On increasing the coupling strength ($\lambda$) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density $\rho \sim k_F^3$ undergoes a change at a critical value, ${\lambda }_T\approx k_F$ [Phys. Rev. B 84, 014512 (2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-$\frac{1}{2}$ fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing $\lambda$. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling $\lambda$. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

Motivated by recent experimental results, we present a systematic theoretical analysis of dark-bright-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component Bose-Einstein condensates. We study analytically the interactions between two dark-bright solitons in a homogeneous condensate and then extend our considerations to the presence of the trap. We illustrate the existence of robust stationary dark-bright-soliton “molecules,” composed of two or more solitons, which are formed due to the competition of the interaction forces between the dark- and bright-soliton components and the trap force. Our analysis is based on an effective equation of motion, derived for the distance between two dark-bright solitons. This equation provides equilibrium positions and characteristic oscillation frequencies of the solitons, which are found to be in good agreement with the eigenfrequencies of the anomalous modes of the system.

We investigate exact matter-wave soliton pairs of two-component heteronuclear atomic Bose-Einstein condensates with tunable interactions and harmonic potentials by using a combination of the homogeneous balance principle and the $F$-expansion technique. Our results show that exact matter-wave soliton pairs are asymmetric where their existence requires some restrictive conditions corresponding to experimentally controllable interactions and harmonic potential parameters. In contrast to homonuclear systems, the potentials for two components in heteronuclear systems are different, which is due to the mass of two components being unequal. Considering two explicit situations of the interaction parameters, we further explore the collision dynamics of the soliton pairs with opposite velocities by synchronously controlling the interaction and potential parameters. The collision dynamics occur during and after the simultaneous evaporative cooling of two condensates. The results show that collisions are elastic and that the solitons after the collision can keep their identities. In addition, we find that the amplitudes of the soliton pairs periodically grow with time during the cooling process and, for the same initial conditions, the collision time of the soliton pair without gain is delayed compared with that with gain. We also discuss how to observe these new phenomena in future experiments.

We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a SU(2)-hopping matrix for the bosons. Using a resummed hopping expansion, we calculate the excitation spectra in the Mott insulating phases and demonstrate that the superfluid-insulator phase boundary displays a nonmonotonic dependence on the gauge-field strength. We also compute the momentum distribution of the bosons in the presence of the non-Abelian field and show that they develop peaks at nonzero momenta as the superfluid-insulator transition point is approached from the Mott side. Finally, we study the superfluid phases near the transition and discuss the induced spatial pattern of the superfluid density due to the presence of the non-Abelian gauge potential.

We numerically demonstrate all-optical logic operations with quantum dots (QDs) embedded in a bimodal photonic-crystal waveguide using Maxwell-Bloch equations in a slowly varying envelope approximation (SVEA). The two-level QD excitation level is controlled by one or more femtojoule optical driving pulses passing through the waveguide. Specific logic operations depend on the relative pulse strengths and their detunings from an inhomogeneouslly broadened (about 1$\%$ for QD transitions centered at $1.5\mu$m) QD transition. This excitation controlled two-level medium then determines passage of subsequent probe optical pulses. Envelope equations for electromagnetic waves in the linear dispersion and cutoff waveguide modes are derived to simplify solution of the coupled Maxwell-Bloch equations in the waveguide. These determine the quantum mechanical evolution of the QD excitation and its polarization, driven by classical electromagnetic (EM) pulses near a sharp discontinuity in the EM density of states of the bimodal waveguide. Different configurations of the driving pulses lead to distinctive relations between driving pulse strength and probe pulse passage, representing all-optical logic and, or, and not operations. Simulation results demonstrate that such operations can be done on picosecond time scales and within a waveguide length of about $10\mu$m in a photonic-band-gap (PBG) optical microchip.

We propose an approach to sensitively probe the chirality of molecules by measuring their coherent optical-absorption spectra. It is shown that quantum dynamics of the cyclic three-level chiral molecules driven by appropriately designed external fields is total-phase dependent. This will result in chirality-dependent absorption spectra for the probe field. As a consequence, the charality-dependent information in the spectra (such as the locations and relative heights of the characteristic absorption peaks) can be utilized to identify molecular chirality and determinate enantiomer excess (i.e., the percentages of different enantiomers). The feasibility of the proposal with chiral molecules confined in hollow-core photonic crystal fiber is also discussed.

We theoretically investigate the dynamic interaction of a quantum dot in a nanocavity with time-symmetric single-photon pulses. The simulations, based on a wave-function approach, reveal that almost perfect single-photon absorption occurs for quantum-dot–cavity systems operating on the edge between strong- and weak-coupling regimes. The computed maximum absorption probability is close to unity for pulses with a typical length comparable to half of the Rabi period. Furthermore, the dynamic control of the quantum-dot energy via electric fields allows the freezing of the light-matter interaction, leaving the quantum dot in its excited state. Shaping of single-photon wave packets by the electric field control is limited by the occurrence of chirping of the single-photon pulse. This understanding of the interaction of single-photon pulses with the quantum-dot–cavity system provides the basis for the development of advanced protocols for quantum-information processing in the solid state.

A physical picture for coherent emission of $\gamma$ rays by a nuclear array excited with synchrotron radiation is given. The particular case of a pure nuclear Bragg reflection from the ${}^{57}$FeBO${}_3$ crystal is analyzed. During free de-excitation of the nuclei, a nuclear exciton polariton is developing inside the crystal and generates at the exit of the crystal a coherent $\gamma$-ray beam. In the crystal the nuclear levels of ${}^{57}$Fe are split because of a combined magnetic and electric interaction. The rich picture of $\gamma$-ray interference is described, which involves geometrical space, energy, and spin domains. In the vicinity of the Néel temperature of the crystal the magnetic splitting of nuclear levels nearly collapses. These conditions lead to drastic changes in the angular, energy, and temporal properties of the emitted radiation. The emission angular function, which in the approximation of a plane incident wave represents the emission intensity for different angular settings of the crystal near Bragg angle, strongly broadens and transforms to a double-hump structure with a central dip between the peaks. The energy and temporal distributions of the emitted radiation crucially depend upon the crystal angular setting. Beyond the central dip, the energy distribution of nuclear scattering acquires a complicated form with several satellites at various energies. In contrast, at the exact angular position of the central dip, the energy spectrum exhibits a single line shape with the line width close to the natural width of the nuclear resonance. The obtained results constitute the theoretical basis for the understanding and for the further elaboration of the ${}^{57}$Fe synchrotron Mössbauer source—the device that provides a collimated beam of intense and polarized $\gamma$ radiation in an energy bandwidth of nanoelectronvolts, the nuclear resonance natural level width.

The motion of a self-propelled cavity soliton in a laser where the pump profile acts as a square billiard is investigated. In the long-term dynamics, only closed trajectories are possible, exhibiting nonspecular reflections with striking similarities to walking droplets in a vibrated liquid bath. Open orbits can be achieved either by introducing scattering defects in the pump profile or in the presence of more than two solitons, due to their interaction. Such dynamical properties can be exploited for applications such as a compact soliton-force microscope.

In this paper, we theoretically discuss the combined chirp effects on the isolated attosecond generation when a model Ar is exposed to an intense 5-fs, 800-nm fundamental chirped pulse combined with a weak 10-fs, 1200-nm controlling chirped pulse. It shows that for the case of the chirp parameters ${\beta }_1$ $=$ 6.1 (corresponding to the 800-nm field) and ${\beta }_2$ $=$ 4.0 (corresponding to the 1200-nm field), both the harmonic cutoff energy and the supercontinuum can be remarkably extended resulting in a 663-eV bandwidth. Moreover, due to the introduction of the chirps, the short quantum path is selected to contribute to the harmonic spectrum. Finally, by superposing a properly selected harmonic spectrum in the supercontinuum region, an isolated pulse as short as 31 as (5 as) is generated without (with) phase compensation.

We investigate analytically and numerically propagation and spatial localization of light in nonlocal media with competing nonlinearities. In particular, we discuss conditions for the modulational instability of plane waves and formation of spatial solitons. We show that the competing focusing and defocusing nonlinearities enable coexistence of dark or bright spatial solitons in the same medium by varying the intensity of the beam.

We show that defocusing Kerr media with parity-time-symmetric potentials can support one- and two-dimensional bright spatial solitons. These solitons are found to be stable over the wide range where they exist. More importantly, we discover an exact one-dimensional solution and a closed two-dimensional solution in the structure.

New extreme-ultraviolet (XUV) light sources such as high-order-harmonic generation (HHG) and free-electron lasers (FELs), combined with laser-induced alignment techniques, enable novel methods for making molecular movies based on measuring molecular frame photoelectron angular distributions. Experiments are presented where CO${}_2$ molecules were impulsively aligned using a near-infrared laser and ionized using femtosecond XUV pulses obtained by HHG. Measured electron angular distributions reveal contributions from four orbitals and the onset of the influence of the molecular structure.

Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on quasientropic measures. The theorem that emerges from this formulation guarantees that the uncertainty of the results of a set of generalized measurements without a common eigenstate has an inviolable lower bound which depends on the measurement set but not the state. A corollary to this theorem yields a parallel formulation of the uncertainty principle for generalized measurements corresponding to the entire class of quasientropic measures. Optimal majorization bounds for two and three mutually unbiased bases in two dimensions are calculated. Similarly, the leading term of the majorization bound for position and momentum measurements is calculated which provides a strong statement of Heisenberg's uncertainty principle in direct operational terms. Another theorem provides a majorization condition for the least-uncertain generalized measurement of a given state with interesting physical implications.

We introduce a non-Markovianity measure for continuous-variable open quantum systems based on the idea put forward in H.-P. Breuer et al. [Phys. Rev. Lett. 103, 210401 (2009);], that is, by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow of information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit.

We present a protocol for generating on-demand, indistinguishable single photons on a silicon photonic integrated chip. The source is a time-multiplexed spontaneous parametric down-conversion element that allows optimization of single-photon versus multiphoton emission while realizing high output rate and indistinguishability. We minimize both the scaling of active elements and the scaling of active element loss with multiplexing. We then discuss detection strategies and data processing to further optimize the procedure. We simulate an improvement in single-photon-generation efficiency over previous time-multiplexing protocols, assuming existing fabrication capabilities. We then apply this system to generate heralded Bell states. The generation efficiency of both nonclassical states could be increased substantially with improved fabrication procedures.

Entangling a mechanical oscillator with an optical mode is an enticing and yet a very challenging goal in cavity optomechanics. Here we consider a pulsed scheme to create Einstein-Podolsky-Rosen-type entanglement between a traveling-wave light pulse and a mechanical oscillator. The entanglement can be verified unambiguously by a pump-probe sequence of pulses. In contrast to schemes that work in a steady-state regime under a continuous-wave drive, this protocol is not subject to stability requirements that normally limit the strength of achievable entanglement. We investigate the protocol's performance under realistic conditions, including mechanical decoherence, in full detail. We discuss the relevance of a high mechanical $Qf$ product for entanglement creation and provide a quantitative statement on which magnitude of the $Qf$ product is necessary for a successful realization of the scheme. We determine the optimal parameter regime for its operation and show it to work in current state-of-the-art systems.

Wavelengths, line strengths, and transition rates are calculated for the multipole ($E1$, $M1$, $E2$, $M2$, $E3$, and $M3$) transitions between the excited $6s^{2}6p^{5}nl$ and $6s6p^{6}nl$ states and the ground $6s^{2}6p^6$ state in Ac${}^{3+}$, Th${}^{4+}$, and U${}^{6+}$ Rn-like ions. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate energies and transition rates for multipole transitions in these hole-particle systems. The RMBPT method agrees with multiconfigurational Dirac-Fock (MCDF) calculations in lowest order, includes all second-order correlation corrections, and includes corrections from negative-energy states. The calculations start from a [Xe]$4f^{14}5d^{10}6s^{2}6p^6$ Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. Evaluated multipole matrix elements for transitions from excited states to the ground states are used to determine the line strengths, transition rates, and multipole polarizabilities. This work provides a number of yet unmeasured properties of these actinide ions for various applications and for benchmark tests of theory and experiment.

Three-body recombination processes are treated numerically for a system of three identical bosons. The two-body model potentials utilized support many bound states, a major leap in complexity that produces an intricate structure of sharp nonadiabatic avoided crossings in the three-body hyperradial adiabatic potentials at short distances. This model thus displays the usual difficulties of more realistic systems. To overcome the numerical challenges associated with sharp avoided crossings, the slow variable discretization approach is adopted in the region of small hyperradii. At larger hyperradii, where the adiabatic potentials and couplings are smooth, the traditional adiabatic method suffices. Despite the high degree of complexity, recombination into deeply bound states behaves regularly due to the dominance of one decay pathway, resulting from the strong coupling between different recombination channels. Moreover, the usual Wigner threshold law must be modified for excited incident recombination channels.

The possibility of controlled direct laser-nuclear excitations is considered from a quantum control perspective. The controllability of laser-driven electric dipole and magnetic dipole transitions among pure nuclear states is analyzed. Within a set of realistic and general conditions, atomic nuclei are demonstrated to possess full state controllability. Additionally, an analysis of the nuclear state excitation probability as a function of the laser control field is conducted. This control landscape is shown to possess a generic topology, which has important physical consequences for achieving optimal nuclear state excitation with laser fields. Last, an assessment is given of the technological challenges that need to be considered when implementing direct nuclear control in the laboratory.