Zitterbewegung of electrons in graphene in a magnetic field

Electric current and spacial displacement due to trembling motion [Zitterbewegung (ZB)] of electrons in graphene in the presence of an external magnetic field are described. Contributions of both inequivalent $K$ points in the Brillouin zone of graphene are considered. It is shown that, when the electrons are prepared in the form of wave packets, the presence of a quantizing magnetic field $B$ has very important effects on ZB. (1) For $B\neq 0$ the ZB oscillations are permanent, for B=0 they are transient. (2) For $B\neq 0$ many ZB frequencies appear, for B=0 only one frequency is at work. (3) For $B\neq 0$ both interband and intraband (cyclotron) frequencies contribute to ZB, for B=0 there are no intraband frequencies. (4) Magnetic field intensity changes not only the ZB frequencies but the entire character of ZB spectrum. An emission of electromagnetic dipole radiation by the trembling electrons is proposed and described. It is argued that graphene in a magnetic field is a promising system for an experimental observation of Zitterbewegung.Comment: 9 pages, 8 figure

Multiphoton Quantum Optics and Quantum State Engineering

We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromnagnetic field, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.Comment: 198 pages, 36 eps figure

Conformational Determinants of Phosphotyrosine Peptides Complexed with the Src SH2 Domain

The inhibition of specific SH2 domain mediated protein-protein interactions as an effective chemotherapeutic approach in the treatment of diseases remains a challenge. That different conformations of peptide-ligands are preferred by different SH2 domains is an underappreciated observation from the structural analysis of phosphotyrosine peptide binding to SH2 domains that may aid in future drug design. To explore the nature of ligand binding, we use simulated annealing (SA) to sample the conformational space of phosphotyrosine-containing peptides complexed with the Src SH2 domain. While in good agreement with the crystallographic and NMR studies of high-affinity phosphopeptide-SH2 domain complexes, the results suggest that the structural basis for phopsphopeptide- Src SH2 interactions is more complex than the “two-pronged plug two-hole socket” model. A systematic study of peptides of type pYEEX, where pY is phosphotyrosine and X is a hydrophobic residue, indicates that these peptides can assume two conformations, one extended and one helical, representing the balance between the interaction of residue X with the hydrophobic hole on the surface of the Src SH2 domain, and its contribution to the inherent tendency of the two glutamic acids to form an α-helix. In contrast, a β-turn conformation, almost identical to that observed in the crystal structure of pYVNV bound to the Grb2 SH2 domain, predominates for pYXNX peptides, even in the presence of isoleucine at the third position. While peptide binding affinities, as measured by fluorescence polarization, correlate with the relative proportion of extended peptide conformation, these results suggest a model where all three residues C-terminal to the phosphotyrosine determine the conformation of the bound phosphopeptide. The information obtained in this work can be used in the design of specific SH2 domain inhibitors