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 et al., Phys. Rev. Lett. 108, 075303 (2012) and G. Zürn et al., Phys. Rev. Lett. 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.

Numerical Solution of the Time Dependent 3D Schrödinger Equation Describing Tunneling of Atoms from Anharmonic Traps

“…where the range of the interaction is fixed to r 0 = 0.1 [4,14] and the interaction strength V 0 is varied. We calculate the total probability P(t) in the box |x 1 , x 2 | ≤ 20.…”

“…Pair correlation plays a major role in quantum tunneling and there are a only few works in the context of ultracold physics which accurately take into account the interatomic interaction [1][2][3][4][5][6][7]. In the present paper, we consider a tunneling of two interacting atoms from an anharmonic optical trap.…”

Tunneling of Two Interacting Fermions

“…The atom-trap potential is taken from [5,9,10] which represents an optical trap and magnetic field gradient (figure 1):…”

“…In the context of ultracold physics, there are only a few works that completely take into account the pair correlation impact in the problem of a decay of a quantum system [1][2][3][4][5][6][7][8]. In this work we present an efficient method [1][2][3][4] which completely takes into account the interatomic interaction and also an external field.…”

“…In this work we present an efficient method [1][2][3][4] which completely takes into account the interatomic interaction and also an external field. This situation corresponds to two cold atoms, subject to an anharmonic optical trap and magnetic field gradient, which have been investigated in the recent experiment of the Heidelberg group on two interacting 6 Li atoms [9,10] and theoretically studied in [5,11,12]. The atoms tunnels through the potential barrier of the trap to open space.…”