Generalized formula for the Landau-Zener transition in interacting Bose-Einstein condensates

Abstract

We present a rigorous analysis of the generalized Landau-Zener problem for the two-level interacting Bose-Einstein condensates. We show that the dynamics of the system is accurately, in detail, described by a two-term variational ansatz that is valid for the whole time domain and is applicable for any set of involved parameters. Applying an exact third order nonlinear differential equation we construct an advanced fifth order polynomial equation for the final transition probability serving as a highly accurate generalized Landau-Zener formula.

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Cited by in corpus (9)

• Thirty five classes of solutions of the quantum time-dependent two-state problem in terms of the general Heun functions
• Fifteen classes of solutions of the quantum two-state problem in terms of the confluent Heun function
• Analytic solutions of the quantum two-state problem in terms of the double-, bi- and tri-confluent Heun functions
• Adiabatic passage through chaos
• A singular Lambert-W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions
• Interaction induced Landau-Zener transitions
• Landau-Zener-Stueckelberg physics with a singular continuum of states
• Many-body adiabatic passage: Quantum detours around chaos
• Demkov-Kunike model in cold molecule formation