Quantum Interference of Dual-Channel Excited Magnons in Spin-1 Bose-Einstein Condensates Atomic Chain

We investigate the quantum interference of spin wave excitations of a spin-1 atomic Bose condensate confined in an optical lattice. Single-channel and dual-channel interactions are employed in our system, and their induced excitations are compared. Also we consider the interplay of magneto-optical excitations, which leads to a constructive or destructive effect for the creation of magnons based on background excitations. The population distributions of excited magnons can be well controlled by steering the long-range dipole-dipole interactions. Such a scheme can be used to demonstrate conventional quantum-optical phenomena like dynamical Casimir effect at finite temperatures.     

Quantum Interference of Dual-Channel Excited Magnons in Spin-1 Bose-Einstein Condensates Atomic Chain

We investigate the quantum interference of spin wave excitations of a spin-1 atomic Bose condensate confined in an optical lattice. Single-channel and dual-channel interactions are employed in our system, and their induced excitations are compared. Also we consider the interplay of magneto-optical excitations, which leads to a constructive or destructive effect for the creation of magnons based on background excitations. The population distributions of excited magnons can be well controlled by steering the long-range dipole-dipole interactions. Such a scheme can be used to demonstrate conventional quantum-optical phenomena like dynamical Casimir effect at finite temperatures.     

Controllable magnetic solitons excitations in an atomic chain of spinor Bose–Einstein condensates confined in an optical lattice

We propose an experimental scheme to show that the nonlinear magnetic solitary excitations can be achieved in an atomic spinor Bose–Einstein condensate confined in a blue-detuned optical lattice. Through exact theoretical calculations, we find that the magnetic solitons can be generated by the static magnetic dipole–dipole interaction (MDDI), of which the interaction range can be well controlled. We derive the existence conditions of the magnetic solitons under the nearest-neighboring, the next-nearest-neighboring approximations as well as the long-range consideration. It is shown that the long-range feature of the MDDI plays an important role in determining the existence of magnetic solitons in this system. In addition, to facilitate the experimental observation, we apply an external laser field to drive the lattice, and the existence regions for the magnetic soliton induced by the anisotropic light-induced dipole–dipole interaction are also investigated.     

Dynamics of confined quantum fluids

We examine the static and dynamic properties of liquid ⁴He in confined geometries. Confinement is modeled by placing the liquid between two rigid, attractive walls with strengths corresponding to Geltech, Vycor, or glass. The liquid arranges itself in a series of layers, with increasing areal density it undergoes a sequence of layering transitions familiar from classical fluids. We identify “bulk” excitations that propagate throughout the film, and “layer” excitations that propagate only close to the substrate. Both have the typical phonon-roton dispersion relation, but the energy of the layer-roton minimum depends sensitively on the substrate strength, thus providing a mechanism for a direct measurement of this quantity. Bulk-like roton excitations are largely independent of the interaction between the matrix and the helium atoms. While the bulk-like rotons are very similar to their true bulk counterparts, the layer modes are not in close relation to two-dimensional rotons and should be regarded as a completely independent kind of excitation.     

Second sound in a laser cooled gas

We show that the second sound can exist in the ultra-cold gas of atoms confined and cooled in a magneto-optical trap. Our approach is based on a two-fluids model, similar to that used for superfluidity. Each of the fluids (the atomic gas and the phonon gas) is described by similar kinetic and fluid equation, which are coupled. The second sound modes are elementary excitations of these two coupled fluids. The ultra-cold gas could be used as an experimental test bed for detailed studies of the dispersion properties of the first and second sound.     

Many-body effects on intersubband resonances in narrow InAs/AlSb quantum wells

Intersubband polarization couples to collective excitations of the interacting electron gas confined in a semiconductor quantum well (QW) structure. Such excitations include correlated pair excitations (repellons) and intersubband plasmons. The oscillator strength of intersubband resonances (ISBRs) strongly varies with QW parameters and electron density because of this coupling. Using the intersubband semiconductor Bloch equations for a two-conduction-subband model, we show that intersubband absorption spectra for narrow wells are dominated by the Fermi-edge singularity (via coupling to repellons) when the electron gas becomes degenerate and in the presence of large nonparabolicity. Thus the resonance peak position appears at the Fermi edge and the peak is greatly narrowed, enhanced, and red shifted as compared to the free particle result. Our results uncover a new perspective for ISBRs and indicate the necessity of proper many-body theoretical treatment in order for modeling and prediction of ISBR line shape.     

Collective excitations of harmonically trapped ideal gases

We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show that the expressions found by the scaling ansatz method are a special case of our solution. Our findings are most useful in case the trap contains more than one phase: we demonstrate how to obtain the oscillation frequencies in case an interface is present between the ideal gas and a different phase.     

Collective excitations of a degenerate Fermi vapour in a magnetic trap

We evaluate the small-amplitude excitations of a spin-polarized vapour of Fermi atoms confined inside a harmonic trap. The dispersion law is obtained for the vapour in the collisional regime inside a spherical trap of frequency , with n the number of radial nodes and the orbital angular momentum. The low-energy excitations are also treated in the case of an axially symmetric harmonic confinement. The collisionless regime is discussed with main reference to a Landau-Boltzmann equation for the Wigner distribution function: this equation is solved within a variational approach allowing an account of non-linearities. A comparative discussion of the eigenmodes of oscillation for confined Fermi and Bose vapours is presented in an Appendix. Received 23 February 1999 and Received in final form 21 April 1999     

Probing collective modes of correlated states of few electrons in semiconductor quantum dots

Low-lying collective excitations above highly correlated ground states of few interacting electrons confined in GaAs semiconductor quantum dots are probed by resonant inelastic light scattering. We highlight that separate studies of the changes in the spin and charge degrees of freedom offer unique access to the fundamental interactions. The case of quantum dots with four electrons is found to be determined by a competition between triplet and singlet ground states that is uncovered in the rich light scattering spectra of spin excitations. These light scattering results are described within a configuration-interaction framework that captures the role of electron correlation with quantitative accuracy. Recent light scattering results that reveal the impact of anisotropic confining potentials in laterally coupled quantum dots are also reviewed. In these studies, inelastic light scattering methods emerge as powerful probes of collective phenomena and spin configurations in quantum dots with few electrons.     

Oscillations of a bose-einstein condensate rotating in a harmonic plus quartic trap

We study the normal modes of a two-dimensional rotating Bose-Einstein condensate confined in a quadratic plus quartic trap. Hydrodynamic theory and sum rules are used to derive analytical predictions for the collective frequencies in the limit of high angular velocities Omega where the vortex lattice produced by the rotation exhibits an annular structure. We predict a class of excitations with frequency sqrt[6]Omega in the rotating frame, irrespective of the mode multipolarity m, as well as a class of low energy modes with frequency proportional to |m|/Omega. The predictions are in good agreement with results of numerical simulations based on the 2D Gross-Pitaevskii equation. The same analysis is also carried out at even higher angular velocities, where the system enters the giant vortex regime.     

Magnetoplasma spectra of two-dimensional electron rings

A hydrodynamical approach is employed to study the collective excitations of a two-dimensional electron gas confined in a ring geometry, under a normal magnetic held. The theory predicts a rich spectrum of magnetoplasma excitations, with several branches of high- and low-frequency resonances. It is shown that the low-frequency resonances can be identified as edge magnetoplasmons localized at the inner and outer boundaries of the ring, exhibiting their characteristic antidot-like and dot-like features. The high-frequency resonances are essentially bulk two-dimensional magnetoplasmons. Our calculated magnetoplasma modes and their associated induced charge densities and dipole moments are compared with a recent experiment, and it is found that most of the experimentally observed features of the spectrum are accounted for with the present theory.     

Two-electron linear intersubband light absorption in a biased quantum well

We point out a novel manifestation of many-body correlations in the linear optical response of electrons confined in a quantum well. Namely, we demonstrate that along with the conventional absorption peak at a frequency omega close to the intersubband energy delta, there exists an additional peak at frequency h omega approximately = 2delta. This new peak is solely due to electron-electron interactions, and can be understood as excitation of two electrons by a single photon. The actual peak line shape is comprised of a sharp feature, due to excitation of pairs of intersubband plasmons, on top of a broader band due to absorption by two single-particle excitations. The two-plasmon contribution allows us to infer intersubband plasmon dispersion from linear absorption experiments.     

Thermodynamic evidence for nanoscale bose-einstein condensation in (4)He confined in nanoporous media

We report the measurements of the heat capacity of (4)He confined in nanoporous Gelsil glass that has nanopores of 2.5-nm diameter at pressures up to 5.3 MPa. The heat capacity has a broad peak at a temperature much higher than the superfluid transition temperature obtained using the torsional oscillator technique. The peak provides definite thermodynamic evidence for the formation of localized Bose-Einstein condensates on nanometer length scales. The temperature dependence of the heat capacity is described well by the excitations of phonons and rotons, supporting the existence of localized Bose-Einstein condensates.     

Dynamics of laser-cooled Ca+ ions in a Penning trap with a rotating wall

We have performed systematic measurements of the dynamics of laser-cooled ⁴⁰Ca⁺ ions confined in a Penning trap and driven by a rotating dipole field (‘rotating wall’). The trap used is a copy of the one used in the SPECTRAP experiment located at the HITRAP facility at GSI, Germany. The size and shape of the ion cloud has been monitored using a CCD camera to image the fluorescence light resulting from excitation by the cooling laser. We have varied the experimental conditions such as amplitude and frequency of the rotating wall drive as well as the trapping parameters. The rotating wall can be used for a radial compression of the ion cloud thus increasing the ion density in the trap. We have also observed plasma mode excitations in agreement with theoretical expectations. This work will allow us to define the optimum parameters for high compression of the ions as needed for precision spectroscopy of forbidden transitions.     

Topology and Geometry of Smectic Order on Compact Curved Substrates

Smectic order on arbitrary curved substrate can be described by a differential form of rank one (1-form), whose geometric meaning is the differential of the local phase field of the density modulation. The exterior derivative of 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. We use the formalism of differential forms to systematically classify and characterize all low energy smectic states on torus as well as on sphere. A two dimensional smectic order confined on either manifold exhibits many topologically distinct low energy states. Different states are not accessible from each other by local fluctuations. The total number of low energy states scales as the square root of the system area. We also address the energetics of 2D smectic on a curved substrate and calculate the mean field phase diagram of smectic on a thin torus. Finally, we discuss the motion of disclinations for spherical smectics as low energy excitations, and illustrate the interesting connection between spherical smectic and the theory of elliptic functions.     

Dynamics of vacuum excitations and quark confinement in quantum field theories

A unified approach to interacting vacuum excitations and quark confinement is formulated in quantum field theories with symmetry breakdown. Vacuum excitations are shown to be coherent clouds of Goldstone bosons or gauge bosons and are interpreted as new asymptotic extended particle states. They correspond to all dynamically possible space-time dependent Bose condensations of the Goldstone bosons in a given theory. Different configurations of vacuum excitations are connected to one another by a family of invariant boson transformations. As an example, the Nambu theory of interacting vortex strings is derived from a Nambu-Heisenberg quark-gluon field theory. The quarks can be completely confined to the strings while the gluons cluster in quantized magnetic flux bundles of penetration width m_v^?1 and provide a short range interaction force.     

Metallic stripe in two dimensions: stability and spin-charge separation

The problems of charge stripe formation, spin-charge separation, and stability of the antiphase domain wall (ADW) associated with a stripe are addressed using an analytical approach to the t- J(z) model. We show that a metallic stripe together with its ADW is the ground state of the problem in the low doping regime. The stripe is described as a system of spinons and magnetically confined holons strongly coupled to the two dimensional spin environment with holon-spin-polaron elementary excitations filling a one-dimensional band.     

Collective excitations of a periodic Bose condensate in the Wannier representation

We study the dispersion relation of the excitations of a dilute Bose-Einstein condensate confined in a periodic optical potential and its Bloch oscillations in an accelerated frame. The problem is reduced to one-dimensionality through a renormalization of the s-wave scattering length and the solution of the Bogolubov-de Gennes equations is formulated in terms of the appropriate Wannier functions. Some exact properties of a periodic one-dimensional condensate are easily demonstrated: (i) the lowest band at positive energy refers to phase modulations of the condensate and has a linear dispersion relation near the Brillouin zone centre; (ii) the higher bands arise from the superposition of localized excitations with definite phase relationships; and (iii) the wavenumber-dependent current under a constant force in the semiclassical transport regime vanishes at the zone boundaries. Early results by Slater [Phys. Rev. 87, 807 (1952)] on a soluble problem in electron energy bands are used to specify the conditions under which the Wannier functions may be approximated by on-site tight-binding orbitals of harmonic-oscillator form. In this approximation the connections between the low-lying excitations in a lattice and those in a harmonic well are easily visualized. Analytic results are obtained in the tight-binding scheme and are illustrated with simple numerical calculations for the dispersion relation and semiclassical transport in the lowest energy band, at values of the system parameters which are relevant to experiment. Received 3 December 1999 and Received in final form 22 March 2000     

Statistical mechanics of confined systems with rotational excitations

New experimental and numerical investigations of confined systems of particles demonstrate the existence of rotational excitations. We develop here a statistical theory of finite systems, including rotational modes, by introducing the angular momentum into the formalism and constructing the relevant distributions. As special applications we study systems driven to a prescribed kinetic energy by negative friction or special isokinetic thermostats. Several distribution functions which are solutions of the Liouville or Fokker–Planck equations are given. The theory is applied to Coulomb clusters confined by parabolic forces.