We report an experimental realization of the geometric Landau-Zener-Stückelberg (LZS) interferometry proposed by Gasparinetti et al. [Phys. Rev. Lett. 107, 207002 (2011)] in a single-trapped-ion system. Unlike those in a conventional LZS interferometer, the interference fringes of our geometric interferometer originate solely from a geometric phase. We also observe the robustness of the interference contrast against noise or fluctuations in the experimental parameters. Our scheme can be applied to other complex systems subject to relatively large errors in system control.

We demonstrate that the process of band-gap creation in periodic solids such as atomic, photonic, or phononic crystals can be viewed as spontaneous $\mathcal{PT}$-symmetry breaking in the framework of a complex frequency band structure. This allows the use of ordinary artificial structures such as Bragg stacks and simple photonic crystals as suitable test beds for the study of phenomena related to $\mathcal{PT}$-symmetry breaking.

We propose a simple method to generate quantum entanglement between two macroscopic mechanical resonators in a two-cavity optomechanical system. This entanglement is induced by the radiation pressure of a single photon hopping between the two cavities. Our results are analytical, so that the entangled states are explicitly shown. Up to local operations, these states are two-mode three-component states, and hence the degree of entanglement can be well quantified by the concurrence. By analyzing the system parameters, we find that, to achieve a maximum average entanglement, the system should work in the single-photon strong-coupling regime and the deep-resolved-sideband regime.

Greenberger-Horne-Zeilinger (GHZ) states are characterized by their transformation properties under a continuous symmetry group, and $N$-body operators that transform covariantly exhibit a wealth of GHZ contradictions. We show that local or noncontextual hidden variables cannot duplicate the predicted measurement outcomes for covariant transformations, and we extract specific GHZ contradictions from discrete subgroups, with no restrictions on particle number $N$ or dimension $d$ except for the general requirement that $N\ge 3$ for GHZ states. However, the specific contradictions fall into three regimes distinguished by increasing demands on the number of measurement operators required for the proofs. The first regime consists of proofs found recently by Ryu et al. [Phys. Rev. A 88, 042101 (2013)], the first operator-based theorems for all odd dimensions $d$, covering many (but not all) particle numbers $N$ for each $d$. We introduce alternative methods of proof that define second and third regimes and produce theorems that fill all remaining gaps down to $N=3$ for every $d$. The common origin of all such GHZ contradictions is that the GHZ states and measurement operators transform according to different representations of the symmetry group, which has an intuitive physical interpretation.

We devise and examine two procrustean entanglement concentration schemes using quantum nondemolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox for use of a much more general, versatile, and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian postmeasurement, the second a non-Gaussian ancillary mode and a Gaussian postmeasurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function-based method in a numerically efficient manner. We then quantify the entanglement increase calculating the logarithmic negativity of the output state and discuss and compare the performance of the protocols.

We propose a simple iterative algorithm to construct the optimal multiconfiguration approximation of an $N$-fermion wave function. Namely, $M\ge N$ single-particle orbitals are sought iteratively so that the projection of the given wave function in the $C_M^N$-dimensional configuration subspace is maximized. The algorithm has a monotonic convergence property and can be easily parallelized. The significance of the algorithm on the study of geometric entanglement in a multifermion system and its implication on the multiconfiguration time-dependent Hartree-Fock (MCTDHF) are discussed. The ground state and real-time dynamics of spinless fermions with nearest-neighbor interaction are studied using this algorithm, discussing several subtleties.

The ($e$,2$e$) recoil peak to binary peak ratio as a function of the ejected-electron energy is reported for helium autoionizing levels ${\left(2p^2\right)}^{1}D$ and ${\left(2s2p\right)}^{1}P$. A special out-of-plane geometry is used where the ejected electrons are detected in a plane that includes the momentum transfer axis but is perpendicular to the scattering plane. The measured recoil peak to binary peak ratio is a dimensionless quantity that can be directly compared with calculations. A second-order model in the projectile-target interaction correctly reproduces the observed energy dependence and magnitude of the ratio, while a first-order model does not.

The complex Kohn variational method, which has been extensively applied to low-energy molecule scattering, is extended to treat molecular ionization by fast electrons under the assumption that the incident and scattered electrons can be described by plane waves. The formulation reduces to the computation of the continuum generalized oscillation strength, which amounts to a generalization of the molecular photoionization problem to which the Kohn method has been successfully applied. To illustrate the approach, we present fully differential cross sections for the case of water, where good experimental data is available for comparison.

We analyze resonant radiation emitted by dispersive shock waves owing to higher-order dispersive corrections of the leading term in the defocusing nonlinear Schrödinger equation. We give criteria for calculating the radiated frequency based on an analytical estimate of the shock velocity and reveal a diversity of scenarios controllable via the corrections, ranging from the radiation-induced transition of the dispersive shock into a classical-type shock to the qualitative modification of the underlying gradient catastrophe or the competition between different breaking mechanisms.

We investigate a hybrid electromechanical system consisting of a pair of charged macroscopic mechanical oscillators coupled to a small ensemble of Rydberg atoms. The resonant dipole-dipole coupling between an internal atomic Rydberg transition and the mechanics allows cooling to its motional ground state with a single atom despite the considerable mass imbalance between the two subsystems. We show that the rich electronic spectrum of Rydberg atoms, combined with their high degree of optical control, paves the way towards implementing various quantum-control protocols for the mechanical oscillators.

Memory (non-Markovian) effect is found to be able to accelerate quantum evolution [S. Deffner and E. Lutz, Phys. Rev. Lett. 111, 010402 (2013).]. In this work, for an atom in a structured reservoir, we show that the mechanism for the speedup is not only related to non-Markovianity but also to the population of excited states under a given driving time. In other words, it is the competition between non-Markovianity and population of excited states that ultimately determines the acceleration of quantum evolution in memory environments. A potential experimental realization for verifying the above phenomena is discussed by using a nitrogen-vacancy center embedded in a planar photonic crystal cavity under current technologies.

A generalization of the box-variational method is developed to describe particle scattering with the Dirac equation. The method is applied to extract phase shifts from all-order single + double relativistic many-body perturbation theory calculations of the electron-helium, electron-neon, and electron-krypton systems. Comparisons with experimental elastic and momentum transfer cross sections are made. Agreement at the $1\%$ to $2\%$ level is achieved for helium and neon. The scattering length for krypton is $4\%$ smaller in magnitude than experimental estimates derived from swarm experiments.

We consider dilute gases of dipolar bosons or fermions in the high-temperature limit in a spherically symmetric harmonic trapping potential. We examine the system using a virial expansion up to second order in the fugacity. Using the Born approximation and assuming purely dipolar interactions, we find that the second-order virial coefficient for both bosons and fermions depends quadratically on the dipole length and is negative at high temperatures, indicating that to lowest order in the dipole-dipole interactions the dipolar single-component quantum gases are repulsive. If the $s$-wave scattering length for the bosonic system is tunable and its absolute value is made small, then the $s$-wave interactions dominate and the dipolar gas behaves like a weakly interacting Bose gas with isotropic $s$-wave interactions. If the generalized scattering lengths for the fermionic system are tunable, then the dipole length can enter linearly in the virial equation of state, enhancing the dipole-dipole effects in the thermodynamic observables.

We theoretically study a superradiant laser, deriving both the steady-state behaviors and small-amplitude responses of the laser's atomic inversion, atomic polarization, and light field amplitude. Our minimum model for a three-level laser includes atomic population accumulating outside of the lasing transition and dynamics of the atomic population distribution causing cavity frequency tuning, as can occur in realistic experimental systems. We show that the population dynamics can act as real-time feedback to stabilize or destabilize the laser's output power, and we derive the cavity frequency tuning for a Raman laser. We extend the minimal model to describe a cold-atom Raman laser using ${}^{87}$Rb, showing that the minimal model qualitatively captures the essential features of the more complex system [Bohnet et al., Phys. Rev. Lett. 109, 253602 (2012)]. This work informs our understanding of the stability of proposed millihertz linewidth lasers based on ultranarrow optical atomic transitions and will guide the design and development of these next-generation optical frequency references.

In view of the increasing importance of non-Gaussian entangled states in quantum information protocols like teleportation and violations of Bell inequalities, the steering of continuous variable non-Gaussian entangled states is investigated. Einstein-Podolsky-Rosen steering for Gaussian states may be demonstrated through the violation of the Reid inequality involving products of the inferred variances of noncommuting observables. However, for arbitrary states the Reid inequality is not always necessary because of the higher-order correlations in such states. One then needs to use the entropic steering inequality. We examine several classes of currently important non-Gaussian entangled states, such as the two-dimensional harmonic oscillator, the photon-subtracted two-mode squeezed vacuum, and the NOON state, in order to demonstrate the steering property of such states. A comparative study of the violation of the Bell inequality for these states shows that the entanglement present is more easily revealed through steering compared to Bell violation for several such states.

The solution of the hyperangular Schrödinger equation for few-body systems using a basis of explicitly correlated Gaussians remains numerically challenging. This is in part due to the number of basis functions needed as the system size grows, but also due to the fact that the number of numerical integrations increases with the number of hyperangular degrees of freedom. This paper shows that the latter challenge is no more. Using a $\delta$ function to fix the hyperradius $R$, all matrix element calculations are reduced to a single numerical integration regardless of system size $n$ or number of dimensions $d$. In the special case of $d$ an even number, the matrix elements of the noninteracting system are fully analytical. We demonstrate the use of the new matrix elements for the three-, four-, and five-body electron-positron systems with zero total angular momentum $L$, positive parity $\pi$, and varied spins $S_{+}$ and $S_{-}$.

We propose a single-photon router using a single atom with an inversion center coupled to quantum multichannels made of coupled-resonator waveguides. We show that the spontaneous emission of the atom can direct single photons from one quantum channel into another. The on-demand classical field perfectly switches off the single-photon routing due to the quantum interference in the atomic amplitudes of optical transitions. Total reflections in the incident channel are due to the photonic bound state in the continuum. Two virtual channels, named the scatter-free and controllable channels, are found, which are coherent superpositions of quantum channels. Any incident photon in the scatter-free channel is totally transmitted. The propagating states of the controllable channel are orthogonal to those of the scatter-free channel. Single photons in the controllable channel can be perfectly reflected or transmitted by the atom.

In this paper we study an application of an information-theoretic distance between two measurements to investigate nonclassical correlations. We postulate the triangle principle, which states that any information-theoretic distance is valid for any sets of measurements, regardless if they can be jointly measured or not. As a consequence, the triangle inequality for this distance is obeyed for any three measurements. This simple principle is valid in any classical realistic theory, however, it may not hold in quantum theory. It leads to the derivation of certain inequalities whose violations are an indicator of nonclassicality. Some of these inequalities formally look the same as those found in the literature on local realism and noncontextuality, but we also derive completely different inequalities. We also show that our geometrical approach naturally implies monogamy of nonclassical correlations.

We introduce two types of two-qubit controlled-phase gates, which operate with trapped ions in a linear Paul trap. Each ion is addressed individually with two sequential bichromatic laser pulses, the two frequency components of which are tuned on exact resonance with the first blue and red vibrational sidebands of the qubit transition frequency. For suitably chosen pulse areas and relative laser phases the dependence on the phonon number vanishes and the net effect is a controlled-phase gate between the electronic qubit states. In contrast to earlier gates, in which the pulses addressing the two ions are separated in time, we use partly overlapping pulses, which make the present gates faster, e.g., by about 26% for rectangular and over 50% for sinusoidal pulses.