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Chemical Physics

Quantum mechanical effects for a hydrogen atom confined in a dielectric spherical microcavity

Dehua Wang, Jie Zhang, Zhaopeng Sun, Zhang Shu-Fang, Gang Zhao

Published Aug 20, 2021• 6 citations
Publisher
DOI
10.1016/j.chemphys.2021.111331

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We calculate the energy and Shannon entropy for a hydrogen atom confined in a dielectric spherical microcavity for the fist time. In contrast to the hydrogen atom in the vacuum microcavity, some unexpected and interesting phenomena appear: First, the turning radius for the bound energy changes from positive to negative depends on the dielectric constant of the spherical microcavity sensitively. With the increase of the relative dielectric constant, the turning radius gets larger. Second, the dielectric spherical microcavity impacts the rearrangement of the excited state energy, and breaks the energy degeneracy of the excited states. At some given radius, there is energy crossover between different orbital. Third, the dielectric in the spherical microcavity affects the Shannon entropy for the confined hydrogen atom greatly. The Shannon entropy in the vacuum microcavity is the smallest and the Shannon entropy increases with the relative dielectric constant. For smaller size spherical microcavity, the Shannon entropy change is always negative, which suggests that the electron density is localized. With the increase of the radius of the microcavity, the Shannon entropy change becomes positive, and the confinement of the electron density gets delocalized. Our results show that we can control the confining effect of the spherical microcavity on the atom by changing the dielectric. This work can guide the future experimental studies for trapping and manipulating of atoms and molecules in the external environment and has some practical applications in metrology and quantum information processing.
The research on the disorder of quantum system plays a very important role in the field of quantum information, and has received much attention from theoretical and experimental researchers. However, it is very difficult to study the disorder of atoms trapped in microcavity due to their complex nonlocal space-time evolution characteristics. To solve this problem, we present a method to study the internal disorder of hydrogenic atoms trapped in microcavity, that is, to characterize and investigate the disorder of the confined system by using the quantum information entropy and shape complexity of the system. The Shannon information entropy and shape complexity in position space and momentum space (Sr, Sp, C[r], C[p]) are calculated and analyzed for different quantum states of hydrogenic atom in InN dielectric spherical microcavity, and pay special attention to the exploration of the influence of quantum confinement effect on the disorder of the system. The results show that when the radius of the spherical microcavity is very small, the quantum confinement effect is more significant, and a series of extreme points appears in the shape complexity curve of the system, which is caused by the joint interaction of information entropy and spatial inhomogeneity. With the increase of the radius of the spherical cavity, the effect of quantum confinement is weakened, and the Shannon information entropy and shape complexity of the confined hydrogenic atom are similar to the counterparts of the hydrogenic atom in free space. Our work provides an effective method to study the internal disorder of a confined quantum. This work provides an effective method for studying the internal disorder of confined quantum systems and presents some references for the information measurement of confined quantum systems.
We present an informational study of a spherically confined hydrogen atom, a hydrogenic ion confined in a strongly coupled plasma, a spherically confined harmonic oscillator, and a particle confined in a cage. For this, we have implemented a numerical procedure to obtain information entropies of these confined quantum systems. The procedure is based on the variational formalism that uses the finite element method (FEM) for the expansion of the wavefunction in terms of local base functions. Such a study is carried out in order to analyze what happens in the rigorous confinement regime. In particular, we have shown that the effects of the interaction potential is no longer important for rigorous confinements and the studied systems start to behave just like an electron confined by a impenetrable spherical cage. When possible, we compared our results with those published in the literature.