Applicability of the eGPE in the molecular droplet regime

Determine whether the extended Gross–Pitaevskii equation remains applicable to microwave-dressed molecular gases in the droplet-forming regime for ellipticities greater than 3.5°, particularly when the imaginary component of the conventional Lee–Huang–Yang correction exceeds 10% of its real component.

Background

The paper benchmarks an extended Gross–Pitaevskii equation (eGPE) against electrostriction measurements in a Bose–Einstein condensate of microwave-dressed NaCs molecules. The model agrees well with experiment over the investigated range, corresponding to ellipticities up to 3.5° and dipolar lengths up to approximately 6,900 a₀.

For larger ellipticities, the system enters a droplet-forming regime and the conventional Lee–Huang–Yang term develops an increasingly significant imaginary component. The paper therefore leaves unresolved whether the eGPE provides a reliable description in this strongly interacting regime, motivating comparisons with variational and quantum Monte Carlo approaches.

References

Beyond the interaction range investigated in this work, the system undergoes droplet formation for $\xi > 3.5\circ$. In this regime, the applicability of the eGPE remains an open question as the imaginary component of the conventional LHY term grows beyond 10\% of its real component (see Appendix).

— Electrostriction in a Bose-Einstein Condensate of Dipolar Molecules  (2608.19180 - Kwak et al., 19 Aug 2026) in Section 6, Conclusions and Outlook

In earlier studies, the imaginary contribution to the LHY integral was simply discarded for relatively small interaction strengths, but the validity of this treatment is unclear at stronger interactions, particularly in the antidipolar regime.

— Electrostriction in a Bose-Einstein Condensate of Dipolar Molecules  (2608.19180 - Kwak et al., 19 Aug 2026) in Appendix, subsection “Lee-Huang–Yang (LHY) term”