Abstract
We investigate the self-bound states of dipolar Dy condensates with the Gaussian-state ansatz which improves the conventional coherent-state ansatz with multimode squeezed coherent states. We show that the self-bound states consist of the experimentally observed self-bound liquid phase and the unobserved self-bound gas phase. The numerically obtained gas-liquid boundary is in good agreement with experimental data. Our theory also allows one to extract the real part of the three-body coupling constant of the Dy atoms from the particle number distribution of the condensates. In particular, we results show that the self-bound states are stabilized by the short-range three-body repulsion. Our study shed a different light to understand the self-bound droplets of Bose-Einstein condensates.
Highlights
Since the observation of the stable liquid droplets in dipolar condensates in the mean-field collapse regime [1,2], this novel quantum phase has received increasing attention in the community
The extended Gross-Pitaevskii equation (EGPE) is applicable only when the condensate is dominated by the coherent component, which excludes its application to the self-bound gas (SBG) phase
Even for the coherent-component-dominant self-bound liquid (SBL) phase one should be very careful about the validity of the EGPE
Summary
Since the observation of the stable liquid droplets in dipolar condensates in the mean-field collapse regime [1,2], this novel quantum phase has received increasing attention in the community. The inclusion of squeezing components in our theory allows us to obtain the unknown real part of the three-body coupling strength by fitting the experimentally measured PND [5] Using this fit, we subsequently map out the phase diagram on the parameter plane formed by the relative dipolar interaction strength and the particle number. The three-body repulsion has been suggested as the mechanism that balances the two-body attraction at high densities [23,24,25], these GPE-based studies implicitly assume that the many-body ground state wave function of the condensate is coherent state. III, we put forward the general properties of our Gaussian ground states by factoringthem into a product of single-mode displaced squeezed vacuum states Using such factorization, we provide concise expressions for the PND and explain how to determine the three-body coupling strength of the Dy atoms.
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