Continuous-variable multimode entanglement in multi-wave mixing

We present a scheme to obtain continuous-variable multimode entanglement via multi-wave mixing. For a four-level atomic system in a diamond configuration, four strong coherence fields are applied to the four dipole-allowed transitions to amplify eight sidebands as cavity fields, respectively. Due to the atomic coherence, the eight side modes constitute a pair of double quantum-beats and combine into two quantum-beat collective modes, which are in a four-wave mixing parametric interaction. As a result, the entanglement occurs between these two collective modes. Correspondingly, any two individual modes from two different collective modes are entangled with each other. This gives rise to continuous-variable eight-mode entanglement with different frequencies, which has extensively application in quantum communication and quantum network.     

On the contribution of nearly critical spin and charge collective modes to the Raman spectra of high-Tc cuprates

We discuss how Raman spectra are affected by nearly critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We show that specific fingerprints of nearly critical collective modes can indeed be observed in Raman spectra and that the selectivity of Raman spectroscopy in momentum space may also be exploited to distinguish the spin and charge contribution. We apply our results to discuss the spectra of high-T_c superconducting cuprates finding that the collective modes should have masses with substantial temperature dependence in agreement with their nearly critical character. Moreover, spin modes should be more diffusive than charge modes indicating that in stripes the charge is nearly ordered, while spin modes are strongly overdamped and fluctuate with high frequency.     

Spectral signatures of critical charge and spin fluctuations in cuprates

We discuss how Raman spectra of high temperature superconducting cuprates are affected by nearly critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We find that specific fingerprints of nearly critical collective modes can be observed and that the selectivity of Raman spectroscopy in momentum space may be exploited to distinguish the spin and charge contribution. We apply our results to discuss the spectra of high-T_c superconducting cuprates finding that the collective modes should have masses with substantial temperature dependence in agreement with their nearly critical character. Moreover spin modes have larger masses and are more diffusive than charge modes indicating that in stripes the charge is nearly ordered, while spin modes are strongly overdamped and fluctuating with high frequency.     

Quantization Scheme of Surface Plasmon Polaritons in Two-Dimensional Helical Liquids

The collective modes of two-dimensional helical electron gases interacting with light have been studied in an extended random phase approximation.An inverse operator transformation that interprets electron oscillations and photons with quasi particles is developed.Because photons are initially included in the model,one can directly derive and compare the static and radiation(or vector)Helds for the excited collective modes.Unlike the traditional quantization scheme that the electron oscillation's contribution is totally hidden in the dielectric function,we can directly investigate their roles when the collective modes interact with other particles.As an example,we find an additional term which plays an important role at small distance arising from electron exchanging effect when the collective modes couple to emitters.     

A comparative study of optic phonon-like excitations in liquid mixtures and molten salts

We report a study of collective excitations in an equimolar Lennard–Jones liquid mixture KrAr and a molten salt NaCl within the parameter-free generalized collective modes (GCM) approach. It is shown that the high-frequency propagating modes in liquid KrAr and molten NaCl correspond to optic phonon-like excitations, caused by fast mass-concentration (charge in NaCl) fluctuations. Dispersion curves for optic collective excitations are discussed.     

Structural-scale transitions in solids with defects and symmetry aspects of field theory

Relaxation and failure mechanisms in solids with mesoscopic defects are considered in the context of a specific class of critical phenomena—structural-scaling transitions. The association of collective modes in mesodefect ensembles with gauge invariance in string theory is discussed. Statistical and thermodynamic properties of deformed solids are studied in relation to dynamics of collective modes of defects.     

Dielectric properties of multiband electron systems II. Collective modes

Starting from the tight-binding dielectric matrix in the random phase approximation we examine the collective modes and electron-hole excitations in a two-band electronic system. For long wavelengths (q → 0), for which most of the analysis is carried out, the properties of the collective modes are closely related to the symmetry of the atomic orbitals involved in the tight-binding states. In insulators there are only inter-band charge oscillations. If atomic dipolar transitions are allowed, the corresponding collectivemodes reduce in the asymptotic limit of vanishing bandwidths to Frenkel excitons for an atomic insulator with weak on-site interactions. The finite bandwidths renormalize the dispersion of these modes and introduce a continuum of incoherent inter-band electron-hole excitations. The possible Landau damping of collective modes due to the presence of this continuum is discussed in detail. In conductors the intra-band charge fluctuations give rise to plasmons. If the atomic dipolar transitions are forbidden, the coupling of inter-band collective modes and plasmons tends to zero as q → 0. On the contrary, in dipolar conductors this coupling is strong and nonperturbative, due to the long range monopole-dipole interactions between intra-band and inter-band charge fluctuations. The resulting collective modes are hybrids of intra-band plasmons and inter-band dipolar oscillations. It is shown that the frequency of the lower hybridized longitudinal mode is proportional to the frequency of the transverse dipolar mode when the latter is small. The dielectric instability in a multi-band conductor is therefore characterized by the simultaneous softening of a transverse and a longitudinal mode, which is an important, directly measurable consequence of the present theory.     

Inelastic scattering of ions at the surface

A systematic study of the interaction between surface collective modes and surface-channeled ions is made. A complex image potential is introduced and the position-dependent stopping power is obtained. It is shown that the surface collective modes play a significant role outside the solid. The energy loss spectra of the surface-channeled ions are obtained by computer simulation.     

Very-short-wavelength collective modes in fluids

The existence of very-short-wavelength collective modes in fluids is discussed. These collective modes are the extensions of the five hydrodynamic (heat, sound, viscous) modes to wavelengths of the order of the mean free path in a gas or to a fraction of the molecular size in a liquid. They are computed here explicitly on the basis of a model kinetic equation for a hard sphere fluid. At low densities all five modes are increasingly damped with decreasing wavelength till each ceases to exist at a cutoff wavelength. At high densities the extended heat mode softens very appreciably for wavelengths of the order of the size of the particles and becomes a diffusion-like mode that persists till much shorter wavelengths than the other modes. Except for the shortest wavelengths these collective modes and in particular the heat mode dominate the dynamical structure factorS(k, ) for all densities. The agreement of the theory with experimentalS(k, ) of liquid Ar seems to imply that very-short-wavelength collective modes also occur in real fluids.     

Collective nature of the boson peak and universal transboson dynamics of glasses

Using probe molecules with resonant nuclei and nuclear inelastic scattering, we are able to measure the density of states exclusively for collective motions with a correlation length of more than approximately 20 A. Such spectra exhibit an excess of low-energy modes (boson peak). This peak behaves in the same way as that observed by conventional methods. This shows that a significant part of the modes constituting the boson peak is of collective character. At energies above the boson peak, the reduced density of states of the collective motions universally exhibits an exponential decrease.     

Dynamical structure functions,collective modes,and energy gap in charged-particle bilayers

The dynamical properties of strongly coupled charged-particle bilayers are investigated by molecular dynamics (MD) simulation and theoretical analysis. The spectra of the current correlation functions show the existence of two (in-phase and out-of-phase) longitudinal and two (in-phase and out-of-phase) transverse collective modes. The out-of-phase modes possess finite frequencies at wave numbers k-->0, confirming the existence of the predicted long-wavelength energy gap in the bilayer system. A theoretical model based on an extended Feynman ansatz for the dynamical structure functions provides predictions on the strength of the collective modes that are verified by the MD experiment.     

Collective electronic excitations in a semiconductor superlattice in the Landau and Wannier-Stark ladder regime

Using a mean-field approximation, we have developed a systematic treatment of collective electronic modes in a semiconductor superlattice (SL) in the presence of strong electric and magnetic fields parallel to the SL axis. The spectrum of collective modes with zero wavevector along the SL axis is shown to consist of a principle magnetoplasmon mode and an infinite set of Bernstein-like modes. For non-zero wavevector along the SL axis, in addition to the cyclotron modes, extra collective modes are found at the frequencies |Nω _c±Mω _s|, which we call cyclotron-Stark modes (ω _c and ω _s are respectively the cyclotron and Stark frequencies, N and M are integer numbers). The frequencies of the modes propagating in “oblique” direction with respect to the SL axis show oscillatory behavior as a function of electric field strength. All the modes considered have very weak spatial dispersion and they are not Landau damped. The specific predictions made for the dispersion relations of the collective excitations should be observable in resonant Raman scattering experiments. Received 29 August 2002 / Received in final form 25 February 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: 612033@inbox.ru     

Batalin-Vilkovisky field-antifield quantisation of fluctuations around classical field configurations

The Lagrangian field-antifield formalism of Batalin and Vilkovisky (BV) is used to investigate the application of the collective coordinate method to soliton quantisation. In field theories with soliton solutions, the Gaussian fluctuation operator has zero modes due to the breakdown of global symmetries of the Lagrangian in the soliton solutions. It is shown how Noether identities and local symmetries of the Lagrangian arise when collective coordinates are introduced in order to avoid divergences related to these zero modes. This transformation to collective and fluctuation degrees of freedom is interpreted as a canonical transformation in the symplectic field-antifield space which induces a time-local gauge symmetry. Separating the corresponding Lagrangian path integral of the BV scheme in lowest order into harmonic quantum fluctuations and a free motion of the collective coordinate with the classical mass of the soliton, we show how the BV approach clarifies the relation between zero modes, collective coordinates, gauge invariance and the center-of-mass motion of classical solutions in quantum fields. Finally, we apply the procedure to the reduced nonlinear O(3) σ-model.     

Diffused vorticity approach to the oscillations of a rotating Bose-Einstein condensate confined in a harmonic plus quartic trap

The collective modes of a rotating Bose-Einstein condensate confined in an attractive quadratic plus quartic trap are investigated. Assuming the presence of a large number of vortices we apply the diffused vorticity approach to the system. We then use the sum rule technique for the calculation of collective frequencies, comparing the results with the numerical solution of the linearized hydrodynamic equations. Numerical solutions also show the existence of low-frequency multipole modes which are interpreted as vortex oscillations.     

Scheme for implementing frequency up-conversion between two collective atomic modes

This paper presents a scheme for realizing the frequency up-conversion between two collective atomic modes. In the scheme two atomic samples are coupled to a cavity mode. Under the large detuning condition, the two collective atomic modes are coupled via the virtual excitation of the cavity mode and the effective Hamiltonian corresponds to the frequency up-conversion. In the scheme the cavity mode is only virtually excited and thus the process is insensitive to cavity decay.     

Transfer matrix theory for the optical absorption spectrum of mixed crystals

We study the density of states and optical absorption spectrum of linear mixed crystals in the one- dimensional alloy transfer matrix approximation. Local modes, which are present in the single impurity limit, develop into collective modes by merging into a band as the impurity concentration increases. The composition dependence of local and collective like optical absorption peaks is discussed, and we show that qualitatively different behaviours are obtained for single band and split bands type density of states.     

On the Molecular-Kinetic Theory of the Collective Motion in Liquids

Starting from the molecular-kinetic approach the upper and lower time limits of validity of VLASOV equation, governing the “collisionless” collective motions in liquids are found. The importance of the relaxation of liquid structure in collective motions is shown. The linear response of a liquid is evaluated, and the conditions of strong and weak damping of collective modes are found.     

Multiscale structural relaxation and adiabatic shear failure mechanisms

Stages of plastic shear instability and adiabatic shear failure are associated with the initiation of collective modes of defect ensembles that have a self-similar nature of autosoliton and "blow-up" structures. Experimental and structural studies have confirmed simulation results for the stages of plastic strain localization and adiabatic shear failure based on the constitutive equations that relate structural relaxation and failure mechanisms to the formation of multiscale collective modes in defect ensembles.     

Bulk and Surface Plasmons in Artificially Structured Materials

The bulk and surface collective charge density excitations of metallic and semiconducting superlattice structures are studied. Because of the new periodicity along the axis of an infinite superlattice, these plasma modes form bands which satisfy Bloch's theorem. The dependence of the band structure on the material parameters is investigated. For finite or semi-infinite systems novel surface plasmons can occur. The coupling of the bulk and surface collective modes to external probes is reviewed.