Feshbach resonance without a closed-channel bound state.

Area of Science:

• Atomic, Molecular, and Optical Physics
• Quantum Mechanics
• Condensed Matter Theory

Background:

• Feshbach resonances are crucial for controlling ultracold atomic gases.
• Understanding resonance conditions, especially in the absence of bound states, is key for advanced applications.
• Analytic models are needed to precisely describe scattering phenomena.

Purpose of the Study:

• To analyze Feshbach resonance physics using analytic expressions for scattering phase shift and scattering length.
• To investigate the conditions under which Feshbach resonance can occur, even without bound states in the closed channel.
• To elucidate the dependence of scattering length sign on coupling strength in the unitary limit.

Main Methods:

• Derivation of analytic expressions for s-wave scattering phase shift and scattering length within a two-channel tight-binding model.
• Unified treatment of bound states and resonances using the Jost function.
• Analysis of Feshbach resonance conditions under strong interchannel coupling.

Main Results:

• Feshbach resonance can occur even when the closed channel lacks a bound state, given strong interchannel coupling.
• Analytic expressions for background scattering length, resonance magnetic field, and energy shift were derived.
• The sign dependence of scattering length on coupling strength in the unitary limit was elucidated.

Conclusions:

• The findings extend the applicability of Feshbach resonance manipulation to a broader range of ultracold atomic systems.
• The derived analytic expressions provide valuable tools for theoretical and experimental investigations of Feshbach resonances.
• This work deepens the understanding of quantum scattering phenomena in interacting many-body systems.