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arXiv:2407.09391 · Physical Review Letters

Dipolar Droplets of Strongly Interacting Molecules

Tim Langen, Jordi Boronat, Juan Sánchez-Baena, Raúl Bombín, Tijs Karman, Ferran Mazzanti

Published Feb 4, 2025• 23 citations
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Abstract

We simulate a molecular Bose-Einstein condensate in the strongly dipolar regime, observing the existence of self-bound droplets, as well as their splitting into multiple droplets by confinement-induced frustration. Our quantum Monte Carlo approach goes beyond the limits of the established effective mean-field theories for dipolar quantum gases, revealing small droplets produced by strong dipolar interactions outside known stable regimes. The simulations include realistic molecular interactions and therefore have direct relevance for current and future experiments.

DOI
10.1103/physrevlett.134.053001

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Abstract Ultracold dipolar droplets have been realized in a series of ground-breaking experiments, where the stability of the droplet state is attributed to beyond-mean-field effects in the form of the celebrated Lee-Huang-Yang (LHY) correction. We scrutinize the dipolar droplet states in a one-dimensional context using a combination of analytical and numerical approaches, and identify experimentally viable parameters for accessing our findings for future experiments. In particular we identify regimes of stability in the restricted geometry, finding multiple roton instabilities as well as regions supporting quasi-one-dimensional droplet states. By applying an interaction quench to the droplet, a modulational instability is induced and multiple droplets are produced, along with bright solitons and atomic radiation. We also assess the droplets robustness to collisions, revealing population transfer and droplet fission.
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We investigate the physics of ultracold dipolar molecules using path-integral quantum Monte Carlo simulations, and construct the complete phase diagram extending from weak to strong interactions and from small to mesoscopic particle numbers. Our calculations predict the formation of self-bound quantum droplets at interaction strengths lower than previous estimates for molecular condensates. Strikingly, we observe that, for stronger interactions, the oblate quantum droplet transitions to a two-dimensional sheet or superfluid membrane with a thickness of a single molecule. As interactions are increased further the system continually loses superfluidity while correlations develop, and is eventually found to undergo a transition to a crystalline monolayer that remains self-bound without external confinement. The spontaneous formation of such two-dimensional phases from a three-dimensional quantum gas is traced back to the peculiar anisotropic form of the dipole-dipole interaction generated by microwave dressing of rotational molecular states. For sufficiently large particle numbers, crystallization takes place for comparably low interaction strengths that do not promote two-body bound states and should thus be observable in ongoing experiments without limitations from three-body recombination.
We investigate beyond-mean-field corrections to the energy of an elongated homogeneous Bose gas strongly confined in two directions, with dipoles aligned along the long axis of the system. When the dipolar interaction reaches its critical strength, the mean-field approach predicts instability. However, similar to the free-space case, beyond-mean-field effects significantly alter the ground state of the system, leading to the formation of a self-bound atomic cloud known as a quantum droplet. Our analysis demonstrates that the beyond-mean-field contribution to the energy in the quasi-1D region, in addition to the confinement induced shift of the mean field energy, is proportional to the third power of the density ∼n3\sim n^3∼n3. Therefore, it can be interpreted as an effective three-body repulsion that stabilizes the gas, preventing collapse and leading to a finite-density solution. We also show that the same effect plays a crucial role in the binding of strongly elongated dipolar droplets under harmonic confinement.