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Europhysics Letters (EPL)

Quantum inelasticity in reflection of a composite particle

Takaaki Sato, Yōsuke Kayanuma

Published Nov 1, 2002• 14 citations
Publisher

Abstract

A collinear reflection of a composite particle made of two harmonically bound atoms at a hard wall is theoretically investigated. It is shown that, in quantum mechanics, the internal vibration is highly excited after collision even when the incident particle hits the wall in its ground state. This is in contrast with the analogous process in classical mechanics, in which the composite particle is reflected elastically as a whole.

DOI
10.1209/epl/i2002-00246-4

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A collinear reflection of a composite particle made of two harmonically bound atoms at a hard wall is theoretically investigated. It is shown that, in quantum mechanics, the internal vibration is highly excited after collision even when the incident particle hits the wall in its ground state. This is in contrast with the analogous process in classical mechanics, in which the composite particle is reflected elastically as a whole.
We investigate how quantum bound states bounce from a hard surface. Our analysis has applications to ab initio calculations of nuclear structure and elastic deformation, energy levels of excitons in semiconductor quantum dots and wells, and cold atomic few-body systems on optical lattices with sharp boundaries. We develop the general theory of elastic reflection for a composite body from a hard wall. On the numerical side we present ab initio calculations for the compression of alpha particles and universal results for two-body states. On the analytical side we derive a universal effective potential that gives the reflection scattering length for shallow two-body states.
Although many quantum mechanics problems of a point particle have been well understood, the realistic physical model is often a composite object consisting of particles bound together, and its quantum mechanics is an important problem with applications in many areas of physics. Unlike a point particle, a composite object possesses internal structure described by some degrees of freedom which are often entangled with each other. We call the entanglement among these degrees of freedom ``internal entanglement'', to distinguish it from any other entanglement they may share with an external object. Examples of internal entanglement include the entanglement between a vibrational and a rotational mode of a molecule, and that between its position and its internal clock-state etc. In this thesis, we study quantum mechanics of composite objects by focusing on the effects of internal entanglement. We first look at the tunnelling of a diatomic molecule type composite object through a half-silvered mirror in continuum space and observe that its spatial superposition state made by the mirror can decohere by emission of radiation due to the fact that its internal degrees of freedom are entangled with radiation fields, and that there exists entanglement between its position and its internal (i.e., relative position) degrees of freedom. Secondly, we study its lattice analog in molecular crystals, namely we replace the diatomic molecule by a biexicton, and the mirror by an impurity. We find that discreteness of a lattice makes the wave vector of a biexicton and the relative distance between two excitons of it entangled with each other. We investigate how this inseparability affects the creation of the biexciton-impurity bound states and the entanglement dynamics. Finally we propose a possible application of our study of internal entanglement to the Anderson model of a composite quasiparticle.
The impulsive collinear collision of an atom and diatomic molecule, modelled as a harmonic oscillator, is expressed in the momentum space representation of quantum mechanics. We find an interesting connection between the quantum and the classical picture (assuming the oscillator to be quantized) and a faster convergence in the quantum mechanical numerical solution. In addition, it provides an analytic approximation that is valid for systems initially in the vibrational ground state, which is analogous to the Franck-Condon overlap integrals.
Some aspects of quantum tunnelling of a composite particle are clarified by a simple model. We calculate the probability that a couple of point particles bound to each other by a square well potential with a hard core tunnel through a rectangular potential barrier. It is shown that resonance structures appear in the transmission spectrum in some cases, which reflects the existence of quasi-bound-states of the centre of mass motion around the potential barrier. It is also shown that an inelastic tunnelling occurs in which the transitions in the relative motion are induced by the tunnelling of the centre of mass.
A variety of physical phenomena have at their foundation the quantum tunneling of particles through potential barriers. Many of these phenomena can be associated with the tunneling of single inert particles. The tunneling of composite systems is more complex than for single particles due to the coupling of the tunneling coordinate with the internal degrees of freedom of the tunneling system. Reported here are the results of a study for the tunneling of a two-component projectile incident on a potential energy system which differs for the two components. A specific linkage is made to sub-Coulomb nuclear reactions.