S. S. Nazin

Quantum cryptography based on quantum dots

Network protocols are formulated for the phase-coding and correlated-photon-pairs quantum cryptosystems. These protocols are free of the restriction imposed on the distance between the two legitimate users by the transmission loss in the optical fiber. A single-photon source and a source of correlated photon pairs based on quantum dots are proposed.

Teleportation of the relativistic quantum field

The process of teleportation of a completely unknown one-particle state of a free relativistic quantum field is considered. In contrast to the non-relativistic quantum mechanics, the teleportation of an unknown state of the quantum field cannot be in principle described in terms of a measurement in a tensor product of two Hilbert spaces to which the unknown state and the state of the EPR-pair belong. The reason is of the existence of a cyclic (vacuum) state common to both the unknown state and the EPR-pair. Due to the common vacuum vector and the microcausality principle (commutation relations for the field operators), the teleportation amplitude contains inevitably contributions which are irrelevant to the teleportation process. Hence in the relativistic theory the teleportation in the sense it is understood in the non-relativistic quantum mechanics proves to be impossible because of the impossibility of the realization of the appropriate measurement as a tensor product of the measurements related to the individual subsystems so that one can only speak of the amplitude of the propagation of the field as a whole.Abstract The process of teleportation of a completely unknown one-particle state of a free relativistic quantum field is considered. In contrast to the non-relativistic quantum mechanics, the teleportation of an unknown state of the quantum field cannot be in principle described in terms of a measurement in a tensor product of two Hilbert spaces to which the unknown state and the state of the EPR-pair belong. The reason is of the existence of a cyclic (vacuum) state common to both the unknown state and the EPR-pair. Due to the common vacuum vector and the microcausality principle (commutation relations for the field operators), the teleportation amplitude contains inevitably contributions which are irrelevant to the teleportation process. Hence in the relativistic theory the teleportation in the sense it is understood in the non-relativistic quantum mechanics proves to be impossible because of the impossibility of the realization of the appropriate measurement as a tensor product of the measurements related to the individual subsystems so that one can only speak of the amplitude of the propagation of the field as a whole.

Electronic structure of the superconducting compounds Tl2Ba2CuO6 and Bi2Sr2CuO6

Abstract The tight-binding method is used to investigate the electronic band structure of Tl 2 Ba 2 CuO 6 and Bi 2 Sr 2 CuO 6 crystals. Partial densities of states on various atoms as well as valences of the elements in these compounds have been determined. The calculated band structure of the considered compounds turns out to have a quasi-two-dimensional nature and strongly resembles that of La 2 CuO 4 . The major contribution to the density of states at the Fermi level was found to come from the hybridized d-orbitals of copper and p-orbitals of oxygen located in the CuO 2 planes.

Quantum cryptography based on the energy-time uncertainty relation

A new cryptosystem based on the fundamental time–energy uncertainty relation is proposed. Such a cryptosystem can be implemented with both correlated photon pairs and single photon states. Quantum cryptography is based on the following two features of quantum theory. First, the stochastic nature of the measurement results in quantum mechanics allows two distant observes to perform measurements of an appropriate physical quantity on a system prepared in some special states to get a pair of perfectly correlated random sequences of zeros and units which can be used as a key [1–9]. Second, any eavesdropper or intruder attempting to affect the key generation procedure can be detected because of the fact that generally the system wavefunction before the measurement cannot be determined from the results of that measurement [10]. Proposed in the present paper is a new cryptosystem whose security is based on the quantum mechanical time–energy uncertainty relation. The cryptosystem is based on a joint measurement of the correlated two-photon (bipho-ton) states of the radiation field, although it will be seen that a cryptosystem of that kind can also be implemented with single-photon states with different frequencies, which is very important from the point of view of its physical realization. A biphoton field is written as |Ψ = exp (−iω 0 t) g(ω)|1 ω |1 ω 0 − ω dω, (1) where |1 ω is the single-photon state with frequency ω, ω 0 is a certain fixed frequency (which is the sum of frequencies of two photons occurring in the biphoton), and g(ω) is the function defining the biphoton spectrum width. The key generation procedure employs the photodetectors with different registration bandwidth. Suppose that the two users A and B register the photons with the photode-tectors having central frequencies ω A,B and bandwidths γ A,B. Let an atom be prepared in the excited state at the moment t = 0 and the photons are detected by the users at t 0 A and t 0 B , respectively. The biphoton field correlation function for a joint measurement by the two users depends on the relative delay of reduced registration moments T = t B − t A , where t A,B = t 0 A,B − r A,B /c (r A,B is the distance between the source and the users, and c is the velocity of light in the medium) [11], and can be written in the following form: P …A new quantum cryptosystem based on the energy-time uncertainty relation is proposed. This cryptosystem can be implemented with both biphotonic states and single photons.

Theory of scanning tunneling spectroscopy: application to Si(100)2 × 1 surface

Abstract Presented is the theory of scanning tunneling microscopy (STM) based on the quasistationary states approach. The tunneling current is calculated as a sum of quasistationary states decay rates. This method naturally takes into account the atomic structure of the tip and crystal surfaces as well as their mutual influence. In the weak tip-to-crystal coupling limit our expression for the tunneling current reduces to that derived in the Bardeen-Tersoff-Hamann method. Tunneling current relief, I – V characteristics and tunneling density of states for the Si(100)2 × 1 surface have been calculated and compared with experimental results.

Theory of scanning tunneling microscopy of the antiferromagnetic Cr(001) surface with nonmagnetic W tips

Abstract We report the results of application of a simple tight-binding method to the calculation of STM images and I-V curves for the (001) surface of antiferromagnetic Cr with two types of model nonmagnetic W tip. Computed STM images exhibit strong dependences on the electronic structure of the tip end. Different tips are found to produce the surface images which differ both quantitatively (the degree of the relief modulation) and qualitatively (positive or negative images). One of the tips shows switching from positive to negative image when the sign of applied voltage is reversed.

Electronic structure of the superconducting compounds TlBa2CaCu2O7 and TlBa2Ca2Cu3O9

Abstract The electronic structure of the two simplest superconducting compounds belonging to the new homologous series TlBa 2 Ca n −1 Cu n O 2( n +1)+1 ( n =2,3) is calculated using the tight-binding method. Total and partial electronic densities of states as well as the valences of individual atoms are obtained. The two-dimensional nature of the electronic spectrum is found to become more prominent with the increase in the number of CuO 2 layers in the primitive unit cell. TlBa 2 CaCu 2 O 7 and TlBaCa 2 Cu 3 O 9 are shown to have hole pockets which disappear after replacement of bivalent Ca with trivalent Y.

Electronic properties of substitutions in the YBa2Cu3O7 anionic sublattice

Abstract The electronic energy band structure of the YBa2Cu3O6X compounds, where X = F, N, Cl, Br and I, has been calculated using a tight-binding method. Br and I atoms were found to have a considerable positive charge which is at variance with the crystal chemistry considerations, indicating that these atoms cannot replace oxygen in this crystal structure. Similar results were obtained for S, Te and P.

Screening and edge states in two-dimensional metals in a magnetic field

The length λ0 at which the lateral electric-field component E⊥ perpendicular to the boundary is conserved near the boundary of two-dimensional (2D) samples, which is covered by 2D electrons, has been determined. The existence of the finite such length follows from the self-consistent process of the screening of the external fields forming the boundaries of real 2D systems by the electrons of the metal. The effect of E⊥ on the structure of magnetic edge states has been taken into account in the mean field approximation in a wide range of the external field from the semiclassical limit (ɛF ≫ ħωc), where ɛF is the Fermi energy of the 2D system and ħωc is the cyclotron energy to the quantum Hall effect (QHE) region (ɛF ≪ ħωc). The positions of the magnetic edge state peaks against the background of their ideal distribution along the perimeter of the 2D circle in the known problem of transverse magnetic focusing have been determined in the semiclassical limit. The systematic description of the structure of the skin layer with λH ≥ λ0, consisting of the set of the so-called integer strips (overlapping or independent), which are carriers of the universal quantum conductance, has been proposed in the QHE regime. A relatively large probability of the overlapping of the fields of adjacent strips, as well as the possibility of describing coupled integer cascades, is remarkable. The existing data on the tunneling current through integer strips in the λH layer providing suitable information on the actual state of the boundary of the 2D system have been commented. A natural analogy between the properties of magnetic edge states and a well-known problem of the details of the ballistic conductance σ‖(H) of narrow electron channels in the magnetic field H has been noticed. The formalisms of both problems are identical under the conditions λH ≥ w, where 2w is the effective width of the quasi-one-dimensional channel. The existing information on the σ‖(H) dependence in a wide range of the magnetic field has been systematized. The attributes of the QHE observed in σ‖(H) convincingly indicate the reality of the formation of various modifications of integer strips in inhomogeneous 2D systems in the quantizing magnetic field.

Minimum energy of a free electron in inert gases

The properties of the minimum energy W of a low-energy free electron in an inert gas are discussed. This quantity is one of the basic characteristics of the electron in problems of the formation of various charged clusters (bubbles or compacts) in low-dimensional electronic states along interfaces. A relation between the energy W and a similar energy W0 determined in the so-called optical approximation, where the energy W0 is proportional to the gas density ng, has been obtained. Comparison makes it possible to determine the ng dependence of the scattering length a0 introduced in the “optical” description of the gaseous medium and to reveal the conditions under which a0(ng) may change sign, which behavior, by definition, is beyond the framework of the optical approximation and is observed experimentally.