Acceleration of spin-orbit coupled Bose-Einstein condensates: analytical description of the emergence of Landau-Zener transitions

TL;DR

This paper provides an analytical framework for understanding how gravitational and harmonic accelerations induce Landau-Zener transitions in spin-orbit coupled Bose-Einstein condensates, incorporating external and internal state dynamics and atomic interactions.

Contribution

It extends the Landau-Zener model to include external forces and atomic interactions in spin-orbit coupled BECs, offering a rigorous analytical description of transition mechanisms.

Findings

Exact reduction of SOC Hamiltonian to Landau-Zener form

Analytical characterization of transition regimes

Assessment of atomic interaction effects on transitions

Abstract

We analytically study the effect of gravitational and harmonic forces on ultra-cold atoms with synthetic spin-orbit coupling (SOC). In particular, we focus on the recently observed transitions between internal states induced by acceleration of the external modes. Our description corresponds to a generalized version of the Landau-Zener (LZ) model: the dimensionality is enlarged to combine the quantum treatment of the external variables with the internal-state characterization; additionally, atomic-interaction effects are considered. The emergence of the basic model is analytically traced. Namely, by using a sequence of unitary transformations and a subsequent reduction to the spin space, the SOC Hamiltonian, with the gravitational potential incorporated, is exactly converted into the primary LZ scenario. Moreover, the transitions induced by harmonic acceleration are approximately cast into the framework of the basic LZ model through a complete analytical procedure. We evaluate how the validity of our picture depends on the system preparation and on the magnitude of atomic-interaction effects. The identification of the regime of applicability and the rigorous characterization of the parameters of the effective model provide elements to control the transitions.