Chinese Physics Letters

Coupled Two-Dimensional Atomic Oscillation in an Anharmonic Trap

Dong Hu, Linxiao Niu, Jiahua Zhang, X. Zou, Shuyang Cao, Xiaoji Zhou

Published Jul 1, 2017• 0 citations

Abstract

In atomic dynamics, oscillation along different axes can be studied separately in the harmonic trap. When the trap is not harmonic, motion in different directions may couple together. In this work, we observe a two-dimensional oscillation by exciting atoms in one direction, where the atoms are transferred to an anharmonic region. Theoretical calculations are coincident to the experimental results. These oscillations in two dimensions not only can be used to measure trap parameters but also have potential applications in atomic interferometry and precise measurements.

DOI: 10.1088/0256-307x/34/7/076701

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Chinese Physics Letters

Coupled Two-Dimensional Atomic Oscillation in an Anharmonic Trap

Dong Hu, Linxiao Niu, Jiahua Zhang, X. Zou, Shuyang Cao, Xiaoji Zhou

Published Jul 1, 2017• 0 citations

Publisher

Abstract

DOI: 10.1088/0256-307x/34/7/076701

Related papers

Tunneling of two bosonic atoms from a one-dimensional anharmonic trap

I. S. Ishmukhamedov, Vladimir S. Melezhik

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.

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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 numerically investigate the following two-body stationary Schrödinger equation (SE):

\left\{ { - \frac{{{{\rlap{--} h}^2}}}{{2m}}\frac{\partial }{{x_1^2}} - \frac{{{{\rlap{--} h}^2}}}{{2m}}\frac{\partial }{{x_2^2}} + V\left( {{x_2}} \right) + g\partial \left( {{x_1} - {x_2}} \right)} \right\}x\Psi \left( {{x_1},{x_2}} \right) = E\Psi \left( {{x_1},{x_2}} \right),

where

{x_1},{x_2} \in \mathbb{R},V\left( {{x_1}} \right) = {V_0}{\sin ^2}\left( {{k_x}{x_i}} \right)

is the potential describing the interaction of atoms with a trap and gδ(x 1–x 2) is the interatomic potential. Previously, a similar problem has been solved analytically for the harmonic interaction

{V_h}\left( {{x_i}} \right) = \frac{1}{2}m\omega x_i^2

with the trap, which leads to the separation of coordinates

y = \frac{{{x_1} + {x_2}}}{{\sqrt 2 }},{\kern 1pt} x = \frac{{{x_1} - {x_2}}}{{\sqrt 2 }}

for the center-of-mass and relative motion. The anharmonicity of the trap couples these motions and, there-fore, the problem becomes significantly more complicated. In previous works, the anharmonicity V a = V–V h of the trap has been taken into account in the framework of perturbation theory. In this work, the energy level shifts of a two-body atomic system are calculated beyond the perturbation theory for different magnitudes of parameter g of the interatomic interaction. The results are compared to those computed using the perturbation theory.