To certify that an experimentally implemented quantum transformation is a certain unitary operation $U$ on a $d$-dimensional Hilbert space, it suffices to determine fidelities of output states for $d+1$ suitably chosen pure input states [Reich et al., Phys. Rev. A 88, 042309 (2013)]. The set of these $d+1$ probe states can consist of $d$ orthogonal states that form a basis and one additional state which is a balanced superposition of all $d$ basis states. Here we provide an analytical lower bound on quantum process fidelity for two-qubit quantum gates which results from the knowledge of average state fidelity for the basis states and the fidelity of the superposition state. We compare this bound with the Hofmann bound that is based on knowledge of average state fidelities for two mutually unbiased bases. We also discuss the possible extension of our findings to $N$-qubit operations.

We report on accurate measurements of the scalar ${\alpha }_S$ and tensor ${\alpha }_T$ polarizabilities of the $5D$ fine structure levels $5D_{3/2}$ and $5D_{5/2}$ in Rb. The measured values (in atomic units) ${\alpha }_S\left({5D}_{3/2}\right)=18400\left(75\right)$, ${\alpha }_T\left({5D}_{3/2}\right)=-750\left(30\right)$, ${\alpha }_S\left({5D}_{5/2}\right)=18600\left(76\right)$ and ${\alpha }_T\left({5D}_{5/2}\right)=-1440\left(60\right)$ show reasonable correspondence to previously published theoretical predictions, but are more accurate. We implemented laser excitation of the $5D$ level in a laser-cooled cloud of optically polarized Rb-87 atoms placed in a constant electric field.

The x-ray spectra resulting from single-electron capture in charge-exchange collisions of Ne${}^{10+}$ with He and Ne atoms are investigated for the projectile energy of 4.54 keV/u using the two-center atomic-orbital close-coupling method. The calculated spectra of the Ne${}^{9+}$ ion produced in Ne${}^{10+}$ + He and Ne${}^{10+}$ + Ne electron-capture collisions have, generally speaking, the same level of agreement with experimental measurements as those calculated previously by the classical trajectory Monte Carlo method, indicating that multi-electron-capture processes, particularly in the case of the Ne${}^{10+}$ + Ne system, significantly affect the considered spectra. The effects of two-electron capture on the spectral line intensity have been demonstrated qualitatively by using the binomial statistics and independent particle model for the target outer-shell electrons. The role of multi-electron-capture processes in the Ne${}^{10+}$ + Ne collision system needs further attention.

We investigate strong-coupling corrections to single-particle excitations in the normal state of a spin-polarized unitary Fermi gas. Within the framework of an extended $T$-matrix approximation, we calculate the single-particle density of states, as well as the single-particle spectral weight, to show that the so-called pseudogap phenomenon gradually disappears with increasing magnitude of an effective magnetic field. In the highly spin-polarized regime, the calculated spin polarization as a function of the effective magnetic field agrees well with the recent experiment on a ${}^6$Li Fermi gas. Although this experiment has been considered to be incompatible with the existence of the pseudogap in an unpolarized Fermi gas, our result clarifies that the observed spin polarization in the highly spin-polarized regime and the pseudogap in the unpolarized limit can be explained in a consistent manner when one correctly includes effects of population imbalance on single-particle excitations. Since it is a crucial issue to clarify whether the pseudogap exists or not in the BCS-BEC crossover regime of an ultracold Fermi gas, our results would be useful for the understanding of this strongly interacting fermion system.

Ultracold atoms in an optical lattice provide a platform for realization of the superfluid (SF) state, a quantum order with paired charge-neutral fermions. In this paper, we study the SF state in the two-dimensional attractive Hubbard model with $\pi$ flux on each plaquette. The SF state in the $\pi$-flux lattice model suffers very strong quantum fluctuations and the ground state becomes a possible quantum phase liquid state. In this phase, there exists Cooper pairing together with a finite energy gap for the atoms, but no long-range SF phase coherence exists at zero temperature. In addition, we discuss the properties of the SF vortices.

The deflection of a vector soliton formed by a solitary wave and an optical vortex in nematic liquid crystals is investigated upon interaction with a localized refractive index defect. The azimuthal instability of the vortex can be triggered by the index perturbation and enhanced by the distortion of the copropagating solitary wave when in the vicinity of the defect. A modulation theory is developed to study the refraction of the vector soliton and is found to be in good agreement with numerical solutions. This model reveals the crucial role of the diffractive radiation shed by both beam components as they evolve, showing that radiation reduces the destabilizing effect of the solitary wave interaction with the vortex, thus enlightening the effect of this continuous spectrum on the evolution of the nonlinear wave packets.

We investigate light transmission obtained from a hybrid optical system composed of a pair of directly coupled photonic crystal cavities called a photonic crystal molecule, a single semiconductor quantum dot, and a waveguide beyond the weak-excitation approximation. We take account of nonlinear terms in the Heisenberg-Langevin equations and give an effective method to deal with such a problem. It is shown, owing to the presence of nonlinear terms, that the efficient generation of high-order sidebands with large amplitudes can be realized with experimentally achievable system parameters. The results obtained here may be useful for gaining further insight into the properties of solid-state cavity quantum electrodynamics (CQED) system and find applications in harnessing the CQED nonlinearity to manipulate photons in a photonic crystal platform.

Two types of inequalities, Kochen-Specker inequalities and noncontextuality inequalities, are both used to demonstrate the incompatibility between the noncontextual hidden variable model and quantum mechanics. It has been thought that noncontextuality inequalities are much more potent than Kochen-Specker inequalities, since the latter are constrained by the Kochen-Specker rules, which are regarded as an extra constraint imposed on the noncontextual hidden variable model. However, we find that a noncontextuality inequality exists in a ray set if and only if a Kochen-Specker inequality exists in the same ray set. This provides an effect approach both for constructing noncontextuality inequalities in a Kochen-Specker set and for converting a Kochen-Specker inequality to a noncontextuality inequality in any ray set.

We present a paradigm for capturing the complementarity of two observables. It is based on the entanglement created by the interaction between the system observed and the two measurement devices used to measure the observables sequentially. Our main result is a lower bound on this entanglement and resembles well-known entropic uncertainty relations. Besides its fundamental interest, this result directly bounds the effectiveness of sequential bipartite operations—corresponding to the measurement interactions—for entanglement generation. We further discuss the intimate connection of our result with two primitives of information processing, namely, decoupling and coherent teleportation.

The “pixel imaging mass spectrometry” camera is used to perform femtosecond laser-induced Coulomb explosion imaging of 3,5-dibromo-3${}^{\prime }$,5${}^{\prime }$-difluoro-4${}^{\prime }$-cyanobiphenyl molecules prealigned in space. The experiment allows the concurrent detection of the correlated two-dimensional momentum images of all the ionic fragments resulting from fragmentation of multiple molecules in each acquisition cycle. The Coulomb explosion studies provide rich information about the parent molecular structure and fragmentation dynamics, and open new opportunities for real-time imaging of intramolecular processes.

We study atoms in optical lattices whose electronic ground state is off-resonantly coupled to a highly excited state with strong binary interactions. We present a time-dependent treatment of the resulting quantum dynamics, which—contrary to recent predictions [Li, Ates, and Lesanovsky, Phys. Rev. Lett. 110, 213005 (2013)]—proves that the strong repulsion between the weakly admixed Rydberg states does not lead to atomic trap loss. This finding provides an important basis for creating and manipulating coherent long-range interactions in optical lattice experiments.

Eigenvalues of a density matrix characterize well the quantum state's properties, such as coherence and entanglement. We propose a simple method to determine all the eigenvalues of an unknown density matrix of a finite-dimensional system in a single experimental setting. Without fully reconstructing a quantum state, eigenvalues are determined with the minimal number of parameters obtained by a measurement of a single observable. Moreover, its implementation is illustrated in linear optical and superconducting systems.

We propose a quantum-enhanced iterative (with $K$ steps) measurement scheme based on an ensemble of $N$ two-level probes which asymptotically approaches the Heisenberg limit ${\delta }_K\propto R^{-K/(K+1)}$, where $R$ is the number of quantum resources. The protocol is inspired by Kitaev's phase estimation algorithm and involves only collective manipulation and measurement of the ensemble. The iterative procedure takes the shot-noise-limited primary measurement with precision ${\delta }_1\propto N^{-1/2}$ to increasingly precise results, ${\delta }_K\propto N^{-K/2}$. We propose an implementation of the algorithm for the measurement of a magnetic field using a two-component atomic cloud of bosons.

We investigate the connection between the concept of affine balancedness (a-balancedness) introduced by M. Johansson et al. [Phys. Rev. A 85, 032112 (2012)] and polynomial local SU invariants and the appearance of topological phases, respectively. It is found that different types of a-balancedness correspond to different types of local SU invariants analogously to how different types of balancedness, as defined by A. Osterloh and J. Siewert, [New J. Phys. 12, 075025 (2010)], correspond to different types of local special linear (SL) invariants. These different types of SU invariants distinguish between states exhibiting different topological phases. In the case of three qubits, the different kinds of topological phases are fully distinguished by the three-tangle together with one more invariant. Using this, we present a qualitative classification scheme based on balancedness of a state. While balancedness and local SL invariants of bidegree $(2n,0)$ classify the SL-semistable states [A. Osterloh and J. Siewert, New J. Phys. 12, 075025 (2010); O. Viehmann et al., Phys. Rev. A 83, 052330 (2011)], a-balancedness and local SU invariants of bidegree $(2n-m,m)$ give a more fine-grained classification. In this scheme, the a-balanced states form a bridge from the genuine entanglement of balanced states, invariant under the SL group, towards the entanglement of unbalanced states characterized by U invariants of bidegree $(n,n)$. As a byproduct, we obtain generalizations to the W state, i.e., states that are entangled, but contain only globally distributed entanglement of parts of the system.

Several types of nonclassical structures within the $N$-qubit Pauli group that can be seen as fundamental resources for quantum information processing are presented and discussed. Identity products (IDs), structures fundamentally related to entanglement, are defined and explored. The Kochen-Specker (KS) theorem is proved by particular sets of IDs that we call KS sets. We also present a theorem that we call the $N$-qubit Kochen-Specker (NKS) theorem, which is proved by particular sets of IDs that we call NKS sets, and whose utility is that it leads to efficient constructions for KS sets. We define the criticality, or irreducibility, of these structures, and its connection to entanglement. All representative critical IDs for up to $N=4$ qubits are presented, and numerous families of critical IDs for arbitrarily large values of $N$ are discussed. The critical IDs for a given $N$ are a finite set of geometric objects that appear to fully characterize the nonclassicality of the $N$-qubit Pauli group. Methods for constructing critical KS sets and NKS sets from IDs are given, and experimental tests of entanglement, contextuality, and nonlocality are discussed. Possible applications and connections to other work are also discussed.

Recently it has been shown that projected entangled-pair states can be considered as a (physically motivated) resource state for measurement-based quantum computation. Here we elaborate on how to construct a deterministic measurement-based quantum computation model on projected entangled-pair states. In particular, we use this scheme to build a four-level many-body model for universal quantum computation on qubits. We also derive a 3-local parent Hamiltonian for this model, whose ground state is nondegenerate.

We show that in one dimension the transfer matrix $\mathbf{M}$ of any scattering potential $v$ coincides with the $S$ matrix of an associated time-dependent non-Hermitian $2\times 2$ matrix Hamiltonian $\mathbf{H}\left(\tau \right)$. If $v$ is real valued, $\mathbf{H}\left(\tau \right)$ is pseudo-Hermitian and its exceptional points correspond to the classical turning points of $v$. Applying time-dependent perturbation theory to $\mathbf{H}\left(\tau \right)$ we obtain a perturbative series expansion for $\mathbf{M}$ and use it to study the phenomenon of unidirectional invisibility. In particular, we establish the possibility of having multimode unidirectional invisibility with wavelength-dependent direction of invisibility and construct various physically realizable optical potentials possessing this property. We also offer a simple demonstration of the fact that the off-diagonal entries of the first-order Born approximation for $\mathbf{M}$ determine the form of the potential. This gives rise to a perturbative inverse scattering scheme that is particularly suitable for optical design. As a simple application of this scheme, we construct an infinite-range unidirectionally invisible potential.

We calculate the probability of inelastic processes in the fullerene shell of an endohedral atom which follow the ionization of the caged atom by a high-energy photon. We demonstrate that the probability is close to unity in a large interval of the photoelectron energies. The inelastic processes are determined mainly by the final-state interactions, which have to be included beyond the perturbative approach. At photoelectron energies $E$ of the order of several keV the probability drops as $1/E$. It is determined by the final-state interactions, which can be treated perturbatively. At still larger energies the probability is determined by the shake-off mechanism and does not depend on energy $E$. A model for calculating the shake-off contribution is also suggested. The actual calculations are carried out for the endohedral atoms $A@{\text{C}}_{60}$ and $A@{\text{C}}_{20}$.

The photo-double-ionization (PDI) of Mg to the Mg${}^{2+}$($3s^{-2}$) state has been studied by photoelectron-photoelectron-coincidence experiments at a photon energy corresponding to the excitation of the 2$p$→3$d$ resonance. The equal energy sharing ($E_1$ = $E_2$ = 16.4 eV) as well as the complementary unequal energy ($E_1$↔$E_2$ = 10.4↔22.4 eV) sharing kinematics have been investigated. From the experimental results without any approximation the symmetrized gerade and ungerade amplitudes have been obtained. The experimental angular correlation patterns as well as the amplitudes are compared to CCC calculations in which the resonant process has been incorporated. The results confirm that the amplitudes of the photo-double-ionization carry the signature of the target radial wave function. The investigation of the triple differential cross sections has been then extended by simulations to a kinematics with the fixed detector at 90${}^o$, which can not be studied experimentally by the present setup. These simulations shed light on results of previous measurements on alkaline-earth-metal atoms in this kinematics, which were not consistent with the common understanding of photo-double-ionization derived from He experiments.

We study numerically the localization of atomic excitation based on the dark states formed through electromagnetically induced transparency using interfering coupling beams. In particular, we examine the formation of dark states in a system exhibiting hyperfine splitting, including the effects of optical pumping in this multilevel system, laser polarization, and finite interaction time, and explore the conditions that lead to optimal spatial resolution of the excitation. We find that optimal localization requires long interaction times, due to the slow approach of the atomic system to steady state near the nodes of the standing wave pattern.