Beam splitter entangler for light fields

We propose an experimentally feasible scheme to generate various types of entangled states of light fields by using beam splitters and single-photon detectors. Two beams of light fields are incident on two beam splitters respectively with each beam being asymmetrically split into two parts in which one part is supposed to be so weak that it contains at most one photon. We let the two weak output modes interfere at a third beam splitter. A conditional joint measurement on both weak output modes may result in an entanglement between the other two output modes. The conditions for the maximal entanglement are discussed based on the concurrence. Several specific examples are also examined.

Topology of toroidal helical fields in non-circular cross-sectional tokamaks

The ordinary differential magnetic field line equations are solved numerically; the tokamak magnetic structure is studied on Hefei Tokamak-7 Upgrade (HT-7U) when the equilibrium field with a monotonic q-profile is perturbed by a helical magnetic field. We find that a single mode (m, n) helical perturbation can cause the formation of islands on rational surfaces with q = m/n and q = (m +/- 1, +/- 2, +/- 3,...)/n due to the toroidicity and plasma shape (i.e. elongation and triangularity), while there are many undestroyed magnetic surfaces called Kolmogorov-Arnold-Moser (KAM) barriers on irrational surfaces. The islands on the same rational surface do not have the same size. When the ratio between the perturbing magnetic field B-r(r) and the toroidal magnetic field amplitude B(phi)0 is large enough, the magnetic island chains on different rational surfaces will overlap and chaotic orbits appear in the overlapping area, and the magnetic field becomes stochastic. It is remarkable that the stochastic layer appears first in the plasma edge region.

Arithmetic of cyclotomic fields and Fermat-type equations

Let l be any odd prime, and ζ a primitive l-th root of unity. Let C_l be the l-Sylow subgroup of the ideal class group of Q(ζ). The Teichmüller character w : Z_l → Z^*_l is given by w(x) = x (mod l), where w(x) is a p-1-st root of unity, and x ∈ Z_l. Under the action of this character, C_l decomposes as a direct sum of C^((i))_l, where C^((i))_l is the eigenspace corresponding to w^i. Let the order of C^((3))_l be l^h_3). The main result of this thesis is the following: For every n ≥ max( 1, h_3 ), the equation x^(ln) + y^(ln) + z^(ln) = 0 has no integral solutions (x,y,z) with l ≠ xyz. The same result is also proven with n ≥ max(1,h_5), under the assumption that C_l^((5)) is a cyclic group of order l^h_5. Applications of the methods used to prove the above results to the second case of Fermat's last theorem and to a Fermat-like equation in four variables are given.

The proof uses a series of ideas of H.S. Vandiver ([Vl],[V2]) along with a theorem of M. Kurihara [Ku] and some consequences of the proof of lwasawa's main conjecture for cyclotomic fields by B. Mazur and A. Wiles [MW]. In [V1] Vandiver claimed that the first case of Fermat's Last Theorem held for l if l did not divide the class number h^+ of the maximal real subfield of Q(e^(2πi/i)). The crucial gap in Vandiver's attempted proof that has been known to experts is explained, and complete proofs of all the results used from his papers are given.

Ion acceleration in laser-excited plasma wake fields

The dynamics of the plasma ions in the wake fields of short, ultraintense laser pulses in underdense plasmas are investigated analytically and numerically. Owing to the large ion-to-electron mass ratio, the motion of plasma ions in-such wake fields has often been assumed to be neglectable. It is shown that when the laser intensity exceeds 10(20) W/cm(2), the ion motion can no longer be ignored. In this case, ion momentum peaks appear behind the laser pulse, which correspond with the ion density peaks. The laser-excited wake field appears to be effective for ion acceleration, in particular to ions with high-charge numbers. The dependence of ion acceleration on the laser intensity, pulse width, and background plasma density is discussed. (c) 2006 Optical Society of America.

Optimization of multi-cycle two-color laser fields for the generation of an isolated attosecond pulse

The effect of the mixing of pulsed two color fields on the generation of an isolated attosecond pulse has been systematically investigated. One main color is 800 nm and the other color (or secondary color) is varied from 1.2 to 2.4 mu m. This work shows that the continuum length behaves in a similar way to the behavior of the difference in the square of the amplitude of the strongest and next strongest cycle. As the mixing ratio is increased, the optimal wavelength for the extended continuum shifts toward shorter wavelength side. There is a certain mixing ratio of intensities at which the continuum length bifurcates, i.e., the existence of two optimal wavelengths. As the mixing ratio is further increased, each branch bifurcates again into two sub-branches. This 2D map analysis of the mixing ratio and the wavelength of the secondary field easily allows one to select a proper wavelength and the mixing ratio for a given pulse duration of the primary field. The study shows that an isolated sub-100 attosecond pulse can be generated mixing an 11 fs full-width-half-maximum (FWHM), 800 laser pulse with an 1840 nm FWHM pulse. Furthermore the result reveals that a 33 fs FWHM, 800 nm pulse can produce an isolated pulse below 200 as, when properly mixed. (c) 2008 Optical Society of America.

Ionization suppression of diatomic molecules in strong laser fields

The ionization rate of molecules in intense laser fields may be much lower than that of atoms with similar binding energy. This phenomenon is termed the ionization suppression of molecules and is caused by the molecular inner structure. In this paper, we perform a comprehensive study of the ionization suppression of homonuclear diatomic molecules in intense laser fields of linear and circular polarizations. We find that for linear polarization the total ionization rate and the ionization suppression depend greatly on the molecular alignment, and that for circular polarization the ionization suppression of molecules in the antibonding (bonding) shells disappears (appears) for laser intensities around 10(15) W/cm(2). We also find that the molecular photoelectron energy spectra are greatly changed by the interference effect, even though the total ionization rate of molecules remains almost the same as that of their companion atoms.

Sub-half-wavelength atom localization via two standing-wave fields

We propose a scheme for sub-half-wavelength atom localization in a four-level ladder-type atomic system, which is coupled by two classical standing-wave fields. We find that one of the standing-wave fields can help in enhancing the localization precision, and the other is of crucial importance in increasing the detecting probability and leading sub-half-wavelength localization.

Photoelectron angular distributions of molecules in bichromatic laser fields of circular polarization

Photoelectron angular distributions (PADs) from above-threshold ionization of O-2 and N-2 molecules irradiated by a bichromatic laser field of circular polarization are Studied. The bichromatic laser field is specially modulated such that it can be used to mimic a sequence of one-cycle laser pulses. The PADs are greatly affected by the molecular alignment, the symmetry of the initial electronic distribution, and the carrier-envelope phase of the laser pulses. Generally, the PADs do not show any symmetry, and become symmetric about an axis only when the symmetric axis of laser field coincides with the symmetric axis of molecules. This study shows that the few-cycle laser pulses call be used to steer the photoelectrons and perform the selective ionization of molecules. (C) 2008 Elsevier B.V. All rights reserved.

Guiding and confining fast electrons by transient electric and magnetic fields with a plasma inverse cone

The fast electron propagation in an inverse cone target is investigated computationally and experimentally. Two-dimensional particle-in-cell simulation shows that fast electrons with substantial numbers are generated at the outer tip of an inverse cone target irradiated by a short intense laser pulse. These electrons are guided and confined to propagate along the inverse cone wall, forming a large surface current. The propagation induces strong transient electric and magnetic fields which guide and confine the surface electron current. The experiment qualitatively verifies the guiding and confinement of the strong electron current in the wall surface. The large surface current and induced strong fields are of importance for fast ignition related researches.

Angular distributions of multiphoton detachment of H- in various infrared laser fields

Using a nonperturbative quantum scattering theory, the photoelectron angular distributions (PADs) from the multiphoton detachment of H- ions in strong, linearly polarized infrared laser fields are obtained to interpret recent experimental observations. In our theoretical treatment, the PADs in n-photon detachment are determined by the nth-order generalized phased Bessel (GPB) functions X-n(Z(f),eta). The advantage of using the GPB scenario to calculate PADs is its simplicity: a single special function (GPB) without any mixing coefficient can express PADs observed by recent experiments. Thus, the GPB scenario can be called a parameterless scenario.

Photoelectron angular distributions from above threshold ionization of hydrogen atoms in strong laser fields

We apply a scattering theory of nonperturbative quantum electrodynamics to study the photoelectron angular distributions (PADs) of a hydrogen atom irradiated by linearly polarized laser light. The calculated PADs show main lobes and jetlike structure. Previous experimental studies reveal that in a set of above-threshold-ionization peaks when the absorbed-photon number increases by one, the jet number also increases by one. Our study confirms this experimental observation. Our calculations further predict that in some cases three more jets may appear with just one-more-photon absorption. With consideration of laser-frequency change, one less jet may also appear with one-more-photon absorption. The jetlike structure of PADs is due to the maxima of generalized phased Bessel functions, not an indication of the quantum number of photoelectron angular momentum states.

Chemical-scale studies of G protein-coupled receptors and ligand-gated ion channels

This dissertation describes studies of G protein-coupled receptors (GPCRs) and ligand-gated ion channels (LGICs) using unnatural amino acid mutagenesis to gain high precision insights into the function of these important membrane proteins.

Chapter 2 considers the functional role of highly conserved proline residues within the transmembrane helices of the D2 dopamine GPCR. Through mutagenesis employing unnatural α-hydroxy acids, proline analogs, and N-methyl amino acids, we find that lack of backbone hydrogen bond donor ability is important to proline function. At one proline site we additionally find that a substituent on the proline backbone N is important to receptor function.

In Chapter 3, side chain conformation is probed by mutagenesis of GPCRs and the muscle-type nAChR. Specific side chain rearrangements of highly conserved residues have been proposed to accompany activation of these receptors. These rearrangements were probed using conformationally-biased β-substituted analogs of Trp and Phe and unnatural stereoisomers of Thr and Ile. We also modeled the conformational bias of the unnatural Trp and Phe analogs employed.

Chapters 4 and 5 examine details of ligand binding to nAChRs. Chapter 4 describes a study investigating the importance of hydrogen bonds between ligands and the complementary face of muscle-type and α4β4 nAChRs. A hydrogen bond involving the agonist appears to be important for ligand binding in the muscle-type receptor but not the α4β4 receptor.

Chapter 5 describes a study characterizing the binding of varenicline, an actively prescribed smoking cessation therapeutic, to the α7 nAChR. Additionally, binding interactions to the complementary face of the α7 binding site were examined for a small panel of agonists. We identified side chains important for binding large agonists such as varenicline, but dispensable for binding the small agonist ACh.

Chapter 6 describes efforts to image nAChRs site-specifically modified with a fluorophore by unnatural amino acid mutagenesis. While progress was hampered by high levels of fluorescent background, improvements to sample preparation and alternative strategies for fluorophore incorporation are described.

Chapter 7 describes efforts toward a fluorescence assay for G protein association with a GPCR, with the ultimate goal of probing key protein-protein interactions along the G protein/receptor interface. A wide range of fluorescent protein fusions were generated, expressed in Xenopus oocytes, and evaluated for their ability to associate with each other.

Structurally engineered cytochromes c with novel ligand-binding properties

Semisynthesis of horse heart cytochrome c and site-directed mutagenesis of Saccharomyces cerevisiae (S. c.) iso-1-cytochrome c have been utilized to substitute Ala for the cytochrome c heme axial ligand Met80 to yield ligand-binding proteins (horse heart Ala80cyt c and S.c. Ala80cyt c) with spectroscopic properties remarkably similar to those of myoglobin. Both species of Fe(II)Ala80cyt c form exceptionally stable dioxygen complexes with autoxidation rates 10-30x smaller and O₂ binding constants ~ 3x greater than those of myoglobin. The resistance of O₂-Fe(II)Ala80cyt c to autoxidation is attributed in part to protection of the heme site from solvent as exhibited by the exceptionally slow rate of CO binding to the heme as well as the low quantum yield of CO photodissociation.

UV/vis, EPR, and paramagnetic NMR spectroscopy indicate that at pH 7 the Fe(III)Ala80cyt c heme is low-spin with axial His-OH^- coordination and that below pH ~6.5, Fe(III)Ala80cyt cis high-spin with His-H₂O heme ligation. Significant differences in the pH dependence of the ¹H NMR spectra of S.c. Fe(III)Ala80cyt c compared to wild-type demonstrate that the axial ligands influence the conformational energetics of cytochrome c.

¹H NMR spectroscopy has been utilized to determine the solution structure of the cyanide derivative of S.c. Fe(III)Ala80cyt c. 82% of the resonances in the ¹H NMR spectrum of S.c. CN-Fe(III)Ala80cyt c have been assigned through 1D and 2D experiments. The RMSD values after restrained energy minimization of the family of 17 structures obtained from distance geometry calculations are 0.68 ± 0.11 Å for the backbone and 1.32 ± 0.14 Å for all heavy atoms. The solution structure indicates that a tyrosine in the "distal" pocket of CN-Fe(III)Ala80cyt c forms a hydrogen bond with the Fe(III)-CN unit, suggesting that it may play a role analogous to that of the distal histidine in myoglobin in stabilizing the dioxygen adduct.