Two-state Bogoliubov theory of a molecular Bose gas
| Autor: | Peden, Brandon M., Wilson, Ryan M., McLanahan, Maverick L., Hall, Jesse, Rittenhouse, Seth T. |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Phys. Rev. A 92, 063624 (2015) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.92.063624 |
| Popis: | 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. Comment: 21 pages, 18 figures, comments welcome |
| Databáze: | arXiv |
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