Tunneling in polymer quantization and the Quantum Zeno Effect

As an application of the polymer quantization scheme, in this work we investigate the one-dimensional quantum mechanical tunneling phenomenon from the perspective of polymer representation of a non-relativistic point particle and derive the transmission and reflection coefficients. Since any tunneling phenomenon inevitably evokes a tunneling time, we attempt an analytical calculation of tunneling times by defining an operator well suited in discrete spatial geometry. The results that we come up with hint at appearance of the Quantum Zeno Effect in polymer framework.     

另类全反射及光学隧穿中的电磁波

讨论了在被称之为受阻全内反射的隧穿过程中发生在由光疏介质到光密介质界面上的一种全反射现象，指出隧穿过程中的隧穿能流密度是隧穿区域内的入射波和反射干涉的结果，进而给出了隧穿区域和透射区域光波的多次反射的表达式。     

Tunneling time distribution by means of Nelson’s quantum mechanics and wave-particle duality

We construct a tunneling time distribution by means of Nelson’s quantum mechanics and investigate statistical properties of the tunneling time distribution. As a result, we find that the relationship between the average and the variance of the tunneling time shows ‘wave-particle duality’.     

Tunneling of an energy eigenstate through a parabolic barrier viewed from Wigner phase space

We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients R or T are then given by the total weight of all classical phase-space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function.     

Tunneling time and stochastic-mechanical trajectories for the double-barrier potential

Quantum motion of particles tunneling a double barrier potential is considered by using stochastic mechanics. Stochastic-mechanical trajectories give us information about complex motion of tunneling particles that is not obtained within the framework of ordinary quantum mechanics. Using such information, we calculate the tunneling times within each of the barriers which depend on the distance between them. It is found that the stochastic-mechanical tunneling time shows better asymptotic behavior than the quantum-mechanical dwell time and presence time.     

Quantum ratchets and quantum heat pumps

Quantum ratchets are Brownian motors in which the quantum dynamics of particles induces qualitatively new behavior. We review a series of experiments in which asymmetric semiconductor devices of sub-micron dimensions are used to study quantum ratchets for electrons. In rocked quantum-dot ratchets electron-wave interference is used to create a non-linear voltage response, leading to a ratchet effect. The direction of the net ratchet current in this type of device can be sensitively controlled by changing one of the following experimental variables: a small external magnetic field, the amplitude of the rocking force, or the Fermi energy. We also describe a tunneling ratchet in which the current direction depends on temperature. In our discussion of the tunneling ratchet we distinguish between three contributions to the non-linear current–voltage characteristics that lead to the ratchet effect: thermal excitation over energy barriers, tunneling through barriers, and wave reflection from barriers. Finally, we discuss the operation of adiabatically rocked tunneling ratchets as heat pumps. Received: 8 February 2002 / Accepted: 11 February 2002 / Published online: 22 April 2002     

New approach to the quantum tunneling process: Characteristic times for transmission and reflection

In [1] we have demonstrated that scattering of a quantum particle on a one-dimensional potential barrier should be considered as a combined process involving two alternative elementary transmission and reflection processes. For symmetric potential barriers, we have found solutions of the Schrödinger equation which describe the transmission and reflection processes in all stages of scattering. The present work studies time aspects of both processes. The local and asymptotic group tunneling times, dwell time, and Larmor tunneling time are determined for each process. Among these time characteristics, the group tunneling times should be considered as auxiliary. As to the dwell and Larmor tunneling times, they are the best estimates (of the expected values) of times the quantum particle in stationary and localized nonstationary states dwells in the barrier region. Moreover, the Larmor time is simply the dwell time averaged over the corresponding ensemble of particles. This characteristic can be measured experimentally and hence the suggested model of scattering can be verified.     

Confronting the Hartman effect with data from frustrated total internal reflection (FTIR)

Over 40 years ago, Hartman noted that the tunneling time τ of a particle through a barrier becomes independent of width for thick barriers. Lately, the Hartman effect has been seen as a support for superluminal tunneling time. By interpreting the reflection and transmission amplitudes in terms of multiple reflection series, we show that τ is linear in barrier width for thin barriers and may be associated with actual traversal time; for thick barriers, τ saturates to the Hartman value because of the suppression of all but the first term of the series due to the smallness of the tunneling factor. For large widths, τ cannot be identified with the propagation time but may be associated with a time to penetrate to a characteristic depth into the barrier, which is independent of width. We discuss data from frustrated internal reflection experiments, which support this view.     

Velocity fluctuations of a column of water streaming down a wire: the possibility of one-dimensional turbulence

In this paper we study the influence of the magneto-coupling effect between the longitudinal motion component and the transverse Landau orbits of an electron on transmission features in single barrier structures. Within the parabolic conduction-band approach, a modified one-dimensional effective-mass Schr?dinger equation, including the magneto-coupling effect generated from the position-dependent effective mass of the electron, is strictly derived. Numerical calculations for single barrier structures show that the magneto-coupling effect brings about a series of the important changes for the transmission probability, the above-barrier quasi-bound states, and the tunneling time. Through examining the variation of the above-barrier resonant-transmission spectrum with the barrier width and observing the well-defined Lorentzian line-shape of the above-barrier resonant peaks, we convincingly show that the above-barrier resonant transmission in single barrier structures is delivered by the above-barrier quasibound states in the barrier region, just as the below-barrier resonant tunneling in double barrier structures is mediated by the below-barrier quasi-bound states in the well. Furthermore, we come to the conclusion that the magneto-coupling effect brings about not only the splitting of the above-barrier quasi-bound levels but also the striking reduction of the level-width of the quasi-bound states, correspondingly, the substantial increase of the density of the quasi-bound states. We suggest that magneto-coupling effects may be observed by the measurements of the optical absorption spectrum associated with the above-barrier quasi-bound states in the single barrier structures. Received: 26 September 1997 / Revised: 26 November 1997 / Accepted: 15 December 1997     

Transmission in pseudospin-1 and pseudospin-3/2 semimetals with linear dispersion through scalar and vector potential barriers

We investigate the tunneling of pseudospin-1 and pseudospin-3/2 quasiparticles through a barrier consisting of both electrostatic and vector potentials, existing uniformly in a finite region along the transmission axis. First, we find the tunneling coefficients, conductivities and Fano factors in the absence of the vector potential. Then we repeat the calculations by switching on the relevant magnetic fields. The features show clear distinctions, which can be used to identify the type of semimetals, although both of them exhibit linear band crossing points.     

Coupling effects of layers on spin transport in ZnSe/Zn 1 - x Mn x Se heterostructures

By use of the scattering matrix method, we investigate the coupling effects of layers on spin-polarized transport through semimagnetic semiconductor heterostructures with triple paramagnetic layers. Due to the coupling between double non-magnetic layers or among triple paramagnetic layers, spin tunneling exhibits interesting and complex features, which are determined by the structural configuration, the external fields as well as the spin orientations. It is shown that for electrons with either spin orientation tunneling through the symmetric or asymmetric heterostructures with triple paramagnetic layers, transmission resonances can approach the optimum under several biases. Moreover, for asymmetric structures, the resonant enhancement can occur under both several positive and negative biases. The spin-dependent resonant enhancement is also clearly reflected in the current density. In addition, for spin electrons traversing the multilayer heterostructure, the resonant splitting occurs in the transmission, which shows rich variations with the bias. These interesting results may be helpful to the development of spintronic devices. Received 28 April 2001     

Angular dependence of tunneling magnetoresistance in magnetic semiconductor heterostructures

Theoretical studies on spin-dependent transport in magnetic tunnel heterostructures consisting of two diluted magnetic semiconductors (DMS) separated by a nonmagnetic semiconductor (NMS) barrier, are carried in the limit of coherent regime by including the effect of angular dependence of the magnetizations in DMS. Based on parabolic valence band effective mass approximation and spontaneous magnetization of DMS electrodes, we obtain an analytical expression of angular dependence of transmission for DMS/NMS/DMS junctions. We also examine the dependence of spin polarization and tunneling magnetoresistance (TMR) on barrier thickness, temperature, applied voltage and the relative angle between the magnetizations of two DMS layers in GaMnAs/GaAs/GaMnAs heterostructures. We discuss the theoretical interpretation of this variation. Our results show that TMR of more than 65% are obtained at zero temperature, when one GaAs monolayer is used as a tunnel barrier. It is also shown that the TMR decreases rapidly with increasing barrier width and applied voltage; however at high voltages and low thicknesses, the TMR first increases and then decreases. Our calculations explain the main features of the recent experimental observations and the application of the predicted results may prove useful in designing nano spin-valve devices.     

Tunneling time in magnetic barrier structures

We adopt the group velocity approach to the issue of tunneling time in two configurations of magnetic barrier structures, which are arranged with identical or unidentical building blocks. The effects of an external electric field are also taken into account. The tunneling time in magnetic barrier structures is found to be strongly dependent on the magnetic configuration, the applied bias, the incident energy as well as the longitudinal wave vector. The results indicate that for electrons with equal energy but different incident angles, the tunneling processes are significantly separated in time within the same magnetic barrier structure. In the configuration arranged with unidentical building blocks, there exists obvious asymmetry of tunneling time in two opposite tunneling directions. Such a discrepancy of the tunneling time varies distinctly with the longitudinal wave vector and the applied bias. Received 4 March 2002 / Received in final form 22 May 2002 Published online 17 September 2002     

Coherent quantum transport in two-dimensional electron gas/superconductor double junctions with Rashba spin-orbit coupling

Based on the extended Blonder-Tinkham-Klapwijk (BTK) approach, we have investigated the coherent quantum transport in two-dimensional electron gas/superconductor (2DEG/SC) double tunneling junctions in the presence of the Rashba spin-orbit coupling (RSOC). It is found that all the reflection coefficients in BTK theory as well as conductance spectra oscillate with the external voltage and energy. The oscillation feature of conductance can be tuned largely by the RSOC for low insulating barriers, while for high insulating barriers it is almost independent of the RSOC. These phenomena are essentially different from those found in ferromagnet/superconductor double tunneling junctions.     

Tunneling-induced ultraslow solitons in triangular quantum dot molecules

We theoretically investigate the propagation of a weak probe laser pulse in a triangular quantum dot molecules scheme based on the tunneling induced transparency. We find that the ultraslow optical solitons can be realized due to the destructive quantum interference induced by the interdot tunneling coupling which can be adjusted by the gate voltage appropriately. This work may provide practical applications such as electro-optic modulated devices and other information processes in semiconductor quantum dots structure.     

Phase Time for the Tunneling of Ultracold V-Type Atoms Through a Mazer Cavity

We study the tunneling time of ultracold V-type atoms interacting a high quality microwave cavity. Here atomic coherence is introduced in the system by a strong driving field which couples the two lower states of the three-level atom. It is found that in the presence of coherence, mazer action or the scattering like nature of the interaction may be examined for extended energies of the incident cold atoms. Our results show that position and amplitudes of the peak values of the phase time(traversal time) may be very effectively controlled by the coherent driving field. Further, here we obtained superclassical values of the phase time corresponding to much higher values of the transmission amplitudes of the tunneling atoms which may be advantageous in the possible experimental realization of the superclassical tunneling time of the traversing cold atoms. In addition, we examine a mirror reflection type symmetry in the phase time curve for a judicious choice of the external driving field.     

Tunneling time in space fractional quantum mechanics

We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for $b\to \infty$ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.     

Effect of Cavity Decay on the Coherent Control of Atomic Tunneling

In this paper we study the influence of cavity decay on the atomic tunneling and entanglement dynamics in a cavity QED system. The system consists of an atom in a double-well potential and a cavity. The results show that the cavity decay affects significantly the tunneling and the entanglement dynamics. The tunneling behaves as a damping-oscillating function of time in this case, while the entanglement shared between the internal and external degree of freedom of the atom exhibits the so-called entanglement sudden death (ESD).     

Tunneling and reflection of an exciton incident upon a quantum heterostructure barrier

We investigate, in one spatial dimension, the quantum mechanical tunneling of an exciton incident upon a heterostructure barrier. We model the relative motion eigenstates of the exciton using a form of the one-dimensional hydrogen atom which avoids difficulties previously associated with 1D hydrogenic states. We obtain probabilities of reflection and transmission using the method of variable transmission and reflection amplitudes. Our calculations may be broadly divided into two sets. In the first set, we consider general qualitative aspects of exciton tunneling, such as the effect of different effective masses for electrons and holes and a relative difference in electron and hole barrier strengths. The second set models the tunneling of an exciton in a GaAs/Al(x)Ga(1-x)As heterostructure. In these calculations we find that, for energies such that the two lowest exciton states are coupled, the probability spectrum for transition from the ground state to the first excited state is identical to that for transition from the first excited state to the ground state. In addition, narrow peaks in the probability spectrum for transition are observed across this energy range for low dopant concentration x. Other interesting phenomena correlated with these peaks in the transition probability are reported.