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EPJ Web of Conferences

Tunneling of Two Interacting Fermions

I. S. Ishmukhamedov, Altay Ishmukhamedov

Published Jan 1, 2018• 0 citations
Publisher

Abstract

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.

DOI
10.1051/epjconf/201817709006

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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 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 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 $(0,2)\ensuremath{\rightleftarrows}(2,0)$ of the spectrum in the limit $g\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}0$ of noninteracting atoms.
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.
A simple theory for the tunneling of two cold atoms out of a trap in the presence of an attractive contact force is developed. Two competing decay channels, for single-atom and bound-pair tunneling, respectively, contribute independently to the decay law of the mean atom number in the trap. The single-atom tunneling rate is obtained through the quasiparticle wave function formalism. For pair tunneling an effective equation for the center-of-mass motion is derived, so the calculation of the corresponding tunneling rate is again reduced to a simpler one-body problem. The predicted dependence of tunneling rates on the interaction strength qualitatively agrees with a recent measurement of the two-atom decay time [G. Z\"urn, A. N. Wenz, S. Murmann, T. Lompe, and S. Jochim, arXiv:1307.5153].
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.
Deterministic preparation of an ultracold harmonically trapped one-dimensional Fermi gas consisting of a few fermions has been realized by the Heidelberg group. Using Floquet formalism, we study the time dynamics of two- and three-fermion systems in a harmonic trap under an oscillating magnetic field. The oscillating magnetic field produces a time-dependent interaction strength through a Feshbach resonance. We explore the dependence of these dynamics on the frequency of the oscillating magnetic field for noninteracting, weakly interacting, and strongly interacting systems. We identify the regimes where the system can be described by an effective two-state model and an effective three-state model. We find an unbounded coupling to all excited states at the infinitely strong interaction limit and several simple relations that characterize the dynamics. Based on our findings, we propose a technique for driving transition from the ground state to the excited states using an oscillating magnetic field.