Time dependence in quantum mechanics

It is shown that the time-dependent equations (Schr?dinger and Dirac) for a quantum system can be derived from the time-independent equation for the larger object of the system interacting with its environment, in the limit that the dynamical variables of the environment can be treated semiclassically. The time which describes the quantum evolution is then provided parametrically by the classical evolution of the environment variables. The method used is a generalization of that known for a long time in the field of ion-atom collisions, where it appears as a transition from the full quantum mechanical perturbed stationary states to the impact parameter method in which the projectile ion beam is treated classically. Received 25 October 1999     

Restoring entanglement in atomic collisions: A gedanken experiment

A new type of collision experiments is discussed, where observations of two successive collisions of the same pair of particles would be possible. When such technology is available, a surprising restoring of entanglement, normally considered broken in usual collision experiments, could be observed. As an illustration the collision partners He⁺ and He⁺⁺ in a collision regime where the resonant charge transfer is dominating are considered. In the analysis it is shown that in such experiments, two spatially widely separated ion paths, corresponding in fact to two different charge states, would contribute coherently to the final amplitudes, describing which of the ions emerges as singly charged, i.e. which carries the single electron involved. The double collision experiments are not trivial, since their overall cross-sections are extremely small. Development of relevant experimental techniques will decide if the proposed phenomena remain in the field of gedanken experiments or enter the world of real experimental physics. Received 2 December 1999 and Received in final form 12 May 2000     

Entangling atoms in photonic crystals

We propose a method for entangling a system of two-level atoms in photonic crystals. The atoms are assumed to move in void regions of a photonic crystal. The interaction between the atoms is mediated either via a defect mode or via a resonant dipole-dipole interaction. We show that these interactions can produce pure entangled atomic states. We analyze the problem with parameters typical for currently existing photonic crystals and Rydberg atoms and we show that the atoms can emerge from photonic crystals in entangled states. Depending on the linear dimensions of the crystal we estimate that a pair of atoms entangled in a photonic crystal can be separated by tens of centimeters. Receive 11 June 1999 and Received in final form 4 October 1999     

特殊磁通量下Aharonov-Bohm散射的简单解法

当ｅΦ／２πｈｃ取半整数时,用抛物从标非常简单地求解了Ａｈａｒｏｎｏｖ－Ｂｏｈｍ解射问题。当ｅΦ／２πｈｃ取整数时,对文献中给出的散射解作了修正。     

Aharonov-Bohm Interferometer in a T-Shaped Quantum Dot Embedded in Majorana Bound States *

We theoretically study the spin-dependent transport properties of anAharonov-Bohm (AB) interferometer composed by a T-shaped quantum dot (QD)embedded in Majorana bound states (MBS). We use the equation of motion method tocalculate the conductance across the interferometer. We note that the conductance exhibitssensitive dependence on the MBS-QD coupling strength as well as the polarization strengthof the leads when the phase factor of AB ring changes periodically. The conductance shows a transitionfrom resonance to anti-resonance when the MBS-QD coupling strength changes from small to large. Also, there is different p-dependence conductance when the leads alignment changesfrom parallel to anti-parallel. These findings suggest that such a model could be used for a sensitivedetection of MBS interactions, exploiting the high sensitivity of conductance to the AB phase in theinterferometer.     

Feynman’s Relativistic Electrodynamics Paradox and the Aharonov-Bohm Effect

An analysis is done of a relativistic paradox posed in the Feynman Lectures of Physics involving two interacting charges. The physical system presented is compared with similar systems that also lead to relativistic paradoxes. The momentum conservation problem for these systems is presented. The relation between the presented analysis and the ongoing debates on momentum conservation in the Aharonov-Bohm problem is discussed.     

Control of tripod-scheme cold-atom wavepackets by manipulating a non-Abelian vector potential

Tripod-scheme cold atoms interacting with laser beams have attracted considerable interest for their role in synthesizing effective non-Abelian vector potentials. Such effective vector potentials can be exploited to realize an all-optical imprinting of geometric phases onto matter waves. By working on carefully designed extensions of our previous work, we show that coherent lattice structure of cold-atom sub-wavepackets can be formed and that the non-Abelian Aharonov-Bohm effect can be easily manifested via the translational motion of cold atoms. We also show that by changing the frame of reference, effects due to a non-Abelian vector potential may be connected with a simple dynamical phase effect, and that under certain conditions it can be understood as an Abelian geometric phase in a different frame of reference. Results should help design better schemes for the control of cold-atom matter waves.     

Effects of external fields on a two-dimensional Klein-Gordon particle under pseudo-harmonic oscillator interaction

We study the effects of the perpendicular magnetic and Aharonov-Bohm(AB) flux fields on the energy levels of a two-dimensional(2D) Klein-Gordon(KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator(PHO).We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter,magnetic field strength,AB flux field,and magnetic quantum number by means of the Nikiforov-Uvarov(NU) method.The non-relativistic limit,PHO,and harmonic oscillator solutions in the existence and absence of external fields are also obtained.     

The Sagnac Phase Shift Suggested by the Aharonov-Bohm Effect for Relativistic Matter Beams

The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a formal analogy with the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and Newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.     

On solutions of Coulomb system and its generalization to the Aharonov-Bohm effect

The paper numerically analyzes the Aharonov-Bohm effect of an infinitely thin magnetic flux for its influence on a two- or three-dimensional (3d) solutions of Coulomb system in momentum and coordinate spaces. For any definitive eigenstate, it is shown that the flux shifts the position of the most probable radius (MPR) of a probability distribution inward or outward in momentum or coordinate spaces, respectively. Moreover, the probability density of the shifted MPR is amplified in the momentum space, while reduced in the coordinate space. Since the Coulomb force among charged particles dominate the structure of matter, shifting of the MPR controlling by the flux effect may be beneficial to the construction of nanostructure by manipulating the atomic and molecular bonds.