In this work we study the effects of collapse and revival, as well as the zitterbewegung (ZB) phenomenon, for the relativistic electron wave packets, which are a superposition of the states with quantum numbers sharply peaked around some Landau level ${n}_{0}$ of the order of few tens. The probability densities as well as average velocities of the packet center and the average spin components were calculated analytically and their evolution is visualized. Our computations demonstrate that due to the dephasing of the states for times larger than the cyclotron period the initial wave packet (which includes the states with the positive energy only) loses the spatial localization so that the evolution can no longer be described classically. However, at the half-revival time $t={T}_{R}/2$ its reshaping takes place first. It is shown that the behavior of the wave packet containing the states of both energy bands (with ${E}_{n}>0$ and ${E}_{n}<0$ ) is more complicated. At short times of a few classical periods such a packet splits into two parts, which rotate with cyclotron frequency in the opposite directions and meet each other every one-half of the cyclotron period. At these moments their wave functions have a significant overlap that leads to ZB, and at the time of fractional revival each of two subpackets is decomposed into few packet fractions. However, at $t={T}_{R}$ each of the two subpackets (with positive or negative energy) restores at various points of the cyclotron orbit, which makes reshaping of the initial wave packet impossible, entirely unlike the wave packet which consists of states with energies ${E}_{n}>0$ only. The obtained results can be useful for the description of electromagnetic radiation and absorption in relativistic plasma on astrophysics objects, where superhigh magnetic field has a value of the order ${10}^{8}--{10}^{9}$ T, as well as for interpretation of experiments with trapped ions.In this work we study the effects of collapse and revival, as well as the zitterbewegung (ZB) phenomenon, for the relativistic electron wave packets, which are a superposition of the states with quantum numbers sharply peaked around some Landau level ${n}_{0}$ of the order of few tens. The probability densities as well as average velocities of the packet center and the average spin components were calculated analytically and their evolution is visualized. Our computations demonstrate that due to the dephasing of the states for times larger than the cyclotron period the initial wave packet (which includes the states with the positive energy only) loses the spatial localization so that the evolution can no longer be described classically. However, at the half-revival time $t={T}_{R}/2$ its reshaping takes place first. It is shown that the behavior of the wave packet containing the states of both energy bands (with ${E}_{n}>0$ and ${E}_{n}<0$) is more complicated. At short times of a few classical periods such a packet splits into two parts, which rotate with cyclotron frequency in the opposite directions and meet each other every one-half of the cyclotron period. At these moments their wave functions have a significant overlap that leads to ZB, and at the time of fractional revival each of two subpackets is decomposed into few packet fractions. However, at $t={T}_{R}$ each of the two subpackets (with positive or negative energy) restores at various points of the cyclotron orbit, which makes reshaping of the initial wave packet impossible, entirely unlike the wave packet which consists of states with energies ${E}_{n}>0$ only. The obtained results can be useful for the description of electromagnetic radiation and absorption in relativistic plasma on astrophysics objects, where superhigh magnetic field has a value of the order ${10}^{8}--{10}^{9}$T, as well as for interpretation of experiments with trapped ions.

arXiv:1107.3983Physical Review AFeb 3, 201212 citations

Superluminal traversal time and interference between multiple finite wave packets

Xi Chen, Chun-Fang Li

The mechanism of superluminal traversal time is investigated from the viewpoint of interference between multiple finite wave packets, due to the multiple reflections inside the well or barrier. In the case of potential well traveling that is classically allowed, each of the successively transmitted constituents is delayed by a subluminal time. When the thickness of the well is much smaller in comparison with a characteristic length of the incident wave packet, the reshaped wave packet with superluminal traversal time in transmission maintains the pro. le of the incident wave packet. In the case of potential barrier tunneling that is classically forbidden, though each of the successively transmitted constituents is delayed by a time that is independent of the barrier thickness, the interference between multiple transmitted constituents explains the barrier thickness dependence of the traversal time for thin barriers and its barrier thickness independence for thick barriers. This manifests the nature of the Hartman effect. Copyright (c) EPLA, 2008.The mechanism of superluminal traversal time is investigated from the viewpoint of interference between multiple finite wave packets, due to the multiple reflections inside the well or barrier. In the case of potential well traveling that is classically allowed, each of the successively transmitted constituents is delayed by a subluminal time. When the thickness of the well is much smaller in comparison with a characteristic length of the incident wave packet, the reshaped wave packet with superluminal traversal time in transmission maintains the pro. le of the incident wave packet. In the case of potential barrier tunneling that is classically forbidden, though each of the successively transmitted constituents is delayed by a time that is independent of the barrier thickness, the interference between multiple transmitted constituents explains the barrier thickness dependence of the traversal time for thin barriers and its barrier thickness independence for thick barriers. This manifests the nature of the Hartman effect. Copyright (c) EPLA, 2008.

arXiv:quant-ph/0611154Europhysics Letters (EPL)Apr 21, 200813 citations

Propagation of wave packets through resonant quantum systems

N. A. Ivanov, V. V. Skalozub

Theoretical and Mathematical PhysicsAug 1, 20114 citations

Program for quantum wave-packet dynamics with time-dependent potentials

Claude M. Dion, A. Hashemloo, G. Rahali

arXiv:1306.3247Computer Physics CommunicationsSep 29, 201335 citations

Quantum random walks and wave-packet reshaping at the single-photon level

P. H. Souto Ribeiro, Stephen Patrick Walborn, Cesar Raitz +2 more

We realize an experimental implementation of one step of a quantum random walk at the single-photon level. After a single step, it is already possible to observe the difference between the quantum and classical random walk. The single photon is obtained using twin photons from parametric down-conversion, in which the detection of one photon of the idler prepares a single-photon state of the signal. We used two different experimental setups, one based on an interferometer and a second using a birefringent crystal. The physical process behind these effects is the spatial reshaping of the single-photon wave packet, which is the spatial analog of the time reshaping observed in tunneling experiments.We realize an experimental implementation of one step of a quantum random walk at the single-photon level. After a single step, it is already possible to observe the difference between the quantum and classical random walk. The single photon is obtained using twin photons from parametric down-conversion, in which the detection of one photon of the idler prepares a single-photon state of the signal. We used two different experimental setups, one based on an interferometer and a second using a birefringent crystal. The physical process behind these effects is the spatial reshaping of the single-photon wave packet, which is the spatial analog of the time reshaping observed in tunneling experiments.

Physical Review AJul 15, 200821 citations

{n}_{0}

of the order of few tens. The probability densities as well as average velocities of the packet center and the average spin components were calculated analytically and their evolution is visualized. Our computations demonstrate that due to the dephasing of the states for times larger than the cyclotron period the initial wave packet (which includes the states with the positive energy only) loses the spatial localization so that the evolution can no longer be described classically. However, at the half-revival time

t={T}_{R}/2

its reshaping takes place first. It is shown that the behavior of the wave packet containing the states of both energy bands (with

{E}_{n}>0

and

{E}_{n}<0

) is more complicated. At short times of a few classical periods such a packet splits into two parts, which rotate with cyclotron frequency in the opposite directions and meet each other every one-half of the cyclotron period. At these moments their wave functions have a significant overlap that leads to ZB, and at the time of fractional revival each of two subpackets is decomposed into few packet fractions. However, at

t={T}_{R}

each of the two subpackets (with positive or negative energy) restores at various points of the cyclotron orbit, which makes reshaping of the initial wave packet impossible, entirely unlike the wave packet which consists of states with energies

{E}_{n}>0

only. The obtained results can be useful for the description of electromagnetic radiation and absorption in relativistic plasma on astrophysics objects, where superhigh magnetic field has a value of the order

{10}^{8}--{10}^{9}

T, as well as for interpretation of experiments with trapped ions.