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arXiv:2503.02644 · PRX Quantum

Quantum Phases for Finite-Temperature Gases of Bosonic Polar Molecules Shielded by Dual Microwaves

Wei Zhang, Kun Chen, Su Yi, Tao Shi

Published Aug 26, 2025• 5 citations
arXivHTMLPDF

Abstract

We investigate the finite-temperature phase diagram of polar molecules shielded by dual microwave fields using the path integral Monte Carlo method combined with the worm algorithm. We determine the critical temperature T c for Bose-Einstein condensations (BECs) and identify two distinct phases below T c : the expanding gas (EG) phase and the self-bound gas (SBG) phase. We further analyze the temperature and interaction-strength dependence of the condensate and superfluid fractions. Notably, in contrast to dilute atomic BECs, the SBG phase displays a low condensate fraction and a high superfluid fraction, resembling the behavior of strongly correlated 4 He superfluids. These significant many-body correlations arise from the interplay between long-range dipole-dipole interactions and the short-range shielding potential. Furthermore, we demonstrate that the aspect ratio of the gas provides a characteristic geometric signature to accurately determine the EG-to-SBG transition, robust against external trapping potentials. Our findings provide unbiased and numerically exact results to guide upcoming experiments with polar molecules.

DOI
10.1103/9cxl-d9zg

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Communications Physics•Jun 2, 2026•1 citation
We investigate the finite-temperature phase diagram of polar molecules shielded by dual microwave fields using the path integral Monte Carlo method combined with the worm algorithm. We determine the critical temperature T c for Bose-Einstein condensations (BECs) and identify two distinct phases below T c : the expanding gas (EG) phase and the self-bound gas (SBG) phase. We further analyze the temperature and interaction-strength dependence of the condensate and superfluid fractions. Notably, in contrast to dilute atomic BECs, the SBG phase displays a low condensate fraction and a high superfluid fraction, resembling the behavior of strongly correlated 4 He superfluids. These significant many-body correlations arise from the interplay between long-range dipole-dipole interactions and the short-range shielding potential. Furthermore, we demonstrate that the aspect ratio of the gas provides a characteristic geometric signature to accurately determine the EG-to-SBG transition, robust against external trapping potentials. Our findings provide unbiased and numerically exact results to guide upcoming experiments with polar molecules.
Bose-Einstein condensation of dipolar molecules can be achieved by shielding loss channels with microwave fields. The microwave coupling can be approximated by effective dipole-dipole interactions with a short-range repulsion. We study properties and stability of these molecular Bose gases with a many-body variational method, the hypernetted-chain Euler-Lagrange method for a wide range of densities and repulsion strengths of the microwave shield. We find a homogeneous gas-like phase which, however, is unstable at low density against density waves: at a critical density, which depends on the repulsion strength, the dipolar fluid undergoes a phase transition to a layer phase. Thus, if the molecular condensate is expanded adiabatically by decreasing the confinement strength, it will spontaneously form layers at the critical density. These quasi-two-dimensional layers can be self-bound, hence form two-dimensional liquids. By varying the microwave shield, the predicted equilibrium densities span more than an order of magnitude.
We investigate the ground-state phases of ultracold gases composed of bosonic microwave-shielded polar molecules (MSPMs). Using a translational symmetry-breaking variational ansatz with Jastrow correlations, we characterize the many-body correlations arising from the large shielding core of the two-body potential in a dense gas. We show that the molecular gases are always stabilized by the shielding potential and support a self-bound gas phase and an expanding gas phase. Furthermore, we find that, analogous to liquid ^{4}He, the condensate fraction is significantly reduced when the size of the shielding core of the two-body potential becomes comparable to the intermolecular distance. For experimental detection, we also identify a bimodal feature in the momentum distribution. Our work invalidates the application of the Gross-Pitaevskii equation to molecular gases and establishes a universal framework to reveal the many-body correlations in dense molecular gases.
We investigate the two- and many-body physics of ultracold polar molecules dressed by dual microwaves with distinct polarizations. Using Floquet theory and multichannel scattering calculations, we identify a regime with the largest elastic-to-inelastic scattering ratio, which is favorable for performing evaporative cooling. Furthermore, we derive and subsequently validate an effective interaction potential that accurately captures the dynamics of microwave-shielded polar molecules (MSPMs). We also explore the ground-state properties of the ultracold gases of MSPMs by computing physical quantities such as gas density, condensate fraction, momentum distribution, and second-order correlation. It is shown that the system supports a weakly correlated expanding gas state and a strongly correlated self-bound gas state. Since the dual-microwave scheme introduces an additional control knob and is essential for creating ultracold Bose gases of polar molecules, our work pave the way for studying the two- and many-body physics of the ultracold polar molecules dressed by dual microwaves. The authors report on a Floquet-theoretical approach to microwave shielding of bosonic ultracold molecules. This clarifies the underlying mechanism behind recently developed dual-microwave schemes and identifies the optimal parameter regime for evaporation.
Using the finite-temperature path integral Monte Carlo method, we investigate dilute, trapped Bose gases in a quasi-two-dimensional (quasi-2D) geometry. The quantum particles have short-range, sss-wave interactions described by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interparticle interaction on the equilibrium properties such as the total energy, the density profile, and the superfluid fraction is discussed. We compare our accurate results with both the semiclassical approximation and the exact results of an ideal Bose gas. Our results show that for repulsive interactions (i) the minimum value of the aspect ratio, where the system starts to behave quasi-2D, increases as the two-body interaction strength increases; (ii) the superfluid fraction for a quasi-two-dimensionally Bose gas is distinctly different from that for both a quasi-1D Bose gas and a true 3D system, i.e., the superfluid fraction for a quasi-2D Bose gas decreases faster than that for a quasi-1D system and a true 3D system with increasing temperature, and shows a stronger dependence on the interaction strength; (iii) the superfluid fraction for a quasi-2D Bose gas lies well below the values calculated from the semiclassical approximation; and (iv) the Kosterlitz-Thouless transition temperature decreases as the strength of the interaction increases.
We use the Ground-State Path Integral Monte Carlo method to study a Bose-Einstein condensate of strongly interacting NaCs polar molecules under the action of a fully anisotropic double microwave shielding potential characterized by a linear and an elliptical polarization field. In particular, we analyze the ground state of the system and its structure as a function of the ellipticity angle ξξξ. While for the circularly polarized case (ξ=0ξ=0ξ=0) a gas phase is realized, one or more self-bound droplets are observed for small ∣ξ∣|ξ|∣ξ∣'s above a threshold value near 3∘3^\circ3∘. With increasing ξξξ, the observed droplets rapidly become tightly bound and are estimated to form a superfluid array. Our results compare favorably to the experimental observations in [Zhang et al., Nature \textbf{651}, 601 (2026)] for positive ξξξ, while moderate differences show up for ξ<0ξ<0ξ<0 where our simulations conform to the expected symmetries of the intermolecular potential.
Abstract Ultracold polar molecular gases provide a powerful platform for exploring quantum many-body physics with strong, long-range, and anisotropic interactions. In this work, we develop an extended Gross-Pitaevskii approach tailored to bosonic dipolar molecules under single-microwave shielding, incorporating their effective interactions and adapting the quantum fluctuation corrections. We benchmark this beyond-mean-field theory against exact path-integral Quantum Monte Carlo simulations. Focusing on the regime of positive scattering lengths, we find excellent agreement across a range of quantum phases, including superfluid, supersolid, and droplet states. We show that elliptic microwave polarization induces anisotropic superfluidity with direction-dependent sound velocities along each spatial axis—an effect absent in atomic dipolar gases. A quasi-one-dimensional theory captures roton softening and predicts roton instabilities tunable via ellipticity. While most experiments rely on double-microwave shielding to reduce losses, we demonstrate that single-shielded molecules already support rich and tunable many-body behavior. Our framework is readily extendable to the double-shielded case. This work establishes a versatile theoretical foundation for ultracold molecular gases and opens the door to future studies with more advanced shielding protocols.