Tunneling dynamics of two interacting one-dimensional particles

Abstract

We present one-dimensional simulation results for the cold atom tunneling experiments by the Heidelberg group [G. Zürn {\em{et al.}}, Phys. Rev. Lett. {\bf{108}}, 075303 (2012) and G. Zürn {\em{et al.}}, Phys. Rev. Lett. {\bf{111}}, 175302 (2013)] on one or two ${}^6$Li atoms confined by a potential that consists of an approximately harmonic optical trap plus a linear magnetic field gradient. At the non-interacting particle level, we find that the WKB (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 non-interacting system to reparameterize the trapping potential. The reparameterized 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.

20 pages (including Appendices A-H), 14 figures

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Experimental Observation of a Generalized Gibbs Ensemble
• How does an interacting many-body system tunnel through a potential barrier to open space?
• Confinement-induced resonances for a two-component ultracold atom gas in arbitrary quasi-one-dimensional traps
• Tunneling Theory for Tunable Open Quantum Systems of Ultracold Atoms in One-Dimensional Traps
• Incorporating exact two-body propagators for zero-range interactions into $N$-body Monte Carlo simulations
• Effective many-body parameters for atoms in non-separable Gaussian optical potentials

Cited by in corpus (19)

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• Macroscopic Quantum Tunneling Escape of Bose-Einstein Condensates
• Tunneling of two bosonic atoms from a one-dimensional anharmonic trap
• Nonexponential tunneling decay of a single ultracold atom
• Dynamics of a few interacting bosons escaping from an open well
• Broken scale-invariance in time-dependent trapping potentials
• Capturing non-exponential dynamics in the presence of two decay channels
• Momentum correlations of a few ultra-cold bosons escaping from an open well
• Imaginary Time Mean-Field Method for Collective Tunneling
• Tuning an effective spin chain of three strongly interacting one-dimensional fermions with the transversal confinement
• Supplemental note for "Two-fermion emission from spin-singlet and triplet resonances in one dimension"
• Dynamics of small trapped one-dimensional Fermi gas under oscillating magnetic fields
• Two Rydberg-dressed atoms escaping from an open well
• Quench dynamics of two interacting atoms in a one-dimensional anharmonic trap
• Decay properties of unstable Tonks-Girardeau gases from a split trap
• Tunneling of two interacting atoms from excited states
• Molecular excited state in the interaction quench dynamics of two different atoms in a two-dimensional anisotropic trap
• Dynamics of mode entanglement induced by particle-tunneling in the extended Bose-Hubbard dimer model