In the present paper we investigate the orientation dependence of the nonsequential double ionization (NSDI) of a hydrogen molecule (H${}_2$) exposed to a strong laser field analytically within the strong-field approximation. Our calculations demonstrate that the NSDI yields can increase with the increase of the molecular alignment angle; i.e., the alignment dependence of the NSDI yields exhibit a reversed tendency compared to that of the single-ionization yields. This striking phenomenon is identified as a signal of quantum interference, which arises from the two-center structure of the diatomic molecule and can lead to the dramatic suppression of the NSDI rates at small alignment angles. Moreover, the interference effect can be altered by both laser intensity and internuclear distance. The above finding indicates that the two-center interference can affect NSDI yields dramatically in certain cases and therefore suggests a feasible way to observe the interference effect indirectly in NSDI experiments.

Level crossing models for two-state quantum systems are applicable to a wide variety of physical problems. We address the special case of level glancing, i.e., when energy levels reach a degeneracy at a specific point of time, but never actually cross. The simplest model with such behavior is the parabolic model, and its generalizations, which we call superparabolic models. We discuss their basic characteristics, complementing the previous work on the related nonlinear crossing models [Vitanov and Suominen, Phys. Rev. A 59, 4580 (1999)].

In this paper, we describe and compare different methods used for the accurate determination of forces acting on matter-wave packets in optical lattices. The quantum interference nature responsible for the production of both Bloch oscillations and coherent delocalization is investigated in detail. We study conditions for the optimal detection of Bloch oscillation for a thermal ensemble of cold atoms with a large velocity spread. We report on the experimental observation of resonant tunneling in an amplitude-modulated optical lattice up to the sixth harmonic with Fourier-limited linewidth. We then explore the fundamental and technical phenomena which limit both the sensitivity and the final accuracy of the atomic force sensor at a ${10}^{-7}$ precision level [Poli et al., Phys. Rev. Lett. 106, 038501 (2011)], with an analysis of the coherence time of the system. We address a few simple setup changes to go beyond the current accuracy.

We study matter-wave dark solitons in atomic Bose-Einstein condensates (BECs) at finite temperatures, under the effect of linear and periodic potentials. Our model, namely, a dissipative Gross-Pitaevskii equation, is treated analytically by means of dark-soliton perturbation theory and the Landau dynamics approach, which result in a Newtonian equation of motion for the dark-soliton center. This reduced model, which incorporates an effective washboard potential and an antidamping term accounting for finite-temperature effects, constitutes an example of an antidamped Josephson junction. We perform a qualitative (local and global) analysis of the equation of motion. We present results of systematic numerical simulations for both zero- and finite-temperature BECs to highlight the differences between the Hamiltonian and dissipative settings. For sufficiently small wave numbers of the periodic potential and weak linear potentials, the analytical results are found to be in good agreement with pertinent ones obtained via a Bogoliubov–de Gennes analysis and direct numerical simulations.

For the multimode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant-generating function. Approximating the exact system of equations at the level of the cumulant-generating function and system operators at lowest order allows us to recover master equation results of the full counting statistics for certain parameter regimes at very low computational cost. The thermodynamic limit, which is not accessible with the master equation approach, can be derived analytically for different approximations.

We study the driven-dissipative dynamics of photons interacting with an array of micromechanical membranes in an optical cavity. Periodic membrane driving and phonon creation result in an effective photon-number-conserving nonunitary dynamics, which features a steady state with long-range photonic coherence. If the leakage of photons out of the cavity is counteracted by incoherent driving of the photonic modes, we show that the system undergoes a dynamical phase transition to the state with long-range coherence. A minimal system, composed of two micromechanical membranes in a cavity, is studied in detail, and it is shown to be a realistic setup where the key processes of the driven-dissipative dynamics can be seen.

We argue that the geometric discord introduced by Dakić, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)] is not a good measure for the quantumness of correlations, as it can increase even under trivial local reversible operations of the party whose classicality or nonclassicality is not tested. On the other hand it is known that the standard, mutual-information-based discord does not suffer this problem; a simplified proof of such a fact is given.

Bell's theorem for systems more complicated than two qubits faces a hidden, as yet undiscussed, problem. One of the methods to derive Bell inequalities is to assume the existence of a joint probability distribution for measurement results for all settings in the given experiment. However, for spin-1 systems, one faces the problem that the eigenvalues of observables do not allow a consistent algebra if one allows all possible settings on each side (Bell's 1966 contradiction), or some specific sets (leading to a Kochen-Specker 1967 contradiction). We show here that by choosing a special set of settings which never lead to inconsistent algebra of eigenvalues, one can still derive multisetting Bell inequalities, and that they are robustly violated. Violation factors increase with the number of subsystems. The inequalities involve only spin observables, we do not allow all possible qutrit observables, still the violations are strong.

We apply a numerical method based on multiconfigurational Ehrenfest trajectories and demonstrate converged results for the Choi fidelity of an entangling quantum gate between two two-level systems interacting through a set of bosonic modes. We consider both spin-boson and rotating-wave Hamiltonians for various numbers of mediating modes (from 1 to 100) and extend our treatment to include finite temperatures. Our results apply to two-level impurities interacting with the same band of a photonic crystal or to two distant ions interacting with the same set of motional degrees of freedom.

Quantum manipulation protocols for quantum sensors and quantum computation often require many single-qubit rotations. However, the impact of phase noise in the field that performs the qubit rotations is often neglected or treated only for special cases. We present a general framework for calculating the impact of phase noise on the state of a qubit, as described by its equivalent Bloch vector. The analysis applies to any Bloch vector orientation and any rotation axis azimuthal angle for both a single pulse and pulse sequences. Experimental examples are presented for several special cases. We apply the analysis to commonly used composite $\pi$ pulse sequences for suppression of static amplitude or detuning errors and also to spin-echo sequences. We expect the formalism presented will help guide the development and evaluation of future quantum manipulation protocols.

We investigate theoretically momentum-resolved radio-frequency (rf) spectroscopy of a noninteracting atomic Fermi gas in a spin-orbit coupled lattice. This lattice configuration has been recently created at MIT [Cheuk et al., Phys. Rev. Lett. 109, 095302 (2012)] for ${}^6$Li atoms, by coupling the two hyperfine spin states with a pair of Raman laser beams and additional rf coupling. Here, we show that momentum-resolved rf spectroscopy can measure single-particle energies and eigenstates and therefore resolve the band structure of the spin-orbit coupled lattice. In our calculations, we take into account the effects of temperatures and harmonic traps. Our predictions are to be confronted with future experiments on spin-orbit coupled Fermi gases of ${}^{40}$K atoms in a lattice potential.

Dynamics of interacting cold atomic gases have recently become a focus of both experimental and theoretical studies. Often cold-atom systems show hydrodynamic behavior and support the propagation of nonlinear dispersive waves. Although this propagation depends on many details of the system, great insight can be obtained in the rather universal limit of weak nonlinearity, dispersion, and dissipation. In this limit, using a reductive perturbation method we map some of the hydrodynamic models relevant to cold atoms to well-known chiral one-dimensional equations such as the Korteweg–de Vries (KdV), Burgers, KdV-Burgers, and Benjamin-Ono equations. These equations have been thoroughly studied in the literature. The mapping gives us a simple way to make estimates for the original hydrodynamic equations and to study the interplay between nonlinearity, dissipation, and dispersion which are the hallmarks of nonlinear hydrodynamics.

The spontaneous emission properties of a two-level emitter embedded in a negative permeability slab near the interface between a negative permeability slab and a negative permittivity slab are investigated. When the impedances of the two slabs are matched and the dissipation of the material is small, the structure forms a very good single-mode cavity for surface plasmons. The extremely high local density of states of surface plasmons results in ultrastrong coupling between the atom and the surface plasmons, and then large vacuum Rabi frequency. A damped vacuum Rabi oscillation occurs in the dynamic evolution of the excited atom close to the interface. The atomic emission spectrum displays an asymmetric two-peak structure with the peak separation equal to the vacuum Rabi frequency.

In this article, we investigate how quantum correlations behave for the so-called Werner and pseudopure families of states. The latter refers to states formed by mixing any pure state with the totally mixed state. We derive closed expressions for the quantum discord and the relative entropy of quantumness for these families of states. For Werner states, the classical correlations are seen to vanish in high dimensions while the amount of quantum correlations remains bounded. For pseudopure states, nearly the opposite effect is observed, with both the quantum and classical correlations growing without bound as the dimension increases and only as the system becomes more entangled. In light of our calculations, we discuss how Werner states could play a role as a quantum one-time pad in cryptographic tasks and, along with isotropic states, could function as a quantum memory device designed to maximize the uncertainty tradeoff between noncommuting measurements on the individual subsystems.

When the scattering length is proportional to the distance from the center of the system, two particles are shown to be trapped about the center. Furthermore, their spectrum exhibits discrete scale invariance, whose scale factor is controlled by the slope of the scattering length. While this resembles the Efimov effect, our system has a number of advantages when realized with ultracold atoms. We also elucidate how the emergent discrete scaling symmetry is violated for more than two bosons, which may shed new light on Efimov physics. Our system thus serves as a tunable model system to investigate universal physics involving scale invariance, quantum anomaly, and renormalization group limit cycle, which are important in a broad range of quantum physics.

Recent experimental advances in light technology necessitate the availability of sophisticated theoretical models which can incorporate an accurate treatment of double-electron continua. We describe here an intermediate-energy $R$-matrix approach to photoionization and photo-double-ionization and illustrate its feasibility by application to photoionization and photo-double-ionization of He and photodetachment and photo-double-detachment of H${}^{-}$. Results are shown to be in excellent agreement with previous theoretical and experimental studies. This work is a key step in the development of a multipurpose $R$-matrix code for multiple-electron ejection.

Quantum-size oscillations of the basic physical characteristics of a confined fermionic condensate are a well-known phenomenon. Its conventional understanding is based on the single-particle physics, whereby the oscillations follow variations in the single-particle density of states driven by the size quantization. Here we present a study of a cigar-shaped ultracold superfluid Fermi gas, which demonstrates an important many-body aspect of the quantum-size coherent effects, overlooked previously. The many-body physics is revealed here in the atypical crossover from the Bardeen-Cooper-Schrieffer (BCS) superfluid to the Bose-Einstein condensate (BEC) induced by the size quantization of the particle motion. The single-particle energy spectrum for the transverse dimensions is tightly bound, whereas for the longitudinal direction it resembles a quasi-free dispersion. This results in the formation of a series of single-particle subbands (shells) so that the aggregate fermionic condensate becomes a coherent mixture of subband condensates. Each time when the lower edge of a subband crosses the chemical potential, the BCS-BEC crossover is approached in this subband, and the aggregate condensate contains both BCS and BEC-like components.

Artificially structured metamaterials hybridized with elements that respond nonlinearly to incident electromagnetic fields can, from a macroscopic perspective, support nonlinear responses that cannot be described by purely electric or magnetic interactions. To investigate the mechanisms and behaviors of such interactions, termed nonlinear magnetoelectric coupling, we develop a set of coupled-mode equations for describing three-wave mixing in a metamaterial, using Bloch modes as the basis. By equating these coupled-mode equations to those of a homogenized system, we derive closed-form expressions for the macroscopic nonlinear susceptibilities. From these expressions, a great deal can be inferred about the nature and construction of magnetoelectric nonlinearities in metamaterials. As an example, we apply this method in the analysis of a prototypical nonlinear magnetoelectric metamaterial. In particular, we show that independent control of the eight second-order susceptibility tensors encompasses a massive parameter space from which new realms of nonlinear interference and wave manipulation can be accessed.

Light scattering by two cases, a hemispherical solid immersion lens (HSIL) and a sphere when illuminated by a focused polarized beam, are discussed. There is a difference between the scattering coefficients of the two scatterers due to multiple reflections inside the sphere, which do not occur in the HSIL. We also derive the Debye series (DS) for the scattering coefficients of the sphere in a focused polarized beam. The DS is derived in a simple and straightforward manner in both mathematical and physical aspects. The applicability of generalized Lorenz-Mie theory (GLMT) is then discussed in terms of the definitions of the incident focused beam. We show that care must be taken when investigating the scattering phenomenon under a focusing condition. This paper aims to give deeper insight into the process of light scattering under focusing conditions.

We study experimentally the dynamics of vertical-cavity surface-emitting lasers (VCSELs) with polarization-rotated (PR) optical feedback, such that the natural lasing polarization of a VCSEL is rotated by 90 deg and then is reinjected into the laser. We observe noisy, square-wave-like polarization switchings with periodicity slightly longer than twice the delay time, which degrade to (or alternate with) bursts of irregular oscillations. We present results of simulations that are in good agreement with the observations. The simulations demonstrate that close to threshold the regular switching is very sensitive to noise, while well above threshold is less affected by the noise strength. The frequency splitting between the two polarizations plays a key role in the switching regularity, and we identify wide parameter regions where deterministic and robust switching can be observed.