Two-state Bogoliubov theory of a molecular Bose gas

TL;DR

This paper develops an analytic Bogoliubov theory for a quasi-2D molecular Bose-Einstein condensate with internal state-dependent dipolar interactions, revealing instabilities and response behaviors relevant for various molecular systems.

Contribution

It provides a novel analytic framework for describing two-component dipolar BECs, including dispersion relations, stability analysis, and correlation functions, applicable to a wide range of molecular gases.

Findings

Identifies three types of instabilities: density-wave, spin-wave, and mixed.

Derives explicit formulas for dispersion relations and structure factors.

Shows susceptibility to density and spin responses depending on polarization.

Abstract

We present an analytic Bogoliubov description of a BEC of polar molecules trapped in a quasi-2D geometry and interacting via internal state-dependent dipole-dipole interactions. We derive the mean-field ground-state energy functional, and we derive analytic expressions for the dispersion relations, Bogoliubov amplitudes, and dynamic structure factors. This method can be applied to any homogeneous, two-component system with linear coupling, and direct, momentum-dependent interactions. The properties of the mean-field ground state, including polarization and stability, are investigated, and we identify three distinct instabilities: a density-wave rotonization that occurs when the gas is fully polarized, a spin-wave rotonization that occurs near zero polarization, and a mixed instability at intermediate fields. These instabilities are clarified by means of the real-space density-density correlation functions, which characterize the spontaneous fluctuations of the ground state, and the momentum-space structure factors, which characterize the response of the system to external perturbations. We find that the gas is susceptible to both density-wave and spin-wave response in the polarized limit but only a spin-wave response in the zero-polarization limit. These results are relevant for experiments with rigid rotor molecules such as RbCs, $\Lambda$-doublet molecules such as ThO that have an anomalously small zero-field splitting, and doublet-$\Sigma$ molecules such as SrF where two low-lying opposite-parity states can be tuned to zero splitting by an external magnetic field.