We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary distinguishability of the branches of the superposition and another based on the ratio of the maximal quantum Fisher information of the superposition to that of its branches, i.e., the relative metrological usefulness of the superposition. A general formula for the effective sizes of these states according to the branch-distinguishability measure is obtained and applied to superposition states of $N$ quantum harmonic oscillators composed of Gaussian branches. Considering optimal distinguishability of pure states on a time-evolution path leads naturally to a notion of distinguishability time that generalizes the well-known orthogonalization times of Mandelstam and Tamm and Margolus and Levitin. We further show that the distinguishability time provides a compact operational expression for the superposition size measure based on the relative quantum Fisher information. By restricting the maximization procedure in the definition of this measure to an appropriate algebra of observables, we show that the superposition size of, e.g., NOON states and hierarchical cat states, can scale linearly with the number of elementary particles comprising the superposition state, implying precision scaling inversely with the total number of photons when these states are employed as probes in quantum parameter estimation of a 1-local Hamiltonian in this algebra.

We present an error analysis of various tomographic protocols based on the linear inversion for the reconstruction of an unknown two-qubit state. We solve the problem of finding a tomographic protocol which is the most robust against errors in terms of the lowest value (i.e., equal to 1) of a condition number, as required by the Gastinel–Kahan theorem. In contrast, standard tomographic protocols, including those based on mutually unbiased bases, are nonoptimal for determining all the 16 elements of an unknown two-qubit density matrix. Our method is based on the measurements of the 16 generalized Pauli operators, where twelve of them can be locally measured, and the other four require nonlocal Bell measurements. Our method corresponds to selectively measuring, one by one, all the real and imaginary elements of an unknown two-qubit density matrix. We describe two experimentally feasible setups of this protocol for the optimal reconstruction of two photons in an unknown polarization state using conventional detectors and linear-optical elements. Moreover, we define the operators for the optimal reconstruction of the states of multiqubit or multilevel (qudit) systems.

We consider the quantum and local hidden variable (LHV) correlations obtained by measuring a pair of qubits by projections defined by randomly chosen axes separated by an angle $\theta$. Local hidden variables predict binary colorings of the Bloch sphere with antipodal points oppositely colored. We prove Bell inequalities separating the LHV predictions from the singlet quantum correlations for $\theta \in (0,\frac{\pi }{3})$. We raise and explore the hypothesis that, for a continuous range of $\theta >0$, the maximum LHV anticorrelation is obtained by assigning to each qubit a coloring with one hemisphere black and the other white.

Secure quantum key distribution with multimode Gaussian entangled states and multimode homodyne detectors is proposed. In general the multimode character of both the sources of entanglement and the homodyne detectors can cause a security break even for a perfect channel when trusted parties are unaware of the detection structure. Taking into account the multimode structure and potential leakage of information from a homodyne detector reduces the loss of security to some extent. We suggest the symmetrization of the multimode sources of entanglement as an efficient method allowing us to fully recover the security irrespectively to multimode structure of the homodyne detectors. Further, we demonstrate that by increasing the number of the fluctuating but similar source modes the multimode protocol stabilizes the security of the quantum key distribution. The result opens the pathway towards quantum key distribution with multimode sources and detectors.

Conditions to achieve an unusually strong Rydberg spin-exchange interaction are investigated and proposed as a means to generate pairwise entanglement and realize a swap-like quantum gate for neutral atoms. Ground-state entanglement is created by mapping entangled Rydberg states to ground states using optical techniques. A protocol involving swap-gate and pairwise entanglement operations is predicted to create global entanglement of a chain of $N$ atoms in a time that is independent of $N$.

In this paper, we propose feedback designs for manipulating a quantum state to a target state by performing sequential measurements. In light of Belavkin's quantum feedback control theory, for a given set of (projective or nonprojective) measurements and a given time horizon, we show that finding the measurement selection policy that maximizes the probability of successful state manipulation is an optimal control problem for a controlled Markovian process. The optimal policy is Markovian and can be solved by dynamical programming. Numerical examples indicate that making use of feedback information significantly improves the success probability compared to classical scheme without taking feedback. We also consider other objective functionals including maximizing the expected fidelity with the target state as well as minimizing the expected arrival time. The connections and differences among these objectives are also discussed.

A combined basis of analytic Gaussian functions and grid-based finite element-discrete variable representation spherical harmonic expansion is specialized for the description of continuum electron dynamics in the presence of electrons held fixed in core molecular orbitals. The applicability of this hybrid representation designed for general problems involving accurate determination of molecular continua wave functions is illustrated for photoionization of second-row diatomic molecules. Accurate descriptions of such electron continuum dynamics are a necessary step towards analyzing correlated double continua photoejections. Examination of this hybrid method in comparison to a more computationally expensive pure grid-based single-center expansion reveals several key advantages that by design make it attractive for describing processes involving one or more electrons moved to the continuum.

We present a measurement of the branching fractions for decay from the long-lived $5D_{5/2}$ level in ${{}^{138}\mathrm{Ba}}^{+}$. The branching fraction for decay into the $6S_{1/2}$ ground state was found to be $0.846{\left(25\right)}_{\mathrm{stat}}{\left(4\right)}_{\mathrm{sys}}$. We also report an improved measurement of the $5D_{5/2}$ lifetime, ${\tau }_{5D_{5/2}}=31.2\left(0.9\right)$ s. Together these measurements provide an experimental determination of transition rates for decay out of the $5D_{5/2}$ level. The low ($<7\times {10}^{-12}$ Torr) pressure in the ion trap in which these measurements were made simplified data acquisition and analysis. Comparison of the experimental results with theoretical predictions of the transition rates shows good agreement.

Anyonic systems are modeled by topologically protected Hilbert spaces which obey complex superselection rules restricting possible operations. These Hilbert spaces cannot be decomposed into tensor products of spatially localized subsystems, whereas the tensor product structure is a foundation of the standard entanglement theory. We formulate bipartite entanglement theory for pure anyonic states and analyze its properties as a nonlocal resource for quantum information processing. We introduce a new entanglement measure, asymptotic entanglement entropy (AEE), and show that it characterizes distillable entanglement and entanglement cost similarly to entanglement entropy in conventional systems. AEE depends not only on the Schmidt coefficients but also on the quantum dimensions of the anyons shared by the local subsystems. Moreover, it turns out that AEE coincides with the entanglement gain by anyonic excitations in certain topologically ordered phases.

Relativistic calculations of the isotope shifts of energy levels in highly charged Li-like ions are performed. The nuclear recoil (mass shift) contributions are calculated by merging the perturbative and large-scale configuration-interaction Dirac-Fock-Sturm (CI-DFS) methods. The nuclear size (field shift) contributions are evaluated by the CI-DFS method including the electron-correlation, Breit, and QED corrections. The nuclear deformation and nuclear polarization corrections to the isotope shifts in Li-like neodymium, thorium, and uranium are also considered. The results of the calculations are compared with the theoretical values obtained with other methods.

We investigate correlations between multiple ionization and fragmentation processes of the ethane molecule in collisions with $580\text{−}\mathrm{keV}{\mathrm{C}}^{+}$ ions under single-electron capture and loss conditions. Employing an electron counting technique, we directly obtain number distributions of ionized electrons, which correspond to distributions of multiple ionization probabilities of ethane. In addition, fragmentation patterns as a function of the charge state $r$ of intermediate parent ions ${\mathrm{C}}_2{{\mathrm{H}}_6}^{r+*}$ are obtained from coincidence measurements between the time of flight of the product ions and the number of electrons emitted. Fragmentation patterns in the different charge-changing conditions reveal a crucial role of the internal excitation in the fragmentation processes. Also, we provide clear evidence of strong selectivity on the parent charge state for formation of the ${{\mathrm{H}}_3}^{+}$ ion, which is exclusively generated through doubly charged parent ions ${\mathrm{C}}_2{{\mathrm{H}}_6}^{2+*}$.

The three-dimensional classical-trajectory Monte Carlo method is employed to investigate low-energy photoelectron spectra in above-threshold ionization by strong laser fields. By connecting the tunneling coordinates with the final momentum-energy spectra, we identify the effects of the Coulomb potential on electron trajectories and the final energy spectra. In addition, we verify that the photoelectron spectra, depending on the energy region, can be controlled with a two-color laser pulse by varying the phase delay. The modulations of the electron spectra and yields as well as the generated photocurrents reveal the connections among them, which support our previous work [Phys. Rev. Lett. 109, 243002 (2012)] on terahertz wave generation from two-color laser pulses.

Yin and Radzihovsky [X. Yin and L. Radzihovsky, Phys. Rev. A 88, 063611 (2013)] recently developed a self-consistent extension of a Bogoliubov theory, in which the condensate number density $n_c$ is treated as a mean field that changes with time, in order to analyze a JILA experiment by Makotyn et al. [P. Makotyn et al., Nat. Phys. 10, 116 (2014)] on a ${}^{85}\mathrm{Rb}$ Bose gas following a deep quench to a large scattering length. We apply this theory to construct a closed set of equations that highlight the role of ${\dot{n}}_c$, which is to induce an effective interaction between quasiparticles. We show analytically that such a system supports a steady state characterized by a constant condensate density and a steady but periodically changing momentum distribution, whose time average is described exactly by the generalized Gibbs ensemble. We discuss how the ${\dot{n}}_c$-induced effective interaction, which cannot be ignored on the grounds of the adiabatic approximation for modes near the gapless Goldstone mode, can significantly affect condensate populations and Tan's contact for a Bose gas that has undergone a deep quench.

We propose a direct readout of symmetry information in matter using nonlinear optics. From combinations of circularly and longitudinally polarized optical fields, we construct irreducible spherical field tensors for second- and third-order nonlinear processes. The coupling of these field tensors to the matter susceptibility tensors allows filtering out of the susceptibility symmetries independently of the sample orientation in the laboratory frame. Experimental demonstrations are conducted on microcrystals, in a microscopy configuration compatible with symmetry order imaging.

We report the experimental observation of coherent population oscillation (CPO-) based light storage in an atomic vapor cell at room temperature. Using the ultranarrow CPO between the ground levels of a $\Lambda$ system selected by polarization in metastable ${}^4\mathrm{He}$, such a light storage is experimentally shown to be phase preserving. As it does not involve any atomic coherences it has the advantage of being robust to dephasing effects such as small magnetic field inhomogeneities. The storage time is limited by the population lifetime of the ground states of the $\Lambda$ system.

We consider the Landau-Zener problem for a two-level system (or qubit) when this system interacts with one harmonic oscillator mode that is initially set to a finite-temperature thermal equilibrium state. The oscillator could represent an external mode that is strongly coupled to the qubit, e.g., an ionic oscillation mode in a molecule, or it could represent a prototypical uncontrolled environment. We analyze the qubit's occupation probabilities at the final time in a number of regimes, varying the qubit and oscillator frequencies, their coupling strength, and the temperature. In particular, we find a surprising nonmonotonic dependence on the coupling strength and temperature.

Photon antibunching is a quantum phenomenon typically observed in strongly nonlinear systems where photon blockade suppresses the probability of detecting two photons at the same time. Antibunching has also been reported with Gaussian states, where optimized amplitude squeezing yields classically forbidden values of the intensity correlation, $g^{\left(2\right)}\left(0\right)<1$. As a consequence, observation of antibunching is not necessarily a signature of photon-photon interactions. To clarify the significance of the intensity correlations, we derive a sufficient condition for deducing whether a field is non-Gaussian based on a $g^{\left(2\right)}\left(0\right)$ measurement. We then show that the Gaussian antibunching obtained with a degenerate parametric amplifier is close to the ideal case reached using dissipative squeezing protocols. We finally shed light on the so-called unconventional photon blockade effect predicted in a driven two-cavity setup with surprisingly weak Kerr nonlinearities, stressing that it is a particular realization of optimized Gaussian amplitude squeezing.

The possibility of the superradiant phase transition in polarizable materials described by the minimal-coupling Hamiltonian with the longitudinal dipole-dipole interaction is examined. We try to reduce the Hamiltonian into the Dicke one in the homogeneous and infinite case, and discuss the stability of normal ground state by the formalism of the Green function in the spatially inhomogeneous case. The presence of the longitudinal dipole-dipole interaction does not enable the superradiant phase transition, if the transverse and longitudinal fields are decoupled. Although the full dipole-dipole interaction can be eliminated in the electric-dipole gauge in the absence of overlap between individual atomic dipoles, we cannot reduce the Hamiltonian to the Dicke one, because the elimination is justified only if all the transverse and longitudinal fields remain. Even if the transverse and longitudinal fields are mixed in spatially inhomogeneous systems, the normal ground state is still stable if the system does not show the superradiant phase transition in the homogeneous case.

We consider a system subject to a quantum optical master equation at finite temperature and study a class of conditional dynamics obtained by monitoring its totally or partially purified environment. More specifically, drawing from the notion that the thermal state of the environment may be regarded as the local state of a lossy and noisy two-mode squeezed state, we consider conditional dynamics (“unravellings”) resulting from the homodyne detection of the two modes of such a state. Thus, we identify a class of unravellings parametrized by the loss rate suffered by the environmental two-mode state, which interpolate between direct detection of the environmental mode alone (occurring for total loss, whereby no correlation between the two environmental modes is left) and full access to the purification of the bath (occurring when no loss is acting and the two-mode state of the environment is pure). We hence show that, while direct detection of the bath is not able to reach the maximal steady-state squeezing allowed by general-dyne unravellings, such optimal values can be obtained when a fully purified bath is accessible. More generally we show that, within our framework, any degree of access to the bath purification improves the performance of filtering protocols in terms of achievable squeezing and entanglement.

Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A third observable is presented which satisfies canonical commutation relations with both position and momentum. The resulting triple of pairwise canonical observables gives rise to a Heisenberg uncertainty relation for the product of three standard deviations. We derive the smallest possible value of this bound and determine the specific squeezed state which saturates the triple uncertainty relation. Quantum optical experiments are proposed to verify our findings.