We show that for tripartite quantum pure states of qubits, all the kinds of entanglement in terms of stochastic local operations and classical communications classification are experimentally measurable by simple projective measurements, provided that four copies of the composite quantum system are available. In particular, the entanglement of reduced density matrices, even though they are mixed states, can be exactly determined in experiment. Concurrence of assistance is also shown to be measurable by introducing an interesting equation with explicit physical meanings.

A trade-off relation on our knowledge about two noncommuting observables of a qubit system in simultaneous measurement is formulated. The obtained inequality offers a quantitative information-theoretic representation of Bohr’s principle of complementarity, and can be interpreted as a trade-off relation on the asymptotic accuracy of the maximum-likelihood estimation of the probability distributions of observables.

We have studied the effect of resonant electronic-state coupling on the formation of ultracold ground-state ${}^{85}\mathrm{Rb}_2$. Ultracold ${\mathrm{Rb}}_2$ molecules are formed by photoassociation (PA) to a coupled pair of $0_u^{+}$ states, $0_u^{+}\left(P_{1∕2}\right)$ and $0_u^{+}\left(P_{3∕2}\right)$, in the region below the $5S+5P_{1∕2}$ limit. Subsequent radiative decay produces high vibrational levels of the ground state, $X{}^1\Sigma _g^{+}$. The population distribution of these $X$-state vibrational levels is monitored by resonance-enhanced two-photon ionization through the $2{}^1\Sigma _u^{+}$ state. We find that the populations of vibrational levels $v^{″}=112–116$ are far larger than can be accounted for by the Franck-Condon factors for $0_u^{+}\left(P_{1∕2}\right)\to X{}^1\Sigma _g^{+}$ transitions with the $0_u^{+}\left(P_{1∕2}\right)$ state treated as a single channel. Further, the ground-state molecule population exhibits oscillatory behavior as the PA laser is tuned through a succession of $0_u^{+}$ state vibrational levels. Both of these effects are explained by a calculation of transition amplitudes that includes the resonant character of the spin-orbit coupling of the two $0_u^{+}$ states. The resulting enhancement of more deeply bound ground-state molecule formation will be useful for future experiments on ultracold molecules.

The oxygen $K$-edge x-ray-emission–threshold-electron coincidence spectrum of ${\mathrm{CO}}_2$ is presented. A two-step model, describing the result as a threshold-photoelectron spectrum free from post-collision interaction effects, predicts the salient features of the measured spectrum. Small discrepancies from the predictions are discussed in terms of threshold ionization dynamics.

The collisions of the isocharged sequence ions of $q=6$ (${\text{C}}^{6+}$, ${\text{N}}^{6+}$, ${\text{O}}^{6+}$, ${\text{F}}^{6+}$, ${\text{Ne}}^{6+}$, ${\text{Ar}}^{6+}$, and ${\text{Ca}}^{6+}$), $q=7$ (${\text{F}}^{7+}$, ${\text{Ne}}^{7+}$, ${\text{S}}^{7+}$, ${\text{Ar}}^{7+}$, and ${\text{Ca}}^{7+}$), $q=8$ (${\text{F}}^{8+}$, ${\text{Ne}}^{8+}$, ${\text{Ar}}^{8+}$, and ${\text{Ca}}^{8+}$), $q=9$ (${\text{F}}^{9+}$, ${\text{Ne}}^{9+}$, ${\text{Si}}^{9+}$, ${\text{S}}^{9+}$, ${\text{Ar}}^{9+}$, and ${\text{Ca}}^{9+}$) and $q=11$ (${\text{Si}}^{11+}$, ${\text{Ar}}^{11+}$, and ${\text{Ca}}^{11+}$) with helium at the same velocities were investigated. The cross-section ratios of the double-electron transfer (DET) to the single-electron capture (SEC) ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ and the true double-electron capture (TDC) to the double-electron transfer ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ were measured. It shows that for different ions in an isocharged sequence, the experimental cross-section ratio ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ varies by a factor of 3. The results confirm that the projectile core is another dominant factor besides the charge state and the collision velocity in slow ($0.35-0.49v_0$; $v_0$ denotes the Bohr velocity) highly charged ions (HCIs) with helium collisions. The experimental cross-section ratio ${\sigma }^{\text{DET}}∕{\sigma }^{\text{SEC}}$ is compared with the extended classical over-barrier model (ECBM) [A. Bárány et al., Nucl. Instrum. Methods Phys. Res. B 9, 397 (1985)], the molecular Coulombic barrier model (MCBM) [A. Niehaus, J. Phys. B 19, 2925 (1986)], and the semiempirical scaling laws (SSL) [N. Selberg et al., Phys. Rev. A 54, 4127 (1996)]. It also shows that the projectile core properties affect the initial capture probabilities as well as the subsequent relaxation of the projectiles. The experimental cross-section ratio ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ for those lower isocharged sequences is dramatically affected by the projectile core structure, while for those sufficiently highly isocharged sequences, the autoionization always dominates, hence the cross-section ratio ${\sigma }^{\text{TDC}}∕{\sigma }^{\text{DET}}$ is always small.

We study the three-body problem in one dimension for both zero- and finite-range interactions using the adiabatic hyperspherical approach. Particular emphasis is placed on the threshold laws for recombination, which are derived for all combinations of the parity and exchange symmetries. For bosons, we provide a numerical demonstration of several universal features that appear in the three-body system, and discuss how certain universal features in three dimensions are different in one dimension. We show that the probability for inelastic processes vanishes as the range of the pairwise interaction is taken to zero and demonstrate numerically that the recombination threshold law manifests itself for large scattering length.

The transmission of highly charged ions through nanocapillaries in insulating polyethylene terephthalate (PET) polymers was investigated. In experiments at laboratories in RIKEN (Japan) and HMI (Germany) different detection methods were applied to study the ion current dependence in a wide range covering two orders of magnitude. At HMI an electrostatic ion spectrometer was used and at RIKEN a two-dimensional position sensitive detector was implemented. New PET samples with parallel capillaries and low density were manufactured. For tilted capillaries, the ions are guided along the capillary axis, since the majority of ions are deflected in a charge patch created in the capillary entrance. The results provide insights into the mechanisms of capillary guiding. The fraction of transmitted ions was found to be nearly independent on the incident ion current indicating a sudden increase in the discharge current depleting the entrance charge patch. The experimental results were well-reproduced by model calculations based on a nonlinear (exponential) expression for the discharge current.

Mode characteristics for two-dimensional equilateral-polygonal microresonators are investigated based on symmetry analysis and finite-difference time-domain numerical simulation. The symmetries of the resonators can be described by the point group $C_{Nv}$, accordingly, the confined modes in these resonators can be classified into irreducible representations of the point group $C_{Nv}$. Compared with circular resonators, the modes in equilateral-polygonal resonators have different characteristics due to the break of symmetries, such as the split of double-degenerate modes, high field intensity in the center region, and anomalous traveling-wave modes, which should be considered in the designs of the polygonal resonator microlasers or optical add-drop filters.

Recently, quantum adiabatic computation has attracted more and more attention in the literature. It is a novel quantum computation model based on adiabatic approximation, and the analysis of a quantum adiabatic algorithm depends highly on the adiabatic conditions. However, it has been pointed out that the traditional adiabatic conditions are problematic. Thus, results obtained previously should be checked and sufficient adiabatic conditions applicable to adiabatic computation should be proposed. Based on a result of Tong et al. [Phys. Rev. Lett. 98, 150402 (2007)], we propose a modified adiabatic criterion which is more applicable to the analysis of adiabatic algorithms. As an example, we prove the validity of the local adiabatic search algorithm by employing our criterion.

The shape of the coherent-population-trapping (CPT) resonances was investigated theoretically and experimentally at different laser powers. The CPT resonances were observed in fluorescence on the degenerate two-level system of the $(F_{\phi }=2\to F_f=1)$ transition of the ${}^{87}\mathrm{Rb}$ $D_1$ line by means of a Hanle effect configuration in an uncoated vacuum cell. Numerical simulations based on the density matrix formalism, which take into account the high-rank polarization moment (HRPMs) influence and the velocity distribution of the atoms, were used to calculate the shape of the nonlinear magnetic resonances. The comparison of the theoretical and experimental shapes of the CPT resonances demonstrated that the HRPMs influence the shape at all laser excitation powers, and this influence can be used to explain some peculiarities at the center of the CPT resonance shape.

We propose an analysis of the time-optimal control of a dissipative two-level quantum system whose dynamics is governed by the Lindblad equation. This simple system allows one to use tools of geometric control theory and to construct its optimal synthesis, i.e., to determine the set of all the optimal trajectories starting from a given initial point. We study different processes such as conversion of a pure state into a mixed state and purification of a mixed state. In particular cases, we show that dissipation is not undesirable and can help accelerating the control.

We present the theory and experimental results of phenomena associated to $J$-coupled nuclear magnetic resonance (NMR) spectroscopy at low magnetic fields $(<{10}^{-4}\mathrm{T})$. So far it was believed that in low field the chemical shift and with it the homonuclear $J$-coupling information is lost. This contribution shows that the network of all homo- and heteronuclear $J$-coupling constants can be measured in low magnetic fields, thus revealing the whole molecular structure even in the absence of any chemical shift information. The chemical group of the form $Y{X}_N$ ($Y$=rare spin $1∕2$, $X$=observed spin $1∕2$, $N$=number of spins $X$) can be identified by the number of lines in the heteronuclear coupled $X$ spectrum if the strong $J$-coupling condition is valid. If two molecular groups, such as $Y{X}_N$ and $A{X}_{M\text{−}N}$ ($A$=group without nuclear spin, $M$=total number of coupled spins$X$), are bound together then all homo- and heteronuclear $J$-coupling constants appear in the $X$-NMR spectrum as pairs of multiplets. A vector model is presented which explains the relation between the molecular structure and the number of observed lines in a multiplet pair. The linewidths of the different NMR lines inside one multiplet are measured to be substantially different and depend on the total spin state of the molecule. If $M$ is an odd number and $M-1$ spins $X$ of the molecule are coupled into $(M-1)∕2$ singlets, then intramolecular dipole-dipole relaxation as well as $J$-coupling mediated relaxation processes are suppressed and very narrow lines are observed.

We analyze a three-variable rate equation model that takes into account carrier capture and Pauli blocking in quantum dot semiconductor lasers. The exponential decay of the relaxation oscillations is analyzed from the linearized equations in terms of three key parameters that control the time scales of the laser. Depending on their relative values, we determine two distinct two-variable reductions of the rate equations in the limit of large capture rates. The first case leads to the rate equations for quantum well lasers, exhibiting relaxation oscillations dynamics. The second case corresponds to dots nearly saturated by the carriers and is characterized by the absence of relaxation oscillations.

The transfer of orbital angular momentum from vortex beams to optically induced photonic lattices is demonstrated. It is found that the sum of the angular momenta of interacting incoherent counterpropagating (CP) beams is not conserved, whereas their difference is. The sum of angular momenta of copropagating (CO) interacting beams is strictly conserved. It is also found that the transfer of angular momentum in CP interacting beams is minimal, amounting to a few percent, whereas the transfer in CO interacting beams is substantial, amounting to tens of percent. In fixed lattices, for both CP and CO beams, angular momentum is never conserved.

We study the threshold of random lasers in the regime of incoherent transport. We present a time-dependent three-dimensional model based on the radiative transfer equation and rate equations, allowing us to describe the various transport regimes (ballistic, multiple scattering, diffusive). Numerical simulations based on this model allow us to describe the main features of the lasing threshold. We develop a modal theory of random lasers with incoherent feedback, based on the disordered-averaged modes of the radiative transfer equation. As a first example, we show that this approach predicts the lasing threshold for systems with sizes $L$ ranging from $L\sim l_s$ (single-scatttering regime) to $L⪢l^{*}$ (diffusive regime).

Our everyday descriptions of the universe are highly coarse grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited powers of observation and computation. But in the modern quantum mechanics of closed systems, some measure of coarse graining is inescapable because there are no nontrivial, probabilistic, fine-grained descriptions. This essay explores the consequences of that fact. Quantum theory allows for various coarse-grained descriptions, some of which are mutually incompatible. For most purposes, however, we are interested in the small subset of “quasiclassical descriptions” defined by ranges of values of averages over small volumes of densities of conserved quantities such as energy and momentum and approximately conserved quantities such as baryon number. The near-conservation of these quasiclassical quantities results in approximate decoherence, predictability, and local equilibrium, leading to closed sets of equations of motion. In any description, information is sacrificed through the coarse graining that yields decoherence and gives rise to probabilities for histories. In quasiclassical descriptions, further information is sacrificed in exhibiting the emergent regularities summarized by classical equations of motion. An appropriate entropy measures the loss of information. For a “quasiclassical realm” this is connected with the usual thermodynamic entropy as obtained from statistical mechanics. It was low for the initial state of our universe and has been increasing since.

We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-correction rates, the encoded state approximately follows an evolution of the type of a single decohering qubit, but with an effectively decreased coupling constant. The factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. The quadratic enhancement depends on the existence of a Zeno regime in the Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze the range of validity of this result and identify two relevant time scales. Finally, we extend the result to more general codes and argue that the performance of continuous error correction will exhibit the same qualitative characteristics.

We investigate macroscopic entanglement in an infinite XX spin-$\frac{1}{2}$ chain with staggered magnetic field, $B_l=B+e^{-i\pi l}b$. Using single-site entropy and by constructing an entanglement witness, we search for the existence of entanglement when the system is at absolute zero, as well as in thermal equilibrium. Although the role of the alternating magnetic field $b$ is, in general, to suppress entanglement as do $B$ and $T$, we find that when $T=0$, introducing $b$ allows the existence of entanglement even when the uniform magnetic field $B$ is arbitrarily large. We find that the region and the amount of entanglement in the spin chain can be enhanced by a staggered magnetic field.