Spectral Properties of Confining Superexponential Potentials

Abstract

We explore the spectral properties and behaviour of confining superexponential potentials. Several prototypes of these highly nonlinear potentials are analyzed in terms of the eigenvalues and eigenstates of the underlying stationary Schrödinger equation up to several hundreds of excited states. A generalization of the superexponential self-interacting oscillator shows a scaling behaviour of the spacing of the eigenvalues which turns into an alternating behaviour for the power law modified oscillator. Superexponential potentials with an oscillating power show a very rich spectral structure with varying amplitudes and wave vectors. In the parity symmetric case doublets of near degenerate energy eigenvalues emerge in the spectrum. The corresponding eigenstates are strongly localized in the outer wells of the potential and occur as even-odd pairs which are interspersed into the spectrum of delocalized states. We provide an outlook on future perspectives including the possibility to use these features for applications in e.g. cold atom physics.

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Feshbach Resonances in Ultracold Gases
• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Few-boson dynamics in double wells: From single-atom to correlated-pair tunneling
• Single atom detection in ultracold quantum gases: a review of current progress
• Control and Manipulation of Cold Atoms in Optical Tweezers
• Sound propagation and quantum limited damping in a two-dimensional Fermi gas
• Superexponential Self-Interacting Oscillator
• Quantum Superexponential Oscillator
• Superexponential Interactions and the Dynamical Unfolding of Confined Degrees of Freedom
• Many-Body Effects in Models with Superexponential Interactions