative x-ray scattering spectra, is tested for fine-scale features that can be obtained with state of the art high-resolution spectroscopy. For that purpose resonant photoelectron (RPE) spectra of the first three outermost singly ionized valence states $X{}^2{\Sigma }_g^{+},$ $A{}^2{\Pi }_u,$ and $B{}^2{\Sigma }_u^{+},$ are measured for selective excitations to different vibrational levels (up to $n=13)$ of the N $1\overrightarrow{s}{\pi }^{*}$ photoabsorption resonance in ${\mathrm{N}}_2$ and for negative photon frequency detuning relative to the adiabatic 0-0 transition of this resonance. It is found that different parts of the RPE spectrum converge to the spectral profile of direct photoionization (fast scattering) for different detunings, and that the RPE profiles are asymmetrical as a function of frequency detuning. The observed asymmetry contradicts the picture based on the simplified notation of a common scattering duration time, but is shown to agree with the here elaborated concept of partial and mean duration times. Results of the measurements and the simulations show that the duration time of the scattering process varies for different final electronic and different final vibrational states. This owes to two physical reasons: one is the competition between the fast “vertical” and the slow “resonant” scattering channels and the other is the slowing down of the scattering process near the zeros of the real part of the scattering amplitude.

Due to the immiscibility of ${}^3\mathrm{He}$ into ${}^4\mathrm{He}$ at very low temperatures, mixed helium droplets consist of a core of ${}^4\mathrm{He}$ atoms coated by a ${}^3\mathrm{He}$ layer whose thickness depends on the number of atoms of each isotope. When these numbers are such that the centrifugal kinetic energy of the ${}^3\mathrm{He}$ atoms is small and can be considered as a perturbation to the mean-field energy, a novel shell structure arises, with magic numbers different from these of pure ${}^3\mathrm{He}$ droplets. If the outermost shell is not completely filled, the valence atoms align their spins up to the maximum value allowed by the Pauli principle.

We describe experiments where two-dimensional (2D) atomic hydrogen gas is compressed thermally at a small “cold spot” on the surface of superfluid helium and detected directly with electron-spin resonance. We reach surface densities up to $5\times {10}^{12}{\mathrm{cm}}^{-2}$ at temperatures $\approx 100\mathrm{mK}$ corresponding to the maximum 2D phase-space density $\approx \mathrm{1.5.}$ By independent measurements of the surface density and its decay rate we make a direct determination of the three-body recombination rate constant and get the upper bound $L_{3b}\lesssim 2\times {10}^{-25}{\mathrm{cm}}^4/\mathrm{s}$ which is an order of magnitude smaller than previously reported experimental results.

In terms of exact solutions of the time-dependent Schrödinger equation for an effective giant spin modeled from a coupled two-mode Bose-Einstein condensate (BEC) with adiabatic and cyclic time-varying Raman coupling between two hyperfine states of the BEC, we obtain analytic time-evolution formulas of the population imbalance and relative phase between two components with various initial states, especially the SU(2) coherent state. We find the Berry phase depending on the number parity of atoms, and particle number dependence of the collapse revival of population-imbalance oscillation. It is shown that self-trapping and phase locking can be achieved from initial SU(2) coherent states with proper parameters.

We prove that the binegativity is always positive for any two-qubit state. As a result, and as suggested by previous work, the asymptotic relative entropy of entanglement in two qubits does not exceed the Rains bound, and the positive partial transposed-entanglement cost for any two-qubit state is determined to be the logarithmic negativity of the state. Further, the proof reveals some geometrical characteristics of the entangled states, and shows that partial transposition can give another separable approximation of the entangled state in two qubits.

Quantum fluctuations of optical fiber-Bragg-grating solitons are investigated numerically by the back-propagation method. It is found that the band-gap effects of the grating act as a nonlinear filter and cause the soliton to be amplitude squeezed. The squeezing ratio saturates after a certain grating length and the optimal squeezing ratio occurs when the pulse energy is slightly above the fundamental soliton energy.

We show that the temporal peak of a quantum wave may arrive at different locations simultaneously in an absorbing medium. The arrival occurs at the lifetime of the particle in the medium from the instant when a point source with a sharp onset is turned on. We also identify other characteristic times. In particular, the “traversal” or “Büttiker-Landauer” time (which grows linearly with the distance to the source) for the Hermitian, non-absorbing case is substituted by several characteristic quantities in the absorbing case. The simultaneous arrival due to absorption, unlike the Hartman effect, occurs for carrier frequencies under or above the cutoff, and for arbitrarily large distances. It holds also in a relativistic generalization but limited by causality. A possible physical realization is proposed by illuminating a two-level atom with a detuned laser.

Sufficient conditions for the nonviolation of the Bell-Clauser-Horne-Shimony-Holt inequalities in a mixed state of a two-qubit system are: (1) the linear entropy of the state is not smaller than 0.457; (2) the sum of the conditional linear entropies is not smaller than -0.086; (3) the von Neumann entropy is not smaller than 0.833; and (4) the sum of the conditional von Neumann entropies is not smaller than 0.280.

We present a scheme to cool the motional state of neutral atoms confined in sites of an optical lattice by immersing the system in a superfluid. The motion of the atoms is damped by the generation of excitations in the superfluid, and under appropriate conditions the internal state of the atom remains unchanged. This scheme can thus be used to cool atoms used to encode a series of entangled qubits nondestructively. Within realizable parameter ranges, the rate of cooling to the ground state is found to be sufficiently large to be useful in experiments.

The properties of some atomic and molecular three-body ions which contain positively charged muons ${\mu }^{+}$ are considered. In particular, the ground states in the muonium ion ${\mathrm{Mu}}^{-}$ (or ${\mu }^{+}{e}^{-}{e}^{-})$ and muon-hydrogen molecular $p^{+}{\mu }^{+}{e}^{-}{,d}^{+}{\mu }^{+}{e}^{-}{,t}^{+}{\mu }^{+}{e}^{-}$ ions are studied in details. The energies of these systems have been determined to high accuracy: $E\left({\mathrm{Mu}}^{-}\right)=-0.52505480624352632929\mathrm{a}.\mathrm{u}.\mathrm{},$ ${E(p}^{+}{\mu }^{+}{e}^{-})=-0.5899037853895877261\mathrm{a}.\mathrm{u}.\mathrm{},$ ${E(d}^{+}{\mu }^{+}{e}^{-})=-0.5902553521522464177\mathrm{a}.\mathrm{u}.\mathrm{},$ and ${E(t}^{+}{\mu }^{+}{e}^{-})=-0.5903740988926828880\mathrm{a}.\mathrm{u}.\mathrm{}$ The interparticle distances, $\delta$ functions, two-particle cusps, and some other bound-state properties are also presented for all considered systems. The photodetachment of the ${\mathrm{Mu}}^{-}$ ion is briefly discussed.

Various total cross sections for collisions of electrons in the energy range 10–2000 eV are calculated for the tetrahedral ${\mathrm{CH}}_4,$ ${\mathrm{SiH}}_4,$ ${\mathrm{GeH}}_4,$ ${\mathrm{CF}}_4,$ ${\mathrm{SiF}}_4,$ and ${\mathrm{CCl}}_4$ targets and ${\mathrm{SF}}_6.$ Molecular total inelastic cross sections determined in the complex potential formalism are partitioned to account for the ionization and cumulative electronic-excitation channels. The present total cross sections and total ionization cross sections are found to be consistent with the previous data. The cumulative total excitation cross sections reported here indicate the relative importance of ionization together with electronic excitation channels including neutral dissociation of these molecules by electron impact.

Electron-impact-induced excitation and dissociation processes between the excited triplet states $a{}^3{\Sigma }_g^{+}\to d{}^3{\Pi }_u,$ $c{}^3{\Pi }_u\to h{}^3{\Sigma }_g^{+},$ and $c{}^3{\Pi }_u\to g{}^3{\Sigma }_g^{+}$ of molecular hydrogen are studied by using the impact-parameter method. The cross sections for ${\nu }_i-{\nu }_f$ resolved vibronic transitions between states have been calculated in the energy range from threshold to 100 eV; their maxima being located in the region of 5–10 eV. A special treatment was required for the transition to the $h{}^3{\Sigma }_g^{+}$ state, whose adiabatic potential-energy curve possesses a barrier at the internuclear distance of about ${5a}_0,$ sustaining three quasi-bound vibrational states with widths of $5.3\times {10}^{-12},$ $1.5\times {10}^{-3},$ and $42.0{\mathrm{cm}}^{-1},$ respectively. The quasistationary character of these vibrational states is taken into account when calculating the $c{}^3{\Pi }_u\to h{}^3{\Sigma }_g^{+}$ excitation and dissociation cross sections.