The $\mathcal{P}\mathcal{T}$-symmetric (PTS) quantum brachistochrone problem is re-analyzed as a quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as a subsystem of a larger Hermitian system, we find nonunitary operator equivalence classes (conjugacy classes) as natural ingredients which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian brachistochrones is demonstrated.

The Markov-chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether quantum computers can speed up classical mixing processes based on Markov chains. To this end, we present a quantum algorithm, making it possible to prepare a quantum sample—i.e., a coherent version of the stationary distribution of a reversible Markov chain. Our algorithm has a significantly better running time than that of a previous algorithm based on adiabatic-state generation. We also show that our methods provide a greater speedup over a recently proposed method for obtaining the ground states of (classical) Hamiltonians.

We study the evolution of one-dimensional quantum lattice systems when the ground state is perturbed by altering one site in the middle of the chain. For a large class of models, we observe a similar pattern of entanglement growth during the evolution, characterized by a moderate increase of significant Schmidt coefficients in all relevant bipartite decompositions of the state. As a result, the evolution can be accurately described by a matrix product state and efficiently simulated using the time-evolving block decimation algorithm.

Tomography of the two-qubit density matrix shared by Alice and Bob is an essential ingredient for guaranteeing an acceptable margin of confidentiality during the establishment of a secure fresh key through the quantum key distribution scheme. We show how the Singapore protocol for key distribution is optimal from this point of view, due to the fact that it is based on so-called symmetric informationally complete positive-operator-valued measure (SIC POVM) qubit tomography which allows the most accurate full tomographic reconstruction of an unknown density matrix on the basis of a restricted set of experimental data. We illustrate with the help of experimental data the deep connections that exist between SIC POVM tomography and discrete Wigner representations. We also emphasize the special role played by Bell states in this approach and propose a protocol for quantum key distribution during which a third party is able to concede or to deny a posteriori to the authorized users the ability to build a fresh cryptographic key.

In this paper, we consider a linear quantum network composed of two distantly separated cavities that are connected via a one-way optical field. When one of the cavities is damped and the other undamped, the overall cavity state obtains a large amount of entanglement in its quadratures. This entanglement, however, immediately decays and vanishes in a finite time. That is, entanglement sudden death occurs. We show that the direct measurement feedback method proposed by Wiseman can avoid this entanglement sudden death, and, further, enhance the entanglement. It is also shown that the entangled state under feedback control is robust against signal loss in a realistic detector, indicating the reliability of the proposed direct feedback method in practical situations.

We numerically studied two-component planar Coulomb crystals (planar bicrystals) in rf traps. The number of ions in the inner shell was found to be limited by the mass difference between the two components and we calculated the maximum possible number of ions in the inner shells for various mass ratios. When large axial potentials are applied the spatial separation between components depends on the trapping parameters as well as on the ion masses and charges. We derived the spatial separation both theoretically and numerically and discussed its effect on the efficiency of sympathetic cooling and on rf heating. We suggest using planar bicrystals for implementing quantum simulation and computation.

For the description of an ${\mathrm{H}}_2$ molecule, an effective one-electron model potential is proposed which is fully determined by the exact ionization potential of the ${\mathrm{H}}_2$ molecule. In order to test the model potential and examine its properties, it is employed to determine excitation energies, transition moments, and oscillator strengths in a range of internuclear distances, $0.8\mathrm{a.u.}<R<2.5\mathrm{a.u}$. In addition, it is used as a description of an ${\mathrm{H}}_2$ target in calculations of the cross sections for photoionization and for partial excitation in collisions with singly charged ions. The comparison of the results obtained with the model potential with literature data for ${\mathrm{H}}_2$ molecules yields a good agreement and encourages therefore an extended use of the potential in various other applications or in order to consider the importance of two-electron and anisotropy effects.

We present experimental kinetic-energy-release distributions in the asymmetric fission processes $\mathrm{C}_{60}{}^{q+}\to \mathrm{C}_{58}{}^{(q-1)+}+\mathrm{C}_2{}^{+}$ and $\mathrm{C}_{70}{}^{q+}\to \mathrm{C}_{68}{}^{(q-1)+}+\mathrm{C}_2{}^{+}$ for highly excited mother ions in charge states $q=4–8$. We find that the distributions for $\mathrm{C}_{70}{}^{q+}$ are considerably narrower and peak at lower energies than for $\mathrm{C}_{60}{}^{q+}$ in the corresponding charge state when $q>4$. Further, semiempirical values for $\mathrm{C}_2{}^{+}$ fission barrier heights were extracted for $q=4–6$ by means of a statistical approach and the measured intensity ratios between fission and ${\mathrm{C}}_2$ evaporation.

We investigate theoretically the time dependence of few-cycle strong-field ionization and excitation in an attosecond-femtosecond–pump-probe scenario. We demonstrate that a combination of simple techniques, relying on perturbation and tunneling theory, are very useful for the description of electron dynamics during the time evolution. Our studies show that half-cycle ionization dynamics is responsible for the difference of the rise time in the ionization steps from the tunneling steps and for the appearance of dips in the ionization probability time dependence.

We present a generalization of the fluid-dynamical scheme developed for nuclear physics to the case of two trapped fermion species with pairing interactions. To establish a macroscopic description of the mass and momentum conservation laws, we adopt a generalization of the usual Thomas-Fermi approach that includes the pairing energy. We analyze the equilibrium density and gap profiles for an equal population mixture of harmonically trapped ${}^6\mathrm{Li}$ atoms for different choices of the local equation of state. We examine slight departures from equilibrium within our formulation, finding that density oscillations can propagate as first sound coupled to pairing vibrations, that in a homogeneous fermion system exhibit a Bogoliubov-like quasiparticle spectrum. In this case, the dispersion relation for the coupled modes displays a rich scenario of stable, unstable, and damped regimes.

We consider the problem of estimating the phase of squeezed vacuum states within a Bayesian framework. We derive bounds on the average Holevo variance for an arbitrary number $N$ of uncorrelated copies. We find that it scales with the mean photon number $n$, as dictated by the Heisenberg limit, i.e., as $n^{-2}$, only for $N>4$. For $N⩽4$ this fundamental scaling breaks down and it becomes $n^{-N∕2}$. Thus, a single squeezed vacuum state performs worse than a single coherent state with the same energy. We find the optimal splitting of a fixed given energy among various copies. We also compute the variance for repeated individual measurements (without classical communication or adaptivity) and find that the standard Heisenberg-limited scaling $n^{-2}$ is recovered for large samples.

We investigate the effect of a phase-modulated pump beam on collective backscattering [also termed collective atomic recoil lasing (CARL)] by a cold, collisionless atomic gas. We show using a numerical analysis that different regimes can be identified in which the atomic dynamics evolves in a qualitatively different manner during the light-atom interaction, depending on the magnitude of the pump modulation frequency. Our results also demonstrate that phase-modulating the pump field can substantially enhance the backscattered field intensity relative to the case of a monochromatic pump which has been used in CARL experiments to date.

An alternative formulation of quantum mechanics is proposed based on a principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a correlation between the positions of a particle at two different times. Under reasonable conditions for the wave function, this correlation implies that the particles follow quasiclassical trajectories. It is also shown that the Born rule is equivalent to a particular case of the evolved principle. These features allow the principle to provide a unified explanation of the results of the statistical experiments and of the quasiclassical macroscopic evolution. There is a strong analogy between the quantum principle and a probabilistic principle which is necessary to derive empirical predictions from the mathematical formalism of probability theory. This principle is referred to by some authors as Cournot’s principle, while other authors use the equivalent notion of typicality. In this paper probability theory and quantum mechanics are formulated in such a way as to explicitly include the two principles and to emphasize the very similar conceptual structure of the two theories.

We describe the application of four-qubit cluster states, built on the simultaneous entanglement of two photons in the degrees of freedom of polarization and linear momentum, for the realization of a complete set of basic operations of one-way quantum computation. These consist of arbitrary single-qubit rotations, either probabilistic or deterministic, and simple two-qubit gates, such as a controlled-NOT (CNOT) gate for equatorial qubits and a universal controlled-phase gate (controlled-$Z$ or CZ) gate acting on arbitrary target qubits. Other basic computation operations, such as the Grover’s search and the Deutsch’s algorithms, have been realized by using these states. In all the cases we obtained a high value of the operation fidelities. These results demonstrate that cluster states of two photons entangled in many degrees of freedom are good candidates for the realization of more complex quantum computation operations based on a larger number of qubits.

Rearrangement reaction in electron scattering from muonic hydrogen $\left(\mu p\right)$ in highly excited states, i.e., $e+\mu p\to \mu +\mathrm{H}$, is theoretically investigated by using the $R$-matrix numerical method, recently developed by the present author [Phys. Rev. A 76, 042513 (2007)]. This process can be identified as dissociative attachment (DA) if we use the terminology of molecular physics. The present study offers a rigorous treatment of the DA to the exotic system $\mu p$ without introducing any type of decoupling approximation. The threshold behavior of the DA cross sections becomes peculiar because of the dipole interaction between $e$ and $\mu p$ and the degeneracy of the hydrogenic $\mu p$ states.

The interatomic Coulombic decay (ICD) following $K$-shell ionization of the Ne dimer and subsequent one-site atomic Auger decay of the $\mathrm{Ne}_2{}^{+}\left(1s^{-1}\right)$ states is studied theoretically. In particular we consider electronic decay of the ${\mathrm{Ne}}^{2+}\left(2s^{-1}2p^{-1}{}^{1}P\right)\mathrm{Ne}$ weakly bound doubly ionized states into the manifold of the ${\mathrm{Ne}}^{2+}\left(2p^{-2}{}^{1}D\right)\text{−}{\mathrm{Ne}}^{+}\left(2p^{-1}\right)$ repulsive triply ionized ones. The total and partial ICD electron spectra are computed within the framework of the time-dependent theory of wave packet propagation. Thereby, we investigate the impact of nuclear dynamics accompanying the electronic decay on the computed spectra in some detail. The computed total ICD electron spectrum is found to be in very good agreement with the recently measured one.

We used cold target recoil ion momentum spectroscopy for a comprehensive study of the decay of a neon dimer $\left({\mathrm{Ne}}_2\right)$ after removal of a $1s$ electron from one of the atoms of the dimer. Multiple decay pathways are found and identified, mostly being connected to different types of interatomic Coulombic decay (ICD) such as the “direct” ICD which happens via the transfer of a virtual photon, the “exchange” ICD via an electron transfer and the electron transfer mediated decay. A quantitative theoretical analysis of these decay processes can be found in the preceding paper by Demekhin et al. [Phys. Rev. A 78, 043421 (2008)], as well as in Stoychev et al. [J. Chem. Phys. 129, 074307 (2008)].

We show that under certain conditions, the inclusion of counter-rotating terms which are usually ignored in the interaction of a two-level atom with the electromagnetic field, leads to significant modifications of the splitting of an atomic beam in the well-known optical Stern-Gerlach effect, which now acquires a “fine” structure.

We investigate the zero-temperature properties of a superfluid Bose-Fermi mixture by introducing a set of coupled Galilei-invariant nonlinear Schrödinger equations valid from weak coupling to unitarity. The Bose dynamics is described by a Gross-Pitaevskii-type equation including beyond-mean-field corrections possessing the correct weak-coupling and unitarity limits. The dynamics of the two-component Fermi superfluid is described by a density-functional equation including beyond-mean-field terms with correct weak-coupling and unitarity limits. The present set of equations is equivalent to the equations of generalized superfluid hydrodynamics, which take into account also surface effects. The equations describe the mixture properly as the Bose-Bose repulsive (positive) and Fermi-Fermi attractive (negative) scattering lengths are varied from zero to infinity in the presence of a Bose-Fermi interaction. The present model is tested numerically as the Bose-Bose and Fermi-Fermi scattering lengths are varied over wide ranges covering the weak-coupling to unitarity transition.

We study the superfluid transition in a quasi-two-dimensional Fermi gas with a magnetic field tuning through a Feshbach resonance. Using an effective two-dimensional Hamiltonian with renormalized interaction between atoms and dressed molecules, we investigate the Berezinskii-Kosterlitz-Thouless transition temperature by studying the phase fluctuation effect. We also take into account the trapping potential in the radial plane and discuss the number and superfluid density distributions. These results can be compared to experimental outcomes for gases prepared in one-dimensional optical lattices.