Dynamics of wavepacket tunneling in a periodic double-well potential

Temporal evolution of wavepacket tunneling in a periodic double-well torsional potential has been studied numerically. Peculiarities of wavepacket tunneling dynamics under conditions of asymmetric distortion of the periodic potential function have been analyzed. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 3, pp. 342–346, May–June, 2008.     

一维时间周期势的量子隧穿

研究了一维时间周期势的量子隧穿,建立了周期势的两种物理模型,并分别在不同情况下对其进行理论研究和推导,证明了一维周期势下的量子隧穿可统一由一种模型处理.     

Nonlinear Landau-Zener tunneling under biharmonic driving

We address the response of a two-mode Bose-Einstein condensate to a biharmonic high-frequency driving field that directly couples the two mode. By use of a high-frequency approximation we find that asymmetric biharmonic high-frequency driving yields new effects on Nonlinear Landau-Zener tunneling as compared to a symmetric off-diagonal modulation. In particular, we detect an unclosed loop structure and the disappearance of the energy level below the loop structure.     

Atomic Landau-Zener tunneling in Fourier-synthesized optical lattices

We report on an experimental study of quantum transport of atoms in variable periodic optical potentials. The band structure of both ratchet-type asymmetric and symmetric lattice potentials is explored. The variable atom potential is realized by superimposing a conventional standing wave potential of lambda/2 spatial periodicity with a fourth-order multiphoton potential of lambda/4 periodicity. We find that the Landau-Zener tunneling rate between the first and the second excited Bloch band depends critically on the relative phase between the two spatial lattice harmonics.     

Linear mobility for coherent quantum tunneling in a periodic potential

The dynamics of a quantum particle moving in a tight binding lattice and coupled to an ohmic heat bath is investigated. Imaginary-time functional integral methods are utilized to determine the self-energy of the velocity-velocity correlation function for weak damping and arbitrary temperatures. Recent results for the linear mobility atT=0 and high temperatures are confirmed and extended to intermediate temperatures. The dominant corrections to the zero temperature mobility are given in terms of a power law.On leave from Dipartimento di Fisica, CISM, Università di Genova Italy     

Landau-Zener tunneling of Bose-Fermi mixture in double-well

The nonlinear Landau-Zener tunneling of a Bose-Fermi mixture in a double-well potential is studied in the present paper. The effect of interaction parameters on bosonic and fermionic tunneling probability is studied for the mixture of ⁴⁰K-⁸⁷Rb. The tunneling phenomena of the system can be controled by adjusting sweeping rate, intraspecies interaction, interspecies interaction and the numbers of bosons and fermions. It is noted that there are three different regions in phase diagram: self-trapping (ST), complete tunneling (CT) and incomplete tunneling (ICT).     

Enhancement of macroscopic quantum tunneling by Landau-Zener transitions

Motivated by recent realizations of qubits with a readout by macroscopic quantum tunneling in a Josephson junction, we study the problem of barrier penetration in the presence of coupling to a spin-1 / 2 system. It is shown that, when the diabatic potentials for fixed spin intersect in the barrier region, Landau-Zener transitions lead to an enhancement of the tunneling rate. The effect of these spin flips in imaginary time is in qualitative agreement with experimental observations.     

Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index

Landau-Zener tunneling is discussed in connection with optical waveguide arrays. Light injected in a specific band of the Bloch spectrum in the propagation constant can be transmitted to another band, changing its physical properties. This can be achieved using two coupled waveguide arrays with different refractive indices. The step in the refractive index causes wave "acceleration" and thus induces strongly nonadiabatic Landau-Zener tunneling. Theoretically, the analysis is performed by considering a Schr?dinger equation in a periodic potential with a step. The region of physical parameters where this phenomenon can occur is analytically determined and a realistic experimental setup is suggested. Its application could allow the realization of light filters.     

Nonlinear Landau-Zener tunneling of Bose-Einstein condensate in a spatially magnetic modulated trap

We study tunneling of a Bose-Einstein condensates confined in a effective double-well potential (a single well with a spatially magnetic modulated scattering length, actually), called pseudo double-well trap, in which the interaction of atoms characterized by the s-wave scattering length a _s can be widely tuned with a magnetic-field Feshbach resonance. As a result, corresponding to different nonlinear parameters, the energy levels of the nonlinear Schrödinger equation can have complex structures in their dependence on the bias between the wells. We discuss the emergence of looped levels, which lead to a breakdown of adiabaticity that the Landau-Zener transition probability does not vanish even in the adiabatic limit. Moreover, we also find that the Landau-Zener tunneling in the pseudo trap show many striking properties distinguished from that of the real trap model (where the barrier is created by the external potential). Possible experimental observation in an opticallyinduced photonic lattices in a photorefractive material is suggested.     

Pure states resulting from decoherence in periodic Landau-Zener transitions

In the paper researches of human's greater circulation, modeled as an electric equivalent circuit were presented. The results of investigations were obtained by applying of electric equivalent circuit and compared with data supplied by a physical, hydrodynamic model of the circulatory system, elaborated by the Biocybernetics Group at the Foundation of Cardiac Surgery Development (Zabrze, Poland).     

Landau-Zener tunneling of fermi superfluid gases in deep BEC regime

The dynamical phenomena of the Landau–Zener tunneling of the superfluid fermi gases in a double-well potential in deep BEC regime is investigated in this paper. The contribution of the higher order term representing the lowest approximation of beyond mean field corrections is considered. By using the corresponding classical Hamiltonian of the system, the fixed points and adiabatic energy levels are studied. The critical parameter for the number of fixed points evolution from two to four is obtained. For the nonlinear Landau–Zener tunneling, the tunneling probability with sweeping rate α$\alpha$ is numerically given. At the adiabatic limit, the tunneling probability is not zero in certain regime, while it goes to zero in the other regime. Exponential dependence of the transition probability on the sweeping rate α$\alpha$ in certain case is obtained.     

Resonant tunneling,eigenvalue and energy band calculation for potential and periodic potential structures

Recursion formulae for the reflection and the transmission probability amplitudes and the eigenvalue equation for multistep potential structures are derived. Using the recursion relations, a dispersion equation for periodic potential structures is presented. Some numerical results for the transmission probability of a double barrier structure with scattering centers, the lifetime of the quasi-bound state in a single quantum well with an applied field, and the miniband of a periodic potential structure are presented.     

Stochastic diffusion in a periodic potential

This paper deals with two equations for classical stochastic diffusion in a potential. First, the full Fokker-Planck equation in phase-space for a Brownian particle in a periodic potential and linearly coupled to an external field is considered. The solution discussed previously by the author and co-worker is improved upon. An alternative approximation is introduced. Then, the simpler Smoluchowski equation, which is derivable from the Fokker-Planck equation under suitable conditions, is solved using Hill's determinant method. Finally a WKB-type method is proposed to solve the Smoluchowski equation for a general class of potentials.     

Quantum friction in a periodic potential

In this paper we study the quantum friction problem using the Hamiltonian of Caldirola-Kanai for a periodic Mathieu's type potential. In the sequel we study the lattice electron with friction we introduce a new effective Hamiltonian of the Caldirola-Kanai form for a Bloch's band. Finally we study the cases of closed solutions of Schrödinger's equation.     

Landau-Zener problem for energies close to potential crossing points

We examine a previously overlooked aspect of the well-known Landau-Zener (LZ) problem, namely, the behavior in the intermediate, i.e., close to a crossing point, energy region, when all four LZ states are coupled and should be taken into account. We calculate the 4×4 connection matrix in this intermediate energy region, possessing the same block structure as the known connection matrices for the tunneling and in the over-barrier regions of the energy and continuously matching those in the corresponding energy regions. Applications of the results may concern various systems of physics, chemistry, or biology, ranging from molecular magnets and glasses to Bose condensed atomic gases.     

Spin-dependent resonant tunneling in a periodic non-magnetic heterostructure with spin-orbit effects

We theoretically investigate the electron transport in a periodic non-magnetic heterostructure with both Dresselhaus and Rashba spin-orbit effects. We show that the transport properties obviously depend on the number of periods and the large spin polarization can be achieved in such a structure. We also show that for m>1, the resonance splitting occurs in the transmission curves of both spin-up and spin-down electrons when the transmission curves are plotted as a function of the electron energy or the well width.     

Browninan motion in a fluctuating periodic potential

A classical Brownian particle is considered in a periodic potential field with a rapidly oscillating phase. The concept of effective potential is used for describing a slow averaged motion of a particle. It is shown that there exists a certain region in which a particle performs a stationary random motion without appreciable drift. By analogy with the ideal case, this region can be called an effective locking region. The situation described is valid for stationary fluctuations of the phase of a potential function, provided that they have a sufficiently small but finite correlation time. The study of the problem is reduced to the analysis of a stochastic system with external noise whose spectral density is zero at zero frequency (“green” noise [1]). The analysis of the first-and second-approximation equations of the averaging method exhibits the high stability of the locking phenomenon. This result has been verified by the numerical solution of appropriate stochastic equations. In this case, a predictor-corrector algorithm was used that allowed one to carry out a numerical simulation to a sufficiently high degree of accuracy. The result of the simulation is in good agreement with the theoretical results. The effective locking bandwidth calculated analytically by the averaging method actually coincides with the value obtained by the simulation.     

Interacting Brownian motion in a periodic potential

We study transport properties of a system composed of Brownian particles immersed in a periodic potential. Interaction among the Brownian particles is treated perturbationally in a framework of a generalized Fokker-Planck equation, which due to the interaction contains a renormalized periodic potential and an extra mean field term. We solve the kinetic equation numerically and discuss effects of the (repulsive) interaction on dynamic response functions and transport coefficients.     

On electron pairing in a periodic potential

A model Hamiltonian is proposed, based on the assumption that two electrons with the same group velocity effectively attract each other, to examine the existence of unconventional electron pairs formed by electrons in a strong periodic potential.