We have investigated the exceptional points (EPs) which are degeneracies of a non-Hermitian Hamiltonian, in the case that three modes are interacting with each other. Even though the parametric evolution of the modes cannot be uniquely determined when encircling more than two EPs once, we can recover the initial configuration of the modes by encircling two EPs three times or three EPs twice. We confirm our expectation by numerically calculating the modes of an open quantum system, two dielectric microdisks, and a $3\times 3$ matrix model.

We generalize Bell's hidden-variable model describing the singlet state of a two-qubit system by extending it to arbitrary states and observables. As in the original work, we assume a uniform, state-independent probability distribution for the hidden variables which are identified with the unit vectors of a three-dimensional real space. By slightly modifying our model, we provide also a minimal hidden variable description of the two-qubit system, relying on a single hidden variable. We discuss the main features and the implications of the model.

We propose a scalable and robust architecture for one-way quantum computation using coupled networks of superconducting transmission line resonators. In our protocol, quantum information is encoded into the long-lived photon states of the resonators, which have a much longer coherence time than the usual superconducting qubits. Each resonator contains a charge qubit used for the state initialization and the local projective measurement of the photonic qubit. Any pair of neighboring photonic qubits are coupled via a mediator charge qubit, and large photonic cluster states can be created by applying Stark-shifted Rabi pulses to these mediator qubits. The distinct advantage of our architecture is that it combines both the excellent scalability of the solid-state systems and the long coherence time of the photonic qubits. Furthermore, this architecture is very robust against the parameter variations.

Total and partial charge transfer cross sections are calculated in collisions of protons with the nitrogen molecule at energies between $0.1$ and 10 keV. Ab initio potential energy curves and nonadiabatic couplings have been obtained for a number of N${}_2$ bond lengths using a multireference configuration interaction method. The influence of the anisotropy of the target molecule is investigated. Results are compared with previous experimental and theoretical data.

Studies of the direct mechanism for dissociative recombination of HCO${}^{+}$ and HOC${}^{+}$ are presented. The calculations involve wave-packet propagation in three dimensions on electronically resonant states of HCO and HOC with the potential-energy surfaces and autoionization widths obtained from ab initio electron scattering and electronic structure calculations. The total cross section and branching ratios for the two molecules and their deuterated isotopologues are calculated and compared to available experiments. The effect of vibrational excitation in DCO${}^{+}$ has been studied as well.

The quantum-statistical cluster expansion method of Lee and Yang is extended to investigate off-diagonal long-range order (ODLRO) in one-component and multicomponent mixtures of bosons or fermions. Our formulation is applicable to both a uniform system and a trapped system without local-density approximation and allows systematic expansions of one-particle and multiparticle reduced density matrices in terms of cluster functions, which are defined for the same system with Boltzmann statistics. Each term in this expansion can be associated with a Lee-Yang graph. We elucidate a physical meaning of each Lee-Yang graph; in particular, for a mixture of ultracold atoms and bound dimers, an infinite sum of the ladder-type Lee-Yang 0-graphs is shown to lead to Bose-Einstein condensation of dimers below the critical temperature. In the case of Bose statistics, an infinite series of Lee-Yang 1-graphs is shown to converge and gives the criteria of ODLRO at the one-particle level. Applications to a dilute Bose system of hard spheres are also made. In the case of Fermi statistics, an infinite series of Lee-Yang 2-graphs is shown to converge and gives the criteria of ODLRO at the two-particle level. Applications to a two-component Fermi gas in the tightly bound limit are also made.

Pulse-to-pulse instability in the emission from a random laser based on Nd:Sc${}_3$(BO${}_3$)${}_4$ ceramic with immobile scatterers was studied below, at, and above the stimulated emission threshold $P_{\mathrm{th}}$. The correlation between pumping and emission intensities was found to be surprisingly low, especially in the vicinity of the lasing threshold. When the sample was excited by reasonably stable (±5$\%$) pumping pulses, a strong fluctuation of output intensities was observed in the range of pumping energies $P_{\mathrm{th}}$/2 < $P$ < 2$P_{\mathrm{th}}$—the range in which the Lévy statistics of emission fluctuations has been predicted in random lasers. We thus report on experimental evidence of the Lévy statistics in a random laser with firmly fixed scatterers.

The propagation of ultrashort optical pulses in an AlGaAs waveguide array is studied using frequency-resolved optical gating measurements. In the nonlinear regime, the measurements show that the pulses at the output of the array evolve toward a set chirp value that is independent of the input chirp. Simulations reproduce the experimental results. The observations can be described as a fixed-point attractor on a chirp-intensity map.

We consider the problem of minimizing the ancillary systems required to realize an arbitrary strategy of a quantum protocol, with the assistance of classical memory. For this purpose we introduce the notion of memory cost of a strategy to measure the resources required in terms of ancillary dimension. We provide a condition for the cost to be equal to a given value, and we use this result to evaluate the cost in some special cases. As an example, we show that any covariant protocol for the cloning of a unitary transformation requires at most one ancillary qubit. We also prove that the memory cost has to be determined globally and cannot be calculated by optimizing the resources independently at each step of the strategy.

We introduce a scheme to reconstruct arbitrary states of networks composed of quantum oscillators—e.g., the motional state of trapped ions or the radiation state of coupled cavities. The scheme involves minimal resources and minimal access, in the sense that it (i) requires only the interaction between a one-qubit probe and a single node of the network; (ii) provides the Weyl characteristic function of the network directly from the data, avoiding any tomographic transformation; (iii) involves the tuning of only one coupling parameter. In addition, we show that a number of quantum properties can be extracted without full reconstruction of the state. The scheme can be used for probing quantum simulations of anharmonic many-body systems and quantum computations with continuous variables. Experimental implementation with trapped ions is also discussed and shown to be within reach of current technology.

I establish a unified view of polygamy of multiqubit entanglement. I first introduce a two-parameter generalization of the entanglement of assistance, namely, the unified entanglement of assistance for bipartite quantum states, and provide an analytic lower bound in two-qubit systems. I show a broad class of polygamy inequalities of multiqubit entanglement in terms of the unified entanglement of assistance that encapsulates all known multiqubit polygamy inequalities as special cases. I further show that this class of polygamy inequalities can be improved into tighter inequalities for three-qubit systems.

We investigate the sensitivity of a recently proposed method for precision measurement [Phys. Rev. Lett. 106, 140502 (2011)], focusing on an implementation based on solid-state spin systems. The scheme amplifies a quantum sensor response to weak external fields by exploiting its coupling to spin impurities in the environment. We analyze the limits to the sensitivity due to decoherence and propose dynamical decoupling schemes to increase the spin coherence time. The sensitivity is also limited by the environment spin polarization; therefore, we discuss strategies to polarize the environment spins and present a method to extend the scheme to the case of zero polarization. The coherence time and polarization determine a figure of merit for the environment's ability to enhance the sensitivity compared to echo-based sensing schemes. This figure of merit can be used to engineer optimized samples for high-sensitivity nanoscale magnetic sensing, such as diamond nanocrystals with controlled impurity density.

We experimentally demonstrated polarization-based entanglement swapping using spatially separated periodically poled lithium niobate waveguides that emit polarization-entangled photon pairs by spontaneous parametric down-conversion (SPDC). Entanglement swapping using such SPDC sources was theoretically analyzed by accounting for losses along photon propagation paths, accidental fourfold coincidence counts (FCC's), and the dead time in single-photon detection. In a partial Bell-state measurement, entanglement was observed between two photons that were initially uncorrelated and that did not directly interact with each other. The obtained fidelity was $52.5\pm 0.8\%$. Accidental FCC's were measured to clarify the effect of simultaneous generation of three pairs in SPDC on the fidelity. The fidelity increased to $80.5\pm 2.9\%$ when accidental coincidence counts were subtracted.

We investigate relationships between computational power and correlation in resource states for quantum computational tensor network, which is a general framework for measurement-based quantum computation. We find that if the size of resource states is finite, not all resource states allow correct projective measurements in the correlation space, which is related to nonvanishing two-point correlations in the resource states. On the other hand, for infinite-size resource states, we can always implement correct projective measurements if the resource state can simulate arbitrary single-qubit rotations, since such a resource state exhibits exponentially decaying two-point correlations. This implies that a many-body state whose two-point correlation cannot be upper bounded by an exponentially decaying function cannot simulate arbitrary single-qubit rotations.

In many important situations, the dominant dephasing mechanism in cryogenic rare-earth-metal-ion–doped systems is due to magnetic field fluctuations from spins in the host crystal. Operating at a magnetic field where a transition has a zero first-order Zeeman (ZEFOZ) shift can greatly reduce this dephasing. Here we identify the location of transitions with a zero first-order Zeeman shift for optical transitions in Pr${}^{3+}$:YAG and for spin transitions in Er${}^{3+}$:Y${}_2$SiO${}_5$. The long coherence times that ZEFOZ can enable would make Pr${}^{3+}$:YAG a strong candidate for achieving the strong-coupling regime of cavity QED, and would be an important step forward in creating long-lived telecommunications wavelength quantum memories in Er${}^{3+}$:Y${}_2$SiO${}_5$. This work relies mostly on published spin-Hamiltonian parameters, but Raman heterodyne spectroscopy was performed on Pr${}^{3+}$:YAG to measure the parameters for the excited state.

The total cross sections for single-charge transfer in H $+$ H, He${}^{+}$ $+$ H, He${}^{+}$ $+$ He${}^{+}$, and Li${}^{2+}$ $+$ H collisions have been calculated in the framework of four-body (4B) formalism of boundary corrected continuum intermediate state (BCCIS) approximation in the energy range 20–5000 keV/amu. The dynamic electron correlation is explicitly taken into account through the complete perturbation potentials. In the initial channel, the passive electron plays the role of screening of the projectile ion. However, continuum states of the target ion and the electron in the field of the residual projectile ion are included. In all cases, total single-electron capture cross sections have been calculated by summing over all contributions up to $n$ $=$ 2 shells and subshells, respectively, except the H-H collision. The present computed results, both in prior and post forms of BCCIS-4B method for symmetric and asymmetric cases have been compared with the available theoretical and experimental results. We found that our computed results, particularly in the prior form, are in better agreement with the experimental observations in comparison to other theoretical findings. Post-prior discrepancy has been found to be within 20$\%$ above 70 keV/amu for all interactions.

Cold and ultracold polar molecules with nonzero electronic angular momenta are of great interest for studies in quantum chemistry and control, investigations of novel quantum systems, and precision measurement. However, in mixed electric and magnetic fields, these molecules are generically subject to a large set of avoided crossings among their Zeeman sublevels; in magnetic traps, these crossings lead to distorted potentials and trap loss from electric bias fields. We have characterized these crossings in OH by microwave-transferring trapped OH molecules from the upper $|f;M=+\frac{3}{2}\rangle$ parity state to the lower $|e;+\frac{3}{2}\rangle$ state and observing their trap dynamics under an applied electric bias field. Our observations are very well fit by a simple Landau-Zener model, yielding insight to the rich spectra and dynamics of polar radicals in mixed external fields.

We address the long-standing issue of accurately partitioning the nonlinear response of silica glass into electronic (Kerr) and nuclear (Raman) contributions to correctly describe the propagation of ultrashort solitons in a unified way independently of their duration. This is done with a semianalytical approach leading to a modified nonlinear coefficient and thus to a modified condition for fundamental soliton propagation valid for durations much less, in the same order, or much greater than the characteristic time scale of the Raman response function. The results provided by this model are in good agreement with numerical integration of the nonlinear Schrödinger equation taking the Raman response into account.

We report on the generation of an intense extreme-ultraviolet (EUV) supercontinuum with photon energies spanning from 35 to 50 eV (i.e., supporting an isolated attosecond pulse with a duration of ∼271 as) by loosely focusing 35 fs, 11 mJ pulses from a femtosecond laser amplifier into a 10-mm-long gas cell filled with krypton gas. The dramatic change in spectral and temporal properties of the driver pulses after passing through the gas cell indicates that propagation effects play a significant role in promoting the generation of the EUV supercontinuum.

Electromagnetic Casimir stresses are of relevance to many technologies based on mesoscopic devices such as microelectromechanical systems embedded in dielectric media, Casimir induced friction in nanomachinery, microfluidics, and molecular electronics. Computation of such stresses based on cavity QED generally requires numerical analysis based on a regularization process. The scheme described below has the potential for wide applicability to systems involving realistic inhomogeneous media. From a knowledge of the spectrum of the stationary modes of the electromagnetic field the scheme is illustrated by estimating numerically the Casimir stress on opposite faces of a pair of perfectly conducting planes separated by a vacuum and the change in this result when the region between the plates is filled with an incompressible inhomogeneous nondispersive dielectric.