We present a calculation of quantum tunneling time based on the transition duration of wave peak from one side of a barrier to the other. In our formulation, the tunneling time comprises a real and an imaginary part. The real part is an extension of the phase tunneling time with quantum corrections whereas the imaginary time is associated with energy derivatives of the probability amplitudes.

A feasible setup of continuous-variable (CV) quantum nondemolishing (QND) interaction at a distance is proposed. If two distant experimentalists are able to locally perform identical QND interactions then the proposed realization requires only a single quantum channel and classical communication between them. A possible implementation of the proposed setup in recent quantum optical laboratories is discussed and an influence of Gaussian noise in the quantum channel on a quality of the implementation is analyzed. An efficient realization of the QND interaction at a distance can be a basic step to possible distributed quantum CV experiments between the distant laboratories.

We propose a unified scheme to generate $W$ states, Greenberger-Horne-Zeilinger (GHZ) states, and cluster states of four distant atoms, which are trapped separately in leaky cavities. The proposed schemes require linear optical elements and photon detectors with single-photon sensitivity. The quantum noise influences the fidelity of the generated states. Further, based on the four-photon coincidence detection, we propose another scheme to generate the $W$ states and GHZ states of four distant atoms. The scheme is insensitive to the quantum noise, but cannot be used to generate the cluster states.

It has been recently suggested that the dynamics of a quantum spin system may provide a natural mechanism for transporting quantum information. We show that one-dimensional rings of qubits with fixed (time-independent) interactions, constant around the ring, allow high-fidelity communication of quantum states. We show that the problem of maximizing the fidelity of the quantum communication is related to a classical problem in Fourier wave analysis. By making use of this observation we find that if both communicating parties have access to limited numbers of qubits in the ring (a fraction that vanishes in the limit of large rings) it is possible to make the communication arbitrarily good.

Entanglement in the ground state of a many-body quantum system may arise when the local terms in the system Hamiltonian fail to commute with the interaction terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy between ground-state entanglement and the phenomenon of frustration in spin systems. In particular, we prove that the amount of ground-state entanglement is bounded above by a measure of the extent to which interactions frustrate the local terms in the Hamiltonian. As a corollary, we show that the amount of ground-state entanglement is bounded above by a ratio between parameters characterizing the strength of interactions in the system, and the local energy scale. Finally, we prove a qualitatively similar result for other energy eigenstates of the system.

We study the stability of entanglement in a quantum computer implementing an efficient quantum algorithm, which simulates a quantum chaotic dynamics. For this purpose, we perform a forward-backward evolution of an initial state in which two qubits are in a maximally entangled Bell state. If the dynamics is reversed after an evolution time $t_r$, there is an echo of the entanglement between these two qubits at time $t_e=2t_r$. Perturbations attenuate the pairwise entanglement echo and generate entanglement between these two qubits and the other qubits of the quantum computer.

A detailed description of the numerical procedure is presented for the evaluation of the one-loop self-energy correction to the $g$ factor of an electron in the $1s$ and $2s$ states in H-like ions to all orders in $Z\alpha$.

In this paper, the Thomas-Fermi model for large atoms is reformulated by incorporating the nonextensive entropy prescription. The entropy nonextensivity contribution dominates the usual thermal correction term in the “low-temperature” limit. On the other hand, the entropy nonextensivity concept appears to provide a useful framework to describe the fractal nature of the Fermi surface in the nondegenerate case. Analytical calculations are given for some atomic properties, such as the total binding energy of the electrons in the atom. The nonextensivity of entropy is indicated to have the potential to provide a means to remedy one of the well-known weaknesses in the Thomas-Fermi model—the boundary effect. The virial theorem has been shown to be a robust result that holds also in the nonextensive entropy regime.

The Ti $K{\alpha }^{″}$ satellite is investigated using a Johann-type spectrometer on the BL15XU undulator beam line of SPring-8 at excitation energies between 4996 and $7000\text{eV}$. The intensity of the $K{\alpha }^{″}$ satellite relative to that of $K{\alpha }_{1,2}$ exhibits an abrupt jump from $0\%$ to $\sim 1\%$ in a range of $10\text{eV}$ around an excitation energy of $5010\text{eV}$. The energy range to reach saturation is $\sim 500\text{eV}$. The creation of spectator holes is implicated to be due to shake-up processes, inducing the emergence of the $K{\alpha }^{″}$ satellite. The onset energy for the appearance of the satellite is $5011.0\text{eV}\pm 0\text{.8}\text{eV}$, corresponding to the $\left[1s3p\right]$ double-ionization threshold energy by a $Z+1$ approximation. The experimental results obtained in this work confirm that the $K{\alpha }^{″}$ satellite originates from a $3p$ spectator hole, as predicted theoretically by Scott [Phys. Rev. A 34, 4438 (1986)].

We have conducted measurements of absolute differential cross sections for the excitation of hydrogen atoms to their $n=3(3S+3P+3D)$ and $4(4S+4P+4D+4F)$ levels. A modulated, crossed-beam method was employed, and the impact energies were 40 and $60\mathrm{eV}$. Comparison of our results with those of others is quite favorable.

The problem of the neutron scattering in the magnetic field of a linear current has been formulated and solved quantum mechanically exactly. The $S$ matrix has been derived in the adiabatic representation and the closed analytical expression for the differential cross section has been obtained. The results reveal the topological phase part at the nonadiabatic collisions.

Partial wave theory of a three dmensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a “hard sphere”-like potential and the magnetic flux is examined. An anomalous total cross section is revealed at the specific quantized magnetic flux at low energy which helps explain the composite fermion and boson model in the fractional quantum Hall effect. Since the nonlocal quantum interference of magnetic flux on the charged particles is universal, the nonlocal effect is expected to appear in a quite general potential system and will be useful in understanding some other phenomena in mesoscopic physics.

We present a diabatization technique in combination with the recently developed hyperspherical close coupling (HSCC) method. In contrast to the strict diabatization, our simple diabatization procedure transforms only sharp avoided crossings in the adiabatic hyperspherical potential curves into real crossings. With this approach, the weak collision channels can be removed from the close-coupling calculations. This method is used to study the antiproton-hydrogen collision at low energies. In the case of a scaled down (anti)proton mass, we show that a 10-channel calculation is enough to obtain converged cross sections at low energies. The results also indicate that protonium formation occurs mostly to the lowest states of the different excited protonium manifolds.

We present a simple exact analytical solution, using the Weyl-Titchmarsh-Kodaira spectral theorem, for the spectral function of the one-dimensional diatomic molecule model consisting of two attractive $\delta$-function wells in the presence of a static external electric field. For sufficiently deep and far apart wells, this molecule supports both an even and an odd state, and the introduction of a static electric field turns these bound states into quasibound states which are Stark-shifted and broadened. The continuum spectrum also inherits an intricate pattern of resonances which reflect the competition between resonant scattering between the two atomic wells and between the linear potential and one or both atomic well(s). All results are analytic and can be easily plotted. The relation between the large orders of the divergent perturbative Stark-shift series and the nonperturbative widths of quasibound levels is studied.

Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent, Mott-insulating domains always coexist with metallic regions, such that global quantities are not appropriate to describe the system. We define a local compressibility that characterizes the Mott-insulating regions and analyze other local quantities. It is shown that the momentum distribution function, a quantity that is commonly considered in experiments, fails in giving a clear signal of the Mott-insulating transition. Furthermore, we analyze a mean-field approach to these systems and compare it with the numerically exact QMC results. Finally, we determine a generic form for the phase diagram that allows us to predict the phases to be observed in the experiments.

In this paper we describe numerical simulations of the response of atoms confined in an optical lattice in the region of a quantum phase transition. We use the increase in the number variance of atoms as the diagnostic of excitations produced by tilting the lattice. We show that this locally determined quantity is a good indicator of the resulting coherence changes as observed in recent experiments. This is found to hold for commensurate and noncommensurate filling of the lattice, implying that our results should hold for a wide range of conditions. In accordance with this view, we find that the qualitative features of our results are in good agreement with recent experiments. We do, however, find extra features in the excitation spectra that may well be of use in future experimental studies. We also show that the variation of the spectra with the duration of the perturbation is a useful diagnostic of the atom dynamics that take place during the tilt.

We theoretically investigate Raman photoassociation of a degenerate Bose-Fermi mixture of atoms and the subsequent prospect for anomalous (Cooper) pairing between atoms and molecules. Stable fermionic molecules are created via free-bound-bound stimulated Raman adiabatic passage which, in contrast to purely bosonic systems, can occur in spite of collisions. With the leftover atomic condensate to enhance intrafermion interactions, the superfluid transition to atom-molecule Cooper pairs occurs at a temperature that is roughly an order of magnitude below what is currently feasible.

We calculate the communication capacity of a broadband electromagnetic waveguide as a function of its spatial dimensions and input power. We analyze the two cases in which either all the available modes or only a single directional mode are employed. The results are compared with those for the free-space bosonic channel.

We experimentally demonstrate a simple classical-field optical heterodyne method which employs postselection to reproduce the polarization correlations of a four-particle entangled state. We give a heuristic argument relating this method to the measurement of multiple quantum fields by correlated homodyne detection. We suggest that using multiple classical fields and postselection, one can reproduce the polarization correlations obtained in quantum experiments which employ multiple single-photon sources and linear optics to prepare multiparticle entangled states. Our experimental scheme produces four spatially separated beams which are separately detected by mixing with four independent optical local oscillators (LO) of variable polarization. Analog multiplication of the four beat signals enables projection onto a four-particle polarization-state basis. Appropriate band pass filtering is used to produce a signal proportional to the projections of the maximally entangled four-field polarization state, $\mid H_1)\mid H_2)\mid H_3)\mid H_4)+\mid V_1)\mid V_2)\mid V_3)\mid V_4)$, onto the product of the four LO polarizations. Since the data from multiple observers is combined prior to postselection, this method does not constitute a test of nonlocality. However, we reproduce the polarization correlations of the 32 elements in the truth table from the quantum mechanical Greenberger-Horne-Zeilinger experiments on the violation of local realism. We also demonstrate a form of classical entanglement swapping in a four-particle basis.

The necessary and sufficient amount of entanglement required for cloning of orthogonal Bell states by local operation and classical communication is derived, and using this result we provide here some additional examples of reversible as well as irreversible states.