Infinite Barriers and Symmetries for a Few Trapped Particles in One Dimension

Abstract

This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are dependent on the specific shapes of the traps and the interactions, this article applies symmetry analysis to identify generic features in the spectrum of stationary states of few-particle, few-well systems. Extended attention is given to a simple but flexible three-parameter model of two particles in two wells in one dimension. A key insight is that two limiting cases, hard-core repulsion and no inter-well tunneling, can both be treated as emergent symmetries of the few-particle Hamiltonian. These symmetries are the mathematical consequences of infinite barriers in configuration space. They are necessary to explain the pattern of degeneracies in the energy spectrum, to understand how degeneracies are broken for models away from limiting cases, and to explain separability and integrability. These symmetry methods are extendable to more complicated models and the results have practical consequences for stable state control in few-particle, few-well systems with ultracold atoms in optical traps.

17 pages in two-column format, 9+ figures; v2 heavily revised (especially introduction) and new references

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Cited by in corpus (12)

• One-dimensional mixtures of several ultracold atoms: a review
• Correlated Tunneling Dynamics of an Ultracold Fermi-Fermi Mixture Confined in a Double-Well
• Magnetic impurity in a one-dimensional few-fermion system
• Topological Exchange Statistics in One Dimension
• Probing the edge between integrability and quantum chaos in interacting few-atom systems
• Morphology of three-body quantum states from machine learning
• Interaction-controlled impurity transport in trapped mixtures of ultracold bosons
• The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps
• Ground-State Magnetization in Mixtures of a Few Ultra-Cold Fermions in One-Dimensional Traps
• Dynamical resistivity of a few interacting fermions to the time-dependent potential barrier
• Topological adiabatic dynamics in classical mass-spring chains with clamps
• Impact of dark states on the stationary properties of quantum particles with off-centered interactions in one dimension