Splitting Of Packets Research Articles

Decoherence of charge density waves in beam splitters for interacting quantum wires

Simple intersections between one-dimensional channels can act as coherent beam splitters for non-interacting electrons. Here we examine how coherent splitting at such intersections is affected by inter-particle interactions, in the special case of an intersection of topological edge states. We derive an effective impurity model which represents the edge-state intersection within Luttinger liquid theory at low energy. For Luttinger K = 1 / 2 , we compute the exact time-dependent expectation values of the charge density as well as the density-density correlation functions. In general a single incoming charge density wave packet will split into four outgoing wave packets with transmission and reflection coefficients depending on the strengths of the tunnelling processes between the wires at the junction. We find that when multiple charge density wave packets from different directions pass through the intersection at the same time, reflection and splitting of the packets depend on the relative phases of the waves. Active use of this phase-dependent splitting of wave packets may make Luttinger interferometry possible. We also find that coherent incident packets generally suffer partial decoherence from the intersection, with some of their initially coherent signal being transferred into correlated quantum noise. In an extreme case four incident coherent wave packets can be transformed entirely into density-density correlations, with the charge density itself having zero expectation value everywhere in the final state.

T^{3} Stern-Gerlach Matter-Wave Interferometer.

We present a unique matter-wave interferometer whose phase scales with the cube of the time the atom spends in the interferometer. Our scheme is based on a full-loop Stern-Gerlach interferometer incorporating four magnetic field gradient pulses to create a state-dependent force. In contrast to typical atom interferometers that make use of laser light for the splitting and recombination of the wave packets, this realization uses no light and can therefore serve as a high-precision surface probe at very close distances.

Surface Hopping Dynamics beyond Nonadiabatic Couplings for Quantum Coherence.

Description of correct electron-nuclear couplings is crucial in modeling of nonadiabatic dynamics. Within traditional semiclassical or mixed quantum-classical dynamics, the coupling between quantum electronic states and classical nuclear trajectories is governed by nonadiabatic coupling vectors coupled to classical nuclear momenta. This enables us to develop a very powerful nonadiabatic dynamics algorithm, namely, surface hopping dynamics, which can describe the splitting of nuclear wave packets and detailed balance. Despite its efficiency and practicality, it suffers from the lack of quantum decoherence due to incorrect accounts for the electron-nuclear coupling. Here we present a new surface hopping algorithm based on the exact electron-nuclear correlation from the exact factorization of molecular wave functions. This algorithm demands comparable computational costs to existing surface hopping methods. Numerical simulations with two-state models and a multidimensional multistate realistic molecule show that the electron-nuclear coupling beyond the nonadiabatic coupling terms can describe the quantum coherence properly.

Observation of small changes in the energy of a neutron in an alternating magnetic field

A method for measuring small changes in the energy of a neutron has been proposed on the basis of the anomalous behavior of the dispersion of the neutron in the crystal near Bragg “resonance.” A high sensitivity of the method allows the observation of the acceleration of the neutron in the alternating magnetic field. It has been found that the small difference between the energies of two spin states of the neutron (parallel and antiparallel to the magnetic field) leads to significant spatial splitting of wave packets and, correspondingly, to the depolarization of the neutron beam.

On the possibility of observing nonadiabatic atomic transitions in a laser field and their application to nanolithography

The scheme of an experiment has been proposed to observe nonadiabatic atomic transitions in the standingwave laser field and splitting of atomic wave packets on the nodes of the standing wave induced by these transitions in a certain range of optical detuning. The effect can be implemented in atomic-optical nanolithography for making spatial atomic structures with a period much smaller than the optical wavelength.

Zitterbewegung of wave packets and conductance of a quasi-one-dimensional channel in the presence of spin-orbit coupling

The electron energy spectrum and wave functions for a quasi-one-dimensional channel with Rashba spin-orbit coupling are calculated. The dynamics of wave packets in thin wires based on GaAs/In0.23Ga0.77As and AlGaAs/GaAs heterostructures with Rashba spin-orbit coupling are studied. Spin polarizations are found. The effect of splitting of wave packets with respect to their centers of mass and Zitterbewegung of their centers are discovered. The characteristics of wave-packet oscillations and spin density for free electrons and under confinement conditions are compared. A method for controlling the conductance of the quasi-one-dimensional channel using a controlling electrode is proposed.

Dynamics of 2D electron wave packets with different initial spin polarization in 2D structures with spin-orbit coupling

The effect of splitting and zitterbewegung of 2D-electrons wave packets in the presence of Rashba spin-orbit coupling has been investigated. It is shown that nonstandard dynamics of wave packets occurs in the systems where the complete system of eigenfunctions is formed by states with different chirality. The time evolution of wave packets depends on the initial electron spin orientation. It is established that the oscillations of packet centers decay with time. Similar effects were studied by us previously for packets with initial spin orientation perpendicular to the 2D electron gas plane.

Linear and nonlinear dynamics of matter wave packets in periodic potentials

We investigate experimentally and theoretically the nonlinear propagation of 87Rb Bose Einstein condensates in a trap with cylindrical symmetry. An additional weak periodic potential which encloses an angle with the symmetry axis of the waveguide is applied. The observed complex wave packet dynamics results from the coupling of transverse and longitudinal motion. We show that the experimental observations can be understood applying the concept of effective mass, which also allows to model numerically the three dimensional problem with a one dimensional equation. Within this framework the observed slowly spreading wave packets are a consequence of the continuous change of dispersion. The observed splitting of wave packets is very well described by the developed model and results from the nonlinear effect of transient solitonic propagation.

Coherent transport of neutral atoms in spin-dependent optical lattice potentials.

We demonstrate the controlled coherent transport and splitting of atomic wave packets in spin-dependent optical lattice potentials. Such experiments open intriguing possibilities for quantum state engineering of many body states. After first preparing localized atomic wave functions in an optical lattice through a Mott insulating phase, we place each atom in a superposition of two internal spin states. Then state selective optical potentials are used to split the wave function of a single atom and transport the corresponding wave packets in two opposite directions. Coherence between the wave packets of an atom delocalized over up to seven lattice sites is demonstrated.

Position-based multicast routing for mobile Ad-hoc networks

In this paper we present Position-Based Multicast (PBM), a multicast routing algorithm for mobile ad-hoc networks which does neither require the maintenance of a distribution structure (e.g., a tree or a mesh) nor resorts to flooding of data packets. Instead a forwarding node uses information about the positions of the destinations and its own neighbors to determine the next hops that the packet should be forwarded to and is thus very well suited for highly dynamic networks. PBM is a generalization of existing position-based unicast routing protocols such as face-2 or GPSR. The key contributions of PBM are rules for the splitting of multicast packets and a repair strategy for situations where there exists no direct neighbor that makes progress toward one or more destinations. The characteristics of PBM are evaluated in detail by means of simulation.

Measuring a Kaluza-Klein radius smaller than the Planck length

Hestenes has shown that a bispinor field on a Minkowski space-time is equivalent to an orthonormal tetrad of one-forms together with a complex scalar field. More recently, the Dirac and Einstein equations were unified in a tetrad formulation of a Kaluza-Klein model which gives precisely the usual Dirac-Einstein Lagrangian. In this model, Dirac's bispinor equation is obtained in the limit for which the radius of higher compact dimensions of the Kaluza-Klein manifold becomes vanishingly small compared with the Planck length. For a small but finite radius, the Kaluza-Klein model predicts the velocity splitting of single fermion wave packets. That is, the model predicts that a single fermion wave packet will split into two wave packets with slightly different group velocities. The observation of such wave packet splits would determine the size of the Kaluza-Klein radius. If wave packet splits were not observed in experiments with currently achievable accuracies, the Kaluza-Klein radius would be bounded by at most ${10}^{\ensuremath{-}25}$ times the Planck length.

Femtosecond Light Wave Packets

We analyze propagation of ultra short light pulses in a transparent, dispersive, nonlinear medium. A general formula for femtosecond wave packet evolution is developed and applied to specific problems. Theoretical and experimental results for wave packet distortion by lenses, wave packet rotation in birefringent media and group velocity matching in sum frequency generation are presented. Numerical results for splitting of femtosecond wave packets in dispersive Kerr media are also presented. PACS numbers: 42.65.Jx, 42.65.Re