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arXiv:1705.05426 · Classical and Quantum Gravity

Quantum tunneling of composite object coupled with quantized radiation field

Fumika Suzuki, Friedemann Queißer

Published Jan 24, 2019• 2 citations
arXivHTMLPDF

Abstract

Abstract We study quantum tunneling of a composite object, which has a dipole or quadrupole moment coupled with quantized (photon or gravitational) radiation field, through a potential barrier. The dipole or quadrupole moment is represented by an oscillator in the relative coordinate of two constituent particles of the object. The center of mass degrees of freedom of the object is not directly coupled with the radiation field. However, we show that, for the object with the oscillator in the excited state, dissipation caused by the radiation field can suppress its quantum tunneling rate in the center of mass degrees of freedom. In addition, when the initial energy of its center of mass motion is similar to that of the excited state of the oscillator, a spatial superposition state of the object prepared by the barrier can decohere due to the radiation field. The main purpose of this article is to investigate how two different interplays (i) among the center of mass, the relative coordinate degrees of freedom and the potential barrier, and (ii) between the relative coordinate degrees of freedom and the radiation field, can affect the quantum tunneling and the creation of the spatial superposition state of the object. Our toy model can give insight into tests of quantum tunneling and quantum superposition of atoms or molecules with its dipole or quadrupole moment coupled with the radiation field.

DOI
10.1088/1361-6382/ab019c

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arXiv:1512.03845•Physical Review A•Nov 21, 2016•5 citations
Abstract We study quantum tunneling of a composite object, which has a dipole or quadrupole moment coupled with quantized (photon or gravitational) radiation field, through a potential barrier. The dipole or quadrupole moment is represented by an oscillator in the relative coordinate of two constituent particles of the object. The center of mass degrees of freedom of the object is not directly coupled with the radiation field. However, we show that, for the object with the oscillator in the excited state, dissipation caused by the radiation field can suppress its quantum tunneling rate in the center of mass degrees of freedom. In addition, when the initial energy of its center of mass motion is similar to that of the excited state of the oscillator, a spatial superposition state of the object prepared by the barrier can decohere due to the radiation field. The main purpose of this article is to investigate how two different interplays (i) among the center of mass, the relative coordinate degrees of freedom and the potential barrier, and (ii) between the relative coordinate degrees of freedom and the radiation field, can affect the quantum tunneling and the creation of the spatial superposition state of the object. Our toy model can give insight into tests of quantum tunneling and quantum superposition of atoms or molecules with its dipole or quadrupole moment coupled with the radiation field.
We study quantum tunneling of a composite object, which has a dipole or quadrupole moment coupled with quantized (photon or gravitational) radiation field, through a {\delta} potential barrier. The dipole or quadrupole moment is represented by an oscillator in the relative coordinate of two constituent particles of the object. The center of mass degrees of freedom of the object is not directly coupled with the radiation field. However, we show that, for the object with the oscillator in the excited state, dissipation caused by the radiation field can suppress its quantum tunneling rate in the center of mass degrees of freedom. In addition, when the initial energy of its center of mass motion is similar to that of the excited state of the oscillator, a spatial superposition state of the object prepared by the barrier can decohere due to the radiation field. The main purpose of this article is to investigate how two different interplays (i) among the center of mass, the relative coordinate degrees of freedom and the potential barrier, and (ii) between the relative coordinate degrees of freedom and the radiation field, can affect the quantum tunneling and the creation of the spatial superposition state of the object. Our toy model can give insight into tests of quantum tunneling and quantum superposition of atoms or molecules with its dipole or quadrupole moment coupled with the radiation field.
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.
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.
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.
The article examines the wave and corpuscular nature of quantum objects using the example of the Mach–Zehnder interferometer and discusses the possibility of the so-called “supertunnel effect”. It is shown how the behavior of a photon in an interferometer is determined not by switching between a wave and a particle, but by the preservation or loss of coherence of its quantum amplitude. Key mechanisms are analyzed: formation of superposition at the beam splitter, interference from coherent amplitude recombination, decoherence induced by path information leakage, and recovery of interference in quantum-eraser schemes. Analogous phenomena for electrons, neutrons, atoms and large molecules are discussed, with attention to dominant decoherence sources (collisions, thermal radiation, internal degrees of freedom) and the shrinking de Broglie wavelength of massive objects. The influence of mass, momentum and barrier parameters on tunneling probability is treated, and practical strategies to enhance tunneling (barrier engineering, resonant tunneling, collective effects, and reducing effective mass) are outlined. The conclusion is that quantum laws are universal: wave-like and particle-like manifestations depend on the experimental context and coherence preservation rather than an intrinsic conversion of the object. The concept of “supertunneling” is framed as potentially realizable only if decoherence and exponential suppression can be overcome, with suggested routes for experimental pursuit.
We consider a composite system consisting of coupled particles, and investigate decoherence due to coupling of the center-of-mass degree of freedom to the internal vibrational degrees of freedom. For a composite system of bound particles, we show that in general such a decoherence effect exists, and leads to suppression of interference between different paths of the center-of-mass. For the special case of harmonically-bound particles moving in an external potential, we show that the coupling between the center-of-mass and internal degrees of freedom takes the form of parametric driving of the vibrational degrees of freedom, and that nontrivial coupling depends on the second derivative of the external potential. We find a solution to this parametric driving problem in one dimension for a fixed center-of-mass trajectory. We also propose a measure of compositeness, which quantifies the extent to which such a composite system cannot be approximated as a single, indivisible particle. We perform numerical simulations for a simple interference experiment, consisting of two wave packets scattering off of a square well, and show a close connection between suppression of interference and entanglement between the center-of-mass and internal degrees of freedom, which depends on the initial state of the internal mode. We also calculate the measure of compositeness for this system.