There are two common settings in a quantum-state discrimination problem. One is minimum-error discrimination where a wrong guess (error) is allowed and the discrimination success probability is maximized. The other is unambiguous discrimination where errors are not allowed but the inconclusive result “I do not know” is possible. We investigate a discrimination problem with a finite margin imposed on the error probability. The two common settings correspond to the error margins 1 and 0. For arbitrary error margin, we determine the optimal discrimination probability for two pure states with equal occurrence probabilities. We also consider the case where the states to be discriminated are multipartite and show that the optimal discrimination probability can be achieved by local operations and classical communication.

We discuss the generation of entanglement between electronic states of two atoms in a cavity using direct quantum feedback schemes. We compare the effects of different control Hamiltonians and detection processes in the performance of entanglement production and show that the quantum-jump-based feedback proposed by Carvalho and Hope [Phys. Rev. A 76, 010301(R) (2007)] can protect highly entangled states against decoherence. We provide analytical results that explain the robustness of jump feedback, and also analyze the perspectives of experimental implementation by scrutinizing the effects of imperfections and approximations in our model.

We address the presence of nondistillable (bound) entanglement in natural many-body systems. In particular, we consider standard harmonic and spin-$\frac{1}{2}$ chains, at thermal equilibrium and characterized by few interaction parameters. The existence of bound entanglement is addressed by calculating explicitly the negativity of entanglement for different partitions. This allows us to individuate a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We discuss how the appearance of bound entanglement can be linked to entanglement-area laws, typical of these systems. Various types of interactions are explored, showing that the presence of bound entanglement is an intrinsic feature of these systems. In the harmonic case, we analytically prove that thermal bound entanglement persists for systems composed by an arbitrary number of particles. Our results strongly suggest the existence of bound entangled states in the macroscopic limit also for spin-$\frac{1}{2}$ systems.

We discuss a method for scaling a neutral-atom Rydberg gate quantum processor to a large number of qubits. Limits are derived showing that the number of qubits that can be directly connected by entangling gates with errors at the ${10}^{-3}$ level using long-range Rydberg interactions between sites in an optical lattice, without mechanical motion or swap chains, is about 500 in two dimensions and 7500 in three dimensions. A scaling factor of 60 at a smaller number of sites can be obtained using collective register encoding in the hyperfine ground states of the rare-earth atom holmium. We present a detailed analysis of operation of the 60-qubit register in holmium. Combining a lattice of multiqubit ensembles with collective encoding results in a feasible design for a 1000-qubit fully connected quantum processor.

We discuss two methods to encode one qubit into six physical qubits. Each of our two examples corrects an arbitrary single-qubit error. Our first example is a degenerate six-qubit quantum error-correcting code. We explicitly provide the stabilizer generators, encoding circuit, codewords, logical Pauli operators, and logical controlled NOT operator for this code. We also show how to convert this code into a nontrivial subsystem code that saturates the subsystem Singleton bound. We then prove that a six-qubit code without entanglement assistance cannot simultaneously possess a Calderbank-Shor-Steane (CSS) stabilizer and correct an arbitrary single-qubit error. A corollary of this result is that the Steane seven-qubit code is the smallest single-error correcting CSS code. Our second example is the construction of a nondegenerate six-qubit CSS entanglement-assisted code. This code uses one bit of entanglement (an ebit) shared between the sender and the receiver and corrects an arbitrary single-qubit error. The code we obtain is globally equivalent to the Steane seven-qubit code and thus corrects an arbitrary error on the receiver’s half of the ebit as well. We prove that this code is the smallest code with a CSS structure that uses only one ebit and corrects an arbitrary single-qubit error on the sender’s side. We discuss the advantages and disadvantages for each of the two codes.

We propose a scheme to engineer an effective spin Hamiltonian starting from a system of electrons confined in micro-Penning-traps. By means of appropriate sequences of electromagnetic pulses, alternated with periods of free evolution, we control the shape and strength of the spin-spin interaction. Moreover, we can modify the effective magnetic field experienced by the particle spin. This procedure enables us to reproduce notable quantum spin systems, such as Ising and $XY$ models. Thanks to its scalability, our scheme can be applied to a fairly large number of trapped particles within the reach of near future technology.

The $L_i$- $\left(i=1–3\right)$ subshell x-ray spectra for the ${}_{52}\text{T}\text{e}$, ${}_{53}\text{I}$, ${}_{55}\text{C}\text{s}$, ${}_{56}\text{B}\text{a}$, and ${}_{57}\text{L}\text{a}$ elements excited by Mn $K\alpha$ ($E_{K{\alpha }_2}=5.888\text{keV}$ and $E_{K{\alpha }_1}=5.899\text{keV}$) x rays have been investigated using the ${}^{55}\text{F}\text{e}$ radioisotope in conjunction with a Cr absorber. A low-energy Ge detector was used to measure the $L$ x rays at an emission angle $\psi =126°$, where the second-order Legendre polynomial term $P_2$ $\left(\text{cos}\psi \right)$ associated with the angular distribution is annulled. In the case of the ${}_{56}\text{B}\text{a}$ and ${}_{57}\text{L}\text{a}$ elements, alignment of the $L_3$-subshell vacancy states was investigated through angular distribution measurements of the emitted $L_3$-subshell x rays. The $L{\alpha }_{1,2}$ and $L{\beta }_{2,15}$ x-ray groups are observed to be nearly isotropic, while the data for the pure $Ll$ $\left(L_3\text{−}{M}_1\right)$ x-ray emission are indicative of a small anisotropic trend, though within experimental error. The integral x-ray fluorescence cross sections are deduced and interpreted in terms of $L_i$-subshell photoionization cross sections, fluorescence and Coster-Kronig yields, and x-ray emission rates. The $L_2$-subshell x-ray cross sections for ${}_{57}\text{L}\text{a}$ measured using targets of lanthanum (III) fluoride and dilanthanum (III) trioxide are found to be unusually higher. The enhancement is observed due to the contribution of the $L_2$-subshell radiative resonant Raman scattering (RRS) of Mn $K\alpha$ x rays having energy around the $L_2$-subshell binding energy of ${}_{57}\text{L}\text{a}$ in these compounds. Also, the observed enhancement of the $L_3$-subshell x-ray cross sections in ${}_{57}\text{L}\text{a}$ is suggestive of intrashell vacancy transfer via $L_2\text{−}{L}_3$ Coster-Kronig RRS transitions. The $L_2$-subshell total RRS cross sections in ${}_{57}\text{L}\text{a}$ have been deduced from the present measured attenuation coefficients for Mn $K\alpha$ x rays in ${\text{La}}_2{\text{O}}_3$ and ${\text{LaF}}_3$. The $L_2$-subshell radiative and total RRS cross sections in ${}_{57}\text{L}\text{a}$ using ${\text{LaF}}_3$ are higher by $\sim 30\%$ than those using ${\text{La}}_2{\text{O}}_3$. The contribution of processes predicted in the framework of Mozouchi’s four-band model involving inner subshells along with the valence and conduction bands of these wide-band-gap insulator compounds is likely to account for the observed results. The $L_2$-subshell radiative and $L_2\text{−}{L}_3$ Coster-Kronig yields and the ratio of the $L_2\text{−}{M}_4$ and $L_2\text{−}{N}_4$ radiative RRS intensities in both La compounds are found to be same and are consistent with values from photoexcited vacancy decay. The $L_2$-subshell radiative RRS was also observed to be isotropic.

We report on the results of a multichannel calculation of fine-structure transition cross sections for collisions of ground-state Ti with He. We find significant suppression of fine-structure level quenching over a wide range of collision energies. We show that the suppression is due to a mechanism proposed by [Hancox et al., Nature (London) 431, 281 (2004)] to explain similar suppression of Zeeman relaxation in collisions of magnetically trapped rare-earth-metal atoms with cold He atoms. We find that the quenching rates are sensitive to the value of the Born-Oppenheimer adiabatic potential surfaces of the Ti-He system in the region of the inner repulsive wall. Adjusting the ab initio potentials for TiHe, available in the literature, we find good agreement with laboratory measurements.

Laser induced field-free alignment of linear molecules is investigated by using a single-shot spatial imaging technique. The measurements are achieved by femtosecond time-resolved optical polarigraphy (FTOP). Individual alignment revivals recorded at high resolution in ${\text{CO}}_2$, as well as simultaneous observation of several alignment revivals produced within the rotational period of the ${\text{O}}_2$ molecule are reported. The data are analyzed with a theoretical model describing the alignment experienced by each molecule standing within the interaction region observed by the detector. The temporal dynamics, intensity dependence, and degree of alignment are measured and compared with the awaited results. The technique is simple and can be easily implemented in a large class of molecular samples. Improvement to extend the performance of the method is discussed. The reported study is a decisive step toward feedback optimization and optimal control of field-free molecular alignment.

High-lying Rydberg states of Xe have been ionized using intense $108\mu \text{m}$ radiation from a free-electron laser. Measured two-dimensional photoelectron images reveal significant above-threshold ionization and contain an indirect contribution resulting from the combined action of the atomic Coulomb field, laser field, and dc electric field of the spectrometer on the electron. The observation of indirect ionization contains information about the electron localization directly after the laser excitation and indicates that the experiments are performed in the multiphoton regime of strong-field ionization. The experiments are compared to and interpreted by means of both classical and quantum-mechanical simulations.

We investigate photo-double-ionization of ${\mathrm{H}}_2$ by circular polarized photons at $h\nu =160\mathrm{eV}$. The previously observed two-center interference pattern in the angular distribution of the electron sum momentum is shown to depend strongly on the internuclear distance and the summed electron momenta.

We study few-boson tunneling in a one-dimensional double well. As we pass from weak interactions to the fermionization limit, the Rabi oscillations first give way to highly delayed pair tunneling (for medium coupling), whereas for very strong correlations multiband Rabi oscillations emerge. All this is explained on the basis of the exact few-body spectrum and without recourse to the conventional two-mode approximation. Two-body correlations are found essential to the understanding of the different tunnel mechanisms. The investigation is complemented by discussing the effect of skewing the double well, which offers the possibility to access specific tunnel resonances.

We introduce an approximate phase-space technique to simulate the quantum dynamics of interacting bosons. With the future goal of treating Bose-Einstein condensate systems, the method is designed for systems with a natural separation into highly occupied (condensed) modes and lightly occupied modes. The method self-consistently uses the Wigner representation to treat highly occupied modes and the positive-$P$ representation for lightly occupied modes. In this method, truncation of higher-derivative terms from the Fokker-Planck equation is usually necessary. However, at least in the cases investigated here, the resulting systematic error, over a finite time, vanishes in the limit of large Wigner occupation numbers. We tested the method on a system of two interacting anharmonic oscillators, with high and low occupations, respectively. The hybrid method successfully predicted atomic quadratures to a useful simulation time 60 times longer than that of the positive-$P$ method. The truncated Wigner method also performed well in this test. For the prediction of the correlation in a quantum nondemolition measurement scheme, for this same system, the hybrid method gave excellent agreement with the exact result, while the truncated Wigner method showed a large systematic error.

We theoretically study harmonically trapped one-dimensional Bose gases (e.g., ${}^7\text{L}\text{i}$, ${}^{23}\text{N}\text{a}$, ${}^{39}\text{K}$, ${}^{87}\text{R}\text{b}$, etc.) with multibands occupied, focusing on effects of higher-energy bands. Combining the Ginzburg-Landau theory with bosonization techniques, we predict that the repulsive interaction between higher-band bosons and the quantum fluctuation can induce the ground state with a finite angular momentum around the trapped axis. In this state, the $Z_2$ reflection symmetry (clockwise or anticlockwise rotations) is spontaneously broken.

There has been a recent resurgence of experimental efforts to quantitatively determine the phase diagram of the Bose-Hubbard model by carefully analyzing experiments with ultracold bosonic atoms on an optical lattice. In many realizations of these experiments, the hopping amplitudes are not homogeneous throughout the lattice, but instead, the lattice has an anisotropy where hopping along one direction is not exactly equal to hopping along a perpendicular direction. In this contribution, we examine how an anisotropy in the hopping matrix elements affects the Mott lobes of the Bose-Hubbard model. For weak anisotropy, we find the phase diagram is only slightly modified when expressed in terms of the average hopping, while for strong anisotropy, one expects to ultimately see dimensional crossover effects.

Two-dimensional Whittaker solitons (WSs) are introduced and investigated numerically in nonlocal nonlinear media. Different classes of stable and unstable higher-order spatial optical solitons are discovered among the solutions of the generalized nonlocal nonlinear Schrödinger equation, in analogy with the linear Whittaker eigenmodes of the quantum harmonic oscillator. Specific values of the modulation depth parameter for different values of the topological charge are discussed. Our results reveal that in media with a Gaussian response function higher-order spatial WSs can exist in various families, such as two-dimensional Gaussian solitons, vortex-ring solitons, half-moon solitons, and symmetric and asymmetric single-layer and multilayer necklace solitons. The stability of WSs is addressed numerically. We establish that two-dimensional Gaussian solitons and vortex-ring solitons are stable, while other families of spatial WSs are unstable, although their stability can be improved by moving into the strongly nonlocal regime.

We numerically demonstrate the possibility of the efficient generation of high-order harmonics and synthesis of subfemtosecond light pulses by superposition of several harmonics in aperiodical nonlinear photonic crystal $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_3$. A simple method of designing such a crystal is presented. Calculations are performed for the fundamental radiation with wavelengths $2.7\mu \mathrm{m}$ and $5\mu \mathrm{m}$, which correspond to the wavelengths of the HF laser and CO lasers.

We experimentally prepare a type of continuous variable genuine four-partite entangled states, the quantum correlation property of which is different from that of the four-mode Greenberger-Horne-Zeilinger and cluster states, and which has not any qubit counterpart to be proposed at present. In the criterion inequalities for the full inseparability of the genuine four-partite entangled states, the amplitude and phase quadrature correlation variances totally consisting of three-party combination from the four entangled modes are involved. The measured correlation variances among the quadratures of the prepared entangled states satisfy the sufficient requirements for the full inseparability.

The dipole polarizabilities of the ground state $n{s}^2{{}^{1}S}_0$ and the metastable state $nsnp{{}^{3}P}_0$ are crucial for estimating the light shifts and blackbody radiation shifts in the optical frequency standard based on alkaline-earth-metal–like atoms. In this paper, the correlative dipole polarizabilities for group IIB atoms were calculated by the method of the $B$-spline configuration interaction with a semiempirical core-polarization model potential. The results are consistent with the experimental values in a reasonable accuracy and agree with other theoretical results as well. With these results, the magic wavelengths, at which the lowest-order light shift of the clock transition $n{s}^2{{}^{1}S}_0\text{−}nsnp{{}^{3}P}_0$ is null, were also obtained. For Zn, Cd, and Hg, they are 413, 420, and 363 nm, respectively.

Momentum distributions of ${\mathrm{Ne}}^{2+}$ and ${\mathrm{Ar}}^{2+}$ ions created by linearly polarized $795\mathrm{nm}$, $25\mathrm{fs}$ laser pulses have been traced at intensities from ${10}^{14}\text{to}3\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ using a “reaction microscope.” Apart from the transition from nonsequential to sequential ionization, characterized by significant changes in longitudinal momentum distributions developing from a double hump, over a triple-peak structure to a narrow single Gaussian observed for both ions, for ${\mathrm{Ar}}^{2+}$ we find a similar behavior but reversed in its intensity dependence in the purely nonsequential regime, pointing to contributions of recollision excitation plus subsequent field ionization, or to the role of “Z trajectories” recently predicted within classical calculations.