Beliaev theory of spinor Bose–Einstein condensates

By generalizing the Green’s function approach developed by Beliaev [S.T. Beliaev, Sov. Phys. JETP 7 (1958) 299; S.T. Beliaev, Sov. Phys. JETP 7 (1958) 289], we study effects of quantum fluctuations on the energy spectra of spin-1 spinor Bose–Einstein condensates, in particular, of a ⁸⁷Rb condensate in the presence of an external magnetic field. We find that due to quantum fluctuations, the effective mass of magnons, which characterizes the quadratic dispersion relation of spin-wave excitations, increases compared with its mean-field value. The enhancement factor turns out to be the same for two distinct quantum phases: the ferromagnetic and polar phases, and it is a function of only the gas parameter. The lifetime of magnons in a spin-1 ⁸⁷Rb spinor condensate is shown to be much longer than that of phonons due to the difference in their dispersion relations. We propose a scheme to measure the effective mass of magnons in a spinor Bose gas by utilizing the effect of magnons’ nonlinear dispersion relation on the time evolution of the distribution of transverse magnetization. This type of measurement can be applied, for example, to precision magnetometry.     

Tunneling of a Dipolar Bose–Einstein Condensate in an Optical Lattice

We have studied the tunneling and fluctuations of a dipolar Bose–Einstein condensate in an optical lattice, it is found that there exist the tunneling and fluctuations between lattices l and l+1, l and l−1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices l and l+1, and that l and l−1, in this case the fluctuations are a constant, and the magnetic soliton appears.     

Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions

We consider an interacting homogeneous Bose gas at zero temperature in two spatial dimensions. The properties of the system can be calculated as an expansion in powers of g, where g is the coupling constant. We calculate the ground state pressure and the ground state energy density to second order in the quantum loop expansion. The renormalization group is used to sum up leading and subleading logarithms from all orders in perturbation theory. In the dilute limit, the renormalization group improved pressure and energy density are expansions in powers of the T ^2B and T ^2Bln(T ^2B), respectively, where T ^2B is the two-body T-matrix. Received 19 April 2002 Published online 13 August 2002     

The Bogoliubov model of weakly imperfect Bose gas

We present a systematic account of known rigorous results about the Bogoliubov model of weakly imperfect Bose gas (WIBG). This model is a basis of the celebrated Bogoliubov theory of superfluidity, although the physical phenomenon is, of course, more complicated than the model. The theory is based on two Bogoliubov's ansätze: the first truncates the full Hamiltonian of the interacting bosons to produce the WIBG, whereas the second substitutes some operators by c-numbers (the Bogoliubov approximation). After some historical remarks, and physical and mathematical motivations of this Bogoliubov treatment of the WIBG, we turn to revision of the Bogoliubov's ansätze from the point of view of rigorous quantum statistical mechanics. Since the exact calculation of the pressure and the behaviour of the Bose condensate in the WIBG are available, we review these results stressing the difference between them and the Bogliubov theory. One of the main features of the mathematical analysis of the WIBG is that it takes into account quantum fluctuations ignored by the second Bogoliubov ansatz. It is these fluctuations which are responsible for indirect attraction between bosons in the fundamental mode. The latter is the origin of a nonconventional Bose condensation in this mode, which has a dynamical nature. A (generalized) conventional Bose–Einstein condensation appears in the WIBG only in the second stage as a result of the standard mechanism of the total particle density saturation. It coexists with the nonconventional condensation. We give also a review of some models related to the WIBG and to the Bogoliubov theory, where a similar two-stage Bose condensation may take place. They indicate possibilities to go beyond the Bogoliubov theory and the Hamiltonian for the WIBG.     

A new perspective on the integrability of Inozemtsev’s elliptic spin chain

The aim of this paper is studying from an alternative point of view the integrability of the spin chain with long-range elliptic interactions introduced by Inozemtsev. Our analysis relies on some well-established conjectures characterizing the chaotic vs. integrable behavior of a quantum system, formulated in terms of statistical properties of its spectrum. More precisely, we study the distribution of consecutive levels of the (unfolded) spectrum, the power spectrum of the spectral fluctuations, the average degeneracy, and the equivalence to a classical vertex model. Our results are consistent with the general consensus that this model is integrable, and that it is closer in this respect to the Heisenberg chain than to its trigonometric limit (the Haldane–Shastry chain). On the other hand, we present some numerical and analytical evidence showing that the level density of Inozemtsev’s chain is asymptotically Gaussian as the number of spins tends to infinity, as is the case with the Haldane–Shastry chain. We are also able to compute analytically the mean and the standard deviation of the spectrum, showing that their asymptotic behavior coincides with that of the Haldane–Shastry chain.     

On the critical point of an interacting two-dimensional trapped Bose gas

We consider a quantized vortex excitation in a two-dimensional, harmonically trapped Bose gas and derive an equation for the Berezinskii-Kosterlitz-Thouless transition temperature based on a simple free-energy argument. We relate the critical phase-space density at the transition to the ratio between the entropy gain and the corresponding cost in energy of creating a free vortex excitation in the system.     

Sum rule for the optical absorption of an interacting many-polaron gas

A sum rule for the first frequency moment of the optical absorption of a many-polaron system is derived, taking into account many-body effects in the system of constituent charge carriers of the many-polaron system. In our expression for the sum rule, the electron-phonon coupling and the many-body effects in the electron (or hole) system formally decouple, so that the many-body effects can be treated to the desired level of approximation by the choice of the dynamical structure factor of the electron (hole) gas. We calculate correction factors to take into account both low and high experimental cutoff frequencies. Received 26 April 2000 and Received in final form 5 December 2000     

Engineering entanglement of a general three-level system interacting with a correlated two-mode nonlinear coherent state

In this article a treatment of a three-level atom interacting with two modes of light in a cavity with arbitrary forms of nonlinearities of both the fields and the intensity-dependent atom-field coupling is presented. A factorization of the initial density operator is assumed, with the privileged field modes being in a pair-coherent state. We derive and illustrate an exact expression for the time evolution of the density operator, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. We show that entanglement can be significantly influenced by different kinds of nonlinearities. The nonlinear medium yields the superstructure of atomic Rabi oscillation. We propose a generation of Bell-type states having a simple initial state preparation of the present system. Received 29 July 2002 / Received in final form 18 October 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: abdelaty@uni-flensburg.dePresent address: Institut für Mathematik, Universit?t Flensburg, Germany.     

The multiphoton ionization rate and the energy shift of atoms interacting with weak dichromatic fields with commensurate frequencies are simple functions of the phase difference

By implementing a time-independent, nonperturbative many-electron, many-photon theory (MEMPT), cycle-averaged complex eigenvalues were obtained for the He atom, whose real part gives the field-induced energy shift, Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ), and the imaginary part is the multiphoton ionization rate, Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ), where ω is the frequency, F is the field strength and ϕ is the phase difference. Through analysis and computation we show that, provided the intensities are weak, the dependence of Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) on ϕ is simple. Specifically, for odd harmonics, Γ varies linearly with cos(ϕ) whilst for even harmonics it varies linearly with cos(2ϕ). In addition, this dependence on ϕ holds for Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) as well. These relations may turn out to be applicable to other atomic systems as well, and to provide a definition of the weak field regime in the dichromatic case. When the combination of (ω ₁, F ₁) and (ω ₂, F ₂) is such that higher powers of cos(ϕ) and cos(2ϕ) become important, these rules break down and we reach the strong field regime. The herein reported results refer to Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) and Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) for He irradiated by a dichromatic ac-field consisting of the fundamental wavelength λ = 248 nm and its 2nd, 3rd and 4th higher harmonics. The intensities are in the range 1.0×10¹²-3.5×10¹⁴ W/cm², with the intensity of the harmonics being 1-2 orders of magnitude smaller. The calculations incorporated systematically electronic structure and electron correlation effects in the discrete and in the continuous spectrum, for ¹S, ¹P, ¹D, ¹F, ¹G, and ¹H two-electron states of even and odd parity. Received 9 July 2000 and Received in final form 2 November 2000     

Effects of properties of the surfactant on its aggregate behavior

The effects of the solvent-surfactant interaction, chain length and stiffness of surfactants on the formation of aggregates and the aggregation degree of surfactants in the two-dimension solution have been investigated using discontinuous molecular-dynamics simulations. When the tail-water repulsion increases or the head-water attraction decreases, the aggregation degree increases. Increasing the chain length and raising the stiffness of surfactants lead to the increment of the aggregation degree. Received 25 July 2001 and Received in final form 7 May 2002     

On the coherent inelastic processes in the interaction of hadrons and <Emphasis Type="Italic">γ</Emphasis>-quanta with nuclei at ultrarelativistic energies

The coherent inelastic processes of the type a→b, which may take place in the collisions of hadrons and γ-quanta with nuclei at very high energies (the nucleus remains the same), are theoretically investigated. The influence of matter inside the nucleus is taken into account by using the optical model based on the concept of refraction index. Analytical formulas for the effective cross-section σ _coh(a→b) are obtained, taking into account that at ultrarelativistic energies the main contribution into σ _coh(a→b) is provided by very small transferred momenta in the vicinity of the minimum longitudinal momentum transferred to the nucleus.     

Highly monochromatic fluorescence via simulation of vacuum-induced coherence

It's shown that the incoherent fluorescence spectrum from a three-level Λ atom with orthogonal atomic transition dipole moments is comprised of a single ultrasharp line by simulating the vacuum-induced coherence (VIC), and the line is on resonance with the driving field. The physical interpretation of the spectral characteristics is given in terms of dressed states.     

Polarized infrared reflectivity study of an oriented ceramic of Bi 2 Sr 2 Ca 2 Cu 3 O 10 + δ (Bi-2223)

The reflectivity spectra of an oriented ceramic of Bi-2223 has been investigated by polarized infrared reflectivity spectroscopy in the energy range 0.005-2.2 eV. It is shown that the data for the polarization parallel to the c axis cannot be fitted with a one-component Drude or extended-Drude model. The conductivity spectrum is then obtained from the best fit of a “double-damping Drude” model to reflectivity spectra, itself derived from the factorized form of the dielectric function, and by a Kramers-Kronig inversion as well. The data and their analysis give a new insight of the 2D character of the system. Received 26 April 2001 and Received in final form 28 August 2001     

From solar proton burning to pionic deuterium through the Nambu-Jona-Lasinio model of light nuclei

Within the Nuclear Nambu-Jona-Lasinio model of light nuclei (the NNJL model), describing strong low-energy nuclear interactions, we compute the width of the energy level of the ground state of pionic deuterium. The theoretical value fits well the experimental data. Using the cross-sections for the reactions _e + d p + p + e^- and _e + d p + n + _e, computed in the NNJL model, and the experimental values of the events of these reactions, detected by the SNO Collaboration, we compute the boron neutrino fluxes. The theoretical values agree well with the experimental data and the theoretical predictions within the Standard Solar Model by Bahcall. We argue the applicability of the constraints on the astrophysical factor for the solar proton burning, imposed by helioseismology, to the width of the energy level of the ground state of pionic deuterium. We show that the experimental data on the width satisfy these constraints. This testifies an indirect measurement of the recommended value of the astrophysical factor for the solar proton burning in terrestrial laboratories in terms of the width of the energy level of the ground state of pionic deuterium.     

Linear and nonlinear optical properties of hydrated and dehydrated silica micro-spheres under an electric bias

The linear refractive indices and nonlinear second-order susceptibility of hydrated and dehydrated silica micro-spheres are studied using attenuated total reflectance (ATR) and the second harmonic generation (SHG) method in direct transmission, respectively. A dramatic change of the effective dielectric constant of silica suspension under an electric bias was observed, which is attributed to particle redistribution in the fluid. Dielectric constants of dehydrated silica spheres change slightly under an electric field due to Pockels effect, for which we measure a linear electro-optical coefficient of r₃₃ ∼3.4±0.7 pm/V. The transmission second harmonic generation comes from the third-order susceptibility χ⁽³⁾, which is a coupling of two photons and the electrostatic field induced by the surface –OH charges as characterized by the Gouy-Chapman model. The SH signal from the dehydrated silica vanishes because of the loss of –OH groups on the particle surfaces. Dehydration of silica beads is irreversible. The optical properties of dried silica spheres do not recover their original hydrated state when distilled water is added.     

Charge and spin density response functions of the clean two-dimensional electron gas with Rashba spin-orbit coupling at finite momenta and frequencies

We analytically evaluate charge and spin density response functions of the clean two-dimensional electron gas with Rashba spin-orbit coupling at finite momenta and frequencies. On the basis of our exact expressions we discuss the accuracy of the long-wavelength and the quasiclassical approximations. We also derive the static limit of spin susceptibilities and demonstrate, in particular, how the Kohn-like anomalies in their derivatives are related to the spin-orbit modification of the Ruderman-Kittel-Kasuya-Yosida interaction. Taking into account screening and exchange effects of the Coulomb interaction, we describe the collective charge and spin density excitation modes which appear to be coupled due to nonvanishing spin-charge response function.     

Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state

A detailed theoretical analysis of the spatiotemporal mode of a single photon prepared via conditional measurements on a photon pair generated in the process of parametric down-conversion is presented. The maximum efficiency of coupling the photon into a transform-limited classical optical mode is calculated and ways for its optimization are determined. An experimentally feasible technique of generating the optimally matching classical mode is proposed. The theory is applied to a recent experiment on pulsed homodyne tomography of the single-photon Fock state [A.I. Lvovsky et al., Phys. Rev. Lett. 87, 050402 (2001)]. Received 16 July 2001     

First principle study of free and surface terminated CdTe nanoparticles

Density functional calculations of structural and electronic properties of stoichiometric and nonstoichiometric CdTe clusters, containing up to few tens of atoms, are carried out using projector augmented wave method. Molecular dynamics has been performed for Cd₁₂Te₁₂ and Cd₁₅Te₁₅ to predict the structure corresponding to global energy minimum. Cage type structures and bulk fragments, both in zinc blende and wurtzite structures, are used as starting geometries and conjugate gradient method is used to locate the local energy minima for other clusters. The aim of these calculations is to get the energetically favorable probable structures, to be compared with the experimentally known structures. Clusters are relaxed both in vacuum and in the presence of surface passivating ligands and the resulting structural rearrangement is analyzed. As expected, passivation increases the stability of an individual cluster, as indicated by specific properties like binding energy, vertical detachment energy, electron affinity etc. Passivation also locks the symmetry for three-dimensional structures but the small Cd_nTe_n (1 ≤ n ≤ 6) clusters, which are planar, attain higher symmetry structures on passivation. We observe `self-healing' mechanism viz., opening of optical gap on relaxation without the aid of passivating ligand, in CdTe clusters as observed in CdSe clusters [A. Puzder et al., Phys. Rev. Lett. 92, 217401 (2004)]. However, we note that 'self-healing' is a stoichiometry dependent phenomenon. Te atoms are found to achieve a total coordination of 4 on passivation, a fact useful in chemical synthesis of nanoclusters.