In this work, we excite $n{D}_{5/2}$ Rydberg states in a dense and cold Rb atomic sample held in a 10.6 $\mu \mathrm{m}$ quasi-electrostatic trap using narrow-bandwidth laser pulses. Our goal is to study the Förster resonance process $n{D}_{5/2}+n{D}_{5/2}\to (n-2)F+(n+2)P_{3/2}$ at zero electric field as a function of the total atomic density using pulsed-field ionization in the range $n=37–47$. Such a process is almost degenerate for $n=43$. Younge and coworkers studied this process [K. C. Younge, A. Reinhard, T. Pohl, P. R. Berman, and G. Raithel, Phys. Rev. A 79, 043420 (2009)] and attributed the observed saturation to many-body effects. Our results show that as the ground-state atomic density increases, the $n{D}_{5/2}$ state population and the population transfer starts to saturate, which is consistent with the onset of Rydberg atom blockade and previously published results. However, since our experiment allows the independent measurement of the $n{D}_{5/2}$ and $(n+2)P_{3/2}$ state populations, we were able to obtain the $(n+2)P_{3/2}$ state population density dependence. Our results clearly show that the $(n+2)P_{3/2}$ state population depends quadratically on the total Rydberg atomic population, and consequently, the Förster resonance is a two-body process for a ground-state atomic density below $3\times {10}^{11}$ ${\mathrm{cm}}^{-3}$.

The Rashba spin-orbit coupling is equivalent to the finite Yang-Mills flux of a static SU(2) gauge field. It gives rise to the protected edge states in two-dimensional topological band insulators, much like magnetic field yields the integer quantum Hall effect. An outstanding question is which collective topological behaviors of interacting particles are made possible by the Rashba spin-orbit coupling. Here we address one aspect of this question by exploring the Rashba SU(2) analogs of vortices in superconductors. Using the Landau-Ginzburg approach and conservation laws, we classify the prominent two-dimensional condensates of two- and three-component spin-orbit-coupled bosons, and characterize their vortex excitations. There are two prominent types of condensates that take advantage of the Rashba spin-orbit coupling. Their vortices exist in multiple flavors whose number is determined by the spin representation, and interact among themselves through logarithmic or linear potentials as a function of distance. The vortices that interact linearly exhibit confinement and asymptotic freedom similar to quarks in quantum chromodynamics. One of the two condensate types supports small metastable neutral quadruplets of vortices, and their tiles as metastable vortex lattices. Quantum melting of such vortex lattices could give rise to non-Abelian fractional topological insulators, SU(2) analogs of fractional quantum Hall states. The physical systems in which these states could exist are trapped two- and three-component bosonic ultracold atoms subjected to artificial gauge fields, as well as solid-state quantum wells made either from Kondo insulators such as ${\mathrm{SmB}}_6$ or conventional topological insulators interfaced with conventional superconductors.

We compare the Landauer, Kubo, and microcanonical [J. Phys.: Condens. Matter 16, 8025 (2005)] approaches to quantum transport for the average current, the entanglement entropy, and the semiclassical full-counting statistics (FCS). Our focus is on the applicability of these approaches to isolated quantum systems such as ultracold atoms in engineered optical potentials. For two lattices connected by a junction, we find that the current and particle number fluctuations from the microcanonical approach compare well with the values predicted by the Landauer formalism and FCS assuming a binomial distribution. However, we demonstrate that well-defined reservoirs (i.e., particles in Fermi-Dirac distributions) are not present for a substantial duration of the quasi-steady state. Thus, on the one hand, the Landauer assumption of reservoirs and/or inelastic effects is not necessary for establishing a quasi-steady state. Maintaining such a state indefinitely requires an infinite system, and in this limit well-defined Fermi-Dirac distributions can occur. On the other hand, as we show, the existence of a finite speed of particle propagation preserves the quasi-steady state irrespective of the existence of well-defined reservoirs. This indicates that global observables in finite systems may be substantially different from those predicted by an uncritical application of the Landauer formalism, with its underlying thermodynamic limit. Therefore, the microcanonical formalism which is designed for closed, finite-size quantum systems seems more suitable for studying particle dynamics in ultracold atoms. Our results highlight both the connection and differences with more traditional approaches to calculating transport properties in condensed matter systems, and will help guide the way to their simulations in cold-atom systems.

Three quasi-Bragg conditions (QBCs) in one-dimensional double-period quasicrystals based on high reflectance from interference are proposed. Analytical formulas for these QBCs are derived using band-edge equations. All of these QBCs have conditions that are different from that of the traditional Bragg condition. The QBC at quarter-wave thickness in double-period quasicrystals is also discontinuous in different regions of the gap map. In contrast, the traditional Bragg condition for periodic cases, which lies at quarter-wave thickness, is continuous in different regions of the gap map. It is found that there are three thickness conditions with the maximum reflectance occurring in the midpoints of the QBCs in double-periodic quasicrystals, which is analogous to the quarter-wave thickness in traditional periodic crystals. These QBCs in double-period cases are different not only from the traditional Bragg condition in periodic cases, but also from those in Fibonacci and Thue-Morse quasicrystals.

We theoretically study high-harmonic generation (HHG) in a composite which consists of ellipsoidal silver nanoparticles in argon. The significant field enhancement in argon in the vicinity of metal nanoparticles allows us to use much lower incident intensities than in typical HHG experiments. A periodic modulation of the nanoparticle concentration provides quasi–phase matching, which mitigates the negative effect of the significant phase mismatch. First, we study the linear optical properties of such a composite and the field enhancement and consider the technological possibilities of creating such a composite. Then the generation of high harmonics is simulated using a propagation equation which includes field enhancement, phase mismatch, absorption of the pump beam and harmonics, and other relevant effects. Generation of harmonics with an efficiency above ${10}^{-7}$ is predicted.

The scalar complex source vortex model is an accurate description of highly focused scalar vortices. We use it to construct a variety of vectorial solutions of Maxwell's equations describing highly focused and variously polarized vector vortex beams accurately. Three different families of optical vector vortex beams are presented and studied in detail. In this model, optical vortices derived within Cartesian symmetry correspond to circularly and linearly polarized highly focused vortex beams in the focus of a high numerical aperture focusing system. In addition, we report on vortical complex-source beams derived within cylindrical and spherical symmetries which exhibit very special and intriguing properties.

We give a complete solution of the problem of constructing a scattering potential $v\left(x\right)$ that possesses scattering properties of one's choice at an arbitrary prescribed wave number. Our solution involves expressing $v\left(x\right)$ as the sum of at most six unidirectionally invisible finite-range potentials for which we give explicit formulas. Our results can be employed for designing optical potentials. We discuss its application in modeling threshold lasers, coherent perfect absorbers, and bidirectionally and unidirectionally reflectionless absorbers, amplifiers, and phase shifters.

Critical excitation in random lasers under picosecond and nanosecond pumping was experimentally studied. The resulting emission intensity statistics were analyzed using fits to $\alpha$-stable distributions. We find that the transition value of $\alpha$, the tail exponent of the stable distribution, is a clear indicator of the threshold of random lasing. We discuss this exponent as an identifier of the threshold. This definition is compared with the conventional definitions for the threshold, namely, the probability of random lasing in the case of coherent random lasers and the intensity enhancement and bandwidth collapse for diffusive random lasing emission. We find a universal applicability of the $\alpha$ exponent as an identifier of the threshold, and hence the criticality, in random lasers.

We study the dynamics of dissipative spin lattices with power-law interactions, realized via few-level atoms driven by coherent laser-coupling and decoherence processes. Using Monte Carlo simulations, we determine the phase diagram in the steady state and analyze its generation dynamics. As opposed to mean-field predictions and nearest-neighbor models, there is no transition to long-range-ordered phases for realistic interactions and resonant driving. However, for finite laser detunings, we demonstrate the emergence of crystalline order. Although the static and dynamical critical exponents of the revealed dissipative phase transition fall into the two-dimensional Ising universality class, the found steady states differ considerably from those of an equilibrium Ising magnet. Two complementary schemes for an experimental implementation with cold Rydberg atoms are discussed.

We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.

The Lipkin-Meshkov-Glick (LMG) model describes critical systems with interaction beyond the first-neighbor approximation. Here we address quantum metrology in LMG systems and show how criticality may be exploited to improve precision. At first we focus on the characterization of LMG systems themselves, i.e., the estimation of anisotropy, and address the problem by considering the quantum Cramér-Rao bound. We evaluate the quantum Fisher information of small-size LMG chains made of $N=2,$ 3, and 4 lattice sites and also analyze the same quantity in the thermodynamical limit. Our results show that criticality is indeed a resource and that the ultimate bounds to precision may be achieved by tuning the external field and measuring the total magnetization of the system. We then address the use of LMG systems as quantum thermometers and show that (i) precision is governed by the gap between the lowest energy levels of the systems and (ii) field-dependent level crossing is a metrological resource to extend the operating range of the quantum thermometer.

Starting from the coupling of a relativistic quantum particle to the curved Schwarzschild space time, we show that the Dirac-Schwarzschild problem has bound states and calculate their energies including relativistic corrections. Relativistic effects are shown to be suppressed by the gravitational fine-structure constant ${\alpha }_G=G{m}_1{m}_2/\left(\hslash c\right)$, where $G$ is Newton's gravitational constant, $c$ is the speed of light, and $m_1$ and $m_2\gg m_1$ are the masses of the two particles. The kinetic corrections due to space-time curvature are shown to lift the familiar $(n,j)$ degeneracy of the energy levels of the hydrogen atom. We supplement the discussion by a consideration of an attractive scalar potential, which, in the fully relativistic Dirac formalism, modifies the mass of the particle according to the replacement $m\to m(1-\lambda /r)$, where $r$ is the radial coordinate. We conclude with a few comments regarding the $(n,j)$ degeneracy of the energy levels, where $n$ is the principal quantum number, and $j$ is the total angular momentum, and illustrate the calculations by way of a numerical example.

We present a unified approach to different recent entanglement criteria. Although they were developed in different ways, we show that they are all applications of a more general principle given by the Cauchy-Schwarz inequality. We explain this general principle and show how to use it to derive not only already known entanglement criteria, but also criteria which were unknown so far. We systematically investigate its potential and limitations to detect bipartite and multipartite entanglement. Furthermore, we describe how to apply our generalized entanglement detection scheme to find the measurement directions to verify the entanglement of a given state experimentally.

A pure quantum state of $N$ subsystems with $d$ levels each is called $k$-multipartite maximally entangled state, which we call a $k$-uniform state, if all its reductions to $k$ qudits are maximally mixed. These states form a natural generalization of $N$-qudit Greenberger-Horne-Zeilinger states which belong to the class 1-uniform states. We establish a link between the combinatorial notion of orthogonal arrays and $k$-uniform states and prove the existence of several classes of such states for $N$-qudit systems. In particular, known Hadamard matrices allow us to explicitly construct 2-uniform states for an arbitrary number of $N>5$ qubits. We show that finding a different class of 2-uniform states would imply the Hadamard conjecture, so the full classification of 2-uniform states seems to be currently out of reach. Furthermore, we establish links between the existence of $k$-uniform states and classical and quantum error correction codes and provide a graph representation for such states.

We investigate optimal discrimination between two projective single-qubit measurements in a scenario where the measurement can be performed only once. We consider general setting involving a tunable fraction of inconclusive outcomes and we prove that the optimal discrimination strategy requires an entangled probe state for any nonzero rate of inconclusive outcomes. We experimentally implement this optimal discrimination strategy for projective measurements on polarization states of single photons. Our setup involves a real-time electrooptical feed-forward loop which allows us to fully harness the benefits of entanglement in discrimination of quantum measurements. The experimental data clearly demonstrate the advantage of entanglement-based discrimination strategy as compared to unentangled single-qubit probes.

A striking scheme called “counterfactual quantum cryptography” gives a conceptually new approach to accomplish the task of key distribution. It allows two legitimate parties to share a secret even though a particle carrying secret information is not, in fact, transmitted through the quantum channel. Since an eavesdropper cannot directly access the entire quantum system of each signal particle, the protocol seems to provide practical security advantages. However, here we propose an eavesdropping method which works on the scheme in a finite key scenario. We show that, for practical systems only generating a finite number of keys, the eavesdropping can obtain all of the secret information without being detected. We also present a improved protocol as a countermeasure against this attack.

We perform relativistic configuration-interaction calculations of the energy levels of the low-lying and core-excited states of berylliumlike iron, ${\mathrm{Fe}}^{22+}$. The results include the QED contributions calculated by two different methods, the model QED operator approach and the screening-potential approach. The uncertainties of theoretical energies are estimated systematically. The predicted wavelengths of the $K\alpha$ transitions in berylliumlike iron improve previous theoretical results and compare favorably with the experimental data.

Recently Zatsarinny and Bartschat [Phys. Rev. Lett. 107, 023203 (2011)] have given an ansatz for extracting ionization amplitudes from close-coupling calculations of electron-impact ionization of atoms. They applied it with extraordinary success to a fully differential cross section of electron-helium single ionization leaving the residual ion in an $n=2$ state. By considering electron-impact ionization of atomic hydrogen we explain the origin of the ansatz and show that it forms an effective interpolation scheme for determining the amplitudes, so long as the pseudostate energy distribution is sufficiently dense.

The velocity map of the above-threshold ionization electron spectrum at long laser wavelength exhibits a characteristic structure normal to the laser polarization, which has the appearance of a trident or a three-pronged fork. The forklike structure vanishes for few-cycle laser pulses. It is explained in terms of the classical-electron-trajectories model of strong-field ionization augmented so as to allow for rescattering. The analysis reveals its relation to the so-called low-energy structure, which was recently observed for very small transverse momenta.

In this paper we explore the rich structure of macroscopic many-particle quantum states for a Bose-Einstein condensate in an optical cavity with a tunable nonlinear atom-photon interaction [K. Baumann et al., Nature (London) 464, 1301 (2010)]. Population inversion, bistable normal phases, and the coexistence of normal-superradiant phases are revealed by adjusting the experimentally realizable interaction strength and pump-laser frequency. For the negative (effective) cavity frequency we observe, remarkably, an inverted quantum phase transition (QPT) from the superradiant to the normal phases with an increase in atom-field coupling, which is just opposite the QPT in the normal Dicke model. Bistable macroscopic states are derived analytically in terms of the spin-coherent-state variational method by taking into account both normal and inverted pseudospin states.