Quantum superarrivals and information transfer through a time-varying boundary

The time-dependent Schrödinger equation is solved numerically for the case of a Gaussian wave packet incident on a time-varying potential barrier. The time evolving reflection and transmission probabilities of the wave packet are computed for several different time-dependent boundary conditions obtained by reducing or increasing the height of the potential barrier. We show that in the case when the barrier height is reduced to zero, a time interval is found during which the reflection probability is larger (superarrivals) compared to the unperturbed case. We further show that the transmission probability exhibits superarrivals when the barrier is raised from zero to a finite value of its height. Superarrivals could be understood by ascribing the features of a real physical field to the Schrödinger wave function which acts as a carrier through which a disturbance, resulting from the boundary condition being perturbed, prpagates from the barrier to the detectors measuring reflected and transmitted probabilities. The speed of propagation of this effect depends upon the rate of reducing or raising the barrier height, thus suggesting an application for secure information transfer using superarrivals.     

Dynamics of ultrashort pulse focusing

The method for studying the transformation of an ultrashort pulse of a spherical wave in the vicinity of the focus was developed. It was shown that the impulse response of the circular aperture contains two components: the transmitted one “cut” by the aperture from the incident wave and the toroidal edge one. Simple algebraic relations describing the propagation process were derived and corresponding software was developed. An example of a change in the pulse shape with Gaussian envelope is given. It was shown that pulses propagating with velocity ν > c, one of which overtakes the primary wave, are formed on the system axis.     

Transmission times of wave packets tunneling through barriers

The transmission of wave packets through barriers by tunneling is studied in detail by the method of quantum molecular dynamics. The distribution of the arrival times of a tunneling packet in front of and behind a barrier and the momentum distribution function of the packet are calculated. The average position and average momentum of the packet and their spread are investigated. It is found that below the barrier a part of the packet is reflected, and a Gaussian barrier increases the average momentum of the transmitted packet and its spread in momentum space. Zh. éksp. Teor. Fiz. 115, 1872–1889 (May 1999)     

Only above barrier energy components contribute to barrier traversal time

A time of arrival operator across a square potential barrier is constructed. The expectation value of the barrier time of arrival operator for a sufficiently localized incident wave packet is compared with the expectation value of the free particle time of arrival operator for the same wave packet. The comparison yields an expression for the expected traversal time across the barrier. It is shown that only the above barrier components of the momentum distribution of the incident wave packet contribute to the barrier traversal time, implying that below the barrier components are transmitted without delay. This is consistent with the recent experiment in attosecond ionization in helium indicating that there is no real tunneling delay time [P. Eckle et al., Science 322, 1525 (2008)].     

On the Traversal Time of Barriers

Fifty years ago Hartman studied the barrier transmission time of wave packets (J Appl Phys 33:3427–3433, 1962). He was inspired by the tunneling experiments across thin insulating layers at that time. For opaque barriers he calculated faster than light propagation and a transmission time independent of barrier length, which is called the Hartman effect. A faster than light (FTL or superluminal) wave packet velocity was deduced in analog tunneling experiments with microwaves and with infrared light thirty years later. Recently, the conjectured zero time of electron tunneling was claimed to have been observed in ionizing helium inside the barrier. The calculated and measured short tunneling time arises at the barrier front. This tunneling time was found to be universal for elastic fields as well as for electromagnetic fields. Remarkable is that the delay time is the same for the reflected and the transmitted waves in the case of symmetric barriers. Several theoretical physicists predicted this strange nature of the tunneling process. However, even with this background many members of the physics community do not accept a FTL signal velocity interpretation of the experimental tunneling results. Instead a luminal front velocity was calculated to explain the FTL experimental results frequently. However, Brillouin stated in his book on wave propagation and group velocity that the front velocity is given by the group velocity of wave packets in the case of physical signals, which have only finite frequency bandwidths. Some studies assumed barriers to be cavities and the observed tunneling time does represent the cavity lifetime. We are going to discus these continuing misleading interpretations, which are found in journals and in textbooks till today.     

Negative refraction of ultra-short electromagnetic pulses

We study pulse propagation across a boundary that separates an ordinary medium from a medium with simultaneously negative dielectric permittivity and magnetic permeability. Solving Maxwell’s equations with two spatial coordinates (one longitudinal, one transverse) and time we find negative refraction as the wave packet undergoes significant and unusual shape distortions. The pulse acquires and maintains a chirp as it traverses the interface, as expected, but with a sign that is opposite to the chirp attained upon traversal into a positive-index material. Both a direct calculation of the spatial derivative of the instantaneous, local phase of the pulse and a Fourier analysis of the signal reveal the same inescapable fact: that inside a negative-index material, a transmitted, forward-moving wave packet is indeed a superposition of purely negative wave vectors. The central findings of this paper are a confirmation that causality is not violated in the short-pulse regime, and that energy and group velocities never exceed the speed of light in vacuum.     

Hidden and unhidden information in quantum tunneling

We discuss the claim that when the peak of a tunneling wave packet appears on the far side of a barrier sooner than would be allowed by causal propagation of the incident peak, this must be interpreted to mean that the transmitted particles originate toward the leading edge of the incident peak. We examine the status of information about where in a wave packet a particle is, both in terms of Bohm's deterministic picture of quantum mechanics and in terms of a recently proposedGedankenexperiment. We find that while there are very real senses in which this interpretation makes sense, attempts to explicitly bring out this extra information in the form of quantum-mechanical observables necessarily fail. It therefore remains hidden information, which we can deduce indirectly from multiple experiments or from the principle of causality, but which we can never observe directly in a single experiment.This work was supported by the U.S. Office of Naval Research under grant N00014-90-J-1259.     

X-ray emission from aluminium under intense, ultrashort irradiation

We present studies of X-ray emission from aluminium under picosecond and femtosecond irradiation in the intensity range 10¹²-10¹⁵ W cm^-2. We use a new and simple method to measure spectrally resolved absolute X-ray yields. It is shown that the X-ray yields can be obtained for arbitrary levels of X-ray flux. We present details of the variation of the absolute yields as a function of wavelength, intensity, polarization and pulse duration of the incident laser radiation. Electron temperatures in the keV range are observed at 10¹⁵ W cm^-2 with femtosecond laser pulses. Received 12 August 1999 and Received in final form 29 November 1999     

Interference and dispersion effects on tunneling time

We study the interplay between pulse width, interference and tunneling for a wave packet incident upon a barrier and, within the context of tunneling time, we offer a complementary insight into the origin of the Hartman effect. We find that interference together with momentum spread lower (increase) the transmission (reflection) tunneling time thereby `breaking the symmetry between transmission and reflection times'. But, within the limits of our method, we are unable to confirm that negative tunneling time can be obtained.     

Salecker-Wigner-Peres clock and average tunneling times

The quantum clock of Salecker-Wigner-Peres is used, by performing a post-selection of the final state, to obtain average transmission and reflection times associated to the scattering of localized wave packets by static potentials in one dimension. The behavior of these average times is studied for a Gaussian wave packet, centered around a tunneling wave number, incident on a rectangular barrier and, in particular, on a double delta barrier potential. The regime of opaque barriers is investigated and the results show that the average transmission time does not saturate, showing no evidence of the Hartman effect (or its generalized version).     

Shocks in non-loaded bead chains with impurities

We numerically investigate the problem of the propagation of a shock in an horizontal non-loaded granular chain with a bead interaction force exponent varying from unity to large values. When is close to unity we observed a cross-over between a nonlinearity-dominated regime and a solitonic one, the latest being the final steady state of the propagating wave. In the case of large values of the deformation field given by the numerical simulations is completely different from the one obtained by analytical calculation. In the following we studied the interaction of these shock waves with a mass impurity placed in the bead chain. Two different physical pictures emerge whether we consider a light or a heavy impurity mass. The scatter of the shock wave with a light impurity yields damped oscillations of the impurity which then behave as a solitary wave source. Differently an heavy impurity is just shifted by the shock and the transmitted wave loses its solitonic character being fragmented into waves of decreasing amplitudes. Received 23 June 1999     

脉冲高斯光束的传输特性与准粒子行为

本文将高斯光束的方法用于研究脉冲高斯光束的传输特性,得出波包扩展以及准粒子行为等有趣结果     

Superluminal pulse propagation in an erbium fiber laser

It is well known that saturating gain media can give rise to superluminal pulse propagation velocity. In most mode-locked lasers the effect is unmeasurably small and has not yet been directly demonstrated. We present experiments on the initial transient of an erbium fiber laser that show a dynamic shift in the propagation velocity to a value larger than the medium’s linear group velocity as the pulse builds up. Received: 14 December 1998 / Revised version: 21 May 1999 / Published online: 25 August 1999     

Dynamical effects of a one-dimensional multibarrier potential of finite range

We discuss the properties of a large number N of one-dimensional (bounded) locally periodic potential barriers in a finite interval. We show that the transmission coefficient, the scattering cross section σ, and the resonances of σ depend sensitively upon the ratio of the total spacing to the total barrier width. We also show that a time dependent wave packet passing through the system of potential barriers rapidly spreads and deforms, a criterion suggested by Zaslavsky for chaotic behaviour. Computing the spectrum by imposing (large) periodic boundary conditions we find a Wigner type distribution. We investigate also the S-matrix poles; many resonances occur for certain values of the relative spacing between the barriers in the potential. Received 1st August 2001 and Received in final form 18 November 2001     

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     

Heat transport through a quantum dot with one-dimensional interacting leads under Coulomb blockade regime

The peculiarities of a low temperature heat transfer through a ballistic quantum dot (a double potential barrier) with interacting leads due to a long-range Coulomb interaction (in the geometrical capacitance approach) are considered. It is found that the thermal conductance K shows periodic peaks as a function of the electrostatic potential of a dot at low temperatures. At the peak maximum it is whereas near the minimum it is . Near the peak maximum the dependence K(T) is essentially nonmonotonic at the temperatures correspondent to the level spacing in the quantum dot. Received 20 October 1999 and Received in final form 20 January 2000     

Use of optical anisotropy for study of ultrafast phase transformations at solid surfaces

A new method of crystalline-order detection in highly absorbing anisotropic crystals is worked out and is demonstrated experimentally on a monocrystal Zn. The method is based on partial transformation of incident p-polarized electromagnetic wave into s-polarizedreflected wave due to optical anisotropy. The method is applicable to anisotropic metals (for example, Zn, Ti, Cd) and makes it possible to follow changes of crystalline structure in thin (10–100 nm) surface layers. It must be emphasized, that the method permits the detection of changes of the long-range order, whereas most of the conventional methods provide information on changes of the short-range order, which need not be changed on melting and amorphization for certain crystals. Using picosecond laser pump pulse (time duration ≈1 ps) and streak camera “Agat”, surface melting and evaporation of Zn are studied. By means of measurement of time dependencies of s- and p-components of a reflected probe pulse (time duration ≈500 ps) the dynamics of melting and evaporation of a surface layer was studied at various flows of energy laser pump pulse. The characteristic time of disappearance of the long-range order is <3 ps. The crystal structure is restored through 100–300 ps after action of a pump pulse. The theoretical analysis of experimental results was performed. Estimations, based on the proposed model, are in satisfactory agreement with the experimental results. Pump-probe experiments with time resolution higher than 3 ps are in progress. Received: 27 November 1998 / Accepted: 21 April 1999 / Published online: 27 October 1999     

高阶效应对超短艾里-高斯脉冲相互作用的影响

本文运用分步傅里叶变换,对满足高阶耦合非线性薛定谔方程的超短艾里脉冲与超短高斯脉冲,利用MATLAB数值模拟了在高阶效应下两脉冲相互作用后的演化过程以及时域上的强度变化。结果表明：负三阶色散效应使超短脉冲相互作用能传输更远距离;正三阶色散效应会减慢超短脉冲相互作用的传输。自陡峭效应通过孤子分裂现象的形式使超短脉冲相互作用产生时域位移,内拉曼效应可以将超短脉冲相互作用的能量由前沿处转移到后沿处。     

3D dissipative motion of atoms in a strongly coupled driven cavity

We develop quantum models for the combined external and internal motion of atoms in a strongly coupled driven cavity mode including the transverse degrees of freedom. Using a simplified Gaussian mode function we determine the parameter regimes and prospects of 3D cooling and confinement of one or two atoms in the cavity field. Analysing the field dynamics for slow atoms traversing the cavity, we show that the spectrum of the transmitted and spontaneously scattered light contains ample information on the motional dynamics of the atom and can be nicely used to investigate the cooling properties of the system. Including several atoms in the dynamics we show how motional correlations build up by the common interaction with the cavity field. This can be looked upon as collisions at far distance and can be monitored via the transmitted field dynamics. Received 5 March 1999 and Received in final form 4 May 1999     

Binary collision approximation for solitary waves in a Y-shaped granular chain

We implement a binary collision approximation to study solitary wave propagation in a two-dimensional double Y-shaped granular chain. The solitary wave was transmitted and reflected when it met the interface of the bifurcated branches of the Y-shaped granular chains. We obtain the analytic results of the ratios of the transmitted and reflected speeds to the incident speed of the solitary wave, the maximum force between the two neighbor beads in a solitary wave, and the total time taken by the pulse to pass through each branch. All of the analytic results are in good agreement with the experimental observations from Daraio et al. [Phys. Rev. E 82 036603 (2010)]. Moreover, we also discuss the delay effects on the arrival of split pulses, and predict the recombination of the split waves traveling in branches in the final stem of asymmetric systems. The prediction of pulse recombination is verified by our numerical results.