We demonstrate that the time operator that measures the time of arrival of a quantum particle into a chosen state can be defined as a self-adjoint quantum-mechanical operator using periodic boundary conditions and applied to wave functions in energy representation. The time becomes quantized into discrete eigenvalues; and the eigenstates of the time operator, i.e., the stroboscopic wave packets introduced recently [Phys. Rev. Lett. 101, 046402 (2008)], form an orthogonal system of states. The formalism provides simple physical interpretation of the time-measurement process and direct construction of normalized, positive definite probability distribution for the quantized values of the arrival time. The average value of the time is equal to the phase time but in general depends on the choice of zero time eigenstate, whereas the uncertainty of the average is related to the traversal time and is independent of this choice. The general formalism is applied to a particle tunneling through a resonant tunneling barrier in one dimension.

We theoretically study dynamic scalar polarizabilities of the ground and select long-lived excited states of dysprosium, a highly magnetic atom recently laser cooled and trapped. We demonstrate that there is a set of magic wavelengths of the unpolarized lattice laser field for each pair of states, which includes the ground state and one of these excited states. At these wavelengths, the energy shift due to laser field is the same for both states, which can be useful for resolved sideband cooling on narrow transitions and precision spectroscopy. We present an analytical formula that, near resonances, allows for the determination of approximate values of the magic wavelengths without calculating the dynamic polarizabilities of the excited states.

On the basis of the virial theorem for finite motion of interacting electrons in a static external field, it is shown that ground-state energy is determined evidently by the one-particle density matrix. The exact expression for ground-state energy is found and can be applied to various problems, in particular, in studying the electronic structure of atoms, molecules, and other bound complexes.

We propose a compact atom interferometry scheme for measuring weak, time-dependent accelerations. Our proposal uses an ensemble of dilute trapped bosons with two internal states that couple to a synthetic gauge field with opposite charges. The trapped gauge field couples spin to momentum to allow time-dependent accelerations to be continuously imparted on the internal states. We generalize this system to reduce noise and estimate the sensitivity of such a system to be $S~{10}^{-7}\frac{\text{m}/{\text{s}}^2}{\sqrt{\text{Hz}}}$.

In quantum computation every unitary operation can be decomposed into quantum circuits—a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-not (cnot) gates. Two measures are important when judging the complexity of the circuit: the total number of cnot gates needed to implement it and the depth of the circuit, measured by the minimal number of computation steps needed to perform it. Here we give an explicit and simple quantum circuit scheme for preparation of arbitrary quantum states, which can directly utilize any decomposition scheme for arbitrary full quantum gates, thus connecting the two problems. Our circuit reduces the depth of the best currently known circuit by a factor of $2$. It also reduces the total number of cnot gates from $2^n$ to $\frac{23}{24}{2}^n$ in the leading order for even number of qubits. Specifically, the scheme allows us to decrease the upper bound from $11$ cnot gates to $9$ and the depth from $11$ to $5$ steps for four qubits. Our results are expected to help in designing and building small-scale quantum circuits using present technologies.

High-resolution measurements of positron interactions with Ne and Ar are presented, as well as theoretical treatments. The data extend over a range of 0.3 to 60 eV and comprise measurements of the grand total, positonium formation, and grand total minus positronium formation cross sections. Theoretical treatments of scattering from Ne and Ar are performed under the relativistic optical potential approach, as well as calculations using the convergent close-coupling method. Comparisons of the present measurements and theories are made with previous theoretical and experimental work.

The polarization dependence of laser-induced radiative recombination (LIR) to ${\mathrm{D}}^{+}$ ions was investigated in the electron cooler of the CRYRING storage ring. The LIR gain as a function of wavelength into $n$ $=$ 3 principal quantum states of deuterium was measured at laser beam polarization angles of 0° and 90° with respect to the direction of the motional electric field in the interaction region. For the case of the polarization vector parallel to the external field, there is a double-peak structure in the gain curve that indicates a polarization effect in the LIR process. The two polarization directions also reveal a different width for the respective gain curves, giving additional evidence for the polarization effect, clearly seen by the behavior of a defined polarization parameter. The obtained polarization effect indicates a high sensitivity in recombination processes to external fields.

The relative yield and momentum distributions of all multiply charged atomic ions generated by a short (30 fs) intense (10${}^{14}$–$5\times {10}^{18}$ W/cm${}^2$) laser pulse are investigated using a Monte Carlo simulation. We predict a substantial shift in the maximum (centroid) of the ion-momentum distribution along the laser polarization as a function of the absolute phase. This effect should be experimentally detectable with currently available laser systems even for relatively long pulses, such as 25–30 fs. In addition to the numerical results, we present semianalytical scaling for the position of the maximum.

In this paper we reveal the rich ground-state properties induced by the strong nonlinear atom-photon interaction which has been found in the recent experiment about a Bose-Einstein condensate coupling with a high-finesse cavity [Nature (London) 464, 1301 (2010)]. Two detuning-dependent phase diagrams are revealed by investigating the experimentally measurable atomic population. In particular, two quantum phase transitions from the superradiant phase or the normal phase to a dynamically unstable phase are predicted in the blue detuning. Moreover, the three-phase coexistence points are found. It is also demonstrated that these predicted quantum phase transitions are the intrinsic transitions governed only by the second-order derivative of the ground-state energy. Finally, we also point out that the region involving coexistence of the superradiant phase and the normal phase previously predicted cannot happen in the ground state.

The dynamics of a phase-separated two-component Bose-Einstein condensate are investigated, in which a bubble of one component moves through the other component. Numerical simulations of the Gross-Pitaevskii equation reveal a variety of dynamics associated with the creation of quantized vortices. In two dimensions, a circular bubble deforms into an ellipse and splits into fragments with vortices, which undergo the Magnus effect. The Bénard–von Kármán vortex street is also generated. In three dimensions, a spherical bubble deforms into toruses with vortex rings. When two rings are formed, they exhibit leapfrogging dynamics.

We investigate possibilities of existence of inhomogeneous dark states of atomic-molecular Bose-Einstein condensates loaded in trap potentials. The system is described by three-coupled equations of the Gross-Pitaevskii type, which account for contributions of the kinetic energy, two-body interactions, and an external potential, and which govern the conversion between atoms and molecules in the stimulated Raman adiabatic passage. We report a class of trapping potentials allowing for the existence of localized stable dark states. The respective atomic and molecular distributions are computed, and their stability and dynamics are discussed.

We analyze excited-state quantum phase transitions (ESQPTs) in three schematic (integrable and nonintegrable) models describing a single-mode bosonic field coupled to a collection of atoms. It is shown that the presence of the ESQPT in these models affects the quantum relaxation processes following an abrupt quench in the control parameter. Clear-cut evidence of the ESQPT effects is presented in integrable models, while in a nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.

It was shown in Augusiak et al. [Phys. Rev. A 77, 030301(R) (2008)] that discrimination between entanglement and separability in a two-qubit state can be achieved by a measurement of a single observable on four copies of it. Moreover, a pseudoentanglement monotone $\pi$ was proposed to quantify entanglement in such states. The main goal of this Brief Report is to show that the close relationship between $\pi$ and concurrence reported there is a result of sharing the same underlying construction of a spin-flipped matrix. We also show that monogamy of entanglement can be rephrased in terms of $\pi$ and prove the factorization law for $\pi$.

Measurements of quantum systems disturb their states. To quantify this nonclassical characteristic, Zurek and Ollivier [Phys. Rev. Lett. 88, 017901 (2001)] introduced the quantum discord, a quantum correlation that can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers the exponential speed-up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy. We also identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.

In this paper, the exact non-Markovian dynamics of open quantum systems in the presence of initial system-reservoir correlations is investigated for a photonic cavity system coupled to a general non-Markovian reservoir. The exact time-convolutionless master equation incorporating with initial system-reservoir correlations is obtained. The non-Markovian dynamics of the reservoir and the effects of the initial correlations are embedded into the time-dependent coefficients in the master equation. We show that the effects induced by the initial correlations play an important role in the non-Markovian dynamics of the cavity but they are washed out in the steady-state limit in the Markovian regime. Moreover, the initial two-photon correlation between the cavity and the reservoir can induce nontrivial squeezing dynamics to the cavity field.

Using recently proposed measures for non-Markovianity [H.-P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)], we study the dynamics of a qubit coupled to a spin environment via an energy-exchange mechanism. We show the existence of a point, in the parameter space of the system, where the qubit dynamics is effectively Markovian and that such a point separates two regions with completely different dynamical behaviors. Indeed, our study demonstrates that the qubit evolution can in principle be tuned from a perfectly forgetful one to a deep non-Markovian regime where the qubit is strongly affected by the dynamical backaction of the environmental spins. By means of a theoretical quantum process tomography analysis, we provide a complete and intuitive characterization of the qubit channel.

We calculate the analytic expression for geometric measure of entanglement for arbitrary superposition of two $N$-qubit canonical orthonormal Greenberger-Horne-Zeilinger (GHZ) states and the same for two $W$ states. In the course of characterizing all kinds of nonclassical correlations, an explicit formula for quantum discord (via relative entropy) for the former class of states has been presented. Contrary to the GHZ state, the closest separable state to the $W$ state is not classical. Therefore, in this case, the discord is different from the relative entropy of entanglement. We conjecture that the discord for the $N$-qubit $W$ state is $\log {}_{2}N$.

A joint experimental and theoretical study of energy loss is presented for 1-to-4-keV fluorine negative ions in grazing scattering on a missing-row reconstructed Au(110) surface. Measurements of energy losses for various azimuthal orientations of the crystal have been performed by means of a time-of-flight method with a pulsed beam. The dependence of the fraction of surviving negative ions on azimuthal angles, was determined. Our energy-loss data are discussed in light of trajectory and stopping-power calculations, where the explicit inclusion of the nonuniform electron density at the surface provides good agreement with the experimental data. The simulation allows us to delineate various trajectory classes that correspond to different contributions in the energy-loss spectra for various azimuthal orientations of the surface.

Field-induced birefringence, also known as cross-polarization wave generation, has played an important role in ultrafast nonlinear optics. In this paper we analyze birefringence induced by relativistic collective motion of electrons driven by a high-intensity laser field. An analytical expression for the phase difference between the parallel and perpendicular polarizations of a weak probe pulse with respect to the polarization of a strong pump pulse as a function of intensity, density, and wavelengths is derived. It is shown that under typical experimental conditions of high-field physics, the effect is well above detection threshold. The analysis is compared with particle-in-cell simulations, and the agreement provides good support for the theory.

We propose a methodology to construct excited states with a fixed angular momentum, namely, “yrast excited states” of finite-size one-dimensional bosonic systems with periodic boundary conditions. The excitation energies such as the first yrast excited energy are calculated through the system-size asymptotic expansion and expressed analytically by dressed energy. Interestingly, they are grouped into sets of almost degenerate energy levels. The low-lying excitation spectrum near the yrast state is consistent with the $\text{U}(1)$ conformal field theories if the total angular momentum is given by an integral multiple of particle number; i.e., if the system is supercurrent.