At the output of a high-finesse cavity a succession of Lissajous patterns may be observed as the cavity length is finely tuned inside a “degenerate region” around a reentrant spherical configuration. This behavior is ascribed to a small parasitic astigmatism of the cavity mirrors. Simple geometrical optics modeling confirms this hypothesis, and then a more realistic analysis using transverse Gaussian modes reveals that the Lissajous patterns correspond to an organization of the astigmatism-split modes into a finer substructure of degenerate modes relative to that of a reentrant spherical cavity. This provides a thorough understanding of the field patterns observed in the degenerate region, including an intriguing spatial symmetry of the patterns corresponding to opposite displacements with respect to a specific central cavity length. This investigation represents a generalization of the theory of reentrant spherical cavities to the astigmatic case.

We present an analysis of a nested Mach-Zehnder interferometer in which an ensemble of identical pre- and postselected particles leaves a weak trace. A knowledge of the weak value partially destroys the quantum interference. The results, contrary to some recent claims [Vaidman, Phys. Rev. A 87, 052104 (2013)], are in accordance with the usual quantum-mechanical expectations.

Misinterpretation in the preceding Comment of my recent analysis of the past of a photon is corrected. There is nothing in this analysis which is “contrary to the usual quantum expectations” but, nevertheless, it does provide “further understanding and interpretation of the system considered.” In particular, it indicates that the common sense argument used in the Comment should be abandoned.

Generalized Schmidt decomposition of pure three-qubit states has four positive and one complex coefficients. In contrast to the bipartite case, they are not arbitrary and the largest Schmidt coefficient restricts severely other coefficients. We derive a nonstrict inequality between three-qubit Schmidt coefficients, where the largest coefficient defines the least upper bound for the three nondiagonal coefficients or, equivalently, the three nondiagonal coefficients together define the greatest lower bound for the largest coefficient. In addition, we show the existence of another inequality which should establish an upper bound for the remaining Schmidt coefficient.

According to the recently proposed density-functional analog of quantum phase transitions (QPTs) the “density” determines the “control parameter” (corresponding to the density-functional theory “external potential”). It was also proved that in the nondegenerate case there is a one-to-one map between the ground-state wave function and the control parameter. It is now shown that there is a one-to-one map between the ground-state subspace and the control parameter. It is pointed out that there is a one-to one map between the subspace density and the control parameter. The Rényi entropies are proved to be strictly monotonic functions of the control parameter in the neighborhood of the transition point. These properties are illustrated with the Dicke model which exhibits a QPT from a normal phase (nondegenerate) to the superradiant case (degenerate) in the thermodynamic limit.

A technique based on summation of dominating classes of correlation diagrams to all orders in Coulomb interaction is used to calculate the energies of the lowest $s,p$, and $d$ states of Ba ii, Ra ii, Fr i, E119 i, and E120 ii. Breit and quantum electrodynamic corrections are also included. Comparison with experiment for Ba ii, Ra ii, and Fr i demonstrates that the accuracy of the calculations is on the level of 0.1%. The technique has been applied to predict the spectra of superheavy elements E119 and E120${}^{+}$. The role of the ladder diagrams [Dzuba, Phys. Rev. A 78, 042502 (2008)], which is the most recent addition to the method, has been emphasized. Their inclusion significantly improves the accuracy of the calculations and expands the applicability of the method.

Electron emission spectra and total electron yields were measured for relatively large (about 5000 atoms) neon clusters that were irradiated by extreme ultraviolet pulses with 20.3 eV, corresponding to the $2p\to 3d$ transition. The present electron emission spectra are remarkably different from those for Ar clusters undergoing sequential ionization [Bostedt et al., Phys. Rev. Lett. 100, 133401 (2008)] and can be interpreted as a superposition of a low-energy exponential tail, dominant at a low free-electron-laser intensity $I$, and an intermediate-energy Gaussian-like peak which grows with $I$. Correspondingly, the total electron yield exhibits interesting $I$ dependence. Especially, a plateau appears in the intermediate $I$ range. These results suggest a crossover in the ionization mechanism from thermal electron to two-photon photoelectron emission. An exciton-Mott transition is proposed for the formation of nanoplasma.

We present a theoretical study of transient absorption spectra of laser-dressed hydrogen atoms, based on numerical solutions of the time-dependent Schrödinger equation. The timing of absorption is controlled by the delay between an extreme ultra violet (XUV) pulse and an infrared (IR) laser field. The XUV pulse is isolated and several hundred attoseconds in duration, which acts as a pump to drive the ground-state electron to excited $p$ states. The subsequent interaction with the IR field produces dressed states, which manifest as sidebands between the 1s-$np$ absorption spectra separated by one IR-photon energy. We demonstrate that the population of dressed states is maximized when the timing of the XUV pulse coincides with the zero crossing of the IR field, and that their energies can be manipulated in a subcycle time scale by adding a chirp to the IR field. An alternative perspective to the problem is to think of the XUV pulse as a probe to detect the dynamical ac Stark shifts. Our results indicate that the accidental degeneracy of the hydrogen excited states is removed while they are dressed by the IR field, leading to large ac Stark shifts. Furthermore, we observe the Autler-Townes doublets for the $n=2$ and 3 levels using the 656 nm dressing field, but their separation does not agree with the prediction by the conventional three-level model that neglects the dynamical ac Stark shifts.

Coherent superpositions of the $49s_{1/2}$ and $48s_{1/2}$ Rydberg states of cold ${}^{87}$Rb atoms were studied near the surface of an atom chip. The superpositions were created and manipulated using microwaves resonant with the two-photon $49s_{1/2}-48s_{1/2}$ transition. Coherent behavior was observed using Rabi flopping, Ramsey sequences, spin echo, and spin locking. These results are discussed in the context of Rydberg atoms as electric field noise sensors. We consider the coherence of systems quadratically coupled to noise fields with $1/f^{\kappa }$ power spectral densities ($\kappa \approx 1$).

The production of very-high-$n$ ($n\sim 300$–500) strontium Rydberg atoms is explored using a crossed-laser-atom-beam geometry. $n$${}^1{S}_0$ and $n$${}^1{D}_2$ states are created by two-photon excitation via the $5s5p$ ${}^1{P}_1$ intermediate state using radiation with wavelengths of $\sim$461 and $\sim$413 nm. Rydberg atom densities as high as $\sim 3\times {10}^5$ cm${}^{-3}$ have been achieved, sufficient that Rydberg-Rydberg interactions can become important. The isotope shifts in the Rydberg series limits are determined by tuning the 461-nm light to preferentially excite the different strontium isotopes. Photoexcitation in the presence of an applied electric field is examined. The initially quadratic Stark shift of the $n$${}^1{P}_1$ and $n$${}^1{D}_2$ states becomes near-linear at higher fields and the possible use of $n{}^1{D}_2$ states to create strongly polarized, quasi-one-dimensional electronic states in strontium is discussed. The data are analyzed with the aid of a two-active-electron (TAE) approximation. The two-electron Hamiltonian, within which the Sr${}^{2+}$ core is represented by a semi-empirical potential, is numerically diagonalized allowing the calculation of the energies of high-$n$ Rydberg states and their photoexcitation probabilities.

The competition between resonant optical excitation of Rydberg states of atoms and their strong, long-range van der Waals interaction results in spatial ordering of Rydberg excitations in a two-dimensional lattice gas, as observed in a recent experiment of Schauß et al. [Nature (London) 491, 87 (2012)]. Here we use semiclassical Monte Carlo simulations to obtain stationary states for hundreds of atoms in finite-size lattices. We show the formation of regular spatial structures of Rydberg excitations in a system of increasing size, and find highly sub-Poissonian distribution of the number of Rydberg excitations characterized by a large negative value of the Mandel $Q$ parameter which is nearly independent of the system size.

We study two observables related to the anomalous breaking of scale invariance in a dilute two-dimensional Fermi gas, the frequency shift and damping rate of the monopole mode in a harmonic confinement potential. For this purpose we compute the speed of sound and the bulk viscosity of the two-dimensional gas in the high-temperature limit. We show that the anomaly in the speed of sound scales as $(2P-\rho c_s^2)/P\sim z/{\left[\ln (T/E_B)\right]}^2$ and that the bulk viscosity $\zeta$ scales as $\zeta /\eta \sim z^2/{\left[\ln (T/E_B)\right]}^6$. Here, $P$ is the pressure, $c_s^2$ is the speed of sound, $\eta$ is the shear viscosity, $z$ is the fugacity, and $E_B$ is the two-body binding energy. We show that our results are consistent with the experimental results of Vogt, Feld, Fröhlich, Pertot, Koschorreck, and Köhl [Phys. Rev. Lett. 108, 070404 (2012)]. Vogt et al. reported a frequency shift $\delta \omega /\omega$ of the order of a few percent and a damping rate smaller than the background rate $\Gamma /{\omega }_0\sim 5\%$.

We study generation and stabilization of vortex rings in atomic Bose-Einstein condensates. We suggest an approach for generating vortex rings by optical tweezers—two blue-detuned optical beams forming a toroidal void in a magnetically or optically confined condensate cloud. We demonstrate that matter-wave vortex rings trapped within the void are energetically and dynamically stable. Our theoretical findings suggest a possibility for the generation, stabilization, and nondestructive manipulation of quantized vortex rings in experimentally feasible trapping configurations.

Attraction of the quantum particle to the center in three-dimensional space with potential $-V_0{r}^{-2}$ gives rise to the quantum collapse, i.e., nonexistence of the ground state (GS) when the attraction strength exceeds a critical value [${\left(V_0^{\left(\mathrm{cr}\right)}\right)}_1=1/8$, in the present notation]. Recently, we have demonstrated that the quantum collapse is suppressed and the GS is restored if repulsive interactions between particles in the quantum gas are taken into account in the mean-field approximation. This setting can be realized in a gas of dipolar molecules attracted to the central charge, with dipole-dipole interactions taken into regard as well. Here we analyze this problem for a binary gas. GSs supported by the repulsive interactions are constructed in a numerical form, as well as by means of analytical approximations for both miscible and immiscible binary systems. In particular, the Thomas-Fermi approximation is relevant if $V_0$ is large enough. It is found that the GS of the miscible binary gas, both balanced and imbalanced, features a weak phase transition at another critical value, ${\left(V_0^{\left(\mathrm{cr}\right)}\right)}_2=1/2\equiv 4{\left(V_0^{\left(\mathrm{cr}\right)}\right)}_1$. The transition is characterized by an analyticity-breaking change in the structure of the wave functions at small $r$. To illustrate the generic character of the present phenomenology, we also consider the binary system with attraction between the species (rather than repulsion) in the case when the central potential pulls a single component only.

Vortex electrons—freely propagating electrons whose wave functions have helical wave fronts—could become a novel tool in the physics of electromagnetic radiation. They carry a nonzero intrinsic orbital angular momentum (OAM) $\ell$ with respect to the propagation axis and, for $\ell \gg 1$, a large OAM-induced magnetic moment $\mu \approx \ell {\mu }_B$ (${\mu }_B$ is the Bohr magneton), which influences the radiation of electromagnetic waves. Here, we consider in detail the OAM-induced effects caused by such electrons in two forms of polarization radiation, namely, in Cherenkov radiation and transition radiation. Thanks to the large $\ell$, we can neglect quantum or spin-induced effects, which are of the order of $\hslash \omega /E_e\ll 1$, but retain the magnetic moment contribution $\ell \hslash \omega /E_e\lesssim 1$, which makes the quasiclassical approach to polarization radiation applicable. We discuss the magnetic moment contribution to polarization radiation, which has never been experimentally observed, and study how its visibility depends on the kinematical parameters and the medium permittivity. In particular, it is shown that this contribution can, in principle, be detected in azimuthally nonsymmetrical problems, for example when vortex electrons obliquely cross a metallic screen (transition radiation) or move near it (diffraction radiation). We predict a left-right angular asymmetry of the transition radiation (in the plane where the charge radiation distributions would stay symmetric), which appears due to an effective interference between the charge radiation field and the magnetic moment contribution. Numerical values of this asymmetry for vortex electrons with $E_e=300$ keV and $\ell =100–1000$ are $0.1\%–1\%$, and we argue that this effect could be detected with existing technology. The finite conductivity of the target and frequency dispersion play crucial roles in these predictions.

We investigate a quantum interferometric lithography system using pair-coherent states as resources to excite an $N$-photon recording medium. The interference pattern is found to have half the period of the classical light interference pattern limited by the Rayleigh criterion. The fringe visibility is nearly unity in the low-flux region and decreases with increasing values of the average photon number. We show that as $N$ increases, the high-flux limit visibility increases and the bright-fringe width decreases; however, the fringe period and spacing remain the same. Compared with the results using two-mode squeezed vacuum states, although our results have the same high-flux limit visibility, we can get higher contrast and narrower bright-fringe patterns under the same conditions of light flux and lithography material. Our approach sheds light on quantum lithography with nonclassical light and reveals how pair-coherent states can be superior to two-mode squeezed vacuum states.

We theoretically and experimentally study the unique spin displacements of a linearly polarized Gaussian beam reflected from an air–multilayer-film interface with effective complex reflection coefficients. It is found that the left- and right-handed spin components exhibit distinct intensity distributions and manifest unequal values of displacements. Furthermore, the displacements are very sensitive to the layers' thickness. This provides an efficient pathway for controlling the spin displacements of light, such as enhancement of spin displacements to microns at specific incident angles. The experimental results with $P$- and $S$-polarized light are in good agreement with the theoretical predictions.

In this paper, we show how continuous-variable dense coding can be implemented using entangled light generated from a membrane-in-the-middle geometry. The mechanical resonator is assumed to be a high reflectivity membrane hung inside a high quality factor cavity. We show that the mechanical resonator is able to generate an amount of entanglement between the optical modes at the output of the cavity, which is strong enough to approach the capacity of quantum dense coding at small photon numbers. The suboptimal rate reachable by our optomechanical protocol is high enough to outperform the classical capacity of the noiseless quantum channel.

We present a general scheme for sharing quantum secrets, and an extension to sharing classical secrets, which contain all known quantum-secret-sharing schemes. In this framework, we show the equivalence of existence of both schemes, that is, the existence of a scheme sharing a quantum secret implies that the extended classical-secret-sharing scheme works, and vice versa. As a consequence of this, we find schemes sharing classical secrets for arbitrary access structures. We then clarify the relationship to quantum error correction and observe several restrictions thereby imposed, which for example indicates that for pure-state threshold schemes the share size $q$ must scale with the number of players $n$ as $q\ge \sqrt{n}$. These results also provide a way of searching for quantum-error-correcting codes.

In the usual treatment of electronic structure, all matter has cusps in the electronic density at nuclei. Cusps can produce nonanalytic behavior in time, even in response to perturbations that are time analytic. We analyze these nonanalyticities in a simple case from many perspectives. We describe a method, the $s$ expansion, that can be used in several such cases and illustrate it with a variety of examples. These include both the sudden appearance of electric fields and disappearance of nuclei in both one and three dimensions. When successful, the $s$ expansion yields the dominant short-time behavior, no matter how strong the external electric field, but agrees with linear-response theory in the weak limit. We discuss the relevance of these results to time-dependent density functional theory.