We investigate the quantum dynamics of two interacting bosonic atoms confined in a one-dimensional anharmonic trap. The tunneling rate, an experimentally measurable parameter of the system, is calculated as a function of the effective coupling interatomic constant $g$ from the ground ( $n=N=0$ ) and first excited atomic states in the trap with respect to relative ( $n=2,N=0$ ) and center-of-mass ( $n=0,N=2$ ) atomic motion. This allows us to investigate the initial population and pair correlation, as well as the effective coupling constant $g$ , of the system by comparing the calculated tunneling rate with the experimental one. We observe that the only possible tunneling scenario is a sequential particle tunneling in the cases we consider. We also analyze a rearrangement $(0,2)\ensuremath{\rightleftarrows}(2,0)$ of the spectrum in the limit $g\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}0$ of noninteracting atoms.We investigate the quantum dynamics of two interacting bosonic atoms confined in a one-dimensional anharmonic trap. The tunneling rate, an experimentally measurable parameter of the system, is calculated as a function of the effective coupling interatomic constant $g$ from the ground ($n=N=0$) and first excited atomic states in the trap with respect to relative ($n=2,N=0$) and center-of-mass ($n=0,N=2$) atomic motion. This allows us to investigate the initial population and pair correlation, as well as the effective coupling constant $g$, of the system by comparing the calculated tunneling rate with the experimental one. We observe that the only possible tunneling scenario is a sequential particle tunneling in the cases we consider. We also analyze a rearrangement $(0,2)\ensuremath{\rightleftarrows}(2,0)$ of the spectrum in the limit $g\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}0$ of noninteracting atoms.

arXiv:1701.06199Physical Review AJun 6, 201719 citations

Juggling Atoms

Anonymous

FocusDec 1, 19980 citations

Dynamical Tunneling and Control

Srihari Keshavamurthy

Tunneling is a supreme quantum effect. Every introductory text [1] on quantum mechanics gives the paradigm example of a particle tunneling through a one-dimensional potential barrier despite having a total energy less than the barrier height. Indeed, the reader typically works through a number of exercises, all involving one-dimensional potential barriers of one form or another modeling several key physical phenomena ranging from atom transfer reactions to the decay of α-particles [2]. However, one seldom encounters coupled multidimenisonal tunneling in such texts since an analytical solution of the Schro¨dinger equation in such cases is not possible. Interestingly, the richness and complexity of the tunneling phenomenon manifest themselves in full glory in the case of multidimensional systems [3]. Thus, for instance, the usual one-dimensional expectation of increasing tunneling splittings as one approaches the barrier top from below is not necessarily true as soon as one couples another bound degree of freedom to the tunneling coordinate. In the context of molecular reaction dynamics, multidimensional tunneling can result in strong mode-specificity and fluctuations in the reaction rates [4]. In fact, a proper description of tunneling of electrons and hydrogen atoms is absolutely essential [5,6] even in molecular systems as large as enzymes and proteins. Although one usually assumes tunneling effects to be significant in molecules involving light atom transfers, it is worth pointing out that neglecting the tunneling of even a heavy atom like carbon is the difference between a reaction occurring or not occurring. In particular, one can underestimate rates by nearly hundred orders of magnitude [7]. Interestingly, and perhaps paradoxically, several penetrating insights into the nature and mechanism of multidimensional barrier tunneling have been obtained from a phase-space perspective [8,9]. The contributions by Creagh, Shudo and Ikeda, and Takahashi in the present volume provide a detailed account of the latest advances in the phasespace-based understanding of multidimensional barrier tunneling.Tunneling is a supreme quantum effect. Every introductory text [1] on quantum mechanics gives the paradigm example of a particle tunneling through a one-dimensional potential barrier despite having a total energy less than the barrier height. Indeed, the reader typically works through a number of exercises, all involving one-dimensional potential barriers of one form or another modeling several key physical phenomena ranging from atom transfer reactions to the decay of α-particles [2]. However, one seldom encounters coupled multidimenisonal tunneling in such texts since an analytical solution of the Schro¨dinger equation in such cases is not possible. Interestingly, the richness and complexity of the tunneling phenomenon manifest themselves in full glory in the case of multidimensional systems [3]. Thus, for instance, the usual one-dimensional expectation of increasing tunneling splittings as one approaches the barrier top from below is not necessarily true as soon as one couples another bound degree of freedom to the tunneling coordinate. In the context of molecular reaction dynamics, multidimensional tunneling can result in strong mode-specificity and fluctuations in the reaction rates [4]. In fact, a proper description of tunneling of electrons and hydrogen atoms is absolutely essential [5,6] even in molecular systems as large as enzymes and proteins. Although one usually assumes tunneling effects to be significant in molecules involving light atom transfers, it is worth pointing out that neglecting the tunneling of even a heavy atom like carbon is the difference between a reaction occurring or not occurring. In particular, one can underestimate rates by nearly hundred orders of magnitude [7]. Interestingly, and perhaps paradoxically, several penetrating insights into the nature and mechanism of multidimensional barrier tunneling have been obtained from a phase-space perspective [8,9]. The contributions by Creagh, Shudo and Ikeda, and Takahashi in the present volume provide a detailed account of the latest advances in the phasespace-based understanding of multidimensional barrier tunneling.

CRC Press eBooksMar 9, 20112 citations

Tunneling Effect of Atom Through Cavity Fields

Wang xiaoguang, Qi Tingzhu

Based on the model proposed by B.G. Englert et al., we study the tunneling effect of an atom through one or two cavities while the atom is slow enough. This is purely the quantum, effect of atom. When an atom is in excited state and cavity fields in single number state, the atom will experience a potential well and a potential barrier. The. transmission probability is obtained as the contributions of two parts, one is the transmission probability through the potential well and another the tunneling probability through the potential barrier.Based on the model proposed by B.G. Englert et al., we study the tunneling effect of an atom through one or two cavities while the atom is slow enough. This is purely the quantum, effect of atom. When an atom is in excited state and cavity fields in single number state, the atom will experience a potential well and a potential barrier. The. transmission probability is obtained as the contributions of two parts, one is the transmission probability through the potential well and another the tunneling probability through the potential barrier.

Communications in Theoretical PhysicsJul 30, 19970 citations

Heavy-Atom Tunneling

Samuel Powell

Jan 1, 20200 citations

g

from the ground (

n=N=0

) and first excited atomic states in the trap with respect to relative (

n=2,N=0

) and center-of-mass (

n=0,N=2

) atomic motion. This allows us to investigate the initial population and pair correlation, as well as the effective coupling constant

g

, of the system by comparing the calculated tunneling rate with the experimental one. We observe that the only possible tunneling scenario is a sequential particle tunneling in the cases we consider. We also analyze a rearrangement $(0,2)\ensuremath{\rightleftarrows}(2,0)$ of the spectrum in the limit $g\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}0$ of noninteracting atoms.