We study the effects of finite size and of vacancies on the photonic band gap recently predicted for an atomic diamond lattice. Close to a $J_g=0\to J_e=1$ atomic transition, and for atomic lattices containing up to $N\approx 3\times {10}^4$ atoms, we show how the density of states can be affected by both the shape of the system and the possible presence of a fraction of unoccupied lattice sites. We numerically predict and theoretically explain the presence of shape-induced border states and of vacancy-induced localized states appearing in the gap. We also investigate the penetration depth of the electromagnetic field which we compare to the case of an infinite system.

We formulate an adiabatic connection for the exchange-correlation energy in terms of pairing matrix fluctuation. This connection opens new channels for density functional approximations based on pairing interactions. Even the simplest approximation to the pairing matrix fluctuation, the particle-particle random phase approximation (pp-RPA), has some highly desirable properties. It has no delocalization error with a nearly linear energy behavior for systems with fractional charges, describes van der Waals interactions similarly and thermodynamic properties significantly better than particle-hole RPA, and eliminates static correlation error for single-bond systems. Most significantly, the pp-RPA is the first known functional that has an explicit and closed-form dependence on the occupied and unoccupied orbitals and captures the energy derivative discontinuity in strongly correlated systems. These findings illustrate the potential of including pairing interactions within a density functional framework.

We consider the cross section for a scattering reaction averaged over a statistical ensemble of incident beam wave packets. We generalize a result known from neutron diffraction that static experiments involving stationary scattering via conservative interactions and steady beam currents cannot distinguish the wave-packet nature of the incident beam. Thus we interpret the results of recent experiments on the loss of interference effects in proton scattering from molecular hydrogen as due to the weak collimation of the incident beam rather than alterations to beam wave packets.

We study the feasibility of nearly degenerate two-photon rovibrational spectroscopy in ensembles of trapped, sympathetically cooled hydrogen molecular ions using a resonance-enhanced multiphoton dissociation (REMPD) scheme. Taking advantage of quasicoincidences in the rovibrational spectrum, the excitation lasers are tuned close to an intermediate level to resonantly enhance two-photon absorption. Realistic simulations of the REMPD signal are obtained using a four-level model that takes into account saturation effects, ion trajectories, laser frequency noise, and redistribution of population by blackbody radiation. We show that the use of counterpropagating laser beams enables optical excitation in an effective Lamb-Dicke regime. Sub-Doppler lines having widths in the 100-Hz range can be observed with good signal-to-noise ratio for an optimal choice of laser detunings. Our results indicate the feasibility of molecular spectroscopy at the ${10}^{-14}$ accuracy level for improved tests of molecular QED, a new determination of the proton-to-electron mass ratio, and studies of the time (in)dependence of the latter.

We study statically homogeneous Bose-Einstein condensates with spatially inhomogeneous interactions and outline an experimental realization of compensating linear and nonlinear potentials that can yield constant-density solutions. We illustrate how the presence of a step in the nonlinearity coefficient can only be revealed dynamically and examine how to reveal it by exploiting the inhomogeneity of the sound speed with a defect-dragging experiment. We conduct computational experiments and observe the spontaneous emergence of dark solitary waves. We use effective-potential theory to perform a detailed analytical investigation of the existence and stability of solitary waves in this setting, and we corroborate these results computationally using a Bogoliubov–de Gennes linear stability analysis. We find that dark solitary waves are unstable for all step widths, whereas bright solitary waves can become stable through a symmetry-breaking bifurcation as one varies the step width. Using phase-plane analysis, we illustrate the scenarios that permit this bifurcation and explore the dynamical outcomes of the interaction between the solitary wave and the step.

The field behind a subwavelength nanohole in a perfectly conducting plate is considered as an idealization of photonic nanostructures. It is stressed that even with nanophotonic or plasmonic structures, the fields in the neighboring free space must satisfy classical electrodynamics. We present scalar and electromagnetic treatments for the fields behind a small hole in a thin, perfectly conducting screen, and give an expression for the total field along the complete axis behind the hole, from near field to far field. Bouwkamp corrected Bethe's expression for the electric field behind the hole. We show that Bouwkamp's solution for the magnetic field needs two additional terms in order for the total field to be given satisfactorily by the sum of the evanescent field and the homogeneous field of a magnetic dipole. The fields are separated into near-field and far-field components, avoiding oscillations caused by interference between them. The variation of the Poynting vector is also considered.

We analyze the ac Stark shift of a cesium atom interacting with far-off-resonance guided light fields in the nanofiber-based two-color optical dipole trap realized by Vetsch et al. [Phys. Rev. Lett. 104, 203603 (2010)]. Particular emphasis is given to the fictitious magnetic field produced by the vector polarizability of the atom in conjunction with the ellipticity of the polarization of the trapping fields. Taking into account the ac Stark shift, the atomic hyperfine interaction, and a magnetic interaction, we solve the stationary Schrödinger equation at a fixed point in space and find Zeeman-state-dependent trapping potentials. In analogy to the dynamics in magnetic traps, a local degeneracy of these state-dependent trapping potentials can cause spin flips and should thus be avoided. We show that this is possible using an external magnetic field. Depending on the direction of this external magnetic field, the resulting trapping configuration can still exhibit state-dependent displacement of the potential minima. In this case, we find nonzero Franck-Condon factors between motional states of the potentials for different hyperfine-structure levels and propose the possibility of microwave cooling in a nanofiber-based two-color trap.

We show that the twisted-photon states, or photon states with large ($>\hslash$) angular momentum projection ($m_{\gamma }$) in the direction of motion, can photoexcite atomic levels for a hydrogenlike atom that are novel and distinct and are not restricted by $m_{\gamma }$, when the symmetry axis of the twisted-photon beam does not coincide with the center of the atomic target. Selection rules are given and interesting implications and observables for the above process are pointed out.

This article surveys quantum correlations dynamics, in the Markovian and non-Markovian regimes, in a system of two harmonic oscillators connected by a time-dependent coupling and in contact with a common heat bath. The results show the survival of the quantum correlations, including entanglement, even at very high temperatures, as well as a remarkable relation between entanglement and the instability of the system. The results also show that the indirect interaction of the oscillators via a bath significantly enhances the quantum correlations and that quantum correlations are much more sensitive to the parameters of the oscillators than the temperature of the bath.

Simulating exotic phases of matter that are not amenable to classical techniques is one of the most important potential applications of quantum information processing. We present an efficient algorithm for preparing a large class of topological quantum states, the $G$-injective projected entangled pair states (PEPS), on a quantum computer. Important examples include the resonant valence bond states, conjectured to be topological spin liquids. The runtime of the algorithm scales polynomially with the condition number of the PEPS projectors and inverse polynomially in the spectral gap of the PEPS parent Hamiltonian.

We demonstrate the creation, characterization, and manipulation of frequency-entangled qudits by shaping the energy spectrum of entangled photons. The generation of maximally entangled qudit states is verified up to dimension $d=4$ through tomographic quantum-state reconstruction. Subsequently, we measure Bell parameters for qubits and qutrits as a function of their degree of entanglement. In agreement with theoretical predictions, we observe that for qutrits the Bell parameter is less sensitive to a varying degree of entanglement than for qubits. For frequency-entangled photons, the dimensionality of a qudit is ultimately limited by the bandwidth of the pump laser and can be on the order of a few millions.

We investigate harmonic generation (HG) from ground-state Ar${}^{+}$ aligned with $M=1$ at a laser wavelength of 390 nm and intensity of $4\times {10}^{14}{\mathrm{W}\mathrm{cm}}^{-2}$. Using time-dependent R-matrix theory, we find that an initial state with magnetic quantum number $M=1$ provides a fourfold increase in harmonic yield over $M=0$. HG arises primarily from channels associated with the ${}^3{P}^e$ threshold of Ar${}^{2+}$, in contrast with $M=0$ for which channels associated with the excited, ${}^1{D}^e$ threshold dominate HG. Multichannel and multielectron interferences lead to a more marked suppression of HG for $M=1$ than $M=0$.

This paper explores the state-to-state transition-probability-control landscape for $n$-level open quantum systems governed by the Lindblad equation. For generic two-level systems, we show analytically that the control landscape does not possess critical points in the space of square-integrable control fields. Numerical simulations show that for a given target state the transition probability reaches its highest value at a particular finite time, and the corresponding control contains temporal subpulses, similar to that for the time optimal control of analogous closed quantum systems with unbounded controls.

We study zero sound in a weakly interacting two-dimensional (2D) gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean-field and many-body (beyond mean field) effects, and the anisotropy of the sound velocity is the same as the one of the Fermi velocity. The damping of zero sound modes can be much slower than that of quasiparticle excitations of the same energy. One thus has wide possibilities for the observation of zero sound modes in experiments with 2D fermionic dipoles, although the zero sound peak in the structure function is very close to the particle-hole continuum.

We propose a mean-field model to describe exciton-polariton condensates in deep periodic external potentials. We derive a set of coupled discrete equations for both condensed and uncondensed components, with interaction and tunneling coefficients obtained within the tight-binding approximation. We use the model to explain the intriguing phenomenon of increasing density modulation in a one-dimensional valley with disorder, reported by F. Manni et al. [Phys. Rev. Lett. 106, 176401 (2011)].

We study the unconventional photon blockade, recently proposed for a coupled-cavity system, in the presence of input and output quantum fields. Mixing of the input or output channels still allows strong photon antibunching of the output field, but for optimal values of the system parameters that differ substantially from those that maximize antibunching of the intracavity field. This result shows that the specific input-output geometry in a photonic system determines the optimal design in view of a single-photon device operation. We provide a compact analytical formula that allows finding the optimal parameters for each specific system geometry.

The time-dependent wave function of a nanoring driven by a laser field is obtained by exploiting the symmetries inherent to the system and used for studying the properties of the electromagnetic radiation emitted by the nanoring as a function of the polarization state of the laser. The diffused radiation has the characteristics of high-order-harmonic generation. For a noncircularly polarized laser field an extension of the expected cutoff position is evident, indicating that nanorings are efficient sources of radiation. The polarization state of the emitted harmonics can be opportunely controlled by varying the parameters of the pump field. The profile of the absorbed angular moment shows that a magnetic moment can be induced depending on the polarization of the driven field.

Enhanced single harmonic generation is analyzed in indium laser ablation plasmas at excitation conditions of multicycle (30 fs) and few-cycle (3.5 fs) pulses. We demonstrate the strong influence of pulse duration, on the emission spectra from the indium plasma. For few-cycle pulses, the enhanced emissions do not coincide with the expected harmonic wavelengths, which is the case for multicycle pulses. We test the coherent properties of an enhanced emission around 20 eV using polarization and double-slit interference techniques. We also characterize the dynamics of the emissions from the indium plasma by tuning the laser pulse duration. A theoretical analysis is presented to describe the indium plasma emission upon excitation by few-cycle pulses.

We propose a scheme to construct the efficient universal quantum circuit for qubit systems with the assistance of possibly available auxiliary Hilbert spaces. An elementary two-ququart gate, termed the controlled-double-not gate, is proposed first in ququart (four-level) systems, and its physical implementation is illustrated in the four-dimensional Hilbert spaces built by the path and polarization states of photons. Then an efficient universal quantum circuit for ququart systems is constructed using the gate and the quantum Shannon decomposition method. By introducing auxiliary two-dimensional Hilbert spaces, the universal quantum circuit for qubit systems is finally achieved using the result obtained in ququart systems with the lowest complexity.

We verified that optical topological charges are conserved in a two-step light-pulse storage and retrieval process based on the electromagnetically-induced-transparency (EIT) effect in a Pr${}^{3+}$:${\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal. Based on this conservation law, one could transfer topological charges from the interacting beams, which may not be overlapped in space and time domains, to the targeted output signal beam, and algebraic operations such as summation and subtraction of topological charges carried by the interacting beams were demonstrated via the EIT-assisted two-step light-pulse storage-retrieval process. The results may be useful for classical and quantum information processing based on optical topological charge buffer memory in EIT media.