Quantum and classical pairwise correlations in two typical collective spin systems (i.e., the Dicke model and the Lipkin-Meshkov-Glick model) are discussed. These correlations in the thermodynamical limit are obtained analytically and in a finite-size system are calculated numerically. Large-size scaling behavior for the quantum discord itself is observed, which has never been reported in another critical system. A logarithmic diverging behavior for the first derivative of the quantum discord is also found in both models, which might be universal in the second-order quantum phase transition. It is suggested that the pronounced maximum or minimum of first derivative of quantum discord signifies the critical point. Comparisons between the quantum discord and the scaled concurrence are performed. It is shown that the quantum discord is very small in one phase and robust in the other phase, while the scaled concurrence shows maximum at the critical point and decays rapidly when away from the the critical point.

We investigate quantum secret-sharing schemes constructed from ${\left[[n,k,\delta ]\right]}_D$ nonbinary stabilizer quantum error-correcting codes with carrier qudits of prime dimension $D$. We provide a systematic way of determining the access structure, which completely determines the forbidden and intermediate structures. We then show that the information available to the intermediate structure can be fully described and quantified by what we call the information group, a subgroup of the Pauli group of $k$ qudits, and we employ this group structure to construct a method for hiding the information from the intermediate structure via twirling of the information group and sharing of classical bits between the dealer and the players. Our scheme allows for the transformation of a ramp (intermediate) quantum secret-sharing scheme into a semiquantum perfect secret-sharing scheme with the same access structure as the ramp one but without any intermediate subsets, and is optimal in the amount of classical bits the dealer has to distribute.

Ab initio calculations of dielectronic recombination rate coefficients of Rh-like gadolinium and tungsten have been performed. Energy levels, radiative transition probabilities, and autoionization rates of Pd-like gadolinium and tungsten for [Zn]4$p^6$4$d^8$4fnl, [Zn]4$p^6$4$d^8$5$l^{\prime }$$nl$, [Zn]4$p^6$4$d^8$6$l^{\prime }$$nl$ and [Zn]4$p^5$4$d^{10}nl,$ [Zn]4$p^5$4$d^9$4fnl, [Zn]4$p^5$4$d^9$5$l^{\prime }$$nl$, [Zn]4$p^5$4$d^9$6$l^{\prime }$$nl$ ($n$ ⩽ 18) complexes were calculated using the flexible atomic code. The contributions from resonant and nonresonant radiative stabilizing transitions to the total rate coefficients are discussed. Results show that the contributions from nonresonant radiative stabilizing transitions are significantly enchanced for W when compared with Gd as a result of lowering of energy levels relative to the ionization limit. In addition, the widely used Burgess-Merts semiempirical formula may underestimate the dielectronic recombination rate coefficients in the temperature regions of interest. The present calculated rate coefficients are fitted to a semiemperical formula. The data obtained are expected to be useful for modelling plasmas both for extreme ultraviolet lithography source development and for fusion applications.

We have explored the spatial distribution of an ion cloud trapped in a linear octopole radio-frequency (rf) ion trap. The two-dimensional distribution of the column density of stored Ag${}_2^{+}$ was measured via photofragment-ion yields as a function of the position of the incident laser beam over the transverse cross section of the trap. The profile of the ion distribution was found to be dependent on the number of loaded ions. Under high ion-loading conditions with a significant space-charge effect, ions form a ring profile with a maximum at the outer region of the trap, whereas they are localized near the center axis region at low loading of the ions. These results are explained quantitatively by a model calculation based on equilibrium between the space-charge-induced potential and the effective potential of the multipole rf field. The maximum adiabaticity parameter ${\eta }_{\max }$ is estimated to be about 0.13 for the high ion-density condition in the present octopole ion trap, which is lower than typical values reported for low ion densities; this is probably due to additional instability caused by the space charge.

We introduce the notion of dissipative periodic lattice as an optical lattice with periodically distributed dissipative sites and argue that it allows one to engineer unconventional Bose-Einstein superfluids with the complex-valued order parameter. We consider two examples: the one-dimensional dissipative optical lattice, where each third site is dissipative, and the dissipative honeycomb optical lattice, where each dissipative lattice site neighbors three nondissipated sites. The tight-binding approximation is employed, which allows one to obtain analytical results. In the one-dimensional case the condensate is driven to a coherent Bloch-like state with nonzero quasimomentum, which breaks the translational periodicity of the dissipative lattice. In the two-dimensional case the condensate is driven to a zero-quasimomentum Bloch-like state, which is a coherent superposition of four-site discrete vortices of alternating vorticity with the vortex centers located at the dissipative sites.

Mean-field dynamics of strongly interacting bosons described by hard-core bosons with nearest-neighbor attraction has been shown to support two species of solitons: one of Gross-Pitaevskii type (GP type) where the condensate fraction remains dark, and a non-Gross-Pitaevskii type (non-GP type) characterized by brightening of the condensate fraction. Here we study the effects of quantum fluctuations on these solitons using the adaptive time-dependent density matrix renormalization group method, which takes into account the effect of strong correlations. We use local observables as the density, condensate density, and correlation functions as well as the entanglement entropy to characterize the stability of the initial states. We find both species of solitons to be stable under quantum evolution for a finite duration, their tolerance to quantum fluctuations being enhanced as the width of the soliton increases. We describe possible experimental realizations in atomic Bose-Einstein condensates, polarized degenerate Fermi gases, and in systems of polar molecules on optical lattices.

This paper investigates bright quantum-matter-wave solitons beyond the Gross-Pitaevskii equation (GPE). As proposals for interferometry and creating nonlocal quantum superpositions have been formed, it has become necessary to investigate effects not present in mean-field models. We investigate the effect of harmonic confinement on the internal degrees of freedom, as the ratio of zero-point harmonic oscillator length to classical soliton length, for different numbers of atoms. We derive a first-order energy correction for the addition of a harmonic potential to the many-body wave function and use this to create a variational technique based on energy minimization of this wave function for an arbitrary number of atoms, and include numerics based on diagonalization of the Hamiltonian in a basis of harmonic oscillator Fock states. Finally we compare agreement between a Hartree product ground state and the Bethe ansatz solution with a Gaussian envelope localizing the center of mass and show a region of good agreement.

We investigate the coherent transport of a single particle and a Bose-Einstein condensate between the two extreme traps of a triple-well potential by means of the spatial adiabatic passage technique. This matter wave transport technique consists of adiabatically following an energy eigenstate of the system that only populates the vibrational ground states of the two extreme wells and presents at all times a node in the central region. Unraveling the (nonlinear) time-dependent Schrödinger equation in terms of Bohmian quantum trajectories, we show that by slowing down the total time duration of the transport process, Bohmian velocities in the central region are orders of magnitude larger than the mean atomic velocities. This leads to a very counterintuitive effect: in the regime of almost perfect adiabaticity, these velocities require relativistic corrections to properly address the transfer process and avoid superluminal propagation.

We have investigated theoretically the interaction between individual quantum dot with broken inversion symmetry and an electromagnetic field of a single-mode quantum microcavity. It is shown that in the strong-coupling regime the system demonstrates nonlinear optical properties and can serve as emitter of the terahertz radiation at Rabi frequency of the system. Analytical results for the simplest physical situations are obtained and a numerical quantum approach for calculating an emission spectrum is developed.

We have excited Li atoms to Rydberg states with a picosecond laser in the presence of a phase-locked microwave field. We have observed energy transfer to higher- and lower-lying Rydberg states depending on the phase of the microwave field at which the picosecond laser excitation occurs. These observations confirm the prediction of a classical picture of the energy transfer and demonstrate that the phase-dependent energy transfer is not limited to processes in which energy transfer occurs across the ionization limit.

A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing for error syndrome recovery with only 2-local measurements in a two-dimensional array of qubits. We study the error threshold for topological subsystem color codes under very general external noise conditions. By transforming the problem into a classical disordered spin model, we estimate using Monte Carlo simulations that topological subsystem codes have an optimal error tolerance of $5.5\left(2\right)\%$. This means there is ample space for improvement in existing error-correcting algorithms that typically find a threshold of approximately $2\%$.

We consider a strongly repulsive fermionic gas in a two-dimensional optical lattice confined by a harmonic trapping potential. To address the strongly repulsive regime, we consider the $t-J$ Hamiltonian. The presence of the harmonic trapping potential enables the stabilization of coexisting and competing phases. In particular, at low temperatures, this allows the realization of a $d$-wave superfluid region surrounded by purely (gapless) normal edges. Solving the Bogoliubov–de Gennes equations and comparing them with the local density approximation, we show that the proximity to the Mott insulator is revealed by a downturn of the Fermi liquid order parameter at the center of the trap where the $d$-wave gap has a maximum. The density profile evolves linearly with distance.

We demonstrate that a simple two-color ionization measurement can be used to extract the time of birth of attosecond extreme ultraviolet pulses. A high-order-harmonic attosecond pulse train generated in xenon gas is used to excite a laser-dressed helium atom, which we model using the Floquet formalism. The interference between ionization paths from different Fourier components of the Floquet states results in the oscillation of ion yield with time delay. Using two IR pulses to create a reference intensity modulation, we obtain the phase of ion-yield oscillations, which provides the absolute timing of attosecond bursts with respect to the driving IR field.

We have calculated electric dipole polarizabilities of the $3s^2{}^1{S}_0,3s3p{}^3{P}_0$, and $3s3p{}^1{P}_1$ states of the ${\mathrm{Si}}^{2+}$ ion using the recently developed configuration interaction $+$ all-order method. A detailed evaluation of the uncertainties of the final results is carried out. Our value for the ground-state electric dipole polarizability 11.670(13) a.u. is in excellent agreement with the resonant excitation Stark ionization spectroscopy value 11.669(9) a.u. [Komara et al., J. Phys. B 38, 87 (2005); Mitroy, Phys. Rev. A 78, 052515 (2008)]. This paper represents a benchmark test of theory and experiment in divalent atoms. The near cancellation of the $n{s}^2{}^1{S}_0$ ground state and the lowest $nsnp{}^3{P}_0$ polarizabilities previously observed in ${{\mathrm{B}}^{+},{\mathrm{Al}}^{+},{\mathrm{In}}^{+},\mathrm{Tl}}^{+}$, and ${\mathrm{Pb}}^{2+}$ is also found in the ${\mathrm{Si}}^{2+}$ ion.

The state dependence of associative ionization of the $ns$ and $nd$ Rydberg series of Ne atoms with $5<n<18$ at thermal collision energies is investigated experimentally using a combination of synchrotron radiation and mass spectrometry in a single-beam experiment. The $n$ dependence of the collisional and associative ionization of the Ne Rydberg atoms have been calculated using the dipole resonant mechanism, in particular the associative ionization rates for $5<n_{\mathrm{eff}}<20$ have been calculated for cell, single beam, and crossed beam conditions. Refinements of the theory implemented previously have been necessary in order to apply the theory to the collisions of rare gas atoms. The results of the theoretical model for the $n$ dependency of the associative ionization rates of the Ne Rydberg atoms are compared to the experimental data.

We consider a harmonically trapped dilute $N$-boson system described by a low-energy Hamiltonian with pairwise interactions. We determine the condensate fraction, defined in terms of the largest occupation number, of the weakly interacting $N$-boson system ($N⩾2$) by employing a perturbative treatment within the framework of second quantization. The one-body density matrix and the corresponding occupation numbers are compared with those obtained by solving the two-body problem with zero-range interactions exactly. Our expressions are also compared with high precision ab initio calculations for Bose gases with $N=2–4$ that interact through finite-range two-body model potentials. Nonuniversal corrections are identified to enter at subleading order, confirming that different low-energy Hamiltonians, constructed to yield the same energy, may yield different occupation numbers. Lastly, we consider the strongly interacting three-boson system under spherically symmetric harmonic confinement and determine its occupation numbers as a function of the three-body “Efimov parameter.”

We study the dynamics of an atomic Bose-Einstein condensate in an optical lattice in which the electronic ground state of each atom is weakly coupled to a highly excited Rydberg state by a far off-resonant laser. This dressing induces a switchable effective soft-core interaction between ground-state atoms which, in the lattice, gives rise to on-site as well as long-range interaction terms. Upon switching on the dressing laser the coherence properties of the atomic superfluid undergo a nontrivial collapse and revival dynamics which can be observed in the interference pattern that is created after a release of the atoms from the optical lattice. This interference signal strongly depends on the strength and the duration of the dressing laser pulse and can be used to probe and characterize the effective interaction between Rydberg-dressed atoms.

The efficient wavelength conversion of images has many potential applications in optical communication, sensing, imaging, and quantum information fields. In this work, we report on a demonstration of an image transfer between light of wavelength 780 nm and light of wavelength 1530 nm by performing two sequential four-wave-mixing processes in two different hot atomic rubidium vapor cells. Furthermore, we confirm experimentally the persistence of coherence of the input light during this sequential process. Our results may be useful to the research fields mentioned above.

We provide a theoretical explanation of the results on the intensity distributions and correlation functions obtained from a random-beam speckle field in nonlinear bulk waveguides reported in the recent publication by Bromberg et al. [Nat. Photonics 4, 721 (2010)]. We study both the focusing and defocusing cases and in the limit of small speckle size (short-correlated disordered beam) provide analytical asymptotes for the intensity probability distributions at the output facet. Additionally we provide a simple relation between the speckle sizes at the input and output of a focusing nonlinear waveguide. The results are of practical significance for nonlinear Hanbury Brown and Twiss interferometry in both optical waveguides and Bose-Einstein condensates.

We use the analytical solution of the quantum Rabi model to obtain absolutely convergent series expressions of the exact eigenstates and their scalar products with Fock states. This enables us to calculate the numerically exact time evolution of $\langle {\sigma }_x\left(t\right)\rangle$ and $\langle {\sigma }_z\left(t\right)\rangle$ for all regimes of the coupling strength, without truncation of the Hilbert space. We find a qualitatively different behavior of both observables which can be related to their representations in the invariant parity subspaces.