Generation of nonground-state condensates and adiabatic paradox

TL;DR

This paper resolves the paradox of generating nonground-state condensates by clarifying the difference between adiabatic and diabatic representations, demonstrating that resonant generation is feasible in the diabatic frame.

Contribution

It shows that the paradox of resonant generation in adiabatic representation is resolved by adopting a diabatic framework, enabling controlled generation of nonground-state condensates.

Findings

Resonant generation is impossible in the adiabatic picture due to time-dependent eigenvalues.

Resonant generation is well-defined in the diabatic representation.

Derived equations describe diabatic mode generation via modulating trapping potential and scattering length.

Abstract

The problem of resonant generation of nonground-state condensates is addressed aiming at resolving the seeming paradox that arises when one resorts to the adiabatic representation. In this picture, the eigenvalues and eigenfunctions of a time-dependent Gross-Pitaevskii Hamiltonian are also functions of time. Since the level energies vary in time, no definite transition frequency can be introduced. Hence no external modulation with a fixed frequency can be made resonant. Thus, the resonant generation of adiabatic coherent modes is impossible. However, this paradox occurs only in the frame of the adiabatic picture. It is shown that no paradox exists in the properly formulated diabatic representation. The resonant generation of diabatic coherent modes is a well defined phenomenon. As an example, the equations are derived, describing the generation of diabatic coherent modes by the combined resonant modulation of the trapping potential and atomic scattering length.