On Critical Velocities in Exciton Superfluidity

The presence of exciton phonon interactions is shown to play a key role in the exciton superfluidity. We apply the Landau criterion for an exciton-phonon condensate moving uniformly at zero temperature. It turns out that there are essentially two critical velocities in the theory. Within the range of these velocities the condensate can exist only as a bright soliton. The excitation spectrum and differential equations for the wave function of this condensate are derived.Comment: 7 pages, Latex; to be published in Phys.Rev.Lett (1997

Semiconductor-cavity QED in high-Q regimes: Detuning effect

The non-resonant interaction between the high-density excitons in a quantum well and a single mode cavity field is investigated. An analytical expression for the physical spectrum of the excitons is obtained. The spectral properties of the excitons, which are initially prepared in the number states or the superposed states of the two different number states by the resonant femtosecond pulse pumping experiment, are studied. Numerical study of the physical spectrum is carried out and a discussion of the detuning effect is presented.Comment: 7 pages, 8 figure

Algebraic varieties with automorphism groups of maximal rank

We confirm, to some extent, the belief that a projective variety X has the largest number (relative to the dimension of X) of independent commuting automorphisms of positive entropy only when X is birational to a complex torus or a quotient of a torus. We also include an addendum to an early paper though it is not used in the present paper.Comment: Mathematische Annalen (to appear

Nonlinear optical spectroscopy of single, few, and many molecules; nonequilibrium Green's function QED approach

Nonlinear optical signals from an assembly of N noninteracting particles consist of an incoherent and a coherent component, whose magnitudes scale \sim N and \sim N(N-1), respectively. A unified microscopic description of both types of signals is developed using a quantum electrodynamical (QED) treatment of the optical fields. Closed nonequilibrium Green's function expressions are derived that incorporate both stimulated and spontaneous processes. General (n+1)-wave mixing experiments are discussed as an example of spontaneously generated signals. When performed on a single particle, such signals cannot be expressed in terms of the nth order polarization, as predicted by the semiclassical theory. Stimulated processes are shown to be purely incoherent in nature. Within the QED framework, heterodyne-detected wave mixing signals are simply viewed as incoherent stimulated emission, whereas homodyne signals are generated by coherent spontaneous emission.Comment: article: 33 pages (preprint format!) ''paper.tex'' figures: 17 figures (.eps) in folder ``figures'

Charge-Transfer Excitations in One-Dimensional Dimerized Mott Insulators

We investigate the optical properties of one-dimensional (1D) dimerized Mott insulators using the 1D dimerized extended Hubbard model. Numerical calculations and a perturbative analysis from the decoupled-dimer limit clarify that there are three relevant classes of charge-transfer (CT) states generated by photoexcitation: interdimer CT unbound states, interdimer CT exciton states, and intradimer CT exciton states. This classification is applied to understanding the optical properties of an organic molecular material, 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA), which is known for its photoinduced transition from the dimerized spin-singlet phase to the regular paramagnetic phase. We conclude that the lowest photoexcited state of TTTA is the interdimer CT exciton state and the second lowest state is the intradimer CT exciton state.Comment: 6 pages, 6 figures, to be published in J. Phys. Soc. Jp

Decay rate and renormalized frequency shift of a quantum wire Wannier exciton in a planar microcavity

The superradiant decay rate and frequency shift of a Wannier exciton in a one-dimensional quantum wire are studied. It is shown that the dark mode exciton can be examined experimentally when the quantum wire is embedded in a planar microcavity. It is also found that the decay rate is greatly enhanced as the cavity length $L_{c}$ is equal to the multiple wavelength of the emitted photon. Similar to its decay rate counterpart, the frequency shift also shows discontinuities at resonant modes.Comment: 12 pages, 2 figures. To appear in P. R. B. September 200

Bosons in a Lattice: Exciton-Phonon Condensate in Cu2O

We explore a nonlinear field model to describe the interplay between the ability of excitons to be Bose-condensed and their interaction with other modes of a crystal. We apply our consideration to the long-living para-excitons in Cu2O. Taking into account the exciton-phonon interaction and introducing a coherent phonon part of the moving condensate, we derive the dynamic equations for the exciton-phonon condensate. These equations can support localized solutions, and we discuss the conditions for the moving inhomogeneous condensate to appear in the crystal. We calculate the condensate wave function and energy, and a collective excitation spectrum in the semiclassical approximation; the inside-excitations were found to follow the asymptotic behavior of the macroscopic wave function exactly. The stability conditions of the moving condensate are analyzed by use of Landau arguments, and Landau critical parameters appear in the theory. Finally, we apply our model to describe the recently observed interference and strong nonlinear interaction between two coherent exciton-phonon packets in Cu2O.Comment: 34 pages, LaTeX, four figures (.ps) are incorporated by epsf. Submitted to Phys. Rev.

Many-body theory of pump-probe spectra for highly excited semiconductors

We present a unified theory for pump-probe spectra in highly excited semiconductors, which is applicable throughout the whole density regime including the high-density electron-hole BCS state and the low-density excitonic Bose-Einstein condensate (BEC). The analysis is based on the BCS-like pairing theory combined with the Bethe-Salpeter (BS) equation, which first enables us to incorporate the state-filling effect, the band-gap renormalization and the strong/weak electron-hole pair correlations in a unified manner. We show that the electron-hole BCS state is distinctly stabilized by the intense pump-light, and this result strongly suggests that the macroscopic quantum state can be observed under the strong photoexcitation. The calculated spectra considerably deviate from results given by the BCS-like mean field theory and the simple BS equation without electron-hole pair correlation especially in the intermediate density states between the electron-hole BCS state and the excitonic BEC state. In particular, we find the sharp stimulated emission and absorption lines which originate from the optical transition accompanied by the collective phase fluctuation mode in the electron-hole BCS state. From the pump-probe spectral viewpoint, we show that this fluctuation mode changes to the exciton mode with decreasing carrier densityComment: RevTeX 11 pages, 10 figures. To appear in Phys.Rev.B1

A new method for detection of exciton Bose condensation using stimulated two-photon emission

Stimulated two-photon emission by Bose-condensed excitons accompanied by a coherent two-exciton recombination, i.e., by simultaneous recombination of two excitons with opposite momenta leaving unchanged the occupation numbers of excitonic states with nonzero momenta, is investigated. Raman light scattering accompanied by a similar two-exciton recombination (or generation of two excitons) is also analyzed. The processes under consideration can occur only if a system contains Bose condensate, therefore, their detection can be used as a new method to reveal Bose condensation of excitons. The recoil momentum, which corresponds to a change in the momentum of the electromagnetic field in the processes, is transferred to phonons or impurities. If the recoil momentum is transmitted to optical phonons with frequency $\omega_0^s$, the stimulated two-photon emission with the coherent two-exciton recombination leads to the appearance of a line at $2\Omega'-\omega$, where $\Omega'=\Omega-\omega_0^s$ and $\Omega$ is the light frequency corresponding to the recombination of an exciton with zero momentum. Formulas for the cross sections at finite temperatures are obtained for the processes under consideration. Our estimates indicate that a spectral line, corresponding to the stimulated two-photon emission accompanied by the coherent optical phonon-assisted two-exciton recombination can be experimentally detected in Cu$_2$O.Comment: 28 pages, 3 Postscript figure

Evaluation of local eggplant cultivars in terms of the suitability as materials for 'Yakuzen' dishes

"Yakuzen" is a form of medicinal cooking based on the theories of Oriental medicine. To prepare Yakuzen dishes, in-season materials with appropriate properties and tastes, "Sei-Mi," are selected according to the health status and constitution of each person. In this study, the suitability of eggplant (Solanum melongena L.) cultivars for Yakuzen was evaluated by sensory tests and by analysis of the functional constituents considered to be closely related to the taste and functionality of Yakuzen dishes. Twenty-two eggplant cultivars including 21 Japanese and 1 Italian cultivar, and a Thai species (Solanum xanthocarpum Schrad & Wendl.) were evaluated. Principal component analysis (PCA) was used for comprehensive evaluation among the cultivars. From the PCA, many of the cultivars with round or oval fruit were characterized as juicy and sweet and considered easy to eat; most of the long-fruit cultivars were characterized as having higher specific amino acid contents. The small and round fruit cultivar Dewako and the Thai species (Makhuea pro) were considered to contain many functional ingredients, such as ash, polyphenols, and specific amino acids, and to have higher suitability for Yakuzen dishes