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arXiv:1707.04201 · Physics Letters A

Effective two-mode description of a few ultra-cold bosons in a double-well potential

Jacek Dobrzyniecki, Tomasz Sowiński

Published Dec 19, 2017• 13 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2017.12.027

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A variationally optimised basis allows an accurate description of the quantum \nbehaviour of ultra-cold atoms, even in the strongly correlated regime. A rescaling \nscheme corrects discrepancies caused by using a reduced Hilbert space. This \napproach also allows the modelling of experimentally realizable double-well potentials, \nwhich still reveals the maximally-entangled states seen in fixed basis models. \nTime dynamics of these double-well systems show macroscopic tunnelling between \nwells for bosons with a sufficient interaction strength. \nThe many-body problem of interacting bosons in the highly-correlated regime \nis difficult. The number of basis states needed to describe this quantum system \naccurately quickly grows beyond computational reach. Rescaling the interaction \nstrength proves a simple and effective method of calculating exact eigenvalues in a \nreduced Hilbert space. \nBosonic systems in the double-well potential are investigated next. First, how \ndifferent eigen-states depend on the interaction strength is examined. The variationally \noptimised method has advantages over a standard fixed basis method with \nthe ability to model experimentally viable systems and explore more stronglycorrelated \nregimes. Secondly, tunnelling dynamics in the double well are studied, \nspecifically for a system where all particles initially occupy a single well. Oscillations \ncorresponding to collective tunnelling between wells are found in regimes \nwhere there are zero interactions or bosons lie in a maximally-entangled state. \nWhat governs the dynamics outside these two regimes is also considered.

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A variationally optimised basis allows an accurate description of the quantum \nbehaviour of ultra-cold atoms, even in the strongly correlated regime. A rescaling \nscheme corrects discrepancies caused by using a reduced Hilbert space. This \napproach also allows the modelling of experimentally realizable double-well potentials, \nwhich still reveals the maximally-entangled states seen in fixed basis models. \nTime dynamics of these double-well systems show macroscopic tunnelling between \nwells for bosons with a sufficient interaction strength. \nThe many-body problem of interacting bosons in the highly-correlated regime \nis difficult. The number of basis states needed to describe this quantum system \naccurately quickly grows beyond computational reach. Rescaling the interaction \nstrength proves a simple and effective method of calculating exact eigenvalues in a \nreduced Hilbert space. \nBosonic systems in the double-well potential are investigated next. First, how \ndifferent eigen-states depend on the interaction strength is examined. The variationally \noptimised method has advantages over a standard fixed basis method with \nthe ability to model experimentally viable systems and explore more stronglycorrelated \nregimes. Secondly, tunnelling dynamics in the double well are studied, \nspecifically for a system where all particles initially occupy a single well. Oscillations \ncorresponding to collective tunnelling between wells are found in regimes \nwhere there are zero interactions or bosons lie in a maximally-entangled state. \nWhat governs the dynamics outside these two regimes is also considered.
Dynamical properties of a few ultra-cold fermions confined in a double-well potential are studied. We show that the dynamics, which is governed by single-particle tunnelings for vanishing interactions, is completely different for strong interactions. Depending on the details of the configuration, for sufficiently strong interactions (repulsions or attractions) the particle flow through the barrier can be accelerated or slowed down. This effect cannot be explained with the single-particle picture. It is clarified with a direct inspection of the spectrum of the few-body Hamiltonian.