We present a general algorithm for finding all classes of pure multiparticle states equivalent under stochastic local operations and classical communication (SLOCC). We parametrize all SLOCC classes by the critical sets of the total variance function. Our method works for arbitrary systems of distinguishable and indistinguishable particles. We also show how to calculate the Morse indices of critical points which have the interpretation of the number of independent nonlocal perturbations increasing the variance and hence entanglement of a state. We illustrate our method by two examples.

Coherent states for a large class of the Lenz-Demkov-Ostrovsky (LDO) potentials are constructed as superpositions of zero-energy Hamiltonian eigenstates. They represent very well-localized stationary wave packets. Moreover, it is shown how to make the packets move along suitable classical orbits. The calculations are performed for a few members of the LDO family of potentials, among them, for the Maxwell's fish-eye model and that used for a theoretical explanation of the periodic system of elements.

We investigate the performance of Grover's quantum search algorithm on a register that is subject to a loss of particles that carry qubit information. Under the assumption that the basic steps of the algorithm are applied correctly on the correspondingly shrinking register, we show that the algorithm converges to mixed states with 50% overlap with the target state in the bit positions still present. As an alternative to error correction, we present a procedure that combines the outcome of different trials of the algorithm to determine the solution to the full search problem. The procedure may be relevant for experiments where the algorithm is adapted as the loss of particles is registered and for experiments with Rydberg blockade interactions among neutral atoms, where monitoring of atom losses is not even necessary.

Most of the schemes for “noiseless” amplification of coherent states, which have recently been attracting theoretical and experimental interest, share a common trait: The amplification is not truly noiseless, or perfect, for nonzero success probability. While this must hold true for all phase-independent amplification schemes, in this work we point out that truly noiseless amplification is indeed possible, provided that the states which we wish to amplify come from a finite set. Perfect amplification with unlimited average gain is then possible with finite success probability, for example, using techniques for unambiguously distinguishing between quantum states. Such realizations require only linear optics, no single-photon sources, and no photon counting. We also investigate the optimal success probability of perfect amplification of a symmetric set of coherent states. There are two regimes: low-amplitude amplification, where the target amplitude is below one, and general amplification. For the low-amplitude regime, analytic results for the optimal amplification success probabilities can be obtained. In this case a natural bound imposed by the ratio of success probabilities of optimal unambiguous discrimination of the source and amplified states can always be reached. We also show that for general amplification this bound cannot always be satisfied.

We demonstrate the control of entanglement in a hybrid optomechanical system comprising an optical cavity with a mechanical end-mirror and an intracavity Bose-Einstein condensate. Pulsed laser light (tuned within realistic experimental conditions) is shown to induce an almost sixfold increase of the atom-mirror entanglement and to be responsible for interesting dynamics between such mesoscopic systems. In order to assess the advantages offered by the proposed control technique, we compare the time-dependent dynamics of the system under constant pumping with the evolution due to the modulated laser light.

We develop a numerical approach for quantifying entanglement in mixed quantum states by convex-roof entanglement measures, based on the optimal entanglement witness operator and the minimax optimization method. Our approach is applicable to general entanglement measures and states and is an efficient alternative to the conventional approach based on the optimal pure-state decomposition. Compared with the conventional one, it has two important merits: (i) that the global optimality of the solution is quantitatively verifiable, and (ii) that the optimization is considerably simplified by exploiting the common symmetry of the target state and measure. To demonstrate the merits, we quantify Greenberger-Horne-Zeilinger (GHZ) entanglement in a class of three-qubit full-rank mixed states composed of the GHZ state, the $W$ state, and the white noise, the simplest mixtures of states with different genuine multipartite entanglement, which have not been quantified before this work. We discuss some general properties of the form of the optimal witness operator and of the convex structure of mixed states, which are related to the symmetry and the rank of states.

We present an approach to the study of entanglement decay which focuses on collective properties. As an example, we investigate the entanglement decay of a two-qubit system produced by local identical reservoirs acting on the qubits for three experimentally and theoretically relevant cases. We study the probability distributions of disentanglement times, a quantity independent of the measure used to quantify entanglement, and the time-dependent probability distribution of concurrence. Analytical results are obtained for initially uniformly distributed pure states. The calculation of these probability distributions gives a complete insight into how different decoherence channels affect the entanglement initially contained in the set of two-qubit pure states. Numerical results are reported for randomly distributed initial mixed states. Although the paper focuses in Markovian noisy channels, we show that our results also describe nonautonomous and non-Markovian channels.

We calculate interaction potentials between three rubidium Rydberg atoms in the absence of external fields. Several three-atom states are considered: $|nS,nS,n^{\prime }S\rangle$ and $|nD,nD,nD\rangle$ $(36<n<75)$. Among the considered states, nonadditive potentials appear in the $S$ states if $n\ne n^{\prime }$ or if $|n-n^{\prime }|$ is small, and also in $D$ states. Interatomic potentials are nonadditive when they induce intensive mixing between three-atom states of the same zero-order energy. The consideration of nonadditive potentials may add a new dimension to the research into Rydberg atoms.

We investigate the phase enhancement of quantum states subject to nonlinear phase shifts. The optimal phase estimation of even entangled coherent states (ECSs) is shown to be better than that of NOON states with the same average particle number $\langle n\rangle$ and nonlinearity exponent $k$. We investigate the creation of an approximate entangled coherent state (AECS) from a photon-subtracted squeezed vacuum with current optical technology methods and show that a pure AECS is even better than an even ECS for large $\langle n\rangle$. Finally, we examine the simple, but physically relevant, cases of loss in the nonlinear interferometer for a fixed average photon number $\langle n\rangle$.

Minimum-error state discrimination between two mixed states $\rho$ and $\sigma$ can be aided by the receipt of “classical side information” specifying which states from some convex decompositions of $\rho$ and $\sigma$ apply in each run. We quantify this phenomena by the average trace distance and give lower and upper bounds on this quantity as functions of $\rho$ and $\sigma$. The lower bound is simply the trace distance between $\rho$ and $\sigma$, trivially seen to be tight. The upper bound is $\sqrt{1-\mathrm{tr}\left(\rho \sigma \right)}$, and we conjecture that this is also tight. We reformulate this conjecture in terms of the existence of a pair of “unbiased decompositions,” which may be of independent interest, and prove it for a few special cases. Finally, we point towards a link with a notion of nonclassicality known as preparation contextuality.

Recently a spin-orbit-coupled Bose condensate has been realized experimentally using two-photon Raman coupling, and this condensate exhibits two distinct equilibrium phases known as the plane wave phase and the stripe phase at equilibrium. In this Rapid Communication we show that such condensate exhibits unique dynamic behaviors, which originate from interactions and are absent in a noninteracting system. In the plane wave phase, a dipole mode will induce a breathing mode in its perpendicular plane and vice versa. This is a cooperation effect between spin-velocity locking and spin-dependent interaction. While in the stripe phase, a breathing mode will induce the sliding mode of the density stripe along its perpendicular direction. This reflects the fact that the sliding mode is the gapless excitation in this phase due to spontaneous spatial translation symmetry breaking.

We propose an encoding scheme to fight against ${\widehat{\sigma }}_x$-type local collective noise. In our scheme, a logical qubit consists of two charge qubits coupled by a variable capacitance, and different logical qubits are coupled by a common inductance. A logical qubit provides a decoherence-free subspace (DFS) immune to the ${\widehat{\sigma }}_x$-type collective noise. We show how to realize universal quantum computation in the DFS. Any two logical qubits can be selectively and controllably coupled by adjusting fluxes through the common inductance and superconducting-quantum-interference-device loops, which makes it possible to scale our scheme up to a large number of logical qubits. Finally, we show how to prepare a logical qubit in the DFS.

Energy levels, radiative transition probabilities, and autoionization rates for [Ne]$3s^{2}3p^{6}3d^{9}4l^{\prime }nl$, [Ne]$3s^{2}3p^{5}3d^{10}4l^{\prime }nl$ ($n=4$–6), and [Ne]$3s^{2}3p^{6}3d^{9}5l^{\prime }nl$ ($n=5$–7) states in Cu-like tungsten (W${}^{45+}$) are calculated using the relativistic many-body perturbation theory method (rmbpt code), the multiconfiguration relativistic Hebrew University Lawrence Livermore Atomic Code (hullac), and the Hartree-Fock relativistic method (cowan code). Autoionizing levels above the [Ne]$3s^{2}3p^{6}3d^{10}$ threshold are considered. It is found that configuration mixing among [Ne]$3s^{2}3p^{6}3d^{9}4l^{\prime }nl$ and [Ne]$3s^{2}3p^{5}3d^{10}4l^{\prime }nl$ plays an important role for all atomic characteristics. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the singly excited [Ne]$3s^{2}3p^{6}3d^{10}nl$ ($n=5$–7) as well as doubly excited, nonautoionizing [Ne]$3s^{2}3p^{6}3d^{9}4s4l$ ($l=s,p,d,f$), [Ne]$3s^{2}3p^{6}3d^{9}4p4l$ ($l=p,d,f$), [Ne]$3s^{2}3p^{6}3d^{9}4d^2$, [Ne]$3s^{2}3p^{5}3d^{10}4s4l$ ($l=s,p,d$), and [Ne]$3s^{2}3p^{5}3d^{10}4p^2$ states in Cu-like W${}^{45+}$ ions. Contributions from the autoionizing doubly excited [Ne]$3s^{2}3p^{6}3d^{9}4l^{\prime }nl$, [Ne]$3s^{2}3p^{5}3d^{10}4l^{\prime }nl$, and [Ne]$3s^{2}3p^{6}3d^{9}5l^{\prime }nl$ states (with $n$ up to 500), which are particulary important for calculating total DR rates, are estimated. Synthetic dielectronic satellite spectra from Cu-like W are simulated in a broad spectral range from 3 to 70 Å. These calculations provide highly accurate values for a number of W${}^{45+}$ properties useful for a variety of applications, including fusion applications.

The process of photon emission by a high-energy electron or positron moving in a bent single crystal with a constant curvature is considered. The relations for differential energy losses of particles and polarization of emitted photons are obtained. Corrections due to multiphoton production are found. The comparison of calculations with existing experimental data is carried out. The process of photoproduction of electron-positron pairs in a bent single crystal is also studied. The differential probabilities of the process taking into account the photon polarization are presented. Equations are obtained which determine the variation of the Stokes parameters of $\gamma$ quanta, and their solutions are given.

This work investigates the utility of femtosecond pulse shaping in increasing the efficiency of Raman excitation of molecules in the strong-field interaction regime. We study experimentally and theoretically the effect of pulse shaping on the strength of nonresonant coherent anti-Stokes Raman scattering in iodine vapor at laser intensities exceeding ${10}^{13}$ W/cm${}^2$. We show that unlike the perturbative case, shaping strong nonresonant laser pulses can increase the signal strength beyond that observed with the transform-limited excitation. Both adiabatic and nonadiabatic schemes of excitation are explored, and the differences of their potential in increasing the excitation efficiency are discussed.

In this paper the authors report that perfect invisibility cloaking could be achieved in a medium designed by a non-Euclidean conformal transformation. Wave behaviors could be controlled as well as the cloaking device configured by the general Euclidean approach dealing with the full Maxwell's equations. The cloaking medium proposed here is totally isotropic and can work in waves without the geometry and polarization limits; thus it is very promising for applications to build a device to hide large objects.

The spontaneous two-photon emission in hydrogenlike ions is investigated within the framework of second-order perturbation theory and Dirac's equation. Special attention is paid to the angular correlation of the emitted photons as well as to the degree of linear polarization of one of the two photons, if the second is just observed under arbitrary angles. Expressions for the angular correlation and the degree of linear polarization are expanded in powers of cosine functions of the two-photon opening angle, whose coefficients depend on the atomic number and the energy sharing of the emitted photons. The effects of including higher (electric and magnetic) multipoles upon the emitted photon pairs beyond the electric-dipole approximation are also discussed. Calculations of the coefficients are performed for the transitions $2s_{1/2}\to 1s_{1/2}$, $3d_{3/2}\to 1s_{1/2}$, and $3d_{5/2}\to 1s_{1/2}$, along the entire hydrogen isoelectronic sequence ($1\le Z\le 100$).

We investigate the low-energy scattering and bound states of two two-component fermionic atoms in pure two-dimensional (2D) and quasi-2D confinements with Rashba spin-orbit coupling (SOC). We find that the SOC qualitatively changes the behavior of the 2D scattering amplitude in the low-energy limit. For quasi-2D systems we obtain the analytic expression for the effective 2D scattering amplitude and the algebraic equations for the two-atom bound-state energy. We further derive the effective 2D contact potential for the interaction between ultracold atoms in the quasi-2D confinement. This effective potential can be used in the research on many-body physics of quasi-2D ultracold Fermi gases with Rashba SOC.

The formations of ${}^{85}{\text{Rb}}_2$ molecules via photoassociation (PA) steered by two-color laser fields are explored theoretically in order to find an efficient and robust PA scheme. The PA processes steered by the PA pulses modulated by two Gaussian pulses and by two chirped pulses are discussed and compared in detail. The two pulses are coherent in the picosecond range and reach their maxima at the same time. The influences of the linear chirp rate, the frequency difference between two pulses, and the phase shift of the modulated envelope with respect to the maximum of the Gaussian envelope on the PA process are investigated. The yield of photoassociated molecules on vibrational levels with a binding energy of $>$1.0 cm${}^{-1}$ with respect to the $5S+5P_{1/2}$ dissociation limit can apparently be enhanced by choosing proper pulse parameters. Especially, the two-color laser field modulated by two chirped pulses can raise the PA efficiency on one side, and weaken the dependence of the PA process on phase shift on the other side.

We experimentally investigate the phenomenon of a quantum ratchet created by exposing a Bose-Einstein condensate to short pulses of a potential which is periodic in both space and time. Such a ratchet is manifested by a directed current of particles, even though there is an absence of a net bias force. We confirm a recent theoretical prediction [M. Sadgrove and S. Wimberger, New J. Phys. 11, 083027 (2009)] that the current direction can be controlled by experimental parameters which leave the underlying symmetries of the system unchanged. We demonstrate that this behavior can be understood using a single variable containing many of the experimental parameters and thus the ratchet current is describable using a single universal scaling law.