Intersite interactions play a crucial role in polar gases in optical lattices even in the absence of hopping. We show that due to these long-range interactions a destabilized stack of quasi-one-dimensional Bose-Einstein condensates develops a correlated modulational instability in the nonoverlapping sites. Interestingly, this density pattern may evolve spontaneously into soliton filaments or into a checkerboard soliton crystal, offering a unique possibility to observe such two-dimensional arrangements in ultracold gases. These self-assembled structures may be observed under realistic conditions within current experimental feasibilities.

We consider the process by which a constant or wide-pulse solution of the nonlinear Schrödinger equation can become converted into an ensemble of solitons by modulational instability. This process is generally believed to be one important step in the generation of supercontinuum in optical fibers. Starting from the Akhmediev breather solution we study the conversion by two methods: One is pulse shape-oriented and uses the soliton relation between width and peak power. The other is eigenvalue-oriented and uses results from scattering theory. It becomes clear that an evolution according to the unmodified nonlinear Schrödinger equation, even in the presence of noise, will not lead to the transformation into solitons. If one takes the Raman effect into account, however, a conversion to a soliton gas takes place.

We investigate experimentally the number statistics of a mesoscopic ensemble of cold atoms in a microscopic dipole trap loaded from a magneto-optical trap and find that the atom-number fluctuations are reduced with respect to a Poisson distribution due to light-assisted two-body collisions. For numbers of atoms $N\gtrsim 2$, we measure a reduction factor (Fano factor) of $0.72\pm 0.07$, which differs from 1 by more than four standard deviations. We analyze this fact by a general stochastic model describing the competition between the loading of the trap from a reservoir of cold atoms and multiatom losses, leading to a master equation. Applied to our experimental regime, this model indicates an asymptotic value of $3/4$ for the Fano factor at large $N$ and in the steady state. We thus show that we have reached the ultimate level of reduction in number fluctuations in our system.

For a system of $N$ identical particles in a random pure state, there is a threshold $k_0=k_0\left(N\right)\sim N/5$ such that two subsystems of $k$ particles each typically share entanglement if $k>k_0$, and typically do not share entanglement if $k<k_0$. By “random” we mean here uniformly distributed on the sphere of the corresponding Hilbert space. The analogous phase transition for the positive partial transpose ($\text{PPT}$) property can be described even more precisely. For example, for $N$ qubits the two subsystems of size $k$ are typically in a $\text{PPT}$ state if $k<k_1:=N/4-1/2$ and typically in a non-$\text{PPT}$ state if $k>k_1$. Since, for a given state of the entire system, the induced state of a subsystem is given by the partial trace, the above facts can be rephrased as properties of random induced states. An important step in the analysis depends on identifying the asymptotic spectral density of the partial transposes of such random induced states, a result which is interesting in its own right.

In a numerical study, we observe Anderson localization of surface modes at the interface between a linear and a nonlinear dielectric medium, containing an optically induced disordered photonic lattice. We discover the threshold for the existence of such localized modes. The influence of Kerr nonlinearity and disorder levels on the transverse localization of light at such an interface is discussed. We demonstrate the suppression of localization for lower disorder levels, as compared to both completely linear and completely nonlinear medium. We also reveal Anderson localization at the linear-nonlinear interface in the presence of a phase-slip defect, and demonstrate the suppression of localization in that case as well.

Global phase factors of topological origin, resulting from cyclic local $\mathit{SU}$ evolution, called topological phases, were first described in [Phys. Rev. Lett. 90, 230403 (2003)], in the case of entangled qubit pairs. In this paper we investigate topological phases in multiqubit systems as the result of cyclic local $\mathit{SU}\left(2\right)$ evolution. These phases originate from the topological structure of the local $\mathit{SU}\left(2\right)$ orbits and are an attribute of most entangled multiqubit systems. We discuss the relation between topological phases and stochastic local operations and classical communication (SLOCC)-invariant polynomials and give examples where topological phases appear. A general method to find the values of the topological phases in an $n$-qubit system is described and a complete list of these phases for up to seven qubits is given.

For any Bell locality scenario (or Kochen-Specker noncontextuality scenario), the joint Shannon entropies of local (or noncontextual) models define a convex cone for which the nontrivial facets are tight entropic Bell (or contextuality) inequalities. In this paper we explore this entropic approach and derive tight entropic inequalities for various scenarios. One advantage of entropic inequalities is that they easily adapt to situations such as bilocality scenarios, which have additional independence requirements that are nonlinear on the level of probabilities, but linear on the level of entropies. Another advantage is that, despite the nonlinearity, taking detection inefficiencies into account turns out to be very simple. When joint measurements are conducted by a single detector only, the detector efficiency for witnessing quantum contextuality can be arbitrarily low.

We study the structure of the revivals in an integrable quantum many-body system, the transverse field $XY$ spin chain, after a quantum quench. The time evolutions of the Loschmidt echo, the magnetization, and the single-spin entanglement entropy are calculated. We find that the revival times for all of these observables are given by integer multiples of $T_{\mathrm{rev}}\simeq L/v_{\max }$, where $L$ is the linear size of the system and $v_{\max }$ is the maximal group velocity of quasiparticles. This revival structure is universal in the sense that it does not depend on the initial state and the size of the quench. Applying nonintegrable perturbations to the $XY$ model, we observe that the revivals are robust against such perturbations: they are still visible at time scales much larger than the quasiparticle lifetime. We therefore propose a generic connection between the revival structure and the locality of the dynamics, where the quasiparticle speed $v_{\max }$ generalizes into the Lieb-Robinson speed $v_{\text{LR}}$.

As a physical principle, information causality has thus far only been studied by using bipartite protocols. In this paper, we consider information causality in multireceiver random access codes, in which no receiver can gain any information only from classical communication. To precisely distinguish physical correlations from nonphysical ones, information causality in the multipartite scenario can be stated as follows: The information gain of total receivers cannot be greater than the amount of classical communication. Operationally, the distributive multiparty physical nonlocal resource can be exploited only for information splitting, rather than for accessing more information. Multipartite information causality is demonstrated to yield entanglement monogamy.

Given an ensemble of systems in an unknown state, as well as an observable $\widehat{A}$ and a physical apparatus which performs a measurement of $\widehat{A}$ on the ensemble, whose detailed working is unknown (“black box”), we study how one can test whether the Lüders or von Neumann reduction rule applies.

We propose an alternative architecture for the measurement-based quantum computation model. This design relies on small composite light-atom primary clusters. These are then assembled into cluster arrays using ancillary light modes and the actual computation is run on such a cellular cluster. We show how to create the primary clusters, which are Gaussian cluster states composed of both light and atomic modes. These are entangled via QND interactions and beam splitters and the scheme is well described within the continuous-variable covariance matrix formalism.

We study an optimized measurement which discriminates $N$ mixed quantum states occurring with given prior probabilities. The measurement yields the maximum achievable confidence for each of the $N$ conclusive outcomes, thereby keeping the overall probability of inconclusive outcomes as small as possible. It corresponds to optimum unambiguous discrimination when for each outcome the confidence is equal to unity. Necessary and sufficient optimality conditions are derived and general properties of the optimum measurement are obtained. The results are applied to the optimized maximum-confidence discrimination of $N$ equiprobable symmetric mixed states. Analytical solutions are presented for a number of examples, including the discrimination of $N$ symmetric pure states spanning a $d$-dimensional Hilbert space ($d⩽N$) and the discrimination of $N$ symmetric mixed qubit states.

The relativistic recoil contributions to the Uehling corrections are revisited. A controversy in recent calculations is considered, which is based on different approaches including Breit-type and Grotch-type calculations. It is found that calculations in those works were in fact done in different gauges and in some of those gauges contributions to retardation and two-photon-exchange effects were missed. Such effects are evaluated and a consistent result is obtained. A correct expression for the Grotch-type approach is presented, which produces a correct gauge-invariant result. A finite-nuclear-size correction for the Uehling term is also considered. The results are presented for muonic hydrogen and deuterium atoms and for muonic ${}^3$He and ${}^4$He ions.

The Casimir interaction between one-dimensional metallic objects (cylinders, wires) displays unconventional features. Here we study the orientation dependence of this interaction by computing the Casimir energy between two inclined cylinders over a wide range of separations. We consider Dirichlet, Neumann, and perfect-metal boundary conditions, both at zero temperature and in the classical high-temperature limit. For all types of boundary conditions, we find that at large distances the interaction decays slowly with distance, similarly to the case of parallel cylinders, and at small distances scales as the interaction of two spheres (but with different numerical coefficients). Our numerical results at intermediate distances agree with our analytical predictions at small and large separations. Experimental implications are discussed.

It is shown that the density-functional-theory exchange and correlation functionals satisfy $0=\gamma E_{hx}\left[{\rho }_N\right]+2E_c^{\gamma }\left[{\rho }_N\right]-\gamma E_{hx}\left[{\rho }_{N-1}^{\gamma }\right]-2E_c^{\gamma }\left[{\rho }_{N-1}^{\gamma }\right]+2\int d^3{r}^{\prime }[{\rho }_{N-1}^0\left(\mathbf{r}\right)-{\rho }_{N-1}^{\gamma }\left(\mathbf{r}\right)]v^0(\left[{\rho }_N\right];\mathbf{r})+\int d^3{r}^{\prime }[{\rho }_{N-1}^0\left(\mathbf{r}\right)-{\rho }_{N-1}^{\gamma }\left(\mathbf{r}\right)]\mathbf{r}·\nabla v^0(\left[{\rho }_N\right];\mathbf{r})+\int d^3{r}^{\prime }{\rho }_N\left(\mathbf{r}\right)\mathbf{r}·\nabla v_c^{\gamma }(\left[{\rho }_N\right];\mathbf{r})-\int d^3{r}^{\prime }{\rho }_{N-1}^{\gamma }\left(\mathbf{r}\right)\mathbf{r}·\nabla v_c^{\gamma }(\left[{\rho }_{N-1}^{\gamma }\right];\mathbf{r})-\int d^3{r}^{\prime }{f}^{\gamma }\left(\mathbf{r}\right)\mathbf{r}·\nabla v_{hxc}^{\gamma }(\left[{\rho }_N\right];\mathbf{r})-2\int d^3{r}^{\prime }{f}^{\gamma }\left(\mathbf{r}\right)v_{hxc}^{\gamma }(\left[{\rho }_N\right];\mathbf{r})$. In the derivation of this equation the adiabatic connection formulation is used, where the ground-state density of an $N$-electron system ${\rho }_N$ is kept constant independent of the electron-electron coupling strength $\gamma$. Here $E_{hx}\left[\rho \right]$ is the Hartree plus exchange energy, $E_c^{\gamma }\left[\rho \right]$ is the correlation energy, $v_{hxc}^{\gamma }\left[\rho \right]$ is the Hartree plus exchange-correlation potential, $v_c\left[\rho \right]$ is the correlation potential, and $v^0\left[\rho \right]$is the Kohn-Sham potential. The charge densities ${\rho }_N$ and ${\rho }_{N-1}^{\gamma }$ are the $N$- and $(N-1)$-electron ground-state densities of the same Hamiltonian at electron-electron coupling strength $\gamma$. $f^{\gamma }\left(\mathbf{r}\right)={\rho }_N\left(\mathbf{r}\right)-{\rho }_{N-1}^{\gamma }\left(\mathbf{r}\right)$ is the Fukui function. This equation can be useful in testing the internal self-consistency of approximations to the exchange and correlation functionals. As an example the identity is tested on the analytical Hooke's atom charge density for some frequently used approximate functionals.

We study the influence of ultracold collisions induced by the inhomogeneous excitation on the clock-transition frequency in one- and two-dimensional shallow blue-detuned (BD) ${}^{87}$Sr optical lattice clocks with a magic wavelength of ${\lambda }_b=389.889$ nm. The minimal lattice potential required to tightly confine atoms in each single lattice site is much larger than that required for a red-detuned (RD) lattice operating at ${\lambda }_r=813.4$ nm because of the relatively smaller magic wavelength. For a deep optical lattice, the two-body interactions of atoms in a single lattice site mainly contribute to the clock-transition frequency shift, while the intersite collisions primarily affect the collisional shift in a shallow optical lattice. For an effective misalignment angle $\Delta \theta \sim 10$ mrad of the probe beam with respect to the lattice axis, the fractional collisional shifts in both one- and two-dimensional BD lattices are at the ${10}^{-16}$ level.

Coherent population trapping (CPT) is theoretically examined as a magnetic-field diagnostic for high-β hydrogen plasma. Time-dependent quantum mechanical Bloch equations, which describe the evolution of the 2$s$ and 3$p$ level populations of the hydrogen atom under CPT conditions, were solved numerically. When the frequency difference of two copropagating lasers equals the energy difference between the atoms’ levels subject to the local magnetic field, a discernable CPT dark line in the Hα emission is predicted, enabling the possibility of noninvasive, localized magnetic-field measurements. The effects of fine and hyperfine level structure, Doppler broadening, plasma-generated electric fields, and degree-of-hydrogen ionization are included in the model. A shift in dark-line position of 15$\%$ of the linewidth is predicted to be caused by contributions from the entire Hα manifold. The laser-induced Hα fluorescence is estimated to be an order of magnitude stronger than the background Hα emission.

We have applied parametric equations of motion (PEM) to study photodissociation dynamics of H${}_2{}^{+}$. This is an application of PEM having frequency as the parameter to a non-Hermitian Hamiltonian. The resonances are extracted using the smooth exterior scaling method. Here we have studied how different resonance states behave with respect to the change in frequency of the laser field. The advantage of this method is that one can easily trace different resonance states that are changing as the parameter changes. It is observed that some higher lying vibrational states remain bound states in continuum with the decrease in frequency.

The Rydberg blockade mechanism has shown noteworthy promise for scalable quantum computation with neutral atoms. Both qubit states and gate-mediating Rydberg state belong to the same optically trapped atom. The trapping fields, while being essential, induce detrimental decoherence. Here we theoretically demonstrate that this Stark-induced decoherence may be completely removed using powerful concepts of magic optical traps. We analyze magic trapping of a prototype three-level system: a Rydberg state along with two qubit states: hyperfine states attached to a $J=1/2$ ground state. Our numerical results show that, while such a magic trap for alkali metals would require prohibitively large magnetic fields, the group IIIB metals such as Al are suitable candidates.

We examine a two-component Bose-Einstein condensate in a double-well potential. We propose a model for the creation of many-particle macroscopic quantum superposition states. The effect of dissipation on the formation of these states is also investigated with the Monte Carlo wave-function technique.