Canonical Transformation Approach to the Ultrafast Non-linear Optical Dynamics of Semiconductors

We develop a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals. Our approach is based on a mapping of the nonlinear optical response of the ``bare'' system onto the linear response of a ``dressed'' system. The latter is characterized by effective time-dependent optical transition matrix elements, electron/hole dispersions, and interaction potentials, which in undoped semiconductors are determined by the single-exciton and two-exciton Green functions in the absence of optical fields. This mapping is achieved by eliminating the optically-induced charge fluctuations from the Hamiltonian using a Van Vleck canonical transformation. It takes into account all many-body contributions up to a given order in the optical fields as well as important Coulomb-induced quantum dynamics to all orders in the optical field. Our approach allows us to distinguish between optical nonlinearities of different origins and provides a physically-intuitive interpretation of their manifestations in ultrafast coherent nonlinear optical spectroscopy.Comment: 24 page

Vortices on Hyperbolic Surfaces

It is shown that abelian Higgs vortices on a hyperbolic surface $M$ can be constructed geometrically from holomorphic maps $f:M \to N$, where $N$ is also a hyperbolic surface. The fields depend on $f$ and on the metrics of $M$ and $N$. The vortex centres are the ramification points, where the derivative of $f$ vanishes. The magnitude of the Higgs field measures the extent to which $f$ is locally an isometry. Witten's construction of vortices on the hyperbolic plane is rederived, and new examples of vortices on compact surfaces and on hyperbolic surfaces of revolution are obtained. The interpretation of these solutions as SO(3)-invariant, self-dual SU(2) Yang--Mills fields on $\R^4$ is also given.Comment: Revised version: new section on four-dimensional interpretation of hyperbolic vortices added

Density of States and NMR Relaxation Rate in Anisotropic Superconductivity with Intersecting Line Nodes

We show that the density of states in an anisotropic superconductor with intersecting line nodes in the gap function is proportional to $E log (\alpha \Delta_0 /E)$ for $|E| << \Delta_0$, where $\Delta_0$ is the maximum value of the gap function and $\alpha$ is constant, while it is proportional to $E$ if the line nodes do not intersect. As a result, a logarithmic correction appears in the temperature dependence of the NMR relaxation rate and the specific heat, which can be observed experimentally. By comparing with those for the heavy fermion superconductors, we can obtain information about the symmetry of the gap function.Comment: 7 pages, 4 PostScript Figures, LaTeX, to appear in J. Phys. Soc. Jp

Measurement of miniband parameters of a doped superlattice by photoluminescence in high magnetic fields

We have studied a 50/50\AA superlattice of GaAs/Al$_{0.21}$Ga$_{0.79}$As composition, modulation-doped with Si, to produce $n=1.4\times 10^{12}$ cm$^{-2}$ electrons per superlattice period. The modulation-doping was tailored to avoid the formation of Tamm states, and photoluminescence due to interband transitions from extended superlattice states was detected. By studying the effects of a quantizing magnetic field on the superlattice photoluminescence, the miniband energy width, the reduced effective mass of the electron-hole pair, and the band gap renormalization could be deduced.Comment: minor typing errors (minus sign in eq. (5)

Polar type density of states in non-unitary odd-parity superconducting states of gap with point nodes

It is shown that the density of states (DOS) proportional to the excitation energy, the so-called polar like DOS, can arise in the odd-parity states with the superconducting gap vanishing at points even if the spin-orbit interaction for Cooper pairing is strong enough. Such gap stuructures are realized in the non-unitary states, F_{1u}(1,i,0), F_{1u}(1,varepsilon,varepsilon^{2}), and F_{2u}(1,i,0), classified by Volovik and Gorkov, Sov. Phys.-JETP Vol.61 (1985) 843. This is due to the fact that the gap vanishes in quadratic manner around the point on the Fermi surface. It is also shown that the region of quadratic energy dependence of DOS, in the state F_{2u}(1,varepsilon,varepsilon^{2}), is restricted in very small energy region making it difficult to distinguish from the polar-like DOS.Comment: 5 pages, 3 figures, submitted to J. Phys.: Condens. Matter Lette

Photoemission spectra of Sr2CuO2Cl2{\rm Sr_2 Cu O_2 Cl_2}: a theoretical analysis

Recent angle resolved photoemission (ARPES) results for the insulating cuprate ${\rm Sr_2 Cu O_2 Cl_2}$ have provided the first experimental data which can be directly compared to the (theoretically) well--studied problem of a single hole propagating in an antiferromagnet. The ARPES results reported a small bandwidth, providing evidence for the existence of strong correlations in the cuprates. However, in the same experiment some discrepancies with the familiar 2D ${\rm t-J}$ model were also observed. Here we discuss a comparison between the ARPES results and the quasiparticle dispersion of both (i) the ${\rm t-t'-J}$ Hamiltonian and (ii) the three--band Hubbard model in the strong--coupling limit. Both model Hamiltonians show that the experimentally observed one--hole band structure can be approximately reproduced using reasonable values for ${\rm t'}$, or the direct oxygen hopping amplitude ${\rm t_{pp}}$.Comment: 11 pages, RevTex version 3.0, 3 postscript figures, LaTeX file and figures have been uuencoded

Kolmogorov condition near hyperbolic singularities of integrable Hamiltonian systems

In this paper we show that, if an integrable Hamiltonian system admits a nondegenerate hyperbolic singularity then it will satisfy the Kolmogorov condegeneracy condition near that singularity (under a mild additional condition, which is trivial if the singularity contains a fixed point)Comment: revised version, 11p, accepted for publication in a sepecial volume in Regular and Chaotic Dynamics in honor of Richard Cushma

Free induction signal from biexcitons and bound excitons

A theory of the free induction signal from biexcitons and bound excitons is presented. The simultaneous existence of the exciton continuum and a bound state is shown to result in a new type of time dependence of the free induction. The optically detected signal increases in time and oscillates with increasing amplitude until damped by radiative or dephasing processes. Radiative decay is anomalously fast and can result in strong picosecond pulses. The expanding area of a coherent exciton polarization (inflating antenna), produced by the exciting pulse, is the underlying physical mechanism. The developed formalism can be applied to different biexciton transients.Comment: RevTeX, 20 p. + 2 ps fig. To appear in Phys. Rev. B1

A possible cooling effect in high temperature superconductors

We show that an adiabatic increase of the supercurrent along a superconductor with lines of nodes of the order parameter on the Fermi surface can result in a cooling effect. The maximum cooling occurs if the supercurrent increases up to its critical value. The effect can also be observed in a mixed state of a bulk sample. An estimate of the energy dissipation shows that substantial cooling can be performed during a reasonable time even in the microkelvin regime.Comment: 5 pages, to appear in Phys. Rev.