Non-classical properties of superposition of two coherent states having phase difference ?

Recently Ahmad et al. [Optik 2009;120;68; Optics Commun. 2007;271:162; Chin. Phys. Lett. 2006;23:2438] have studied non-classical properties of superposition of two-coherent states of the form, |ψ〉=K[|α〉+eiξ|αei?〉] for the special cases with values ? = π/2,  3π/2,  and π, and for arbitrarily fixed values of ξ. We point out that some of their results are special cases of our recently published work [Physica A 319, 305 (2003); Physica A 341, 201(2004)] on the most general superposition of two arbitrary coherent states of the form ∼(Z₁|α〉+Z₂|β〉), where X_1,2, α and β are arbitrary and only restriction on these is the normalization condition for the superposed state. To make our point we first obtain results for (i) squeezing of the most general Hermitian operator X_θ = X₁ cos θ + X₂ sin θ, with X₁ + iX₂ = a, is the annihilation operator, and (ii) sub-Poissonian photon statistics, for the superposed state |ψ〉 with a general ? and, then obtain results of Ahmad et al. for ? = π/2,  3π/2,  and π and for θ = 0 and π/2. It is interesting to note that the arbitrarily fixed values ξ = |α|² and −|α|² for ? = π/2 and 3π/2, respectively by Ahmad et al. are the values at which we get maximum squeezing working in a rigorous way.     

A measurement of e+e− → pp for (1975 ⩽ s ⩽ 2250) MeV

The $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{p}\text{p}$ cross section has been measured in the energy interval (1975 ? 2E ? 2250) MeV for |cosθ| < 0.7. The measurement is based on ～ 100 events, thus improving by a factor 3 on the previous existing statistics in this energy interval. The form factor |G|² is given as a function of energy under the assumption |G_E| = |G_M|. We also give the first measurement of the differential cross section, averaged over the energy interval, and estimate the ratio G_M|/|G_E| from it.     

Rotational coupling of the β 1 and E 0+ ion-pair states of lodine bromide

The $\text{E(}\text{Ω}\text{= 0}{}^{\mathrm{+}}\text{)}$ and $\text{β(}\text{Ω}\text{= 1)}$ ion-pair states of IBr are coupled by an electronic Coriolis interaction. A nonlinear, least-squares fit of term values for both states yields a set of potential and rotational constants purged of the effects of this interaction. The magnitude of the coupling constant, |W_1,0| = 2.41 cm^?1, is 98% of the value predicted for pure precession. Principal constants of the previously unreported β state of I⁷⁹Br are T_e = 39507.76, ω_e = 122.09, ω_eχ_e = 0.2546, B_e = 0.02937, and α_e = 8.2 × 10^?4cm^?1.     

Thermoelectric power of semiconductors in the extreme quantum limit—I: The ‘electron-diffusion’ contribution

A study is made of the effect of the quantization of the electron energy levels in a strong magnetic field on the ‘electron-diffusion’ contribution, S_e, of the transverse thermoelectric power of a high-purity isotropic semiconductor (n-type gallium arsenide GaAs) in the extreme quantum limit, when all the carriers in the conduction band are in the lowest Landau level. A theoretical expression for S_e is derived, taking into account of spin splitting. The sign of S_e is either positive or negative, depending on the sign of the conducting carriers. The transition to nondegeneracy, which takes place when the lowest Landau level is driven through the Fermi level, has a large effect on the variation of S_e with magnetic field. This effect is characterized by a large and rapid increase in |S_e|. Spin splitting effects, even with a small effective mass ($\text{m1 = 0·07 m}{}_0$, where m₀ is the free-electron mass) and a very small g-factor (g ≈ 0·32), greatly modify and reduce |S_e| a a function of field. For large fields, |S_e| increases monotonically with H. Calculations are carried out for n-type GaAs at T = 0·5°K with N = 1·2 × 10¹⁶cm^?3 carriers.     

Thermo-optical properties of uniaxial NaT(XO4)2 laser host crystals (where T = Y, La, Gd or Bi, and X = W or Mo)

Thermo-optic coefficients dn _o/dT and dn _e/dT were measured in tetragonal double tungstate and double molybdate crystals NaT(XO₄)₂ (where T = Y, La, Gd or Bi and X = W or Mo) by a laser beam deviation method in the spectral range 0.4–1.1 μm. Thermal expansion coefficients in the directions of a and c crystallographic axes were also measured. Analytical expressions for thermo-optic dispersion formulas were derived as series in 1/λ ². All dn/dT values for NaT(XO₄)₂ crystals were found to be negative. Their absolute values satisfy the relation |dn _e/dT| > |dn _o/dT| for crystals without Bi and |dn _o/dT| > |dn _e/dT| for crystals with Bi. A clear tendency for dn/dT values to decrease with the increase of the volumetric thermal expansion coefficient α _vol of the crystal was observed. This is related with dominant contribution of volumetric thermal expansion effect to the temperature dependence of the refractive index. Thermal coefficients of the optical path W = dn/dT + (n ? 1)α _T governing thermal lensing effect were calculated for different light propagation directions and polarizations as well as crystal athermal directions.     

Photoemission study of electronic structure evolution across the metal-insulator transition of heavily B-doped diamond

We studied the electronic structure evolution of heavily B-doped diamond films across the metal-insulator transition (MIT) using ultraviolet photoemission spectroscopy (UPS). From high-temperature UPS, through which electronic states near the Fermi level (E_F) up to ∼5k_BT can be observed (k_B is the Boltzmann constant and T the temperature), we observed the carrier concentration dependence of spectral shapes near E_F. Using another carrier concentration dependent UPS, we found that the change in energy position of sp-band of the diamond valence band, which corresponds to the shift of E_F, can be explained by the degenerate semiconductor model, indicating that the diamond valence band is responsible for the metallic states for samples with concentrations above MIT. We discuss a possible electronic structure evolution across MIT.     

Pattern guided structure formation in polymer films of asymmetric blends

Two off-critical blends of poly(2-vinylpyridine) and polystyrene, 2:3 and 3:2 (w:w) PVP:PS, were spin-cast (with varied domain scale R) onto periodically (λ = 4 μm) patterned substrate. The pattern consisted of two alternating symmetric stripes: Au attracting PVP and neutral self-assembled monolayer. The resulting droplet-type morphologies were recorded with Scanning Force Microscopy and examined with integral geometry approach. PVP-rich islands of the 2:3 PVP:PS films form, for a wide R/λ range, strongly anisotropic morphologies. They show up, for R/λ ∼ 0.5, a weak λ/2-substructure of smaller PVP droplets in addition to the domains periodic with λ. The 3:2 blend exhibits morphologies with dominant λ-structure of PVP ribbons, which encircle PS droplets. For R/λ ∼ 0.5, smaller PS domains are also present but no λ/2-substructure is formed. The |χ_E|-values of droplet surface density are reduced, as compared to homogeneous substrate, for the 3:2 blend (with |χ_E| → 0 for R ∼ λ). This effect is absent for the 2:3 mixture.     

Optimization of optical parametric chirped pulse amplification with different pump wavelengths

Optical parametric chirped pulse amplification with different pump wavelengths was investigated using LBO crystal, at signal central wavelength of 800 nm. According to our theoretical simulation, when pump wavelength is 492.5 nm, there is a maximal gain bandwidth of 190 nm centered at 805 nm in optimal noncollinear angle using LBO. Presently, pump wavelength of 492.5 nm can be obtained from second harmonic generation of a Yb:Sr₅(PO₄)₃F laser. The broad gain bandwidth can completely support ∼6 fs with a spectral centre of seed pulse at 800 nm. The deviation from optimal noncollinear angle can be compensated by accurately tuning crystal angle for phase matching. The gain spectrum with pump wavelength of 492.5 nm is much better than those with pump wavelengths of 400, 526.5 and 532 nm, at signal centre of 800 nm.     

Search for a parity violation induced by neutral currents in the 6S–7S transition of atomic cesium

Parity violating, time-reversal invariant, weak neutral currents can induce an electric dipole transition moment, E₁^p.v., between atomic states of same parity. We report here on the preliminary results of an experiment designed to measure E₁^p.v. in the 6S–7S transition of atomic cesium, using a polarization effect characteristic of the interference of E₁^p.v. with the electric dipole transition moment E₁^ind. induced by a d.c. electric field. At a 90% confidence level we find the upper limit: |E₁^p.v.| < 2.0 × 10^?9|e|a₀. As a consequence the coupling constant of the electron-nucleon interaction involving the product of an axial electronic neutral current by a vector nucleonic one must be less than 44 G_F.     

Very high field magnetization and AC susceptibility of native horse spleen ferritin

The magnetization of native horse spleen ferritin protein is measured in pulsed magnetic fields to 55 T at T=1.52 K. The magnetization rises smoothly with negative curvature due to uncompensated Fe³⁺ spins and with a large high field slope due to the underlying antiferromagnetic ferritin core. Even at highest fields the magnetic moment is only ∼4% of the saturation moment of the full complement of Fe³⁺ in the ferritin molecule. The AC magnetic susceptibility, χ_AC(T,f), responding to the uncompensated spins, reaches a maximum near the superparamagnetic blocking temperature with the temperature of the maximum, T_M, varying with excitation frequency, T_M⁻¹ α log f for 10?f?10⁴ Hz.     

Nonlinear optical properties and phase-relaxation processes in single-walled carbon nanotubes

We have investigated third-order nonlinear optical properties of bundled and isolated semiconducting single-walled carbon nanotubes (SWNTs) by means of Z-scan method, pump-probe method, and two-beam time-resolved degenerate four-wave mixing (DFWM) method. The figures of merit Im χ⁽³⁾/α in both bundled and isolated SWNTs samples were found to be enhanced with increasing tube diameter. The measured Im χ⁽³⁾/α value in the bundled SWNTs was an order of magnitude smaller than that in the isolated SWNTs. Both population relaxation time T₁ and phase-relaxation time T₂ for bundled samples were smaller than those in the isolated samples. These experimental results can be explained by an increase in nonradiative recombination rate and phase-relaxation rate in the bundled sample. The phase-relaxation time T₂ is considered to have a significant role in the enhancement of Im χ⁽³⁾/α.     

Broadband four-wave optical parametric amplification in bulk isotropic media in the ultraviolet

We report on four-wave optical parametric amplification of the ultrashort ultraviolet light pulses in bulk fused silica and CaF₂. Exact phase-matching in these isotropic media is achieved by means of non-collinear interaction with cylindrical beam focusing. Four-wave optical parametric amplifier efficiently operates in the UV spectral range with 1-ps laser pulses, delivering amplified signal energy exceeding 50 μJ using millijoule pump pulses in the visible (527 nm). Results of scanning of the parametric gain profile suggest that broad amplification bandwidth as wide as ∼20 nm (at FWHM) under these experimental settings is achieved, which might support amplification of sub-10-fs ultraviolet pulses with central wavelength around 330 nm. It is also shown experimentally and verified theoretically that the parametric gain profile exposes a distinct inhomogeneity and its bandwidth notably broadens due to effects of self- and cross-phase modulation imposed by the intense pump beam.     

The spectra and structure of indium iodide: The rotational and vibrational constants of the B 1 state

The rotational constants of the B 1 state of indium iodide are reported for the first time as B_e = 0.037533 cm⁻¹ and α_e = 0.000289 cm⁻¹ while T_e = 25050.60 cm⁻¹ for the B1-X0⁺ transition. Accurate vibrational constants are also computed from measured Q heads as ω_e= 146.36 cm⁻¹ and ω_eχ_e = 2.20 cm⁻¹.     

The nature of the rectilinear diameter singularity

The rigorous explanation for the term |t|^2β in the rectilinear diameter equation is given (t=(T_c−T)/T_c, β is the critical exponent for the asymptotic form of the equation of state). The optimal order parameter, for which the branches of binodal are symmetric, is constructed within the canonical formalism. It is shown that the ratio of the amplitudes for the diameter singularity of the order parameter before |t|^1−α and |t|^2β, where α determines the behavior of the heat capacity and β is the critical exponent of the order parameter, takes the universal character modulo non-universal factor which depends on the thermodynamic class of the corresponding states. The analysis of entropy for argon and water leads to β=0.33 and the corresponding amplitude ratio .     

Perturbation theory with a tridiagonal zeroth-order hamiltonian

We generalize the Rayleigh-Schrödinger perturbation formalism to the hamiltonians H=H₀+λH₁ where the correction λH₁ is small and the unperturbed operator H₀ is represented by an infinite tridiagonal matrix. This enables us to construct the solutions E=E₀+λE₁+λ²E₂+… and |ψ〉 = |ψ₀〉+λ|ψ₁〉+λ²|ψ₂〉+… in terms of the analytic continued fractions.     

Study of optical nonlinearity of functionalized multi-wall carbon nanotubes by using degenerate four wave mixing and Z-scan techniques

The phase conjugation geometry of degenerate four wave mixing (DFWM) technique has been employed to study the third-order optical nonlinear susceptibility (χ³) and second-order hyperpolarizability of multi-wall carbon nanotubes (MWCNTs). MWCNTs were grown by thermal chemical vapor deposition method and, subsequently functionalized with carboxylic acid group to improve their solubility in an organic solvent, ethylene glycol. The average hyperpolarizability for each carbon atom has been found to be 4.74 × 10⁻⁴⁶ m⁵/V² for the pump pulse of 8 ns at 532 nm. Decreasing the pulse width of the pump laser decreases the average value of hyperpolarizability. The absorption spectra show a monotonous increase from IR through visible and give an opportunity to estimate the imaginary part of the χ³ by the open aperture Z-scan technique.     

Temperature-dependent photoluminescence in La2/3Ca1/3MnO3

Visible photoluminescence and its temperature dependence of La_2/3Ca_1/3MnO₃ in the temperature range 138-293 K were measured. It was observed that the main broad band centered at ∼1.77 eV with the shoulders at ∼1.57 and ∼1.90 eV existed in the entire temperature range. It can be well fitted by three Gaussian curves B₁, B₂ and B₃ centered at ∼1.52, ∼1.75 and ∼1.92 eV, respectively. The intensities of the peak B₁ and B₂ vary as temperature increases. In the entire temperature range, the intensity of B₁ increases with increasing temperature, whereas that of B₂ decreases. The photoluminescence mechanisms for La_2/3Ca_1/3MnO₃ are presented based on the electronic structures formed by the interactions among spin, charge and lattice, in which B₁ was identified with the charge transfer excitation of an electron from the lower Jahn-Teller split e_g level of a Mn³⁺ ion to the e_g level of an adjacent Mn⁴⁺ ion, B₂ is assigned to the transition between the spin up and spin down e_g bands separated by Hund's coupling energy E_J and B₃ is attributed to the transition, determined by the crystal field energy E_C, between a t_2g core electron of Mn³⁺ to the spin up e_g bands of Mn⁴⁺ by a dipole allowed charge transfer process.     

Z-scan measurements of optical nonlinearity in acid blue 29 dye

The third order nonlinear optical properties of acid blue 29 solutions have been studied using Z-scan technique. Experiments are performed using a CW He–Ne laser at 632.8 nm wavelength and 3 mW power. The linear absorption coefficient α₀, nonlinear absorption coefficient β, nonlinear refractive index n₂, Re χ³, and Im χ³ are measured at three different concentrations. Our results show that higher concentration gives better nonlinear optical properties. Also, it was found that there is an increasing trend in the value of the nonlinear refractive index n₂ as the concentration increases.     

Averaged local field intensities in composite films

The photophysical properties of molecules adsorbed in composite films (e.g. surface island films) depend on the local electromagnetic field within the film. The ratio between the average field intensity 〈|E|²〉 in the film and the intensity |E_I|² associated with the incident field is a measure of the electromagnetic contribution to the surface influence on molecular photophysical phenomena. This ratio depends on the film composition and morphology, on the dielectric properties of the pure components making the film and on the frequency, direction and polarization of the incident radiation. Calculations of this ratio as a function of these parameters for several models of composite films are presented. Image interactions and retardation effects as well as radiative damping and finite size contributions to the dielectric response of the films are taken into account. In addition, an estimate of the field inhomogeneity within the film is obtained by calculating also the ratio 〈|E|²〉_shell/|E_I|² associated with the field in thin shells surrounding the dielectric particles which constitute the film.     

Relaxor behavior of (Ba,Sr)(Zr,Ti)O3 ferroelectric ceramics

We examine the ferroelectric-relaxor behavior of (Ba_0.65Sr_0.35)(Zr_0.35Ti_0.65)O₃ (BSZT) ceramics in the temperature range from 80 to 380 K. A broad dielectric maximum, which shifts to higher temperature with increasing frequency, signifies the relaxor-type behavior of these ceramics. The value of the relaxation parameter γ∼2 estimated from the linear fit of the modified Curie-Weiss law, indicates the relaxor nature of the BSZT ceramics. The dielectric relaxation rate follows the Vogel-Fulcher relation with T_VF=107 K, E_a=0.121 eV, and ν₀=6.83×10¹⁴ Hz, further supports such relaxor nature. The slim P-E hysteresis loop and ‘butterfly’ shape dc bias field dependence of permittivity at T>T_m (T_m, the temperature of permittivity maximum) clearly signifies the occurrence of nanopolar clusters, which is the typical characteristic of ferroelectric relaxor. At 300 K and 10 kHz, the dielectric constant and loss tan δ are ∼1100 and 0.0015, respectively. The high tunability (∼25%) and figure of merit (∼130) at room temperature show that the BSZT ceramics could be a promising candidate for tunable capacitor applications.