This paper addresses and expands on the contents of the recent Letter [Phys. Rev. Lett. 111, 030502 (2013)] discussing private quantum subsystems. Here we prove several previously presented results, including a condition for a given random unitary channel to not have a private subspace (although this does not mean that private communication cannot occur, as was previously demonstrated via private subsystems) and algebraic conditions that characterize when a general quantum subsystem or subspace code is private for a quantum channel. These conditions can be regarded as the private analog of the Knill-Laflamme conditions for quantum error correction, and we explore how the conditions simplify in some special cases. The bridge between quantum cryptography and quantum error correction provided by complementary quantum channels motivates the study of a new, more general definition of quantum error-correcting code, and we initiate this study here. We also consider the concept of complementarity for the general notion of a private quantum subsystem.

We study the energy shift and the Casimir-Polder force of an atom out of thermal equilibrium near the surface of a dielectric substrate. We first generalize, adopting the local source hypothesis, the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji [J. Phys. (Paris) 43, 1617 (1982); J. Phys. (Paris) 45, 637 (1984)], which separates the contributions of thermal fluctuations and radiation reaction to the energy shift and allows a distinct treatment of atoms in the ground and excited states, to the case out of thermal equilibrium, and then we use the generalized formalism to calculate the energy shift and the Casimir-Polder force of an isotropically polarizable neutral atom. We identify the effects of the thermal fluctuations that originate from the substrate and the environment and discuss in detail how the Casimir-Polder force out of thermal equilibrium behaves in three different distance regions in both the low-temperature limit and the high-temperature limit for both the ground-state and excited-state atoms, with special attention devoted to the distinctive features as opposed to thermal equilibrium. In particular, we recover the distinctive behavior of the atom-wall force out of thermal equilibrium at large distances in the low-temperature limit recently found in a different theoretical framework, and furthermore we give a concrete region where this behavior holds.

We study the diamagnetic interaction between a ground-state atom, which is located at a distance $z$ from a planar body, e.g., a perfect mirror or a nondispersive and nonabsorbing dielectric substrate, and the body-assisted electromagnetic fields from vacuum, equilibrium, and out of equilibrium thermal fluctuations. We find that the diamagnetic potential at zero temperature is always proportional to $z^{-4}$ in both the retarded and the nonretarded zones, and the Casimir-Polder (CP) force is attractive. The CP potential due to the thermal fluctuations at equilibrium dominates over that due to the zero-point fluctuations in the long-distance or high-temperature limit and behaves like $T/z^3$, and the corresponding force is attractive. However, in the case of out of thermal equilibrium, the CP potential exhibits a different behavior with slower dependence on the distance and stronger dependence on temperature in the same limit, and it decays like $(T_e^2-T_s^2)/z^2$, where $T_e$ is the temperature of the environment and $T_s$ is that of the substrate, yielding a CP force that can either be attractive or repulsive. Meanwhile, in the short-distance or low-temperature limit the CP potential is always dominated by the contribution due to the vacuum fluctuations.

Photoionization spectra of beryllium atoms in the region of $1s$ excitation have been measured by synchrotron radiation. The photon energy region reported in this article is between $1s2s^2$ and $1s\left(2s2p{}^{3}P\right)4s$ corresponding to 122.3 and 127 eV, respectively. The configurations which have the unique characteristics due to the configuration mixing between $2s$ and $2p$ are discussed. Comparisons with the previous paper by L. VoKy et al. [Phys. Rev. A 46, 3945 (1992)] calculating the photoionization spectrum of this energy region were made and the assignments of the resonances were performed. The Fano parameters were also derived for the observed states.

Inelastic cross sections for collisions between thorium (Th) and helium (${}^3\mathrm{He}$) are measured. For Th[${}^3{F}_2$]–${}^3\mathrm{He}$, we determine the ratio of momentum transfer to Zeeman relaxation cross sections to be $\gamma \sim 500$ at 800 mK. For Th[${}^3{P}_0$]–${}^3\mathrm{He}$, we find no quenching of this metastable state during ${10}^6$ collisions. We measure the radiative lifetime of Th[${}^{3}P{}_0$] to be $\tau >130$ ms. The observed stability of Th[${}^3{P}_0$] opens up the possibility of trapping this metastable species.

We measure the ratio $\gamma$ of the momentum transfer–to–vibrational quenching cross section for molecular thorium monoxide (ThO) [$X{(}^1{\Sigma }^{+})$, $v=1$, $J=0$] in collisions with atomic helium between 800 mK and 2.4 K. We find $\gamma \sim {10}^4$. We also observe indirect evidence for ThO-He van der Waals complex formation, which has been predicted by theory [Tscherbul, Sayfutyarova, Buchachenko, and Dalgarno, J. Chem. Phys. 134, 144301 (2011)], and in conjunction, we determine the three-body recombination rate constant at 2.4 K, ${\Gamma }_3=8\pm 2\times {10}^{-33}$ ${\mathrm{cm}}^6$ ${\mathrm{s}}^{-1}$.

Antihydrogen production has reached such a level that precision spectroscopic measurements of its properties are within reach. In particular, the ground-state level population is of central interest for experiments aiming at antihydrogen spectroscopy. The positron density and temperature dependence of the ground-state yield is a result of the interplay between recombination, collisional, and radiative processes. Considering the fact that antihydrogen atoms with the principal quantum number $n=15$ or lower quickly cascade down to the ground state within 1 ms, the number of such states is adopted as a measure of useful antihydrogen atoms. It has been found that the scaling behavior of the useful antihydrogen yield is different depending on the positron density and positron temperature.

We use $R$-matrix theory with time dependence (RMT) to investigate multiphoton ionization of ground-state atomic carbon with initial orbital magnetic quantum number $M_L=0$ and $M_L=1$ at a laser wavelength of 390 nm and peak intensity of ${10}^{14}{\mathrm{W}/\mathrm{cm}}^2$. Significant differences in ionization yield and ejected-electron momentum distribution are observed between the two values for $M_L$. We use our theoretical results to model how the spin-orbit interaction affects electron emission along the laser polarization axis. Under the assumption that an initial C atom is prepared at zero time delay with $M_L=0$, the dynamics with respect to time delay of an ionizing probe pulse modeled by using RMT theory is found to be in good agreement with available experimental data.

The concept of measure synchronization between two coupled quantum many-body systems is presented. In general terms we consider two quantum many-body systems whose dynamics gets coupled through the contact particle-particle interaction. This coupling is shown to produce measure synchronization, a generalization of synchrony to a large class of systems which takes place in absence of dissipation. We find that in quantum measure synchronization, the many-body quantum properties for the two subsystems, e.g., condensed fractions and particle fluctuations, behave in a coordinated way. To illustrate the concept we consider a simple case of two species of bosons occupying two distinct quantum states. Measure synchronization can be readily explored with state-of-the-art techniques in ultracold atomic gases and, if properly controlled, be employed to build targeted quantum correlations in a sympathetic way.

We present a method for investigating nonequilibrium dynamics of an ultracold system that is initially at thermal equilibrium. Our procedure is based on the classical fields approximation and appropriately prepared initial state for antiferromagnetic condensate with fixed magnetization. As an application of the method, we investigate the influence of thermal fluctuations on the quantum phase transition from an antiferromagnetic to phase separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We find that at temperatures significantly lower than the critical condensation temperature $T_c$ the scaling law for the number of created spin defects remains intact.

We analytically calculate the critical phenomena of a Bose-Einstein condensation of an ideal gas in an arbitrary trap with any mesoscopic or macroscopic number of particles and find all universality classes of the system's statistics and thermodynamics. In particular, we find analytically the universal fine structure of the famous discontinuity in the value or/and derivative of the specific heat in the critical region around the $\lambda$ point.

We investigate the soliton behaviors of laser beams in two types of two coupled $\mathcal{PT}$-symmetric dissipative gratings which contain different coupling forms (constant coupling and periodic coupling). The dynamics of such systems is governed by coupled nonlinear time-dependent Schrödinger-like equations and the corresponding soliton solutions are obtained. Long-time soliton oscillations are observed in the case of constant coupling, but absent in the case of periodic coupling. The stable regions of the parameters for gain or loss strength and modulation frequency are estimated by the variational method and numerical simulation. It is interesting that the stable region in the parameter space in the periodic-coupling case is wider than that in the constant coupling case.

We describe a method for measuring the field profile of x-ray ultrashort pulses including phase information. The scheme is based on spectrally interfering two replicas of the same pulse, which are spectrally shifted via three-wave mixing with IR or visible beams. Using a single-shot spectrometer the scheme can be used for the inspection of individual ultrashort x-ray pulses with random amplitudes and phases. Examples for characterization of stochastic pulses with a bandwidth of 1 eV are given, including criteria for a successful measurement.

We describe the absorption by the walls of a quantum electrodynamical cavity as a process during which the elementary excitations (photons) of an internal mode of the cavity exit by tunneling through the cavity walls. We estimate by classical methods the survival time of a photon inside the cavity and the quality factor of its mirrors.

We investigate the creation of electron-positron pairs in a combination of static electric and magnetic fields. The electric and magnetic fields point along the $x$ direction and $z$ direction, respectively, and vary along the $x$ direction. In the case when the spatial extensions of the two fields are not equal to each other, the quantum field theoretical solutions to the Dirac equation suggest a complete suppression of the pair-creation process as long as an effective scalar potential is subcritical, even though the effective electric field may still be supercritical.

It has been shown by Oreshkov and Brun that any two-outcome quantum measurement can be decomposed into a continuous stochastic process using a feedback loop. In this article, we characterize which of these decompositions are possible when each iteration of the feedback loop consists of a weak measurement caused by an interaction with a probe system. We restrict ourselves to the case when the probe is a qubit and the interaction Hamiltonian between the probe and system is constant. We find that even given the ability to perform arbitrary unitary pulses throughout the continuous decomposition, only generalized measurements with two distinct singular values are achievable. However, this is sufficient to decompose a generalized qubit measurement using a qubit probe and a simple interaction Hamiltonian.

We investigate the behavior of genuine multiparticle entanglement, as quantified by the generalized geometric measure, in gapless-to-gapped quantum transitions of one- and two-dimensional quantum spin models. The investigations are performed in the exactly solvable one-dimensional $XY$ models, as well as two-dimensional frustrated $J_1–J_2$ models, including the Shastry-Sutherland model. The generalized geometric measure shows nonmonotonic features near such transitions in the frustrated quantum systems. We also compare the features of the generalized geometric measure near the quantum critical points with the same for measures of bipartite quantum correlations. The multipartite quantum correlation measure turns out to be a better indicator of quantum critical points than the bipartite measures, especially for two-dimensional models.

We describe a method to perform any generalized purity-preserving measurement of a qubit with techniques tailored to superconducting systems. First, we consider two methods for realizing a two-outcome partial projection: using a thresholded continuous measurement in the circuit QED setup and using an indirect ancilla qubit measurement. Second, we decompose an arbitrary purity-preserving two-outcome measurement into single-qubit unitary rotations and a partial projection. Third, we systematically reduce any multiple-outcome measurement to a sequence of such two-outcome measurements and unitary operations. Finally, we consider how to define suitable fidelity measures for multiple-outcome generalized measurements.

Nonlocal properties of an ensemble of diagonal random unitary matrices of order $N^2$ are investigated. The average Schmidt strength of such a bipartite diagonal quantum gate is shown to scale as $lnN$, in contrast to the $ln{N}^2$ behavior characteristic of random unitary gates. Entangling power of a diagonal gate $U$ is related to the von Neumann entropy of an auxiliary quantum state $\rho =A{A}^{†}/N^2$, where the square matrix $A$ is obtained by reshaping the vector of diagonal elements of $U$ of length $N^2$ into a square matrix of order $N$. This fact provides a motivation to study the ensemble of non-Hermitian unimodular matrices $A$, with all entries of the same modulus and random phases and the ensemble of quantum states $\rho$, such that all their diagonal entries are equal to $1/N$. Such a state is contradiagonal with respect to the computational basis, in the sense that among all unitary equivalent states it maximizes the entropy copied to the environment due to the coarse-graining process. The first four moments of the squared singular values of the unimodular ensemble are derived, based on which we conjecture a connection to a recently studied combinatorial object called the “Borel triangle.” This allows us to find exactly the mean von Neumann entropy for random phase density matrices and the average entanglement for the corresponding ensemble of bipartite pure states.

We present experimental and theoretical results on single- and multiple-electron capture, and fragmentation, in ${\mathrm{C}}^{6+}+{\mathrm{C}}_{60}$ collisions at velocities in the $v_{\text{col}}=0.05-0.4$ a.u. range. We use time-of-flight mass spectrometry and coincidence detection of charged fragments to separate pure target ionization from processes in which the ${\mathrm{C}}_{60}$ target is both ionized and fragmented. The coincidence technique allows us to identify different types of fragmentation processes such as ${\mathrm{C}}_{60}^{q+}\to {\mathrm{C}}_{58}^{q+}+{\mathrm{C}}_2$ and ${\mathrm{C}}_{60}^{q+}\to {\mathrm{C}}_{58}^{(q-1)+}+{\mathrm{C}}_2^{+}$. A quasimolecular approach is employed to calculate charge transfer and target excitation cross sections. First-order time-dependent perturbation and statistical methods are used to treat the postcollisional processes: the calculated rate constants for ${\mathrm{C}}_2$ and $\mathrm{C}{}_2^{+}$ emission from the excited and charged fullerene are then used to evaluate the fragmentation dynamics. We show that the target ionization cross section decreases with the induced target charge state and the impact energy. ${\mathrm{C}}_2$ emission from $\mathrm{C}{}_{60}^{q+}$ is found to dominate when $q\le 2$ while $\mathrm{C}{}_2^{+}$ emission dominates when $q\ge 5$, in agreement with the present and previous experimental results.