Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1701.06199 · Physical Review A

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

I. S. Ishmukhamedov, Vladimir S. Melezhik

Published Jun 6, 2017• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.95.062701

Related papers

Tunneling of Two Interacting Fermions

I. S. Ishmukhamedov, Altay Ishmukhamedov

We consider two interacting atoms subject to a one-dimensional anharmonic trap and magnetic field gradient. This system has been recently investigated by the Heidelberg group in the experiment on two 6Li atoms. In the present paper the tunneling of two cold 6Li atoms, initially prepared in the center-of-mass and relative motion excited state, is explored and full time-dependent simulation of the tunneling dynamics is performed. The dynamics is analyzed for the interatomic coupling strength ranging from strong attraction to strong repulsion.

EPJ Web of Conferences•Jan 1, 2018•0 citations

Quantum dynamics of two bosons in an anharmonic trap: Collective versus internal excitations

Christian Matthies, Sascha Zöllner, Hans‐Dieter Meyer +1 more

We deal with the effects of an anharmonic trap on an interacting two-boson system in one dimension. Our primary focus is on the role of the induced coupling between the center of mass and the relative motion as both anharmonicity and the (repulsive) interaction strength are varied. The ground state reveals a strong localization in the relative coordinate, counteracting the tendency to fragment for stronger repulsion. To explore the quantum dynamics, we study the system's response upon (i) exciting the harmonic ground state by continuously switching on an additional anharmonicity and (ii) displacing the center of mass, this way triggering collective oscillations. The interplay between collective and internal dynamics materializes in the collapse of oscillations, which are explained in terms of few-mode models.

arXiv:0705.3205•Physical Review A•Aug 8, 2007•16 citations

Tunneling dynamics of two interacting one-dimensional particles

Seyed Ebrahim Gharashi, D. Blume

We present one-dimensional simulation results for the cold-atom tunneling experiments by the Heidelberg group [Z\"urn et al., Phys. Rev. Lett. 108, 075303 (2012); Z\"urn et al., Phys. Rev. Lett. 111, 175302 (2013)] on one or two $^{6}\mathrm{Li}$ atoms confined by a potential that consists of an approximately harmonic optical trap plus a linear magnetic-field gradient. At the noninteracting particle level, we find that the Wentzel-Kramers-Brillouin approximation may not be used as a reliable tool to extract the trapping potential parameters from the experimentally measured tunneling data. We use our numerical calculations along with the experimental tunneling rates for the noninteracting system to reparametrize the trapping potential. The reparametrized trapping potentials serve as input for our simulations of two interacting particles. For two interacting (distinguishable) atoms on the upper branch, we reproduce the experimentally measured tunneling rates, which vary over several orders of magnitude, fairly well. For infinitely strong interaction strength, we compare the time dynamics with that of two identical fermions and discuss the implications of fermionization on the dynamics. For two attractively interacting atoms on the molecular branch, we find that single-particle tunneling dominates for weakly attractive interactions, while pair tunneling dominates for strongly attractive interactions. Our first set of calculations yields qualitative but not quantitative agreement with the experimentally measured tunneling rates. We obtain quantitative agreement with the experimentally measured tunneling rates if we allow for a weakened radial confinement.

arXiv:1509.00931•Physical Review A•Sep 28, 2015•27 citations

Two-body atomic system in a one-dimensional anharmonic trap: The energy spectrum

I. S. Ishmukhamedov, D. Aznabayev, S. A. Zhaugasheva

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.

Physics of Particles and Nuclei Letters•Sep 1, 2015•7 citations

Tunneling theory for tunable open quantum systems of ultracold atoms in one-dimensional traps

Rikard Lundmark, C. Forssén, J. Rotureau

The creation of tunable open quantum systems is becoming feasible in current experiments with ultracold atoms in low-dimensional traps. In particular, the high degree of experimental control over these systems allows detailed studies of tunneling dynamics, e.g., as a function of the trapping geometry and the interparticle interaction strength. In order to address this exciting opportunity we present a theoretical framework for two-body tunneling based on the rigged Hilbert space formulation. In this approach, bound, resonant, and scattering states are included on an equal footing and we argue that the coupling of all these components is vital for a correct description of the relevant threshold phenomena. In particular, we study the tunneling mechanism for two-body systems in one-dimensional traps and different interaction regimes. We find a strong dominance of sequential tunneling of single particles for repulsive and weakly attractive systems, while there is a signature of correlated pair tunneling in the calculated many-particle flux for strongly attractive interparticle interaction.

arXiv:1412.7175•Physical Review A•Apr 13, 2015•28 citations

Few-Boson Dynamics in Double Wells: From Single-Atom to Correlated Pair Tunneling

Sascha Zöllner, Hans‐Dieter Meyer, Peter Schmelcher

We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensitive to both atom number and initial configuration.

arXiv:0709.3163•Physical Review Letters•Jan 29, 2008•145 citations
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 ggg from the ground (n=N=0n=N=0n=N=0) and first excited atomic states in the trap with respect to relative (n=2,N=0n=2,N=0n=2,N=0) and center-of-mass (n=0,N=2n=0,N=2n=0,N=2) atomic motion. This allows us to investigate the initial population and pair correlation, as well as the effective coupling constant ggg, 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⇄(2,0)(0,2)\ensuremath{\rightleftarrows}(2,0)(0,2)\ensuremath⇄(2,0) of the spectrum in the limit g\ensuremath→\ifmmode±\else\textpm\fi0g\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}0g\ensuremath→\ifmmode±\else\textpm\fi0 of noninteracting atoms.
We consider two interacting atoms subject to a one-dimensional anharmonic trap and magnetic field gradient. This system has been recently investigated by the Heidelberg group in the experiment on two 6Li atoms. In the present paper the tunneling of two cold 6Li atoms, initially prepared in the center-of-mass and relative motion excited state, is explored and full time-dependent simulation of the tunneling dynamics is performed. The dynamics is analyzed for the interatomic coupling strength ranging from strong attraction to strong repulsion.
We deal with the effects of an anharmonic trap on an interacting two-boson system in one dimension. Our primary focus is on the role of the induced coupling between the center of mass and the relative motion as both anharmonicity and the (repulsive) interaction strength are varied. The ground state reveals a strong localization in the relative coordinate, counteracting the tendency to fragment for stronger repulsion. To explore the quantum dynamics, we study the system's response upon (i) exciting the harmonic ground state by continuously switching on an additional anharmonicity and (ii) displacing the center of mass, this way triggering collective oscillations. The interplay between collective and internal dynamics materializes in the collapse of oscillations, which are explained in terms of few-mode models.
We present one-dimensional simulation results for the cold-atom tunneling experiments by the Heidelberg group [Z\"urn et al., Phys. Rev. Lett. 108, 075303 (2012); Z\"urn et al., Phys. Rev. Lett. 111, 175302 (2013)] on one or two 6Li^{6}\mathrm{Li}6Li atoms confined by a potential that consists of an approximately harmonic optical trap plus a linear magnetic-field gradient. At the noninteracting particle level, we find that the Wentzel-Kramers-Brillouin approximation may not be used as a reliable tool to extract the trapping potential parameters from the experimentally measured tunneling data. We use our numerical calculations along with the experimental tunneling rates for the noninteracting system to reparametrize the trapping potential. The reparametrized trapping potentials serve as input for our simulations of two interacting particles. For two interacting (distinguishable) atoms on the upper branch, we reproduce the experimentally measured tunneling rates, which vary over several orders of magnitude, fairly well. For infinitely strong interaction strength, we compare the time dynamics with that of two identical fermions and discuss the implications of fermionization on the dynamics. For two attractively interacting atoms on the molecular branch, we find that single-particle tunneling dominates for weakly attractive interactions, while pair tunneling dominates for strongly attractive interactions. Our first set of calculations yields qualitative but not quantitative agreement with the experimentally measured tunneling rates. We obtain quantitative agreement with the experimentally measured tunneling rates if we allow for a weakened radial confinement.
We numerically investigate the following two-body stationary Schrödinger equation (SE): {−–h22m∂x12−–h22m∂x22+V(x2)+g∂(x1−x2)}xΨ(x1,x2)=EΨ(x1,x2),\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),{−2m–h2​x12​∂​−2m–h2​x22​∂​+V(x2​)+g∂(x1​−x2​)}xΨ(x1​,x2​)=EΨ(x1​,x2​), where x1,x2∈R,V(x1)=V0sin⁡2(kxxi){x_1},{x_2} \in \mathbb{R},V\left( {{x_1}} \right) = {V_0}{\sin ^2}\left( {{k_x}{x_i}} \right)x1​,x2​∈R,V(x1​)=V0​sin2(kx​xi​) 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 Vh(xi)=12mωxi2{V_h}\left( {{x_i}} \right) = \frac{1}{2}m\omega x_i^2Vh​(xi​)=21​mωxi2​ with the trap, which leads to the separation of coordinates y=x1+x22,x=x1−x22y = \frac{{{x_1} + {x_2}}}{{\sqrt 2 }},{\kern 1pt} x = \frac{{{x_1} - {x_2}}}{{\sqrt 2 }}y=2​x1​+x2​​,x=2​x1​−x2​​ 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.
The creation of tunable open quantum systems is becoming feasible in current experiments with ultracold atoms in low-dimensional traps. In particular, the high degree of experimental control over these systems allows detailed studies of tunneling dynamics, e.g., as a function of the trapping geometry and the interparticle interaction strength. In order to address this exciting opportunity we present a theoretical framework for two-body tunneling based on the rigged Hilbert space formulation. In this approach, bound, resonant, and scattering states are included on an equal footing and we argue that the coupling of all these components is vital for a correct description of the relevant threshold phenomena. In particular, we study the tunneling mechanism for two-body systems in one-dimensional traps and different interaction regimes. We find a strong dominance of sequential tunneling of single particles for repulsive and weakly attractive systems, while there is a signature of correlated pair tunneling in the calculated many-particle flux for strongly attractive interparticle interaction.
We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensitive to both atom number and initial configuration.